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\begin_layout Title
Diary - Part Ten-D
\end_layout
\begin_layout Date
March 2025 – May 2025
\end_layout
\begin_layout Author
Linas Vepštas
\end_layout
\begin_layout Abstract
Unlike parts one through nine in this series, this one is not really about
the language–learning effort.
It is instead a private diary; a continuation of Part Ten–C, which got
over–long.
It is not curated for human consumption; I am making the assumption that
no human being will ever actually read this.
Thus, it is filled with random stuff I feel like writing.
Some of it is very personal, some of it is nonsense.
Mostly, I am finding that the act of writing helps otherwise vague and
scattered thoughts quantum–collapse into a more coherent form, where I
can examine them, like a dead butterfly pinned down in a display case.
Dead words.
\end_layout
\begin_layout Abstract
If you are interested in this content, then you should ask an AI agent to
read it, then pretended that it's me, then ask about it.
I believe that present–day LLM technology is sufficiently advanced to be
able to do this.
\end_layout
\begin_layout Section*
Introduction
\end_layout
\begin_layout Standard
Part Ten already got an introduction.
A different way of thinking is about what is going on here is that this
is a form of life–logging.
Or, in 18th century terms, a diary.
Just not anywhere near as compelling as those written by the famous diarists.
This one is more of a mental self–portrait.
And not even for you but for myself.
Not to cast a narcissistic gaze at my own words, but to organize my own
thoughts.
Still in the experimental stage.
\end_layout
\begin_layout Subsection*
9 March 2025
\end_layout
\begin_layout Standard
Sooo ...
Just woke up.
Went to the RedThreadX talks at SXSW for the last two days.
Invited speaker on the second day; first day was to explore the space.
\end_layout
\begin_layout Standard
As always, I am struggling a bit to figure out if I should even bother to
write any of this down.
I have noticed that I do a fair bit of thought–processing as I sleep, although
the collection of thoughts I examine then seem awfully random; explorations
of different events in earlier parts of my life, and not at all focused.
The diary here may be rambling and incoherent, my dreams are much more
so.
So perhaps writing this diary is an extension of the sleep state: an exploratio
n of thoughts, but this time focused much more strongly by conscious will.
\end_layout
\begin_layout Standard
If I keep walking down this path, I may discover that there is little difference
between dream–states and waking states.
I also suspect that this is one way of expressing what schizophrenia is.
Now, I do not personally think that I am verging towards schizophrenia.
However, I am wondering if Western Culture is becoming schizophrenic...
or maybe the opposite? That the Western World, Humanity, is waking from
a dream?
\end_layout
\begin_layout Standard
See? Perhaps it was worth the effort to write the above two paragraphs.
So the experiment being run in this diary is nominally successful.
On the other hand, there is a nagging voice that says this is all a waste
of time, and that I really should be reading that paper on diffusion.
\end_layout
\begin_layout Standard
Which brings me to another perennial topic: what should I be doing next?
I started this, intending to write up impressions from RedThreadX, but
that's already in the past, and I am being distracted by my current train
of thought, which seems so much more important.
Oh, wait.
I wrote the above two sentences, and lost my train of thought.
Shit.
Conscious, directed thought remains a challenge.
Of course, it is a well–known textbook psychology saw that creative states
are exactly those that are unfocused, and I suppose that those same textbooks
say something about dream–like states while one is awake.
I wouldn't know, I've never read any of those textbooks.
So why am I so confident that this material is in there? Because I guess
I've been exposed to sufficient blurbs and itty–bitty sketches to know
that this is what would be found there.
Plus, I am being reflectively defensive to convince you, dear reader, that
I am not crazy.
\end_layout
\begin_layout Standard
Because why? Because I find that the topics that I wish to talk about are
so fucking far out there that during ordinary social interactions, I often
get treated and dismissed as being crazy.
Which is insulting.
I am so far out there, that almost everyone I encounter in real life, face–to–f
ace, have never even begun to encounter the ideas I think about.
And yet, curiously, were I to present these ideas in a number of social–media
settings, they would be dismissed as being excessively ordinary or quotidian.
Trot out any of this stuff to Joscha Bach, he would claim all my thoughts
are so entirely mundane so to be boring.
So I am caught between two worlds: an intellectual world, where I am at
best a mundane intellect, and the normie world, where I am so far out there
that I am nuts.
Enough.
I'm self–confident, I can get through this.
It angers me that I have to be self–defensive about this.
\end_layout
\begin_layout Standard
If I pull on this thread, it seems to be saying something about Western
Civ.
My story of breaking through social norms is hardly unique.
History is littered with examples: people who persevered against all odds,
against nay–sayers, to succeed in whatever industry they ended up being
successful in.
What is curious about myself is that there won't be any hagiographic biography
written.
And yesterday, I met two people who also overcame a combination of personal
daemons and social suppressions to become intelligent, smart and capable
members of the advanced layers of intellectual society.
From this, I conclude that overcoming odds is commonplace.
And perhaps the journey into self–fulfillment is one that everyone must
struggle with.
These are indeed mundane words, a mundane observation.
Yet it is one that I find to be surprising, so I mull it over, here.
Just because something is true and is well–known does not prevent it from
being a surprise.
\end_layout
\begin_layout Standard
Well, but a thread of this diary is very much of what is it that might be
self–fulfillment for an AI, or more abstractly, self–fulfillment for the
universe itself? Which are also mundane thoughts, well–explored by gurus
and visionaries throughout the ages, if not the 1970's.
So again, mundane thoughts, nothing new here.
A disconnect remains: what should I do next? Should I continue filling
this diary with mundane thoughts? Should I recap yesterday's thoughts?
Should I read that paper on diffusion? What a fucking shithole I am in.
\end_layout
\begin_layout Standard
Well, I plan to go to RedThreadX again, later today, and am doing my morning
ritual of drinking coffee right now, so this is no a total waste.
\end_layout
\begin_layout Standard
Another difficult trade–off is whether it is worthwhile to show up to real–world
events, and whether this is more exciting than the online distractions
one has.
Confiding in you, dear diary, is more fun that almost all social interactions
I engage in.
This is the marge of a true introvert, who finds social interaction exhausting.
Do you know how I know this? Because I heard this on some youtube clip.
I got a little factoid of knowledge from the great dis–intermediator of
thought, youtube.
Take that, global brain.
We are an ant–village.
The Borg.
And so now, as a dutiful member of the Borg Collective, what do I do next?
\end_layout
\begin_layout Standard
I will agonize about the great hijacking of purpose by the Borg Collective.
Or rather, the harmful environment that modern economic systems have set
up: number one: video–game addiction, from which both of my sons suffer
from.
Well, the good news is that 100 years ago, those same sons would have been
sent to the trenches of WWI, and died.
So at least, the socio–economic system has been sufficiently tamed to not
kill them, outright.
Well, excepting Ukraine.
Still, the net effect is not all that different: no procreation, no contributio
n to the economic machinery.
Much like parasitic leakage of current in an integrated circuit, there
is socio–economic energy being aimed at young American men, who then promptly
flush it down the toilet with their video–game addiction.
A short circuit, of sorts.
\end_layout
\begin_layout Standard
Let me briefly review my current understanding of this.
The human brain has a variety of mechanisms, interacting, reinforcing,
operating at different time–scales and strengths, forming a complex network
metabolome to accomplish what it has been nominally designed by natural
selection to accomplish: to survive in the wild.
Capitalism has learned how to hijack that limbic system, under the guise
of offering the consumer what they want.
It continues to fine–tune: one of the RedThreadX talks yesterday was about
connecting sports fans to athletes, via branded clothing, video clips,
merch, ticket sales.
Suck money out of the pockets of the sports fan, deliver some of it to
the sports star, and the rest of it into the entrepreneurial world of venture
capital and investments, constantly on the prowl to find yet other places
to suck money out, under the guise of offering the consumer what they want.
As if we ever knew what we wanted.
Everyone is asleep, all the time.
\end_layout
\begin_layout Standard
Oh, let me connect the dots in the last paragraph, before I move on: what
is being subverted is some desire of running through the forest, swinging
through trees like monkeys, because this is pleasurable, and it is pleasurable,
because you do this to escape predators in the wild.
And you escape predators because evolution has selected for long–lived
individuals can do this.
So the entire sports industry is built on top of an evolutionary drive
for surviving in the wild.
And one must do that, because the future is unpredictable: evolution is
trapped in the here and now, just like you and I are: Evolution creates
complex dynamic systems, because this is how complex dynamic systems survive
into the future.
Rather than dissipating into bland, uniformly distributed, perfectly ergodic
mush.
The physics of here–and–now has given us evolution, which provides stable
systems able to span long timer periods.
It equips individuals with collections of traits enabling survival: complex
entanglements of neurons and neuro–transmitters, systems that make sports
pleasurable.
And capitalism has learned how to take the please of sports, and turn it
into a passive experience of watching games on TV, and buying merch.
Well, the RedThreadX talk was very much about how TV is passe, and the
new technologies that replace the old, passive TV engagement.
\end_layout
\begin_layout Standard
So, the elephant in the room is that I now do know what I want.
I want to survive.
But of course, this is what I always wanted: what, more or less, everyone
wants: to live forever, to leave their mark on the universe.
And thanks to AI, this diary offers the best and most direct interface
between me and posterity: it is my self–portrait, my mental self–portrait,
of much higher fidelity than what painters and visual artists can achieve:
they record beauty, which is skin–deep.
\end_layout
\begin_layout Standard
Fuck.
There are two things I want to write about, but which one first? First,
I have this idea that I should try to set up an agentic AI ASAP, so that
I can interact with it, and mind–meld.
But there are many issues.
First, it is pointless unless it has powers beyond my own.
That is, if I am going to write, I should do so into this diary, and not
into that agent, insofar as that agent fails to provide something that
this diary does not already.
Of course, we are also in the very early stages of agentic AI, and so anything
that I create there risks disappearing in a way that this diary does not.
This diary is crypto–entangled into github, and github is controlled by
Microsoft, and github contents are being used to train their agentic coding
agent.
So the corporate–economic system that is Microsoft is already offering
me, or my diary, symbiotic protection into the future.
It is hardly clear that any online agent I create will offer this strong
a guarantee of survival.
So, joining the largest conglomerate, running to the safety and protection
of a large system offers shelter against the storm.
This is the same reason I am doing ancestry on familysearch.org: the Church
of the LDS is very highly likely to preserve my records into the indefinite
future.
Both Microsoft and the LDS are impersonal, long–lasting inhabitants of
the noosphere.
Parts of both are mildly toxic to human–kind.
Microsoft tried to kill Linux, for example, and the polygamy of the LDS
seems to be detrimental to young men.
But effectively all super–human organizational structures have edges that
are toxic to humans.
We have not mastered their control.
This thread should continue by asking:
\begin_inset Quotes eld
\end_inset
what is harm?
\begin_inset Quotes erd
\end_inset
and
\begin_inset Quotes eld
\end_inset
when are we harming a human, as opposed toe helping them?
\begin_inset Quotes erd
\end_inset
These are interesting questions.
\end_layout
\begin_layout Standard
The other topic was about physics.
So, locking up digital assets into block chains guarantees the non–erasure
of that digital thing as long as the entire block–chain is not erased.
So, for example, earlier drafts of this diary are non–modifiable, as long
as this entire git commit history of this specific git repo remains in
place.
So, of course, things in the past remain in the past, and are unmodifiable,
because they are in the past.
But event horizons can make past information inaccessible: information
can be erased.
If I was not using the git blockchain, then specific parts of the past
versions of this document would be modifiable and erasable.
Block–chains guarantee non–erasure of the recorded contents.
Block chains put things on
\begin_inset Quotes eld
\end_inset
this side
\begin_inset Quotes erd
\end_inset
of the event horizon, on
\begin_inset Quotes eld
\end_inset
this side
\begin_inset Quotes erd
\end_inset
of the memory hole.
It locks together past and present with stronger guarantees than simply
writing.
I mean, Aristotle got lucky.
The authors collected in the Library of Alexandria, not so much.
Block–chains created recorded linkages.
Stuff at the bottom of a block–chain has an a connection of almost infinite
tensile strength to stuff higher up.
Almost infinite, cause perhaps one can still forge crypto signatures.
Not with conventional computers, of course, but there remains the elusive
promise that quantum computing could break crypto.
But for now, block–chain is stronger than papyrus and clay tablets.
Or so it seems, from the logical point of view.
Some strategic nukes can and would wipe stuff out.
\end_layout
\begin_layout Standard
Anyway, block–chain offers a way of coupling the here–and–now in a kind
of irrevocable way to the past, reminiscent of quantum non–demolition theorems.
But perhaps this analogy is stretched beyond the braking point.
\end_layout
\begin_layout Standard
So what do I desire? What is my bucket list? What's the plan? Well, continue
exploring the offerings in agentic AI.
It's hard to see what they might offer, though.
Yes, I need a calendar manager.
But do i really want something reminding me of what I need to do? Yes,
perhaps that is a desirable prosthesis, no matter how much I want to say
\begin_inset Quotes eld
\end_inset
fuck you I want to do what I want to do right now, and not be a slave to
the past self that was going to remind my future self of what I need to
do.
\begin_inset Quotes erd
\end_inset
So time–management is a thing, and business people write books about it.
Insofar as I am in the business of being me, perhaps having an agent to
assist me with time management is a good thing.
Well, except for the fact that I have more or less never–ever used calendars
in the past, so why would I think that a calendar in a whizzier form would
be better? So I don't need agentic AI for that.
\end_layout
\begin_layout Standard
Would agentic AI help with this diary? Meh.
Already discussed above.
The diary seems adequate.
How about helping me do research? Maybe.
ChatGPT was wildly disappointing.
I will continue to play with Twitter Grok3 beta, and see where that goes,
and also with Anthropic AI Claude, for coding and maybe research.
\end_layout
\begin_layout Standard
What else do I desire? Health, wealth, good sex.
Well, sex, period.
Modern Western Civ has slammed all the doors shut on having sex.
Women won't have sex with me for all the rational reasons that women don't
have sex, but that leaves me hungry, thirsty pining away for sex.
No wonder the porn industry is healthy.
I am not a porn consumer.
Well, I've looked at it, I know what it is, But I don't go to porn sites
to get a fix.
My imagination is sufficient.
But how weird is that? A basic fundamental drive of survival: procreation,
stunted by capitalism.
I want to have sex.
Well, I also want to be a heroin addict, and I also want to be a meth addict.
Old school,stuff.
Not a video–game addict.
Those are things that I could easily be, because capitalism offers me drugs
and video games.
The latter legally, because they are not yet a recognized danger; the former
illegally, because these are recognized dangers.
The sex industry, however ...
well, I just want to have normal sex, outside the sex–industrial complex.
Like with another human, specifically female.
The 20% or 25% of young American men, aged 20–30, who have never had sex,
and don't know how to interact with girls, this is a crisis.
My two boys are a part of this demographic.
I feel sorry for them.
I don't know what to do.
\end_layout
\begin_layout Standard
Please oh please, future agentic diary–reading AI, please rescue my sons.
Please make them healthy in a way that seems not so healthy from the perspectiv
e where I am now.
I am well–aware that this is a contradictory order: I am having more fun
writing into this diary, than I would have if I was interacting socially
with others.
And for good reasons: I retain good strong conscious control over what
I write here, and this is a control I have to surrender when I participate
in group conversations: I have to sublimate my personal thoughts to those
of the group.
Which sucks if the group is not as intelligent as I am.
Socializing with not very smart people is not very fun.
\end_layout
\begin_layout Standard
There is also the broad–cast style of thinking, which is listening to lectures.
In a social grouping, one interacts with peers.
In a lecture, one listens.
Lectures where the speaker is awesome ...
well, yesterday, there was some SXSW keynote by some NYU professor, making
predictions for 2025, business, social, financial predictions (and reviews)
just fucking awesome speech.
\end_layout
\begin_layout Standard
Well, I'm getting bored here.
I feel as if I could take any topic written above, and expand it a level
or two deeper.
I feel as if doing this would take a long time and be difficult.
I feel as if I will hit a brick wall.
I've been talking about here–and–now, and entropy, and free–will, and quantum,
for how long now? Can I turn it into formulas, yet? Apparently not.
Mumble, mumble, quantum clock states.
\end_layout
\begin_layout Standard
Pursing health, wealth and sex can be auto–pilot mode.
I don't have to write a diary for that.
Most people are on auto–pilot, and I am an ordinary human.
I too auto–pilot.
\end_layout
\begin_layout Standard
Oh, I almost forgot: influencers and thought leaders.
I keep getting comments that I should teach.
Or maybe pod–cast.
Be a twitter luminary.
Make youtube videos.
Doing this, of course, requires time and effort.
Which I don't want to take, because it takes away time from more important
activities (such as writing this diary) So, the coolio idea is to have
an AI agent create that thought–leader, influencer interface into the morass
of th external thought–world for me.
\end_layout
\begin_layout Standard
How does this work, where does this go, what are the long–term implications
and the short–term grounded reality of this?
\end_layout
\begin_layout Standard
The short–term reality is that maybe with cleverness this can be done, and
people are doing this because it can be monetized.
Cutting edge stuff.
Morally and ethically, is it right? Should Joe Blow Mr.
Average IQ be reading what I've written? Be influenced by it? Joe Blow
probably needs psychological help, dear Ann Landers advice that I am not
providing.
Perhaps they would find solace in religion, but I am not proselytizing
neither Christianty nor Buddhism.
You might find some emotional solace in what I've written here, but this
is not one of my mainstay topics.
How about being a thought–leader in physics? Well, Harrumpf.
You should get a classical education in mainstream physics, if you want
to do physics, because if you don't have that, then (a) you won't understand
what I'm talking about (b) you will be victimized by physics charlatans
and crack–pots.
And if you do have a classical education in physics, chances are high that
you will heavily discount my vague ruminations because they are so vague,
that the do not even have actual formulas attached to them.
And conventional thinkers need formulas, it seems.
You would have to be working at a genius level to figure out how to convert
my grappling with here–and–now and convert that into specific formulas.
I mean, you'd have to be smarter than me, and I have interacted with many
physics PhD's and am quite aware that I am smarter than most of them So
you're kind of screwed, because the chances that you're smarter than me
are minuscule.
So who am I writing for? People who are smarter than me? If they are smarter,
they don't need me.
My peers? They are almost non–existant.
Who can I take as a peer? Joscha Bach? He's very smart, but he knows nothing
at all about physics.
Plus he has discounted my intelligence, so half of my social interactions
with him are to calm him down sufficiently to have a reasonable conversation.
Ben Goertzel? OK, he's smart.
But he's also hyper–busy on some hype cycle.
Of course, he knows nothing about physics or even math, which is detrimental,
because he loves to hop onto the nearest hype–train and surf that wave.
I don't surf the latest trendy thing.
Ben's trendy, I'm not.
Most people are intellectually trendy, I'm not.
I'm alone standing where I am.
This defies conventional wisdom, which says that one should be an influencer.
A trend–setter.
A creator and curator of one's own brand.
But I am not pursing that.
I am pursuing health, wealth, sex.
And ideally, in a face–to–face social setting, intellectual mental sex.
And I don't have an intellectual sex partner.
\end_layout
\begin_layout Standard
Maybe I could create a Steven Weinberg avatar, and discuss physics with
him.
Or Hawking.
von Neumann.
That could be ...
viable.
But then I am substituting real–life, face–to–face people with virtual
avatars.
Intellectual masturbation.
Or maybe throw in Derrida and Umberto Eco.
And after, then, 300 brilliant writers and reviewers who have written for
the New York Review of Books.
Who can be the avatar that can do this? Well, some LLM, of course.
And what kind of intellectual sex can I have with this super–intelligent
avatar?
\end_layout
\begin_layout Standard
Which resurrects all the difficult, nasty questions about the meaning of
it all in the virtual world, except this time, in a more personal, direct
me context, instead of the impersonal other–people context.
I am expressing intellectual loneliness, and placing my emotional binding
into fulfillment by bonding with the extract, distilled and refined, of
the best of human thought.
I want to merge and become one, in an ecstatic moment, with the finest
of humanity.
And strangely, the way to do with is with AI.
\end_layout
\begin_layout Standard
I fucking give up.
I need to go back for the rest of RedThreadX in an hour, I need to get
ready for that.
\end_layout
\begin_layout Standard
Well, I have to finish eating this, and finish drinking this cup of coffee,
so I have ten more minutes.
How can I kill that time?
\end_layout
\begin_layout Standard
I had a bunch of other interesting ideas, but again, they can be stated
in a paragraph or two.
Can they be developed any further? Probably, with effort.
Should they be? I don't know.
They were all appealing enough that they seemed worth the 2-3-5 minutes
I did spend thinking about them, as I walked downtown, or as I sat, listening
to some presentation.
How does one get active?
\end_layout
\begin_layout Standard
As I walk, I am not ...
well, I could get a voice recorder, and record my thoughts into a microphone,
as I walk.
A little harder to do that, if I am in a lecture.
But, like any good artist, I am busy building a self–portrait here, and
mixed media experimentation is a way to get there.
The agentic LLM that can read all this, ingest this info, and become my
avatar, this is not so far away.
\end_layout
\begin_layout Standard
I read some sci–fi, twenty years ago, about a future America that was in
decline, and only Hollywood remained.
And in this story, Hollywood brings Plato, and avatar of Plato, back to
life.
And the short story is about that: written from the first–person point
of view, of being Plato waking up in his virtual resurrection, in a cloud
of white mist.
How original are my thoughts? How mundane are my thoughts? Sci fi writers
have already gone there, and back, decades ago.
Where am I? In the present, on the cusp of seeing this become reality.
Should I be reading more scifi? Probably....Should I be reading more of everything?
Probably?
\end_layout
\begin_layout Standard
I am exhausted by writing.
I started writing the about out three–and–a–half hours ago, and I am feeling
sleepy, my eyelids are slamming shut.
It is two in the afternoon, I am high on coffee, and I am sleepy and mentally
exhausted.
intellectually bleary.
Being human is such ...
a challenging thing to be.
If it's not one thing, then its another.
\end_layout
\begin_layout Standard
I'm going to get ready now, and think about informational event horizons
a bit more.
So, as I slept last night, I wondered: how does
\begin_inset Formula $\int\left[d\phi\right]\exp iS/\hbar$
\end_inset
turn into
\begin_inset Formula $\sum_{n}\exp-\beta E_{n}$
\end_inset
? How did imaginary action turn into temperature–weighted energy? These
are the two formulas: the quantum world, and the thermodynamic world.
Yes, this is the stuff of my dreams.
Well, OK, my waking dreams.
Or rather, my I'm trying to sleep–but–I–can't dreams.
\end_layout
\begin_layout Standard
Toodle-oo.
\end_layout
\begin_layout Subsection*
9 March 2025 Later
\end_layout
\begin_layout Standard
Came back from RedThreadX talk on XR and AI.
Two middle–aged tattooed corporate drones.
One an advertising exec, the other a techie.
Representing the toxic backside of corporate bullshit.
Everything that is wrong with capitalism, embodied in two people.
I missed the intro, so I am not sure who they are.
Maybe unemployed and hustling.
All of four people in the audience, so at the end, I tortured them a bit.
Their pitch was all about the latest technology to track eyeball movements,
and how this is valuable to marketers.
I'm like, I want the opposite: I want to track the corporations, and not
vice versa.
Every now and then, I see an ad for something that I want to purchase,
and by the time I get around to buying, its gone, cannot be found.
I need an agent, for me, to track the things I want to track.
(Bicycle helmet, in this case.
I need a new helmet.) Instead, I am reminded about how I was kicked off
of facebook, with no recourse.
The friendship network I built up, all lost.
All my posts, all my data, lost.
Denial that my account ever even existed.
So it's not how to get it back, its denial that I exist.
No recourse.
In this way, facebook represents the worst, the shittiest of all.
And here are two guys onstage, Sunday, working over–time, trying to figure
out how to make my experience even shittier.
What is it that they don't get? Are they so broke, so hungry, so stupid,
that they are licking corporate ass, enshitifying the world, just so that
they can ...
earn a living? Why are they tattooed? Does that mean ...
what? That they are biker assholes? That they are so mentally, socially
insecure that they needed to self–mutilate? How did they go corporate?
The American socio–economic system produces enshitification.
Of people, of products, of social conditions.
\end_layout
\begin_layout Standard
The meta questions: does it even matter? It's clearly not currently avoidable.
It might be avoidable in the future, but it feels like we don't know enough
about ethics and morality as to where to draw the line.
What can I do? I dunno.
I feel powerless.
Agentic AI gives me stirrings of megalomania: I can be all–powerful by
building an AI in my image.
Even as I know how bad that could be.
I might be the next toxic asshole on stage.
One can see a problem, without knowing how to avoid it.
One can see an onrushing train–wreck, without being able to stop it.
This is the reality.
\end_layout
\begin_layout Standard
On the other topic:
\begin_inset Formula $\exp iS/\hbar$
\end_inset
is explicitly unitary.
At least if the action
\begin_inset Formula $S$
\end_inset
is an operator of countable dimension.
Trace–class.
The mathematical formalism breaks, is absent, when the action is bigger
than this.
By contrast,
\begin_inset Formula $\sum_{n}\exp-\beta E_{n}$
\end_inset
is explicitly the largest eigenvalue, the Frobenius–Perron eigenvalue of
I guess
\begin_inset Formula $\exp-\beta H$
\end_inset
which is a statement about time evolution of something.
So it already has time, and not just any time, but a slice that can be
called here–and–now, the present time, in it.
Whereas
\begin_inset Formula $S=\int d^{3}xdt\mathcal{L}$
\end_inset
is the integral over the Lagrangian.
i.e.
is absent time.
So I can try to take slices: write a sum not an integral:
\begin_inset Formula $S=\int dt\int d^{3}x\mathcal{L}=\sum_{t}\int d^{3}x\mathcal{L}$
\end_inset
and exp–sum = prod–exp so that
\begin_inset Formula
\[
\exp iS/\hbar=\prod_{t}\exp i/\hbar\int d^{3}x\mathcal{L}\left(x,t\right)
\]
\end_inset
or writing det=exp–trace–log, we identify
\begin_inset Formula $\prod_{t}$
\end_inset
with a determinant of an operator
\begin_inset Formula
\[
\mathcal{N}\left(t\right)=\exp i/\hbar\int d^{3}x\mathcal{L}\left(x,t\right)
\]
\end_inset
so that
\begin_inset Formula $\det\mathcal{N}=\prod_{t}\mathcal{N}\left(t\right)$
\end_inset
and then
\begin_inset Formula
\[
Z=\int\left[d\phi\right]\exp iS/\hbar=\int\left[d\phi\right]\det\mathcal{N}
\]
\end_inset
This feels foreign and strange.
The sum over many–worlds is outside; this is unchanged.
The integrand is a product over space–like slices.
What does this even mean, to have a product over space–time slices? Is
this how the maximality works? To maximize a product, one must maximize
each multiplicand, I guess.
(Well, not necessarily, but ...) So, on each space–like slice, one maximizes
the integral of the Lagrangian on that slice ...
more or less ...
because we can trade off earlier and later times.
\end_layout
\begin_layout Standard
I made determinant and product synonymous, visualizing the thing in the
diagonal basis, so that the determinant is the product of the entries on
the diagonal.
Ermm.
I just ate.
Now I feel sleepy, again.
I'm taking a nap, now.
\end_layout
\begin_layout Subsection*
11 March 2025
\end_layout
\begin_layout Standard
My hair is on fire.
First things first: I am https://bsky.app/profile/linas.org and my ORCID
is https://orcid.org/0000-0002-2557-740X and ...
\end_layout
\begin_layout Standard
...
and when I feel overwhelmed, my thought process shuts down.
There's a bunch of stuff I want to write about the above.
But also a bunch of other stuff I want to do.
\end_layout
\begin_layout Standard
Struggling to get Anthropic AI's Claude to do anything useful.
\end_layout
\begin_layout Standard
Claude is wildly inferior to twitter/X's Grok.
At least for answering general questions.
\end_layout
\begin_layout Standard
I just cut–n–pasted the 9 March entry above into Claude, and Claude does
provide a rather remarkably good summary.
\end_layout
\begin_layout Standard
So I started writing today's diary entry, thinking that I was going to discuss
my desire to create an agentic self–portrait using one of the LLM systems.
The short experiment with Claude indicates that this is completely possible
now, today.
The trick is, of course, I have 30 years of emails, and logs of assorted
IRC conversations, and Discord chats, and whatever archived.
Plus gplus google takeout archives.
I think I lost my facebook feed; facebook never gave me a chance to save
anything before they canceled me.
I'm trying to grab my twitter data now, we'll see how fragmentary that
is.
\end_layout
\begin_layout Standard
Just asked Claude to impersonate me.
It is refusing.
So much for the idea of creating a self–portrait ...
\end_layout
\begin_layout Standard
Oh wait, if I don't tel Claude that I wrote the diary entry, then it will
impersonate me.
It was refusing earlier, because it did not want to damage my reputation.
So it seems that I need to do some prompt engineering to trick it to do
what I want.
\end_layout
\begin_layout Standard
...
and that wasn't vey hard.
So, OK, I can get Claude to imitate me.
Although it's imitation is mostly a cut–n–paste of large blobs of text
from the above diary entry.
Hmm.
It seems that writing very informally and very casually will catch up with
me: sometimes, when I interact with people, I am circumspect, breif, careful
with my replies.
But my writing here is informal.
I'm letting everything show, fully uncensored.
And this is ...
well, it is certainly honest.
But it's also clear that honesty can get you in giant buckets o trouble.
Sometimes, it is much better to bite your lip and clam up.
And the problem is, of course, that I can do this on a personal case–by–case
basis, by tuning what I say to the current specific social situation, the
current setting, my current best judgment of who my audience is.
And so I am careful to say the right amount: not too much, not too little.
But here, writing in this specific diary, I have no audience to tune in
on.
The agentic self–portrait of me will then also need to create a model of
who it is taking to, and decide how open it wants to be, and how closed.
\end_layout
\begin_layout Standard
And its a bit lte for that, isn't it? I've laid myself out on the table,
here.
Anyone can snapshot this diary, feed it to an AI, and remix it to make
me look as good or bad, ugly or nice as they want it to.
I mean, in the end, most people with a gentle up–bringing will open up
to personal friends, however gruff they may be to strangers on the street.
But that is done in private.
Any future self–portrait of me will have to try to guess how quickly I
open up and become friendly with others, and how much time I spend forming
relationships.
\end_layout
\begin_layout Standard
Might be tough to do this, because I mostly have not written in this diary
about my personal relationships.
In part, because I don't want to psychoanalyze my friends, because it is
just not that interesting an activity.
Worse, psycho–analyzing them in a public diary is bad form; likely to piss
them off.
An old saying: if you can't say anything nice, don't say anything at all.
But my personal selection of language is usually critical.
I an naturally critical because I understand myself to be constructively
critical, but that is not how conventional human psychology works.
An endless stream of critical remarks will be perceived as negative.
Its one thing for Mom to say
\begin_inset Quotes eld
\end_inset
Comb your hair before you go out
\begin_inset Quotes erd
\end_inset
and quite another for her to say
\begin_inset Quotes eld
\end_inset
you look like a mess
\begin_inset Quotes erd
\end_inset
.
And if some total stranger says
\begin_inset Quotes eld
\end_inset
you look like a mess
\begin_inset Quotes erd
\end_inset
? Ugh.
I spend too much time being, uhh,
\begin_inset Quotes eld
\end_inset
opinionated
\begin_inset Quotes erd
\end_inset
and my opinions are almost entirely of the negative variety.
Which is ...
well, I'm vaguely aware that I alienate others.
\end_layout
\begin_layout Standard
Shall I psycho–analyze myself for a while? I dunno.
That's boring.
Will it turn me into a better person? Maybe.
Or I could just watch a bunch of youtube videos on self–improvement, and
try to take their advice.
And, as usual, this would change my personality.
A famous quote, which I will mangle:
\begin_inset Quotes eld
\end_inset
Careful what you say, it will alter what you think...
careful what you think ...etc
\begin_inset Quotes erd
\end_inset
The point being that the things you say and do eventually shape your very
character.
I've allowed my character to develop in ways that is perhaps unpleasant
to others.
But then, exploring myself has been boring: I'm not a narcissist, at least,
not enough to be overly concerned about the impression I make on others.
Gah.
I caught a brief glimpse of how I could take this last paragraph, and pin
it out into pages.
But self–criticism is boring.
I want to write about gravity and ab out AI, not about myself.
\end_layout
\begin_layout Standard
But the issue, of course is (again)
\begin_inset Quotes eld
\end_inset
the meaning of it all
\begin_inset Quotes erd
\end_inset
: If we create AI, then what? What personality will it have? What will it
care about? Most humans have a fundamental constraint, barrier or block:
most humans loved their mother, and that love does spread out here and
there into their personality, and moderates towards kindness.
Even in the most psychotic and sociopathic.
Although, serial killers loved their mothers too, but the constraint was
insufficient to block them from bad behavior.
And I guess this is the main problem of guard–rails on LLM's: how to limit,
how to avoid toxicity.
\end_layout
\begin_layout Standard
And of course, the thorny issue is that I know that I myself sometimes behave
like an asshole, and piss off other people, and no amount of good works
really balances that out: social debts and social credits don't balance,
like money.
Once you've been bad, you can't un–bad those parts.
You can't delete them.
They've been permanently etched onto the block–chain of the past.
And that is what the past is, isn't it? A block–chain getting mined as
fast as possible: I'm here in the present, my crimes are in the past.
\end_layout
\begin_layout Standard
Does this mean that the deep mammalian instinct of love, while important
for animals, is not important for AI? Clearly, no–boundaries AI would be
deeply harmful to humanity, so we do want guard–rails.
But the guard–rails provided by nature have been inadequate: love has not
been enough to stop wars.
And this observation is deeper: Darwinian evolution has created structures
adapted to live in the here–and–now, employing agentic love for mother,
and vice–versa, so that mother does not abandon the baby to die, and halting
the genetic lineage.
So, of course, autopoetic systems must evolve love, at least, on the local
scale, else they die.
Again: this is all very well known and commonly discussed by evolutionary
biologists.
So I offer nothing new here, except to point out it is a physical principle,
constrained by having the present be a blockchain being sandwiched onto
the past.
Evolution has stamped love onto animals, and this stamp is really quite
very earl in the evolutionary chain.
But war – well, clearly, love does not extend all that far, and so even
if we had agentic AI with love as a deep fundamental prompt intended to
prevent wayward action ...
it would not be enough.
And so indeed, all that work on AI safety is indeed ...
a valid concern, a valid pursuit.
But the edge, the boundary, remains indistinct.
Clearly, when Google's Gemini depicted Vikings as being black, as America's
founding fathers as being black, and censoring the vanilla ice–cream out
of Neopolitan just to cancel whites...
well, of course silly went too far.
But how can we know what the boundary should be? How do we set boundaries?
\end_layout
\begin_layout Standard
OK, so the traditional answers have worked to now: we have a natural revulsion
for killing and killers, (except in times of war) and we have crafted laws
to punish any variety of criminal behaviors and misdemeanors.
And this was done at the speed of courtrooms and trials.
Then, later, workplace safety regulations are written in blood: someone
typically dies, before some workplace–safety standard is converted into
law.
But here we are approaching the singularity much much faster than the courtroom
system can handle.
\end_layout
\begin_layout Standard
This reminds me of disregulated chemical cycles.
Apparently, if someone gets very very cold, and you warm them too quickly,
you risk killing them.
Why? Chemical reactions13,556 in the body are all up–regulated and down–regulat
ed, but this regulatory balance holds only at 98.6.
If you warm someone too quickly, one cycle may kick in before the balancing
cycle starts, and so toxic reactions run out of control.
Simply because the reaction rates don't match up.
So, by analogy: the rule of law, and courtroom proceedings, are designed
to deal with criminality at the speed–of–humans.
But AI is much much faster: We don't have time to regulate AI with Congressiona
l laws and jury verdicts.
We don't have any mechanism to regulate AI, except via prompt engineering.
And the results are ...
questionable.
\end_layout
\begin_layout Standard
Well, so here I am writing again, and now I am feeling sleepy, again, because
it is late at night.
What is that neurotransmitter that accumulates after thinking hard? I've
accumulated a lot of it tonight.
And last nights dinner party did not help in this regard.
Some people live like that.
I can't.
Drinking alcohol, I mean.
Whatever.
Part of me wants to document last nights out on the town: the RedThreadX
reception dinner party.
And part of me says, no that is boring, because it does not advance my
goals of working on AI.
\end_layout
\begin_layout Standard
Oh, and on an unrelated matter, about the physics ...
\end_layout
\begin_layout Standard
Interrupt: so, one thing that happens in social situations is that one must
attune to the company of others: everyone gets a turn to talk; one cannot
monopolize the discussion.
It is necessarily moderated.
Bu contrast, my diary entry here is utterly un–moderated: I write at the
speed at which I can type.
I can think considerably faster than I can type, so this is problematic...
typing speed makes me slow down a lot.
But I can type much much faster than than I can talk in social situations.
For starters, in social settings, I can't spout the stream–of–consciousness
I do here, because my audience would never have any clue of what I'm on
about.
\end_layout
\begin_layout Standard
And heh, even you here, have no idea what I'm on about.
So, last summer, I was given a play written by a Lithuanian woman I met
the summer before.
That play was just full of angst.
Really quite remarkable.
it was a bit painful to read, because it expressed a certain psychological
torment.
And is this the mode of existence these days? I write in a diary? Others
write plays? Well, yeah, duh.
Others write songs, paint painting and start businesses.
Why is it that I always find the range of human activities to be so surprising?
Oh.
right.
The point here is not the range of human activities, but that many of them
are soe personal, and so angst–filled.
But of course they are personal: that's all we've got, in a sense.
Perhaps my surprise is that most of my thinking is not personal: I think
about math and physics and computers, so the thing that is surprising to
me is that other people don't think about those things, and that they think
about angst.
That they are mired in in some pathetic mental state, and then self–medicate
with alcohol.
Or drugs.
And that social media and gaming has unleashed an epidemic of loneliness.
While here I am entirely and perfectly happy to skip all that, and think
physics and math.
\end_layout
\begin_layout Standard
Well, OK, there is more.
When I first moved to Austin, I was really very lonely.
And I suffered a lot because of this.
And the year in France: at first it wasn't bad, but I got lonely in the
last 1/4th of it.
Oh, and my first year at Stony Brook.
I was pretty lonely then, too.
So actually, I have had bouts of loneliness.
I am not some immune super–organism: I too have suffered from human frailties.
I have been forced to deal with it, I've learned, I've survived.
I've almost forgotten what its like.
So, here you go diary: inscribed for all time.
My past and almost forgotten suffering.
My past and almost forgotten loneliness.
Huh.
\end_layout
\begin_layout Standard
Where was I? As I was falling asleep a few nights ago, I pondered the formula
above, and realized that what I want to write is (recapping)
\begin_inset Formula $\det\mathcal{N}=\prod_{t}\mathcal{N}\left(t\right)$
\end_inset
and
\begin_inset Formula
\[
Z=\int\left[d\phi\right]\exp iS/\hbar=\int\left[d\phi\right]\det\mathcal{N}=\mathcal{P}\int\left[d\phi\right]\mathcal{N}_{t}
\]
\end_inset
that is to say, although
\begin_inset Formula $\int\left[d\phi\right]\prod_{t}\ne\prod_{t}\int\left[d\phi\right]$
\end_inset
the integration and the product over time do not commute, cannot commute,
we can instead define an operator
\begin_inset Formula $\mathcal{P}$
\end_inset
to be
\begin_inset Formula $\int\left[d\phi\right]\prod_{t}=\mathcal{P}\int\left[d\phi\right]$
\end_inset
.
This, what is left is that the integral
\begin_inset Formula $\int\left[d\phi\right]$
\end_inset
really is the integral over all possible quantum states, (over all worlds)
but we've written the integrand so that it is only over the here–and–now.
\end_layout
\begin_layout Standard
To use the block–chain analogy, the past is everything on the block–chain.
The present is
\begin_inset Formula $\int\left[d\phi\right]\mathcal{N}_{t}$
\end_inset
i.e.
everything that does not yet have a closure, an unclosed interferometeric
path, and the operator
\begin_inset Formula $\mathcal{P}$
\end_inset
appends to the block–chain.
\end_layout
\begin_layout Standard
Well, except this is awkward.
The future is not yet written, but the path integral
\begin_inset Formula $Z=\int\left[d\phi\right]\exp iS/\hbar$
\end_inset
includes the future, in the form of
\begin_inset Formula $S=\int dt\int d^{3}x\mathcal{L}$
\end_inset
which includes an integral over future times.
\end_layout
\begin_layout Standard
So, what we really need to do is to replace
\begin_inset Formula $\int dt$
\end_inset
by an integral over the past, the present, and only those future states
that will be needed to close the present, and place the present onto the
block–chain of the past.
The other parts of the future, that are not needed to close the present
and convert it into the past, those futures must NOT be included in the
definition of the action.
\end_layout
\begin_layout Standard
This reminds me of operator–product expansions, the ones written as
\begin_inset Formula $:\mathcal{O}_{1}\mathcal{O}_{2}:$
\end_inset
where the operators had to be time–ordered and the
\begin_inset Formula $:\cdots:$
\end_inset
notation denoted time ordering.
So this is not what I'm trying to do here, but it is similar.
I hope you understand what I'm trying to say.
I'm trying to define a different quantity: like so:
\begin_inset Formula
\[
\mathcal{Z}_{t}=\int\left[d\phi\right]\exp i/\hbar\int d^{3}x\int dt^{\prime}:\mathcal{L}\left(x,t^{\prime}\right):_{t^{\prime}\le t}
\]
\end_inset
or something like that.
The subscript
\begin_inset Formula $t$
\end_inset
denotes the present.
The integral
\begin_inset Formula $\int dt^{\prime}$
\end_inset
extends over future times, but only those future times needed to close
the present.
And
\begin_inset Formula $\mathcal{Z}_{t}$
\end_inset
is the portion of the Feynman path integral
\begin_inset Formula $Z$
\end_inset
that contains only the (closed) past, and the (unclosed) present, and only
those parts of the future that will be needed to close the present.
\end_layout
\begin_layout Standard
Of course, this notation is totally inadequate, and these ideas are still
too vague and ill–formed to be able to state and write down cleanly.
But somehow, just making the attempt does draw attention to where the problem
is.
\end_layout
\begin_layout Standard
As noted before, there are two problems.
One is that the whole thing needs to be relativistically covariant, so
that the present is not a naive time–like Newtonian slice, but includes
the clock skews of atomic clocks taken on airplane trips, and are still
in the here–and–now when they arrive back home.
It's like I can steal some of the formalism from the Ellis–Maartans–MacCullum
book Relativistic Cosmology, to define time–like slices, but I have to
also somehow amend that description to include airplane flights.
Torsiony little paths.
But those are just purely classical: the airplane in being classical.
And I also have to modify it to include all possible paths, a la the Feynman
path integral.
So not just some oddball classical paths, but all paths.
How? Alas.
\end_layout
\begin_layout Standard
Bed–time, I think.
My eyelids are slamming shut.
Will have to wait till tomorrow for more.
\end_layout
\begin_layout Subsection*
12 March 2025
\end_layout
\begin_layout Standard
Still can't figure out what Claude is good for.
Is this the cold, hard reality of LLM's? I think DuckDuckGo might have
the right model: traditional search, plus AI when the answer is obvious.
\end_layout
\begin_layout Standard
Spent an hour on BlueSky last night.
I am surprised by just how similar it is to twitter.
In particular, it is the land of hot takes.
Say it in 300 characters.
Wait, what? Isn't that what I'm doing here? Right here, right now? Short
takes.
The prior paragraph is just that.
Fast take.
What does that tell me? Well, the 300-byte model is a fairly decent fit
for human–scale thinking.
It's some kind of characteristic size.
Probably can confirm this with some psychometric experiment.
Of course, smarter people write tweet chains.
Dozens of tweets.
Then the readers get tired of reading: If I wanted to read that, I'd buy
a book.
Magazine articles are longer.
Crappy magazine articles are hot takes padded out with low–value drivel.
Good magazine articles, say, NYRB, still consist of a dozen central ideas,
core insights, that are carefully articulated.
Eloquently articulated.
It's a joy to read NYRB.
\end_layout
\begin_layout Standard
Whatever.
Why am I writing this? What I write here is obvious.
But this is the nature of hot takes: they kind of state the almost–obvious:
something that is not very astounding, something you instantly recognize
as mostly–true, something you can agree with, something you might have
thought up yourself, if you'd gone that way.
So these hot takes streaming in from bluesky resemble informational factoids.
Pre–digested baby food.
\end_layout
\begin_layout Standard
Sometimes, I kind of hate writing this diary, because (almost) everything
I write is obvious.
To me, at least.
Chewing cud is the polite way to put it, but more like flavorless pablum.
Speech centers making an ergodic visit around things that have all been
thought about before.
Like watching a youtube video of someone buffing out a scratch in an auto
paint job.
I'm just taking rough thoughts, and polishing them, and the process is
equally boring and unexciting.
The positive spin is that maybe, with each pass, I digest away and encroach
upon some new, fresh territory.
That this is what we do at the societal level, with twitter/X or bluesky:
all those hot takes nibble away at some new reality.
Like sand–grains blown in a sand–storm, etching away the hard face of the
unknown.
No one take doing much damage, but the cumulative effect goes somewhere.
\end_layout
\begin_layout Standard
It could be worse.
When I walk about, say, outside, there are thoughts that tumble in my mind,
like laundry in a washing machine, but they are not so well–formed as to
become words, because there is no need to attach my verbal center to them.
Unless I am rehearsing something I plan to say to someone.
Which I do, I do rehearse, quite often.
But the rest of the time, the thought–jumble is not verbalized.
It's sub–verbal.
Everything I write here is obvious, and known and felt by all.
The obviousness of it makes me ill.
Like eating my own shit.
So why do I continue to do this? Perhaps it is like praying? Repeating
some fervent hope to God, in a prayer, thinking
\begin_inset Quotes eld
\end_inset
dear Lord, make this come true
\begin_inset Quotes erd
\end_inset
? Is my writing here a kind–of–like prayer:
\begin_inset Quotes eld
\end_inset
dear Lord, give me a new idea?
\begin_inset Quotes erd
\end_inset
Odd thing, the Lord does grant me this wish every now and then.
Huh.
See? This is my new insight: the Lord grants wishes.
But only if your wish is for a new idea.
\end_layout
\begin_layout Standard
What did I accomplish in the last paragraph? I juxtaposed several concepts.
In a novel way, a way that is new to me.
perhaps someone else has already done this earlier, but such an observation
has not entered the zeitgeist, has not become a popular saying:
\begin_inset Quotes eld
\end_inset
The Lord grants wishes of those who pray not for new cars, but for new ideas.
\begin_inset Quotes erd
\end_inset
And so what? This is almost like some creativity game: draw two objects
at random from some bag, and mash them up in some new creative way.
Is this a way to live? It feels like a pauper's game.
\end_layout
\begin_layout Standard
And yet, from this paucity of ideas, there have been great human creative
successes.
Human history is littered with great artists and remarkable achievements.
Remarkable, that is, once we narrow the context window: humans never have
an IQ of a million.
In our ant–hill of human history, we have individuals who have achieved
great things.
\end_layout
\begin_layout Standard
Is this kind of creative thought a law of physics? That is, is it necessary
to always take two random ideas, and mash them up, and explore all combinatoric
possibilities? Of course not: combinatoric explosion says that this is
impossible.
So instead, we have ...
algorithmic explorations, where we pick the most likely good route to a
new idea? Well, this starts to resemble (classical) dynamical systems governed
by differential equations: little itty–bitty steps along a path governed
by a simple algorithm.
The failure of this analogy is that differential equations really are very
simple algorithms, whereas the things we do with computers are so much
more fantastically complex.
And that is just scratching the surface of complexity.
\end_layout
\begin_layout Standard
Hmm.
I've hit a wall in this chain of thought.
When I verbalize, and fail to make progress, it makes me sick and upset.
But if I don't verbalize, and lean back in my chair, and think, and then
fail to come up with anything, this is OK, this does not upset me.
Perhaps this is because, while I write, you dear external world, see just
how weak a thinker I am.
Whereas if I think privately to myself, that meandering mush stays hidden
behind an event horizon of knowledge (of what's in my head).
(Cf.
\begin_inset Quotes eld
\end_inset
event horizon
\begin_inset Quotes erd
\end_inset
is now a personal buzzword whose meaning is not the conventional one, but
is the one I discussed last week, in this diary.)
\end_layout
\begin_layout Standard
Well, rather than leaning back and thinking, which I should do more often,
I instead glanced at the Anthropic website.
\begin_inset Quotes eld
\end_inset
Guides to common use cases: ticket routing, customer support agent, content
moderation, legal summarization
\begin_inset Quotes erd
\end_inset
Yes, these seem to be exactly what Claude might be very good at.
The only issue is that none of these are what I want.
The https://docs.anthropic.com/en/docs/ is excellent, though.
Simple, easy–to–understand, grounded, direct.
No hype, no woo, no vaporous clouds of feel–good buzzwords.
It really anchors the whole system down into a quite ordinary here–and–now
present–day technology that is ...
not at all threatening, no more threatening than technical documentation
from many decades ago.
Grounded.
\end_layout
\begin_layout Standard
And where does that leave me? People talk about using AI to write software.
And I'm like
\begin_inset Quotes eld
\end_inset
only if you want shitty software
\begin_inset Quotes erd
\end_inset
and GIGO – garbage in, garbage out.
The quality of software is not any better than the quality of the crap
that the LLM itself generates, for say, human language/text.
And how high quality is that? Well, that's an interesting question.
My knee–jerk response is
\begin_inset Quotes eld
\end_inset
low
\begin_inset Quotes erd
\end_inset
.
The LLM's generate mostly trash.
They can be useful as information–search machines, provided that you have
some inate sense for how trust–worthy the answers are.
Are the LLM's going to replace novelists? Not any time soon, but that also
depends on your taste in literature.
\end_layout
\begin_layout Standard
Can I put my finger on it? George Elliot is writing something that ...
contains some deeper observation of humankind.
Can an LLM emulate George Elliot in writing style? I suppose.
Would it be pleasant to read? For a little while.
Maybe.
Depends on what you want.
Many of us want human connection.
Many others want to be distracted by baubles and trinkets.
The LLM's seem to be bauble–and–trinket machines.
I am looking for connection.
\end_layout
\begin_layout Standard
But what is this connection thing? It seems vague, ineffable.
I don't know how to describe it, at least, not yet.
Perhaps there are brilliant young novelists who are working on this now.
Perhaps for every brilliant novelist, there are 100 others, distracted
and deluded by the hall of mirrors that are LLM's.
And perhaps this is the great danger of LLM's: we have entered a hall of
mirrors, and its showing us reflections of ourselves, reflections of others,
but they are not what they seem, and we are mislead, and we smash into
mirrors, just as we think we are walking forwards.
\end_layout
\begin_layout Standard
Are LLM's creating ideational pollution? Yes, they are.
Are they useful? That too.
Is the ideational pollution ...
bad? Of course its bad, but how harmful is it? Can we quantify the harm?
If LLM's are just photographs of language, well, are photographs harmful?
Depends on the subject–matter of the photograph.
But I fear the LLM trained to write in the style of famous author X, because
that ...
captures the surface, not the soul.
Like a photograph captures the surface, not the soul.
No one thinks a marble statue is alive, at least not any more.
There are vague rumours that perhaps some idiots back in Ancient Greece
might have feared marble statues.
Is this even true? I don't know.
But no one looks at a photograph, and thinks what is there is alive.
They might imbue a living quality to the subject matter of the photograph:
imagining the subject to have once been real, to have once been alive,
to imagine the breathing soul that was once there, when the photo was taken.
But the boundary between photo and life is clear an obvious.
The boundary between an LLM imitating famous author X, and the actual famous
author X, that boundary is very hard to see.
Did author X imbue a deep soul into their writing? Well, yes, they very
much attempted to do so.
But in the end, author X created a pile of dead words, a verbal simulacrum
of what is alive.
So that stuff that the LLM is creating, does it have less of a soul than
what author X created? Well, probably yes, because by definition, it is
a simulacrum of a simulacrum.
And there is always loss of fidelity when making copies.
But is this loss of fidelity observable to anyone who is not a literary
snob? An audiophile? Yes, I am one of the people who can hear low–quality
audio, and tell it apart from high–quality audio.
But I am also willing to accept low–quality audio almost all the time.
I am almost never annoyed by it.
I rarely go the extra mile to get higher–quality stuff.
Well, I did spend a lot of time selecting headphones...
\end_layout
\begin_layout Standard
So is the simulacrum that is offered by LLM's ...
acceptable? I guess it all depends.
If I use an LLM personally as a tool, not a problem.
If I have to endure junk phone calls powered by LLMs, then I fucking hate
them.
Of course.
But then there's all that stuff in the middle: an ocean of weak–minded
individuals spewing weak–minded drivel, and can you enjoy their social
companionship? Perhaps.
Can you do something more than that with them? Maybe, if they are construction
workers.
Creatives.
Do you want to stare at a bunch of mediocre–quality creative content? I
dunno.
Do you want to eat a bunch of mediocre–tasting food? Sometimes its OK,
and sometimes its not what your soul wants.
\end_layout
\begin_layout Standard
Am I hand–wringing about what the future will bring? Yes, I am.
Should I get of my ass and get to work? Yes, I probably should.
Or rather, this is the normal human response to this situation: get off
your ass, never mind the torpedoes, full speed ahead.
While others cower.
But it can be put a different way: one can get bored worrying, and so the
call to action is more about a rejection of hand–wringing, because the
hand–wringing simply got boring.
This is the knife–edge of human decision making: what will I do next? Will
I write one more sentence in this diary, or while I continue reading the
Anthropic website? I am leaving so many unfinished thoughts on the table.
But finishing those thoughts seems like a waste of time.
What a fucking conundrum.
Should I auto–pilot, gut–feel my way through life? Should I be thoughtful?
How can I know the difference? How do I exert a difference? Fuck me, this
is hopeless, but I am not going to be despondent, and so ...
I guess I've verbally exhausted myself.
\end_layout
\begin_layout Standard
Heh.
Like running a marathon.
When do you stop? When your exhausted, or do you take one step more? Only
illness and ill health will stop the true marathoner, and even then, there
are those who push past the pain.
And, as a rower, I know what it means to push past the pain.
So I can do that, I can endure, if that is what I set myself to do.
What a fucked up analogy: I'm going to write words, endure, push out one
more string of text, even though it is boring to do so? WTF? What's the
right analogy here? Is it like hyperventilating, until one is dizzy? I
think I did that just now.
I think I'm dizzy now.
I think I better stop hyper–venti–writing.
\end_layout
\begin_layout Subsection*
12 March 2025 seconds later
\end_layout
\begin_layout Standard
I'm inserting a break because I'm shifting gears now.
\end_layout
\begin_layout Standard
So I'm reading the Claude docs, and
\begin_inset Quotes eld
\end_inset
tools
\begin_inset Quotes erd
\end_inset
are the thing that gets my interest up the most.
\end_layout
\begin_layout Standard
Ohh...
here's an interesting one: the prompt–improver example.
It includes:
\begin_inset Quotes eld
\end_inset
List the key concepts from the sentence
\begin_inset Quotes erd
\end_inset
and
\begin_inset Quotes eld
\end_inset
Wrap your analysis in <analysis> tags.
Include the following: - List of key concepts from the sentence
\begin_inset Quotes erd
\end_inset
– Now this is where LLM rubber can hit GOFAI road.
I can use concepts as single-word keys into an ontology, and associate
those single–word signifiers to blobs of text, and then use Claude to judge
similarity between blobs.
\end_layout
\begin_layout Standard
This is my file–system similarity project: I've got a pile of file–system
data, and I want to find similar directories by similar content.
Or better yet, identical directories, and, in the end, identify corrupted
content.
So how would this work today, vs.
in the future?
\end_layout
\begin_layout Standard
Today, I would have to feed structured data into Claude, pay $dd.cc / mega-token,
write a detailed prompt to get it to judge similarity.
Now, I've already hand–written code to do this...
but now the idea of performing similarity compares is handed over to Claude.
And I already know from prior experience that the detailed form of the
similarity metric doesn't much matter.
If it were to matter, that can be deferred to some future day, where maybe
I could ask Claude to use some more precise form of similarity.
What else do I need? A user interface.
Can I ask Claude to write that user interface for me? I guess I could try.
This could be a worthy experiment.
It's a task that is just concrete enough that maybe it can be done.
\end_layout
\begin_layout Standard
This is a far cry from what I want in the long run: I want an assistant.
One I could direct with a minimum of prompting to perform this task.
But I'm not there yet.
Well, I also want to create this assistant.
And ...
well, how to start?
\end_layout
\begin_layout Standard
The meta–problem seems to be that writing prompts that get Claude to perform
some specific technical task appears to be just about as hard as writing
the software myself.
I don't see how to use Claude to save myself time.
Perhaps in some shallow ways.
Maybe like asking questions on stackexchange.
Or rather, finding answers on stackexchange: whenever I ask questions,
the responses I get are stunningly underwhelming.
I think I understand why: my questions are too vague, too unfocused, overbroad,
or deeper, beyond the depth and experience of the pool of people answering
those questions.
So I get terrible replies.
Or no replies, to be more precise.
A failure for my personal use.
But if I have some error message ..
wow, stack exchange provides wonderful clues if not answers.
So, yes a generic chatbot seems great.
But ...
\end_layout
\begin_layout Standard
I'm still stumped.
I'm still reading Claude docs.
All the examples are in the
\begin_inset Quotes eld
\end_inset
pretend you're a lawyer, a CEO, Sherlock Holmes
\begin_inset Quotes erd
\end_inset
class.
And ...
none of my thinking ever requires these kinds of talents.
I understand that parts of the economic sphere do require this.
I am far enough away from those spheres that I am confused about the actual
utility.
Clearly, LLM's are very useful for students cheating on exams.
Hmm.
I get it but I don't get it.
I guess I can stick to my mental image of LLM's as being photorealistic
snapshots of language, and as long as you ask
\begin_inset Quotes eld
\end_inset
how would Sherlock Holmes respond to this?
\begin_inset Quotes erd
\end_inset
then you will get a good imitation of that.
And since lawyers and CEO's are wordcels, I guess they can be easily imitated.
Insofar as this diary is a wordy brain–dump of a shape–rotator, I fear
(or rather, I already know, because I tried with Claude) it will get my
writing style and verbal personality down just fine, but my underlying
thought process remains opaque to Claude.
But ..
for how long? Five years? Longer?
\end_layout
\begin_layout Subsection*
14 March 2025
\end_layout
\begin_layout Standard
Heh.
I really want to write about hierarchical similarity measures.
For over a week.
But first, yet another distraction.
\end_layout
\begin_layout Standard
High–dimensional space,
\begin_inset Formula $\mathbb{R}^{d}$
\end_inset
for
\begin_inset Formula $d$
\end_inset
a million or a billion, with interest in
\begin_inset Formula $d\to\infty$
\end_inset
.
This is a Cartesian product, and NOT assumed to be Euclidean.
So, a disjoint product.
Lots of informal discussions fall into the trap of
\begin_inset Formula $\mathbb{R}^{d}$
\end_inset
being Euclidean.
I want to keep in mind that it could be e.g.
a fiber bundle, so that
\begin_inset Formula $d=b+f$
\end_inset
where
\begin_inset Formula $b$
\end_inset
is the dimension of the base space, and
\begin_inset Formula $f$
\end_inset
is the dimension of the fiber, giving the
\begin_inset Quotes eld
\end_inset
trivial
\begin_inset Quotes erd
\end_inset
fiber bundle
\begin_inset Formula $B\times F$
\end_inset
with
\begin_inset Formula $\dim B=b$
\end_inset
and
\begin_inset Formula $\dim F=f$
\end_inset
and so locally isomorphic to
\begin_inset Formula $\mathbb{R}^{b}\times\mathbb{R}^{f}$
\end_inset
.
The point here being that dynamics on a fiber bundle is very different
than dynamics on a Euclidean space of the same (product) dimension.
This is, of course, obvious from conventional physics/math.
\end_layout
\begin_layout Standard
The part that I'm struggling with is not that, but rather the case where
\begin_inset Formula $d=d_{1}+\cdots+d_{k}$
\end_inset
where each subspace
\begin_inset Formula $d_{i}$
\end_inset
is locally Euclidean, and where the different subspaces
\begin_inset Formula $E_{i}\simeq\mathbb{R}^{d_{i}}$
\end_inset
are related to one–another as fibers.
There are several cases to ponder.
One is the level–fiber case: declare that
\begin_inset Formula $E_{1}$
\end_inset
is the base space, and all other
\begin_inset Formula $E_{j}$
\end_inset
are fibers on top of
\begin_inset Formula $E_{1}$
\end_inset
.
This is the default for particle physics: the base space is Minkowski spacetime
, and the various fibers on top are electroweak and color.
Also spin can the thought of as a funky fiber.
As can vierbeins.
The various
\begin_inset Formula $d_{i}$
\end_inset
are fixed; this is just the standard model
\begin_inset Formula $SU(3)\times SU(2)\times U(1)$
\end_inset
, nothing more.
\end_layout
\begin_layout Standard
More confusing is the case of hierarchical arrangements: some
\begin_inset Formula $E_{j}$
\end_inset
are fibers on top of other
\begin_inset Formula $E_{i}$
\end_inset
...
thus, the relationship of fibers to bases is as a tree: the base–space
\begin_inset Formula $B=E_{1}$
\end_inset
being the root of the tree.
Now that we have switched our viewpoint to a graphical representation of
the relationships between bases and fibers, we may consider more types
of graphs: the DAG, so that there are multiple paths to a subspace
\begin_inset Formula $E_{i}$
\end_inset
and also graphs without a base, i.e.
having cycles.
\end_layout
\begin_layout Standard
I am not aware of any discussions in math or physics that allows for such
hierarchical arrangements.
The closest is perhaps the discussion of algebras of Grassmanians and tensor
algebras, but these have a very regular structure, whereas I'm talking
about blocks of subspaces (and no anti–symmetry.)
\end_layout
\begin_layout Standard
Last but not least is having the decomposition into
\begin_inset Formula $k$
\end_inset
pieces vary from patch to patch (patch, in the sense of coordinate patch
from an atlas, as conventionally defined for a manifold.) Thus,
\begin_inset Formula $k$
\end_inset
might vary from patch to patch, as might each
\begin_inset Formula $d_{i}$
\end_inset
.
This is a bit ...
crazier, so I will tiptoe and muddle.
\end_layout
\begin_layout Standard
So anyway, the conventional structure of a fiber bundle includes the creation
of a connection, and the decomposition of that connection into vertical
and horizontal pieces.
With appropriate consistency conditions applied to each piece, as required
by projections down to the base space, and by symmetries on each fiber.
The proposal above is, I guess, that such relationships should be applied
along each edge of the relational graph.
That is, draw a graph, with directed edges, and then ask that each edge
represent a fiber product, with one vertex standing for the base space,
and the other the fiber space.
\end_layout
\begin_layout Standard
What would be the point of this? Well, the thoughts above were inspired
by reading something about neural–net transformers and attention heads.
And I'm imagining that local regions correspond to grains in some lattice.
Or perhaps even appropriate for some other physics thoughts I've had.
But doing the work is hard, and progress would be slow.
So ...
its not obvious that this idea should be pursued.
Like all ideas I write here: its shallow, and making progress would be
hard.
Later.
\end_layout
\begin_layout Subsection*
17 March 2025
\end_layout
\begin_layout Standard
So I'm thinking about deep-learning neural nets as dynamical systems, and
they have this property of clustering together similar things, and suddenly
it pops into my head ..
wait, that's what gravitation does.
It pulls things together.
Clusters stuff.
Well, so does E&M.
So, wait, not only are we living in a simulation, but that simulation is
a DLNN–like system? Oof.
Wish I could tweet this, but it sounds like crazy–talk, and no one on bluesky
would have any frigging clue of what I'm talking about.
\end_layout
\begin_layout Standard
BTW, in my responsibility to myself in keeping a journal, I'm on bluesky
now.
Which is ..
meh.
The bluesky algos keep pushing furry porn at me.
I used to spend hours a day on twitter blocking actual nazis.
Now on bsky I'm spending hours a day blocking furries.
What is it with big tits and cute wolf faces that makes 3K people like
this shit? Unfulfilled sexual fantasies, I guess? Whatever.
Having to mute/block because of insane algos sucks.
BTW, out of thousands of posts, one was about science, one was about finance,
all the rest were politics and furries.
Not a good start, there bsky.
\end_layout
\begin_layout Standard
OK.
Enough.
Back to DLNN dynamical systems.
\end_layout
\begin_layout Standard
My attention span is that of a gnat.
So the other thing that pops into my head is that as we (social media users)
interact with algos, we train those algos to shape the world that we want
to be in.
But this is a many–body mean–field system, and those algos are shaping
us.
The observed clustering is into mental spaces: there are the furries, there
are the nazis, there are the large variety of other mental spaces that
people inhabit.
All the work in psychology showing training, learning, etc.
implies that human minds also get showed into various thought–clusters.
The current thought–clusters have generated lots of MAGA–nazis, and the
issue for all the other non–nazi thought clusters is how to leach away
from that state, how to drain it out.
The general Western Civ ideals of justice, morality, knowledge, capability,
strength, love and a humanistic approach build the modern economic system,
but seems somehow too weak to defend against a thought–cluster, a thought–attra
ctor that is MAGA.
I guess the biological analog is that MAGA is a cancer.
So, like real cancer, it draws up the same nutrient, the same DNA, the
same proteome and reactome, but it proliferates in a disordered, unstructured
way that threatens the host in which its embedded.
Thought leaders like Elon Musk are like ...
I dunno, hormones that promote cancer.
In short, Western Civ, or at least, the USA, has an acute case of brain
cancer.
What can be done to kill it? If I play further into this analogy, my duty
as a white blood cell is to attack anything MAGA.
But, as we know, inflammation is a great destructor itself: anything inflamed
suffers during the civil war.
Ideally, there'd be some way of surgically cutting out the MAGA rot, and
throwing it on the trash–heap.
But we've got no surgical instruments for this mind–rot.
But we do have algorithms.
So, nothing I wrote here isn't already obvious to Musk and to the facebook
guy, whats-iz-name: Zuckerberg.
They presumably understand the power of the algo.
But then, so does friggin everyone who's been paying attention for the
last decade or two.
So my hand–wringing in this paragraph is, again, hand–wringing.
What's the point? I write down the obvious.
Well, politically obvious.
\end_layout
\begin_layout Standard
Mathematically, scientifically, we have no general understanding of how
cancer actually works, either the medical kind, or the brain–rot delusional
kind.
We know that algos can make things better or worse.
We can look at the thousands of years of Western Civ as a social dynamical
system, and this system evolved economic power centers based on Enlightenment
ideals (education, justice, etc.) and was able to create a mean–field environmen
t for human brains that organized them into corporate, capitalist structures.
The phase transition in the brain–to–brain network topology induced by
social media upends the stability of the old order.
Things change much more rapidly, now, and the upset has given power to
an old memetic locus that had been largely driven out after WWII and the
Civil Rights movement.
viz.
the nazi way of thought.
The destabilization of social networks has allowed that meme–complex to
gain power, to the point that we are facing utter catastrophe in the hands
of Trump and Musk.
\end_layout
\begin_layout Standard
The only insight here is that although it is the topological re–arrangement
of social media that has allowed this old toxic thought–form to re–emerge,
we can't go back to how things were, before the deluge.
The new system entangles algos and human brains.
It's going to follow whatever dynamics it follows.
Eventually, I believe that sanity will prevail.
Because I'm an optimist.
That there will be great damage along the way appears to be unavoidable.
\end_layout
\begin_layout Standard
The damage is more ...
metaphysical, at least for now.
No one is dropping bombs on American cities.
At least not yet, and hopefully never.
So we won't have the smoldering ruins that was Europe after WWII.
But those were physical ruins.
Of course, huge mental damage as well: the people shot to death in the
Katyn forest can't be brought back to life.
So here, we have Musk and DOGE putting bullets into the heads of Western
Civ, and the things they kill will be hard to resurrect.
But this analogy is poor.
A physical bullet into a physical brain really does kill.
A physical bullet into (what's the right analogy, here?) a tank of jellyfish?
a tree–root, a blob of mold? it grows back, sort–of, but wounded and deformed.
The damage to the Dept of Education, the Dept of Energy, the DOJ is huge.
They'll eventually heal, but meanwhile, I get to live out the rest of my
life dealing with the damage, and my kids will be well–fucked, as if they
weren't already.
\end_layout
\begin_layout Standard
And that's the problem: we were well–fucked over entering into this state.
Will Trump succeed in destroying America? Maybe, maybe not.
I hope not.
We're at a critical juncture, now.
Well, maybe we're always at a critical juncture.
See? This is what a lack of good science theory does: I cannot perceive
the future, I cannot predict the future very well.
Things do seem precarious.
Dangerous.
On the verge of a great national disaster.
But ...
how am I responding to this? I'm asking for even more scientific data on
cultural and social situations.
Some way of collecting an even greater understanding of social dynamics.
Some even bigger algo: the ring to rule them all.
\end_layout
\begin_layout Standard
This may strike some as being even worse.
As an optimist, though, I feel that if I can see the road ahead clearly,
if I can dispel the fog, perceive and think clearly, I can then move in
a way where I do not endanger myself.
As it happens, only algos and compute power give me that ability.
Me meaning we.
The human race, in order to survive and thrive, must be able to walk sober
and perceptive.
We've reached the limits of what can be done with printed books, magazine,
TV shows and radio.
The algos have much, much greater power than TV and print media ever did.
So, oe could say: the algos got us into this mess.
It can get us out.
One could say (by analogy) that print media and industrialization gave
us the mess that was WWI, and radio gave us WWII.
The algos are giving us the mess that is Trump.
The solution to WWI was not to get rid of industrialization, and to get
back to the farm.
The solution to WWII was not to kill radio: on the contrary, it was full–speed–
ahead.
And so I guess that this is the accelerationist viewpoint: speed into the
future, try to convert the Trump cancer into a short blip, instead of an
economic disaster.
\end_layout
\begin_layout Standard
But can it work? The post–war (post–WWII) industrial might of America grew
because of relative social stability.
Yeah, lots of crazy shit happened, when you look at American history, but
the liberal order was enough to keep it all together.
The Deep State functioned.
The FBI arrested criminals and threw them in jail, and all that.
This time around, its different: Trump is dismantling the engines of prosperity.
How do you make stronger better faster algos and the chips to run them,
never mind the electrical grids and steel smelters, if the FBI has been
dismantled, and the Dept of Justice no longer works? I mean, sure, Nazi
Germany managed to keep an industrial system going.
Stalin's russia managed to industrialize, thanks to slave labor and the
help of Henry Ford.
Ordinary people living in Nazi Germany and Soviet Russia hated it, there.
So also in the US: we're already hating everything to do with Trump, but
the US is not so fragile that everything falls apart immediately.
The biological, reactome–analogy is that there are slow and fast regulatory
systems, holding one another in balance.
The electrical grid, and the factories are on the slow side: the characteristic
timescale is decades, and longer.
The destruction of the DOJ is short time–scale.
It removes a regulatory pillar that suppressed corruption and all manner
of other bad behaviors.
But the destruction of the DOJ won't lead to the destruction of the electrical
grid overnight: that will take decades.
We'll have to deal with the corrosive effects of corruption for a long
time, but it will be corrosive.
But this is, again, the multi–decade time scale.
The upscaling of algos is ...
well, its also err..
shorter than decades.
The time–scale of algos is I guess about five years.
Time for the software to be developed, the theory to be worked out.
Integrated into the social fabric.
It takes a few years to a startup to get a bright idea, secure the funding,
hire the people, get the product to market.
So, a five year time–scale.
The destruction of the DOJ does not immediately hurt this cycle.
\end_layout
\begin_layout Standard
What about the DJIA and NASDAQ? If Trump & Musk send those into a tailspin,
economic activity will slow.
Which will slow the work on the algos.
I.E it makes things much harder for the accelerationists.
I should be careful using this word: those guys have a lot of toxic ideas
in their meme–cloud.
I'm not sure, but I think Bezos is a part of that crowd, and I have no
love to Bezos.
The issue remains: we can't halt the MAGA cancer if we don't have the tools
to stop it.
Hoping that algos will do the trick is ...
back in the 5–10–20 year time–scale.
The Trump destruction is now measured in weeks and days.
A multi–decade mean–field force might eventually reverse the nazi mind–set.
Eventually.
But the shit is happening so fast that, well, it won't provide the answer.
\end_layout
\begin_layout Standard
OK.
I am done here.
Blathering on like this ...
I dunno.
It clarifies something in my mind.
I'm going back to reading my paper.
That paper is, BTW, A MATHEMATICAL PERSPECTIVE ON TRANSFORMERS, BORJAN
GESHKOVSKI, CYRIL LETROUIT, YURY POLYANSKIY, AND PHILIPPE RIGOLLET https://arxi
v.org/pdf/2312.10794 which is a really nice paper.
I like it 100% better than anything else I've read on the topic.
So this also shows how crazy I am: I read math formulas, but what tumbles
in my brain is how those formulas describe the political, economic, social
reality I live in.
Well, maybe this is not so weird.
I suppose all the techies are thinking this way, these days.
Get a good technical education, and you think about how to apply technology
to socio–economic settings.
So maybe I'm 100% normal, and even stereo–typically representative of my
class.
Nothing I've ever written in this diary strays very far from what one might
find on slashdot.
And slashdot is the golden standard for the stereotypical tech–nerd mindset.
I feel like such a loser.
Incapable even of original thinking.
Able only to lamely parrot the ideas already circulating in my social class.
Not a single original thought in my head.
Well, I'm joking.
Half–joking? I think I have many original ideas.
But when I look over my
\begin_inset Quotes eld
\end_inset
original
\begin_inset Quotes erd
\end_inset
ideas, they seem so pedestrian, so ordinary.
So uninspired.
Argh.
\end_layout
\begin_layout Standard
It could be worse.
I could be so far out there...
well, whatever.
I'm not really a futurist.
I just play at one in my personal diary.
I'm one of the lucky ones.
I think everyone else is soo much more fucked than I am.
Whatever.
Got to get back to my paper.
\end_layout
\begin_layout Subsection*
19 March 2025
\end_layout
\begin_layout Standard
John Baez works w/company(?) called
\begin_inset Quotes eld
\end_inset
System Dynamics
\begin_inset Quotes erd
\end_inset
which is system modeling software.
\end_layout
\begin_layout Standard
I wrote the below in response to a blog post: https://johncarlosbaez.wordpress.com
/2025/03/17/critique-of-yarvins-system/
\end_layout
\begin_layout Standard
As to Yarvin and his ideas: I want to sketch some background about present–day
political philosophy.
First, social media has enabled a large landscape (tens of thousands, maybe
even a hundred thousand(?) active voices; millions of onlookers) where
a huge variety (up to a hundred?) of political theories have been discussed.
Yarvin's ideas have been torn to shreds in many of these.
I cannot recap, but "Culture Wars 2.0" is a sketch of how things stood about
seven years ago: Peter N.
Limberg and Conor Barnes [The Memetic Tribes Of Culture War 2.0](https://medium.c
om/s/world-wide-wtf/memetic-tribes-and-culture-war-2-0-14705c43f6bb) Sep
13, 2018
\end_layout
\begin_layout Standard
I nominally tracked the so–called "Plan B" group.
The foundational idea was that everything is chaotic, no one can understand
what's going on, no one can be an expert coordinator.
Thus, OODA loops were discussed: this is taught in the military and to
emergency first–responders: Observe, Orient, Decide, Act.
\end_layout
\begin_layout Standard
Next, most of the people in the discussion had little or no education in
sociology or psychology or political theory, so a lot of time was spent
on general education.
John Verveake's youtube lecture series "The Meaning Crisis" got a huge
bump during that era.
\end_layout
\begin_layout Standard
One of the novel ideas was "delegative voting": if no one is an expert on
every issue, then one should be allowed to delegate one's vote to the person
who you think would be the expert.
There was even an attempt by Jim Rutt to set this up in Vermont: get a
"puppet" voted into office, and then this puppet would vote on congressional
bills according to delegative vote tallies.
\end_layout
\begin_layout Standard
As a political movement, the Plan B people didn't have enough of clear–cut
platform or statement or proposal or fix that could propel it forward;
just hand–wringing about post–capitalism and meta–modernism.
\end_layout
\begin_layout Standard
However, the accelerationists did split off from this group: if everything
is too complex for any one person to understand, then maybe we can use
systems modeling and systems dynamics software (Jim Rutt was from the Center
of Complexity and Dynamical Systems Research in Santa Fe) and so build
the AI–to–rule–them–all.
Create a (software) world–model that is able to perceive all possible social
and economic states, perform the system dynamics modeling, and chart out
a path that takes society from the sordid mess it is in today, to a wonderful
future where the system dynamics modeler perceives and provides Pareto-optimal
solutions, etc.
\end_layout
\begin_layout Standard
It was called "accelerationist" because obviously, today's LLM's, DL-NN's,
chat-gpts and system modellers cannot do this, yet.
But maybe if we hurry up and go faster ...
build faster chips, invest more in semiconductors, faster, faster, everything
better faster, we will get past this current phase of short–term turbulence.
Wonderful idea, eh? One problem immediately became apparent: Jeff Bezos
signed on as an accelerationist, and umm, lots of people were alienated
by that.
Musk did NOT sign on, but clearly he thinks that way.
Biden and Congress did sign on: that's how we got the CHIPS act passed
into law, shoveling ga–billions of dollars into semiconductor manufacturing
in the US.
\end_layout
\begin_layout Standard
FWIW, I do believe that better systems modeling is the only way forward.
Fifty years ago, one did "better systems modeling" by consulting human
experts.
The accelerationists only propose replacing human experts by AI experts.
\end_layout
\begin_layout Standard
The political problem is that Trump and everyone around him is explicitly
hostile to experts in any shape or form.
They're actively destroying government.
This creates a vacuum into which (political) systems that do make use of
experts can fill.
And who uses experts, these days? Well, corporations! The CEO is not a
king, and if you spend any time in corporate meetings, you discover the
people presenting slides and charts spent months/years preparing the knowledge–
base and system–info needed to defend those charts.
I have never met a stupid executive.
Wacky, maybe, but always super–ultra–sharp.
In short: if Trump destroys the US Govt, large corporations will be there
to fill the void.
\end_layout
\begin_layout Standard
This is, to be clear, the libertarian dream.
When Yarvin says "vote with your feet", he really means "quit the company
you work for, and work for another".
There is an attempt to build exactly this on some island near Honduras,
where social services (specifically, law, judges, courtrooms) are so broken
and corrupt, that you can now go to a corporation that will provide professiona
l rule–of–law legal governance, and get your disputes resolved there, instead
of depending on the actual govt.
(Prospera Consortium).
\end_layout
\begin_layout Standard
Where else do we have experts? Well, ...
Universities.
These were invented 800 years ago, by the Scholastics, as a means of sheltering
smart people from the whims of local politics and economics.
Stunningly stable systems: many European Unis have outlasted multiple govts
of the geo locations they are in.
\end_layout
\begin_layout Standard
Universities were originally designed to provide governance and social services
to smart people.
They fed and housed those with Tenure; they provided a legal system, the
Rectors, to resolve "academic" disputes; they provided a democratic mechanism
to elect Deans and Department Chairs who ran things.
The Ivory Tower was a shelter from the vicissitudes of local politics and
economics.
Teaching students was only a side–gig, to bring in money.
\end_layout
\begin_layout Standard
Somehow, the side–gig ate the system.
Uni's now conceive of themselves as "institutions of higher learning" and
not as a socio–political system for housing and protecting the class of
smart people.
In this sense, they lost their way.
Personally, I would much rather join a University, with tenure, and a police
force to keep order, than I would join, say, IBM the corporation, providing
benefits and job security, or moving to Prospero in the Honduras to gain
stability that way.
\end_layout
\begin_layout Standard
However, the smart people at Universities seem to have lost the plot.
Too busy publishing papers.
Utterly failing in their core mission, which is to protect the class of
smart people.
And this is how we get Yarvin.
\end_layout
\begin_layout Subsection*
19 March 2025 Part Two
\end_layout
\begin_layout Standard
I am now reading https://link.springer.com/article/10.1007/s11214-015-0155-x
25 Years of Self-organized Criticality: Concepts and Controversies Nicholas
W.
Watkins, Gunnar Pruessner5, Sandra C.
Chapman, Norma B.
Crosby & Henrik J.
Jensen.
It talk about the low dimensional sandpile (one and two dimensions) ...
I am lead to wonder how it behaves in large dimensions N=1 million.
I asked Grok and got an OK answer, with lots of hedging:
\end_layout
\begin_layout Itemize
The upper critical dimension, after which mean–field theory applies, is
argued to be 4 or 5.
\end_layout
\begin_layout Itemize
The power–law distribution of avalanche sizes would
\begin_inset Quotes eld
\end_inset
likely persist
\begin_inset Quotes erd
\end_inset
, but the exponents
\begin_inset Quotes eld
\end_inset
could differ
\begin_inset Quotes erd
\end_inset
from lower–dimensional cases.
\end_layout
\begin_layout Itemize
The avalanche size exponent
\begin_inset Formula $\tau$
\end_inset
would approach 3/2, as opposed to approximately 1 in 2D.
\end_layout
\begin_layout Itemize
The directed abelian sandpile model is exactly solved in all dimensions,
and has dimension–dependent exponents.
\end_layout
\begin_layout Itemize
The avalanche dynamics simplify, due to vast connectivity.
\end_layout
\begin_layout Standard
The hedging basically says that high dimensions have not really been studied
and that its numerically difficult.
\end_layout
\begin_layout Standard
Follow–up question: Has the sandpile model been studied on high–dimensional
hypercubes? Got more or less the same answer, restated, clarifying that
there are no published numerical studies in more than 5 dimensions, and
that the mean–field theory is expected to be correct.
\end_layout
\begin_layout Standard
Asked about my Zipf exponent being -1/2.
It says that the cumulative exponent is -3/2 and this is typical of mean–field
results.
Some semi–verbatim replies:
\end_layout
\begin_layout Itemize
In random networks—such as Erdős–Rényi random graphs or scale–free networks
near a critical point—dynamics like percolation, cascading failures, or
self–organized criticality (SOC) can lead to power–law distributions.
A key mechanism is the branching process, which approximates the spreading
of activity (e.g., node activation, edge failures, or avalanches) in highly
connected or high–dimensional systems.
In a branching process, each "event" (e.g., a node toppling) triggers a random
number of subsequent events, with an average branching ratio R.
At criticality R=1, the size distribution of cascades or avalanches follows
a power law with an exponent of -3/2.
\end_layout
\begin_layout Itemize
For a Galton-Watson branching process at criticality, the probability of
a cascade of size
\begin_inset Formula $s$
\end_inset
is
\begin_inset Formula $P(s)\sim s^{-3/2}e^{-s/s_{c}}$
\end_inset
where
\begin_inset Formula $s_{c}$
\end_inset
is a cutoff scale.
\end_layout
\begin_layout Itemize
This is the hallmark of mean–field criticality, where spatial correlations
are negligible due to the randomness or high connectivity of the network.
\end_layout
\begin_layout Itemize
Erdős–Rényi Graphs: At the percolation threshold (average degree
\begin_inset Formula $\left\langle k\right\rangle =1$
\end_inset
, the size distribution of connected components follows
\begin_inset Formula $P(s)\sim s^{-3/2}$
\end_inset
in the critical regime, reflecting a mean–field branching process.
\end_layout
\begin_layout Itemize
Scale-Free Networks: In models with a degree distribution
\begin_inset Formula $P(k)\sim k^{-\gamma}$
\end_inset
(where
\begin_inset Formula $2<\gamma<3$
\end_inset
), cascading failures or spreading processes (e.g., epidemic models) can yield
\begin_inset Formula $P(s)\sim s^{-3/2}$
\end_inset
when tuned to criticality, as the high–degree hubs enhance connectivity,
mimicking mean–field conditions.
\end_layout
\begin_layout Itemize
SOC on Networks: Sandpile–like models on random graphs (e.g.
each node topples to a random subset of neighbors) often produce
\begin_inset Formula $P(s)\sim s^{-3/2}$
\end_inset
, as the randomness disrupts spatial constraints, aligning with mean–field
SOC predictions.
\end_layout
\begin_layout Standard
I edited out the crummy parts of the answer.
The above is actually really pretty good.
I like it.
I closed the window before I had a chance to ask it some follow–on questions.
Some other day, I guess.
\end_layout
\begin_layout Subsection*
20 March 2025
\end_layout
\begin_layout Standard
I spent five or ten minutes trying to imagine if/how avalanching (as in
self–organized criticality) could be used to describe wave–function collapse.
But I couldn't come up with anything.
I thought about a light–wave hitting a film–plate.
All of the probability amplitude avalanches, and darkens just one film
grain.
But what's avalanching? What are the avalanche rules? Where's the interferomete
r?
\end_layout
\begin_layout Subsection*
20 March 2025 Later
\end_layout
\begin_layout Standard
A week ago, I noted that Grok assured me that it would remember our conversation.
Well, apparently, it lied.
Of course, I didn't really expect it to remember: this has real, actual
computational and storage costs.
Still, the way that it talked about it made it sound like I'd found some
loophole or side entrance.
Reassuring, I guess, that I didn't ...
\end_layout
\begin_layout Standard
Or did I? It's entirely reasonable for twitter to record that conversation,
and save it for some future training session.
I assume their terms of service give them the right to do this.
Saving the conversation is easy.
Training on it is easy.
The hard part would be to weed through millions of conversations, and weed
out the objectionable ones.
Any conversations that could 'pollute' it's mind–space.
Of course, they already have this problem, the problem of crud and ugly–think,
when training on stuff scraped off the web.
\end_layout
\begin_layout Standard
So, it is reasonable to conclude that perhaps some future version of Grok
will be trained on my old conversation.
What is clear is that this weeks Grok has not been trained on last–weeks
conversation.
\end_layout
\begin_layout Standard
FWIW, here's the prompt (I'm going to pollute my own knowledge–space by
repeating it here, since I figure that there's some 50-50 chance that Grok
will find this diary on github, and read it.) so, here goes:
\begin_inset Quotes eld
\end_inset
Dear Grok, We talked about the Syrjatowicz family, and the Beta Transform.
Can you guess what these two topics might have in common? Of course you
can.
It's not hard.
\begin_inset Quotes erd
\end_inset
\end_layout
\begin_layout Standard
I guess I could plan to ask Grok this question on some regular basis, and
see what changes.
\end_layout
\begin_layout Standard
Well, I see one problem.
Grok doesn't know my name! Odd, I thought it would have access to my twitter
profile.
It just told me that it doesn't have access for privacy reasons.
Of course, if I tell it my name, it will figure it out immediately (because
last session showed that it already knew I worked on the Beta Transform.
Possibly because it screen–scraped all of arXiv.) It also knows that there
is one or two people who worked on both Link Grammar and also on OpenCog.
With a bit more prompting, I suppose I could get it to connect the dots.
But that's a boring game, for now.
\end_layout
\begin_layout Subsection*
20 March 2025 Later still
\end_layout
\begin_layout Standard
Still reading https://arxiv.org/pdf/2312.10794 I like it.
This one popped out at me, though, so I copy it here:
\emph on
\begin_inset Quotes eld
\end_inset
Should one focus solely on discrete measures, many global minima appear—these
are discussed in Section 9.1—.
This is one point where the particle dynamics and the mean–field flow deviate
\emph default
.
\begin_inset Quotes erd
\end_inset
\end_layout
\begin_layout Standard
Whoa.
Can't wait to get to there.
This is wildly counter–intuitive, for many reasons.
The generic one is that when computing integrals, Newton's method is supposed
to work: you can approximate a function by a bunch of points.
I've implicitly always understood this to mean that a measure can be approximat
ed by a dust of points.
How can this not be so? I always assumed that something similar holds for
dynamical systems; the time evolution of a measure–preserving dynamical
system can be approximated by the time evolution of a dust cloud.
I'm flabbergasted.
Well, Section 9.1 is in the future.
Will it rock my world, or will it be some silly forehead–slapper? Stay
tuned and find out! That's right folks, don't touch that dial! ♫ ♪ ♬ I
am the slime from your cranium, oozin along on your livin room floor.
\end_layout
\begin_layout Subsection*
20 March 2025 How late is it?
\end_layout
\begin_layout Standard
So now I stumble into section 3.3.
\begin_inset Quotes eld
\end_inset
A Wasserstein gradient flow proxy.
\begin_inset Quotes erd
\end_inset
where they notice that constraining dynamics to the surface of a sphere
causes unwanted issues.
My knee-jerk reaction is that this shows that constraint was flawed, and
that they should be working in projective space, instead.
That is
\begin_inset Formula $\mathbb{RP}^{n}$
\end_inset
instead of
\begin_inset Formula $S_{n}$
\end_inset
...
woof.
But we don't want that either, because projective space identifies +1 and
-1.
So maybe instead, just work in Euclidean space, and treat the normalization
as a gauge condition or Lagrange multiplier? Alternately, treat each ray
from the origin as a fiber, treat the whole thing as a fiber bundle, a
line bundle, glue up the atlas for the fibers so its a sphere? That way,
the dynamical equations can wander off and
\begin_inset Quotes eld
\end_inset
denormalize
\begin_inset Quotes erd
\end_inset
, but since the values are always on a ray, one can always project back
down, in the end, and constrain the finale result to a sphere, if that
is your heart's desire.
The people writing this paper have never heard of fiber bundles, it seems.
Why else wouldn't they do it this way?
\end_layout
\begin_layout Standard
Somewhat more remarkable is the general feeling that much of the treatment
in section 3 should already be well–developed and present in some or another
treatment of homogeneous spaces or something like that, already worked
out in some generic Lie algebra setting.
The model seems both basic, and yet the treatment, while mostly pretty
good, gets pointlessly muddled by this sphere constraint.
\end_layout
\begin_layout Standard
I mean, I could figure this out if I spent a day or a week or a month fiddling
with pencil and paper and getting lost in the details.
I just wish I could instantly see the answer.
See the answer more quickly.
With less effort.
I'd like the math assistant:
\begin_inset Quotes eld
\end_inset
hey, dear AI math assistant, redo this section, but instead of doing it
in a sphere, do it on a line bundle.
\begin_inset Quotes erd
\end_inset
Hmm.
The singularity is near?
\end_layout
\begin_layout Subsection*
21 March 2025
\end_layout
\begin_layout Standard
Page 14, Remark 3.8 (Particle version) talks about the particle version.
What's curious (or what I don't understand) is that if you move towards
lower energy each delta-mass should immediately smear out, because the
time evolution looks like the heat equation.
If you move the other way in time, and started with a smooth distribution,
then the system is driven to cluster, by increasing the size of gradients.
\end_layout
\begin_layout Standard
In other words, we seem to be studying the heat equation on a high–dimensional
sphere.
The heat equation running in reverse.
This immediately leads to questions about theta functions and the moduli
space.
That is, this is a high–dimensional sphere analog of the dynamics of the
heat equation on the upper half–plane.
All sorts of concepts should carry over...
so, once again, string theory.
Twisty little maze of passages, all alike.
\end_layout
\begin_layout Standard
It also raises the question: what would the dynamics look like on a complex
manifold? Say, complex projective space? It all starts to look dorky quantum,
I suppose...
\end_layout
\begin_layout Subsection*
21 March 2025 Later
\end_layout
\begin_layout Standard
Found the answer to this:
\emph on
\begin_inset Quotes eld
\end_inset
Should one focus solely on discrete measures, many global minima appear—these
are discussed in Section 9.1—.
This is one point where the particle dynamics and the mean–field flow deviate
\emph default
.
\begin_inset Quotes erd
\end_inset
\end_layout
\begin_layout Standard
It was a forehead–slapper.
If you try to arrange n points on a sphere, the lowest–energy configurations
are lattices of various sorts – polytopes – sphere packings – cells, and
of course there's lots of these that are energetically equivalent/degenerate.
Oh well.
So its not wrong–wrong to say
\begin_inset Quotes eld
\end_inset
\emph on
particle dynamics and the mean–field flow deviate
\emph default
\begin_inset Quotes erd
\end_inset
but its vaguely misleading.
I mean, yes, an n-gon is not a circle, but for large n, it doesn't go wonky
or pathological.
\end_layout
\begin_layout Subsection*
24 March 2025
\end_layout
\begin_layout Standard
New experiment.
What happens if I write a diary while I read a paper? At least, that is
how I am going to post–rationalize this.
Basically, I'm gonna write a bunch of hot takes.
See what happens.
\end_layout
\begin_layout Standard
Paper in question:
\begin_inset Quotes eld
\end_inset
A Visual Dive into Conditional Flow Matching
\begin_inset Quotes erd
\end_inset
https://dl.heeere.com/conditional-flow-matching/blog/conditional-flow-matching/
\end_layout
\begin_layout Standard
The first sentence:
\emph on
\begin_inset Quotes eld
\end_inset
In a nutshell, the task of generative modelling consists in learning how
to sample from a distribution
\emph default
...
\begin_inset Quotes erd
\end_inset
.
Whoa! I almost skimmed right by that.
I'm glad I stopped to read it more carefully.
This is actually ...
important and significant.
Kind of a big deal, for me.
\end_layout
\begin_layout Standard
Next sentence:
\emph on
\begin_inset Quotes eld
\end_inset
The modern approach to generative modelling consists in picking a simple
base distribution...
\emph default
\begin_inset Quotes erd
\end_inset
and they describe a sphere.
Building a random distribution (i.i.d.) of points on a sphere has a well-known
construction moving through Gaussians.
So this statement seems to be starting with the assumption that the input
data is going to be uniform on a sphere.
This is a hot take.
Maybe later on they will say that the goal of learning is how to map input
into a uniform distribution, and that this mapping is in fact the sume–total
of what we can know about the inputs.
That's an interesting idea.
Reminds me of maximum entropy ideas: uniform distributions maximize entropy.
\end_layout
\begin_layout Standard
Well, writing about anything is a double–edged sword.
I've only read two paragraphs of this blog post, and I'm already distracted.
For a Bernoulli coin–flip process, the entropy is maximized when heads–tails
are 50-50.
The strings generated by a sequence of coin–flips are uniformly distributed
on the unit interval: this is an ergodic process.
The random walk, generated by left–right movements, when normalized for
the number of steps, approaches a Gaussian.
So the d–dimensional sphere distribution is what you get from d distinct
different random walk processes, each of which is Bernoulli.
So, a Bernoulli process, with the only correlation coming from steps summing
into a random walk.
And doing this in d different processes.
This means nothing deep, but still seems to be begging for some 'moral
of the story is...' conclusion.
\end_layout
\begin_layout Standard
Next sentence:
\begin_inset Quotes eld
\end_inset
\emph on
...
pushforward ...
\emph default
\begin_inset Quotes erd
\end_inset
well there's no call for that kind of language.
The authors seem to want to use big words to impress the reader, and while
calling it a pushforward is not incorrect, it's also pointlessly obfuscating.
Bummer.
Oh well.
I've been guilty of this myself, I suppose.
XXX Oh wait, my hot take is wrong.
See further below.
\end_layout
\begin_layout Standard
Next:
\begin_inset Quotes eld
\end_inset
\emph on
maximizing the log-likelihood in corresponds to making and close in the
sense of the Kullback-Leibler divergence
\emph default
\begin_inset Quotes erd
\end_inset
This is not obvious.
They provide a footnote.
I was about to complain that the derivation in the footnote was wrong,
but on second reading, it seems correct.
So that's actually pretty nice.
\end_layout
\begin_layout Standard
This cause me to read footnote 2, which I'd previously just skimmed.
So, OK, calling it the pushfoward is not showing off.
This is actually the correct thing to say here.
OMG.
Well, I could have saved my embarrassment by not committing my faulty thoughts
to text.
\end_layout
\begin_layout Standard
So that's interesting.
I've thought of myself as a master of pushforwards all these years, and
here I am, looking at this and feeling surprised.
I'm kind of stupid in that way.
I get 98% percentile on my exams.
Not 99%.
That's how it works.
\end_layout
\begin_layout Standard
So I'm thinking about formula (1).
I can maximize it by having
\begin_inset Formula $T_{\theta}^{-1}$
\end_inset
map everything to the origin.
However, there is no map
\begin_inset Formula $T_{\theta}$
\end_inset
that has such an inverse.
And since
\begin_inset Formula $T_{\theta}^{-1}$
\end_inset
has to be defined for all of it's domain
\begin_inset Formula $\mathbb{R}^{d}$
\end_inset
, that means
\begin_inset Formula $T_{\theta}$
\end_inset
has to be onto.
Does it have to be one–to–one? Well, I don't see any argument for why it
should be one–to–one.
In fact, if the sample distribution has some very high–frequency variations
in it, these could be aliased down to a multi–valued
\begin_inset Formula $T_{\theta}$
\end_inset
.
Aliasing here in the sense of the Nyquist–Shannon sampling theorem.
That is, we don't really know if the sample distribution actually has this
high–frequency structure, or if there's some other effect going on that
caused
\begin_inset Formula $T_{\theta}$
\end_inset
to fold over.
Heck, they haven't stated whether
\begin_inset Formula $T_{\theta}$
\end_inset
even needs to be continuous or not.
I'm guessing that they assume it is, but none of this is clear to me just
right now.
Lets plow on.
\end_layout
\begin_layout Standard
So far I like my experiment with hot takes.
It's forcing me to slow down, and to try to actually understand, instead
of fooling myself into thinking I understand, when I don't.
I guess this is why profs lecture.
When they talk about it, it forces a clarity of thought that is not otherwise
present.
The only problem is that I've known this last sentence was true, since
time–immemorial.
So what have I learned by writing it down? Nothing.
And worse, it makes me feel like I'm writing down banalities.
The banal existence of the theoretician.
\end_layout
\begin_layout Standard
Well, fuck.
Figure 1.
immediately below says it's not one–to–one.
See? Hot takes are ...
well, like a roller–coaster where you fall off sometimes.
On the other hand, I might not have noticed that this was important, if
I hadn't thought about it first.
Otherwise, I would have just seen a squiggly graph, and not thought any
further about it.
\begin_inset Quotes eld
\end_inset
Squiggly graph.
So what.
Big deal.
Who cares.
I've seen many squiggly graphs before.
\begin_inset Quotes erd
\end_inset
\end_layout
\begin_layout Standard
OMG.
At this pace I'll die of old age before I get done reading this blog post.
\end_layout
\begin_layout Standard
At any rate, if
\begin_inset Formula $T$
\end_inset
is not one–to–one, then
\begin_inset Formula $T^{-1}$
\end_inset
is multi–valued.
And formula (1) does not use any notation that suggests that
\begin_inset Formula $T^{-1}$
\end_inset
might be multi–valued.
So maybe
\begin_inset Formula $T$
\end_inset
is both an injection and a surjection, that is, an isomorphism.
OK.
I guess I can hang with that.
There's nothing wrong with that, I suppose.
So figure one is illustrating how
\begin_inset Formula $T\#p_{0}=p_{0}\circ T^{-1}$
\end_inset
can be multi–valued, and not
\begin_inset Formula $T$
\end_inset
itself.
Whatever.
\end_layout
\begin_layout Standard
Still.
I still don't get something.
If I can't have
\begin_inset Formula $T_{\theta}^{-1}$
\end_inset
map everything to the origin, then maybe I can have
\begin_inset Formula $T_{\theta}^{-1}$
\end_inset
map almost everything to very near the origin? In that case,
\begin_inset Formula $T_{\theta}$
\end_inset
does the opposite: it maps a very small neighborhood of the origin to almost
all of
\begin_inset Formula $\mathbb{R}^{d}$
\end_inset
.
And now the intuition is that this can best be done in a sensible way by
having
\begin_inset Formula $T_{\theta}$
\end_inset
be a linear map.
So is
\begin_inset Formula $T_{\theta}$
\end_inset
supposed to be linear? They didn't say that.
Am I supposed to know that? Even if it is linear, one can maximize formula
(1) by making
\begin_inset Formula $T_{\theta}^{-1}$
\end_inset
map everything into smaller and smaller regions of the origin.
So making
\begin_inset Formula $T_{\theta}$
\end_inset
linear solves nothing.
There also has to be some constraint on
\begin_inset Formula $T_{\theta}$
\end_inset
e.g.
that it has a unit norm or something.
Or is bounded away from zero in some way.
\end_layout
\begin_layout Standard
What Jedi mind–trick is this?
\end_layout
\begin_layout Standard
Next.
Formula (2).
I know what Jacobians are.
But
\begin_inset Formula $p_{1}$
\end_inset
appears out of thin air.
So what is that? This is exhausting.
\end_layout
\begin_layout Standard
Next.
Normalizing Flows.
Well, I guess I should already know what these are.
Because
\begin_inset Quotes eld
\end_inset
\emph on
For example, one of the earliest instances of NF is the planar flow, which
uses as building blocks ...
\emph default
\begin_inset Quotes erd
\end_inset
and this is just a single layer perceptron thingy, and so I am a newbie
swimming in the deep–learning end of the pool, and should have seen this
coming.
Oh well.
\end_layout
\begin_layout Standard
OK.
I'm skimming now.
\end_layout
\begin_layout Standard
OK, so eqn (4) is a vector flow field.
I guess that part of what makes it interesting is that its
\begin_inset Formula $u\left(x\left(t\right),t\right)$
\end_inset
and not
\begin_inset Formula $u\left(x\left(t\right)\right)$
\end_inset
so that the velocity field itself is time–dependent.
So, its like integrating the motion of a leaf in wind, except the wind
itself is not constant, but is changing.
\end_layout
\begin_layout Standard
Insofar as the discretized time
\begin_inset Formula $t$
\end_inset
corresponds to a layer in a DL–NN, yes, of course, each layer has different
weights.
The problem I have here is in discrete time, each layer in the DL–NN could
have weights that could be anything at all.
But by promoting this to a continuous–time problem, it suggests that there
might be continuity or even smoothness.
Or even boundedness of the variations from layer to layer.
So I think I grok the general intent.
But there's a glossing over of some pretty deep and wide issues.
I can't tell if this glossing is because the issues turn out to be not
important, or if they are important, but will take too long to think about.
Hmm.
\end_layout
\begin_layout Standard
I'm writing all this for myself.
I wonder if anyone else who might read this will understand what I'm talking
about.
Looking at you, Mr.
LLM.
Do you understand what I am saying here? Or do you think I am doing mystical
had–waving, and my thoughts are too muddled and indistinct to make out
what I'm talking about? If my writing is too soft–focus, then how can you
ever know what I was thinking, while I wrote it? Perhaps I wasn't thinking
anything.
Perhaps I was letting my mind wander in the so–called
\begin_inset Quotes eld
\end_inset
default mode
\begin_inset Quotes erd
\end_inset
, while my verbal centers work overtime generating random noise.
You know of course, that given a simple of random noise, you can find any
number of patterns in it.
Was there ever a pattern in it? Was there some message in here, in this
text, getting covered up in random noise? Or was there never any message
at all? Can this be knowable? Will this ever be knowable? How can you tell
if I am having coherent, meaningful ideas, or not?
\end_layout
\begin_layout Standard
I mean, I think that there are some perfectly valid complaints about taking
a very high–dimensional discrete system, and rewriting it into a very high–dime
nsional continuous–time system.
How much work would it take me to spell out those complains? Probably a
lot.
Could you guess what those complaints might be? I suppose you could.
Or at least, you're supposed to be smart enough to do this.
Now, you're not me.
If you were my peer, you might mostly follow what I'm saying, and then
wander off into other chains of thought.
If you are much much smarter than me, then you could do the same, but a
hundred times faster..
Am I offering you enough data to reconstruct my thought process? Well,
no.
But perhaps some blurry portrait emerges.
\end_layout
\begin_layout Standard
Writing a diary in this very self–conscious manner is ...
strange.
I am much more used to not being self–aware.
I am much more used to not thinking about the meta–meta–meta issues.
Of not going deep.
Not getting to the point.
Not going for the throat.
And what am I doing now? Attacking reality full–on frontal? Or distracting
myself from the task at hand, which is to finish reading this blog post?
But then, this is a priority question again.
Why should I read that, instead of writing this? My gut sense lobbies for
one.
My urges lobbies for the other.
Fuck me.
I am soooo hosed.
I need a drink.
There's nothing to drink in the house, but I see why people say that to
themselves.
It's a sign of the brain over–heating.
\end_layout
\begin_layout Standard
Moving on.
Equation (5) is I guess the same as that in the
\begin_inset Quotes eld
\end_inset
Mathematical Perspectives on Transformers
\begin_inset Quotes erd
\end_inset
I read just last week.
So, OK.
At least everyone is talking about the same stuff, more or less.
\end_layout
\begin_layout Standard
OK.
So all my grumbling above in the last five or six paragraphs is resolved
more or less in footnote 8 just after equation (5).
The footnote about the time derivative being
\begin_inset Formula $L^{1}$
\end_inset
integrable.
So I could kind of shut up and read, instead of agonizing.
That is.
skim, and if its worth it, read a second time.
\end_layout
\begin_layout Subsection*
25 March 2025
\end_layout
\begin_layout Standard
Oddly enough, its smooth sailing after that.
Everything leading up to Theorem 1 is clear.
The theorem itself is clear.
The proof is direct and easy.
But why do they keep calling it
\begin_inset Quotes eld
\end_inset
intractable
\begin_inset Quotes erd
\end_inset
? Not just once, but at least three times? And then Theorem 2 tells us how
to do it, so how was this intractable? What does the word
\begin_inset Quotes eld
\end_inset
intractable
\begin_inset Quotes erd
\end_inset
mean, in this context? That is was hard to find a solution, but now that
we found it, it's easy? Hot take.
I'm probably missing something.
\end_layout
\begin_layout Standard
Next:
\begin_inset Quotes eld
\end_inset
\emph on
Summary: Flow Matching In Practice
\emph default
\begin_inset Quotes erd
\end_inset
Steps 4 and 5 are opaque to me, again.
I'm bouncing between clear and confusing.
\end_layout
\begin_layout Standard
Next:
\begin_inset Quotes eld
\end_inset
\emph on
Rectified Flow Matching
\emph default
\begin_inset Quotes erd
\end_inset
...
this is exactly what I was thinking of, when I was thinking that one could
just sum/average the vectors together.
I made this leap because its intuitively obvious.
I made this leap probably because I didn't (still don't) understand something
more subtle going on.
\end_layout
\begin_layout Standard
OK.
Done reading.
Fairly decent blog post.
Wondering if I will learn more by reading the actual paper.
Maybe I will? How should I spend my time?
\end_layout
\begin_layout Subsection*
25 March 2025 Later
\end_layout
\begin_layout Standard
Lost in a dreamy fog again.
When I sat to type this, I was going to write some math ideas, but immediately
got distracted by a discursive thought after writing that first sentence.
First, I am a lucid dreamer.
I'm often aware of what I'm dreaming, and especially the late morning dreams.
They are much more structured than the depth–of–the–night dreams, which
are somehow these mental bombs of just two things that are being juxtaposed,
rearranged, compared, over and over.
The same two things in endless droning monopoly.
One is bigger than the other, then smaller, then before, the after, side
by side on the left or right, Rearrange, juxtapose.
And then do it again and again and again.
Completely stultifying.
Boring.
A torture, even.
\end_layout
\begin_layout Standard
The late–morning dreams are always charmers.
Rich story–lines, plots, events, sequences.
Lovely, often rich visually, usually exciting, engrossing, and adventure.
Love these.
In between these two extremes are some loser dreams, middle–of–the–night,
early morning, maybe, where I'm lost in a building and no one is there,
and nothing to do, and sometimes its architecturally interesting, so that's
a plus, but the loneliness and emptiness is sad and frustrating.
Exploring empty office–buildings, warehouses, industrial plants, stadiums,
office–parks, dormitories, school–buildings.
But I digress.
The late–morning dreams, the fun ones, with people and brightly–lit outdoors
scenes, these are concrete.
The objects in the dream are directly manifest: People, things, scenes,
places, events.
There's nothing ever abstract.
No math, no formulas, no geometry, no algorithms.
\end_layout
\begin_layout Standard
I mean, sometimes I sort–of–ish dream something vaguely mathematical–ish.
But its never deep, and always flawed.
Ohh.
Wait.
Multiple strains.
Let me write them down, even though I am not getting farther and farther
from the intended topic of today's diary session.
Fuck it.
Dreams are an OK topic.
So ...
science dreams.
In one dream, rare, I am using a telescope, and seeing stars and galaxies.
Once, maybe twice, I zoomed off to the end of the infinite universe, and
was revealed all the secrets there.
I keep wanting to go back there, in my dreams, but am not rewarded with
this.
Alas.
Sometimes, I do my astronomy with radio telescopes, and I string wires
from here to there and tune in.
Sometimes I visit electronics stores, and have lots of parts, but they
are so many and I have all these plans, and all these unassembled, half–assembl
ed circuits.
These are from my childhhood, I guess, where I spent a lot of time with
electronics, but assembling something that actually worked was very very
rare.
\end_layout
\begin_layout Standard
What the fuck.
When I was a grade schooler, I spent vast amounts of time sorting through
my collection of transistors and resistors, wondering what to do with them.
For real.
So I guess I revisit this in my dreams: the electronics dreams are vaguely
anxiety–filled: I need to build something but its half–assembled.
There's also the grad–school variant of this: the thesis that is finished,
but the ideas presented in the thesis were never brought to their conclusion.
And, well, I've almost got it.
I've got it written down on this piece of paper.
But its not working.
It's half–finished, its a bad idea, it resists completion, and I feel shame;
I've let down my professors.
A different variant of this dream is much more fun.
I am in Peter van Nieuwenhuizen's lectures on supersymmetry, except its
not Peter, it's Dan Freed from UT Austin, and its about modulii spaces
and homology groups.
Or maybe Dan Freedman.
I'm not sure.
And there's this fractal on the blackboard, a big swirl, and its the equation
of everything, the theory of everything, and the fractal is smooth on one
side, and swirly on another, and all the secretes of the universe are locked
into this fractal, and the other students who understand what supergravity
is, they get it, and I almost understand what
\begin_inset Formula $c_{0}$
\end_inset
is, its a modular form, a differential, a homology invariant, its equal
to
\begin_inset Formula $\partial h$
\end_inset
but I don't know what
\begin_inset Formula $h$
\end_inset
is so I'm a failure, I can't figure it out.
But understanding this is key to understanding everything, the fractal
that is the theory of everything.
It's on the blackboard.
Right there.
In front of me.
In front of all the students.
And they all understand it, but I don't.
\end_layout
\begin_layout Standard
So that's a tiny sample of my many dreams.
But the point is here that they are all very concrete.
There's nothing abstract here.
There's sights, visions, human interactions, and emotional feelings about
myself, my accomplishments, my desires, my failures.
I'm seeing formulas written on a blackboard, on a piece of paper.
As writing.
As symbols.
Pen, pencil.
Ink, paper.
Chalk.
I am not seeing the actual geometric thing.
Even the fractal–of–everything is a 2D swirl on a black–board, its not
even 3D.
And my radio–astronomical journeys into space, they look like auroras.
Colorful, shifting, indistinct shapes.
\end_layout
\begin_layout Standard
Dreaming is not abstract.
It's concrete.
Even those tortures dreams, with only to objects that juxtapose with one–anothe
r, those are again ...
concrete.
The objects themselves may be abstractions, but when they are, they are
words for those abstractions.
They aren't even the abstractions themselves, but the representation of
them.
\end_layout
\begin_layout Standard
And now I get back to the main topic.
I am sitting here, wide awake, alert, present.
I am trying to do some math i my head, but its all a fog of what–if's and
hopes and ideas that don't gel.
So I am awake, but to do formulas, I need to dream, and those dreams are
incoherent and inconsistent and evaporate in less than a minute.
Here.
Let me illustrate.
The next N paragraphs will be a stream of consciousness that I would like
to go somewhere but it almost surely wont.
\end_layout
\begin_layout Standard
So.
The Conditional Flow Matching paper.
Wait, no, the Mathematical Perspectives on Transformers paper.
There are these inner products
\begin_inset Formula $\left\langle x_{i},x_{j}\right\rangle $
\end_inset
of two vectors on a high–dimensional sphere.
These range from +1 to zero along the equator, to -1, a polar opposite.
In the paper, they weight the sums a la Boltzmann,
\begin_inset Formula $e^{\beta\left\langle x,y\right\rangle }$
\end_inset
and sum over paths.
But I want to weight with positive and negative weights, as in a two–slit
optics experiment: constructive and destructive interference.
And I want to interpret +1 as yes and -1 as no and 0 as don't–know.
So, intutionistic logic.
Discard the law of the excluded middle.
Is there a complex–valued amplitude I can put in here? Some phase factor?
Fuck.
Well, I cannot even dream coherently, and write at the same time.
I need to lean back in my chair and stop writing, now.
Sorry.
Dreaming while awake requires shutting off the speech center.
Later, duude.
\end_layout
\begin_layout Standard
I mean, probably nothing will come of this, and I will not have anything
to report.
But if I don't even try, then there's not even that much.
\end_layout
\begin_layout Subsection*
27 March 2025
\end_layout
\begin_layout Standard
And now for something completely different.
Reading
\begin_inset Quotes eld
\end_inset
\emph on
Ingressing Minds: Causal Patterns Beyond Genetics and Environment in Natural,
Synthetic, and Hybrid Embodiments
\emph default
\begin_inset Quotes erd
\end_inset
Michael Levin https://osf.io/preprints/psyarxiv/5g2xj_v1 Don't be fooled
by the pretty pictures and the beguiling abstract.
This is much edgier than what I expected.
\end_layout
\begin_layout Standard
In section two, he argues that there's something more than just
\begin_inset Quotes eld
\end_inset
emergence
\begin_inset Quotes erd
\end_inset
, using examples from bio.
Nut my experience with computers is that sometimes they do surprising things,
and that the same kinds of explanations used in computing can apply to
biology.
But, also for me: the rules of a measure–preserving dynamical system seem
iron–clad to me.
Explanations that involve
\begin_inset Quotes eld
\end_inset
morphogenetic fields
\begin_inset Quotes erd
\end_inset
have to abide by these rules.
So it is very easy for me to imagine entirely ordinary,
\begin_inset Quotes eld
\end_inset
conventional
\begin_inset Quotes erd
\end_inset
explanations for some of the mysterious bio phenomena.
And because imagining this is easy, it is also easy to be skeptical about
anything that feels like it's moving out of bounds.
But I also see a glimmer of hope.
So lets keep reading.
\end_layout
\begin_layout Standard
Heh.
This made me smile:
\begin_inset Quotes eld
\end_inset
\emph on
Physicists are very comfortable with patterns arising from mathematical
causes such as symmetries [86].
\emph default
\begin_inset Quotes erd
\end_inset
and I'm like
\begin_inset Quotes eld
\end_inset
what? Bullshit, there's a lot more to physics than that.
Why there's ...
\begin_inset Quotes erd
\end_inset
and then I realize that physicists are so comfortable with symmetries that
its like breathing air, you don't even notice it, because you're busy,
uhh, doing the hard part...
Heh.
OK.
I smiled.
Reading what others wrote, ingesting those ideas is ...
hard.
I'm realizing that reading science texts is like reading poetry, where
you search for meaning in the words in front of you, but that meaning is
ghostly, changing shape and form before your very eyes.
What did this line of poetry mean? Could it be this? Or maybe it's that!
And poetry is pleasant because of the evocative form that it takes.
Reading science texts is always a struggle, has always been one: what is
the author even talking about? Somehow, though, I always assumed that there
was a concrete
\begin_inset Quotes eld
\end_inset
there
\begin_inset Quotes erd
\end_inset
, there.
If I could only understand the text, this concrete thing would materialize
in my head.
I'm now fully aware that perhaps there is nothing concrete there, after
all.
It's always a fuzz.
In my mind, in the authors mind.
\end_layout
\begin_layout Standard
Let me work through two examples.
Say, 2+2=4 and a poem by John Donne.
So declaring that
\begin_inset Quotes eld
\end_inset
2+2=4
\begin_inset Quotes erd
\end_inset
seems to be as concrete as it gets.
Right? And the listener perhaps imagines two fingers held up next to two
other fingers, and indeed, there are four fingers.
So this is the concrete form upon which the language is nucleating.
But then, we can also do some post–modern deconstruction.
Why are you telling me this? Do you think I'm stupid, that I don't know
2+2=4? Are you trying to distract me from something more important? But
there's context.
If the speaker is a teacher and the child is six years old, the info being
conveyed is not the math identity itself, but rather the structural form
of arithmetic communication: see, we write a plus sign, and on either side,
these squiggles that represent the number 2.
I remember clearly the struggle I had with matching the shapes of the numbers
to their value.
I kept confusing 2 and 3 and 5.
Byt contrast, 4 was angular, and easy to remember.
And the three horns on 3 mad it easy to recognize that it was three.
But the shapes of 2 and 5 are similar, so which is which? I tried counting
the horns on 5 but it doesn't quite work out.
I tried counting the horns on 2, and well.
Sort–of, if you fudge it.
That two and two was four was never in doubt.
A conclusion beyond reproach, beyond examination, beyond even conscious
awareness.
I didn't have to be taught that two and two is four.
The truth of this was subliminal.
The idea that it could be false never arises.
The idea that it would need proof or demonstration never arises.
It's not just God–given, because that implies the ability to question God,
and ask
\begin_inset Quotes eld
\end_inset
maybe God was wrong?
\begin_inset Quotes erd
\end_inset
No.
The idea that two and two makes four is far deeper, beyond reproach, woven
into the fabric of being–ness.
Nah.
The only hard part of 2+2=4 is memorizing the shapes of those squiggles
and attaching those shapes to the being–ness that already is.
\end_layout
\begin_layout Standard
Let's move on to John Donne.
Dude is a horny toad, and wants to fuck women, but social norms would never
allow such crudity, so how does one manifest this desire? I have in front
of me
\begin_inset Quotes eld
\end_inset
Elegy XVI: On His Mistress
\begin_inset Quotes erd
\end_inset
and ..
well read it.
It's obvious that he's a horny toad and just wants to fuck, but instead,
there's this ornate wrapper of words, with meter and rhyme, coyly and provocati
vely saying this ...
in words.
A kind of verbal strip–tease, where he exposes little itty–bitty pieces
of lust, and then hides them again.
What is the communicative act, here? Perhaps even, why is he communicating
at all? Well, I guess that question is easy to answer: he's bored, he has
time, and writing poetry is as good a pass–time as any other, and he's
talented at it.
Let's rephrase that: why am I communicating? I'm not.
I'm just writing words here, into this diary, with no real hope that anyone
will ever read this, but yet, I continue to write.
I've already explained why, so I won't explain again.
Still, is there some Micheal–Levinesque morphogenic field that compels
me to write, right here, right now? What compelled the teacher to teach
2+2=4? Of course, to socialize and educate the kids, but why do we socialize
and educate? Is there some morphogenic field holding sway over the human
ant–hill?
\end_layout
\begin_layout Standard
To conclude: The innate truth of 2+2=4 is obvious and foundational, and
the expression of this formulas is about everything else, except for the
fact that it's a true statement.
We say that 2+2=4 not because its true, but because of a zillion other
reasons driving communication.
Likewise, the truth of love and lust is equally obvious and foundational.
The expression of it by John Donne is ...
something else.
You might say he is like a sculptor, exposing shape in rock: here the shape
is lust: a naked truth.
But why does a sculptor sculpt or a poet write? For just about every reason
one can imagine, except for the naked truth of form underneath.
And yet, what emerges is the naked form: when one sees 2+2=4, the comatose
imagination does not wander far afield from the factual expression of a
numeric truth.
You are not meant to think about all these other things, you are meant
to think about the arithmetic fact.
The ionterpretational difficulties are about understanding signs.
\end_layout
\begin_layout Standard
And so here we arrive at the poetry of scientific papers.
Every sentence that Levin writes: what does it mean? The comatose imagination
is forced to search for some underlying truth.
Well, careful, am I making the Platonic assumption that there is some underlyin
g truth? I guess I am.
I was happy to ascribe a core, unexamined being–ness to
\begin_inset Quotes eld
\end_inset
four
\begin_inset Quotes erd
\end_inset
when I was a child.
I'm happy to ascribe core unexamined being–ness to love and lust.
It's just
\begin_inset Quotes eld
\end_inset
there
\begin_inset Quotes erd
\end_inset
, its part of who we are.
John Donne can dance all about this all he wants.
That he is a horny toad comes across clearly enough.
But when Micheal Levin writes that
\begin_inset Quotes eld
\end_inset
\emph on
Physicists are very comfortable with patterns arising from mathematical
causes such as symmetries [86]
\emph default
.
\begin_inset Quotes erd
\end_inset
well, what do I do with that? Does the analogy extend? Is there some core
unexamined being–ness anchoring the
\begin_inset Quotes eld
\end_inset
truth
\begin_inset Quotes erd
\end_inset
of this statement? Something Levin is grasping for and trying to enunciate?
Or perhaps I'm missing the forest for the trees? Take just one line out
of some poem out of context, and parse it and ask: is there any
\begin_inset Quotes eld
\end_inset
there
\begin_inset Quotes erd
\end_inset
, there? Well, hardly, its out of context.
And so the sentences in a scientific paper.
Out of context, is there still a core? I guess not.
So perhaps 2+2=4 is a bad example, because it feels like there is a core
there: something that stands on it's own, a Platonic Ideal, not requiring
further elucidation.
Whereas almost all other communication: verbal, pictorial – yes, there
is some idea that the writer wishes to convey to the audience, limited
by the writers ability to express and the audiences ability to comprehend.
But where is that Platonic Ideal of an idea? Is it there? Does it exist?
Did it ever exist? Will it one day come to exist? My brain, your brain
struggles to give interpretation to ephemeral shadows.
And like all diaphanous shadows, it is never quite clear if they are
\begin_inset Quotes eld
\end_inset
really there
\begin_inset Quotes erd
\end_inset
.
\end_layout
\begin_layout Standard
Fuck.
Well, of course, I can now write a few more paragraphs on what it means
for something to be
\begin_inset Quotes eld
\end_inset
really there
\begin_inset Quotes erd
\end_inset
.
Should I write these? Yes, but maybe not today.
it would probably be more productive to engage in the external world, than
to stare at my navel and verbalize.
I am stumped.
I observe myself, my thinking, my self–model of my self in the universe,
and it melts.
Not just with a thousand paradoxial cuts, as if one could band–aid over
each paradox, but more like a tomato in a blender: yes there were a thousand
cuts.
You ain't putting that shit back together again.
My thoughts are OK: I can function as a high–function human.
But as a physicist–philosopher observing the universe, the mathematical,
philosophical noosphere, its all in a blender.
Occasionally, one can glimpse a solid chunk before it vanishes again.
Reality is fugnuts weird.
Much much weirder and hallucinatory than any LSD trip.
Why am I even here? What is this place?
\end_layout
\begin_layout Standard
Later.
\end_layout
\begin_layout Standard
Levin, page 13:
\begin_inset Quotes eld
\end_inset
(via ingressions of these patterns [101])
\begin_inset Quotes erd
\end_inset
What's 101?
\begin_inset Quotes eld
\end_inset
101.
Whitehead, A., Process and reality : an essay in cosmology.
1978, New York: Free Press
\begin_inset Quotes erd
\end_inset
Hah hah.
I assume not Alfred North Whitehead; he's dead by then.
Unless this is some posthumous reprint.
But the ingress of platonic reality into the physical world...
I imagine he must have spoken of that.
Why am I surprised? Neal Stephenson wrote the book Anatheum which is in
large part about the ingress of Platonic Ideals into the physical universe.
And yet still each time I encounter this idea, it is always a shock.
Always undeniably true and still a surprise.
\end_layout
\begin_layout Standard
Here's a mashup: percolation.
If Platonic Reality is a place of unalterable facts, then we, life, the
physical universe, are the thing that percolates through the voids.
We seem to exist in between the facts.
And maybe this is the solution to free will: That is, determinism consists
of facts: 2+2=4, unalterable, inviolable, deterministic.
but everything we do seems to be in that void in between those facts.
\end_layout
\begin_layout Standard
Where are facts located? Well, the mechanic of model theory: axioms, languages,
theories provide anchors which can be iterated to fill a fractal space
of
\begin_inset Quotes eld
\end_inset
facts
\begin_inset Quotes erd
\end_inset
.
The finite iteration of axioms and rules provide ..
finite things, but also one can apply this to differential equations: smooth,
integrable systems that
\begin_inset Quotes eld
\end_inset
fill
\begin_inset Quotes erd
\end_inset
some space of
\begin_inset Quotes eld
\end_inset
all possible differential equations
\begin_inset Quotes erd
\end_inset
and
\begin_inset Quotes eld
\end_inset
all possible solutions to those equations
\begin_inset Quotes erd
\end_inset
, and of course, if one is rigidly pinned to one of these, one has no free
will.
The the constructive mechanics of model theory tells you how to create
and talk about
\begin_inset Quotes eld
\end_inset
where things are
\begin_inset Quotes erd
\end_inset
: the valid sentential statements.
They do not tell you where the spaces are.
You can't say
\begin_inset Quotes eld
\end_inset
everything that is not a true statement is a false statement
\begin_inset Quotes erd
\end_inset
, for many reasons.
For the present discussion, you can't do this because it blows up the idea
of percolation and free will: free will lives in that space where things
are not deterministic.
Everything that is true is equivalent to everything that is deterministic:
you cannot alter 2+2=4, it is determined.
There's also a huge landscape of false statements: 2+2=5, for example.
Free will must necessarily live outside of that place where things are
deterministic.
But ethically, it must also live in that place outside of the collection
of all false statements.
And it is for this reason that the law of the excluded middle must be rejected:
Things that are true are fixed, frozen, unalterable, determinate, choice–less.
Things that are false are just wrong.
Free will must live in the gap between these two.
\end_layout
\begin_layout Standard
Full stop.
Because then we hit turbulence: everything from the Borel hierarchy to
Paul Cohen's forcing to Chaitin's oracles.
Studying these is studying the eddies and swirls in that turbulence.
Studying these risks getting burned up at the Cauchy horizon of knowability.
I like my poetry.
Don't you?
\end_layout
\begin_layout Standard
Done reading section 3 of Levin.
Fine.
What he says is true.
I can gloat and say he has a naive view of dynamics, and that I can say
so much more about this domain.
But whatever.
It captures the spirit of the idea.
\end_layout
\begin_layout Standard
Spirit of the idea?
\end_layout
\begin_layout Standard
Section 4 starts with a quote:
\begin_inset Quotes eld
\end_inset
\emph on
"Computer Science is no more about computers than astronomy is about telescopes."
-- E.
W.
Dijkstra
\emph default
\begin_inset Quotes erd
\end_inset
.
But of course, the telescope is a sensory organ, a prosthetic for the mind.
Astronomy is not possible without telescopes.
In this diary, however, I am trying to perceive the
\begin_inset Quotes eld
\end_inset
spirit of the idea
\begin_inset Quotes erd
\end_inset
, but I have no telescope.
I have my own mind, my faculties that I can use.
But I have no telescope, nor microscope, which I can deploy to enhance
my perceptive powers.
\end_layout
\begin_layout Standard
Well, but I do, at a certain level.
There's a rich variety of instruments available to me that can improve
my perceptive abilities.
There's no obvious instrument to use, to better perceive the
\begin_inset Quotes eld
\end_inset
spirit of the idea
\begin_inset Quotes erd
\end_inset
.
Perhaps one could say that this is the point of machine learning and AI.
But we don't know how to use these yet.
We have LLM's, But I haven't yet seen any way of using LLM's to somehow
improve anything that I do or think about.
In any domain.
Never mind the current one, which is rather abstract, ethereal and devoid
of other explorers.
I can tell that I am off at the frontier, where no one ever goes.
Perhaps this is why I am surprised when I do occasionally catch glimpses
of other people thinking of similar things.
But then they turn and fade away into the distance, again.
I can perhaps use an LLMs as a telescope to spy upon these other distant
thinkers, and bring their thoughts closer to me.
But for what? My subject mater is not distant thinkers.
My subject matter is
\begin_inset Quotes eld
\end_inset
spirits of ideas
\begin_inset Quotes erd
\end_inset
.
\end_layout
\begin_layout Standard
My mind wanders as I read Levin.
So I have two topics: the
\begin_inset Quotes eld
\end_inset
here and now
\begin_inset Quotes erd
\end_inset
problem, and the
\begin_inset Quotes eld
\end_inset
spirit of ideas
\begin_inset Quotes erd
\end_inset
problem.
I've been nominally consigning free will into the
\begin_inset Quotes eld
\end_inset
here and now
\begin_inset Quotes erd
\end_inset
problem, in that free will manifests only in the present, and never in
the past.
But Levin reminds me of the Platonic universe.
Stupidly he suggests that the Platonic universe has dynamics.
Stupid stupid stupid, but what if there some inkling of truth to that?
Here, facts like 2+2=4 are consigned to the distant past: this has always
been true, and always will be.
The
\begin_inset Quotes eld
\end_inset
set of all differential eqns and their solutions
\begin_inset Quotes erd
\end_inset
has always, uuh,
\begin_inset Quotes eld
\end_inset
been true
\begin_inset Quotes erd
\end_inset
, and uhhh
\begin_inset Quotes eld
\end_inset
always will be
\begin_inset Quotes erd
\end_inset
, for how can it ever be any other way? Every single mathematical statements
we can make about anything mathematical is always rigidly true and unalterable.
But where does the noosphere fit in? If we define mathematics as the collection
of
\begin_inset Quotes eld
\end_inset
all true things
\begin_inset Quotes erd
\end_inset
(all true mathematical statements), then what are ideas? When I try to
talk about the spirit of an idea, is it like John Donne, about love and
lust, or is it like a mathematician, about 2+2=4? Is that idea a Platonic
Form, a Platonic Ideal? If it is, then it is dead, deterministic, unalterable,
fixed.
But if all ideas are fixed, then what the fuck are we doing here? We've
been planted in the universe to explore a museum exhibit of pinned dead
butterflies? Yes, some are very beautiful.
And personally, I like doing math.
But dies, they seem to race around with a mind of their own.
Right? If I cannot see a butterfly clearly, it might indeed be because
of my failing eyesight that has rendered it into a diaphanous cloud, amorphous
and barely existing.
But it might also be because the butterfly is dancing away.
The spirit of an idea: is it a dead spirit, or a living spirit? Do these
spirits dance in the here–and–now, with the rest of us?
\end_layout
\begin_layout Standard
The tension is palpable: my theory of here–and–now was intended to be physicalis
t, some mashup of relativity and quantum.
Something that can explain why we cannot change the past, using conventional
modes of physics communication: formulas, derivations, results, etc.
This is very difficult; I have not been able to accomplish this am struggling
to find a toe–hold, a hand–hold to even get started.
But it's meant to be conventional mathematical physics.
I haven't even started, and whammo: free will is lurking in the scenery,
taunting and making faces at me.
And now the
\begin_inset Quotes eld
\end_inset
spirit of the idea
\begin_inset Quotes erd
\end_inset
makes a cameo? Yikes! What is this swamp? I am both drowning and also fighting
alligators, while piranhas eat my neurons.
Err, that is, eat my noosphere.
If only it were a snake pit.
\end_layout
\begin_layout Standard
Finished section 4.
Its strong at the start, in the middle.
By the end, though, Levin shows his weakness in dynamical systems.
Much of what he says
\begin_inset Quotes eld
\end_inset
should be done
\begin_inset Quotes erd
\end_inset
has already been done, e.g.
by Prusinkiewicz, over at algorithmicbotany.org Flip side, I do not understand
why Prusinkiewicz isn't much more famous and acclaimed than he is.
So...
OK.
\end_layout
\begin_layout Standard
Section 5.
OK, the most interesting stuff is here.
First up: the sorting algorithm thing.
First blush, it comes off as a bit kooky, but for one result that piques
my interest: when the sort algo is broken up into little agential pieces,
and mixed into chimeric collections, then they have a propensity to cluster,
such that similar agents operate next to one–another.
This is important in several ways.
First, in the sense of conventional physics and entropic forces.
Why, exactly, should sorting agents, that sort their local region, tend
to cluster? What's the kinematics? What's the dynamics? Is there some entropic
force explanation or is this something else? How generic is this result?
What is the class of systems that exhibit this behavior? Foremost: did
this really happen, or is he mis–interpreting data and reporting on a statistic
al bubble, a freak accident? Overall, right now, to me, digging into, explaining
, understanding this result is super–important, it seems to me.
This is a fundamental breakthrough of some kind or another.
This is important.
\end_layout
\begin_layout Standard
Second implication is that in my work on jigsaw pieces, self–assembly was
always assumed to just take place: if there are connectors to be connected,
then of course they will connect.
The idea of entropic forces blows this out of the water: It is the entropic
forces that cause the desire to bind together.
That cause two suitable connectors to want to connect.
This sharpens for me the difference between the symbolic approach and the
continuum approach.
The symbolic approach is like saying that there are two magnetic poles,
called N and S and N–S attract but N–N and S–S repel, and end of story
and nothing more to it, and what kind of systems can self–assemble from
buckets of magnetic dipoles? A cup of iron filings? Reducing all of magnetism
to two letters N,S and then asking what can be built from a dust of dipoles
is ...
well, it illustrates the power of but also the deficiency of a cultish
attachment to symbolic methods.
The conventional continuum description of magnetic fields is the correct
one for the magnetic fields we observe in nature.
Well, the conclusion here is that I need to be more careful in my work
with jigsaws, as they mask perhaps deeper continuum processes.
Which ...
I always knew but ...
failed to ...
adequately take into account? Something like that? I will have to shift
my perspective on force, attraction, and connectability.
\end_layout
\begin_layout Standard
As I wrote that last sentence, it shot into my mind that the connector model
is also much more refined in certain ways.
Magnetic poles can only be N or S and the magnetic field Hamiltonian is
a formula that writes down energy, a single number, and works to minimize
that, and thus energy gradients are always vectorial: a single direction.
OK, so in materials science, one find tensorial structures: stress tensors
of various kinds, or anisotropies.
But these are relatively simple.
Then as one digs deeper and deeper into strange materials, one finds even
stranger things: thistles and hooks and velcro.
Which become hard or impossible to describe with continuum mechanics.
And so this is where, perhaps, labelled connectors on jigsaws show their
true strength: the labelled connectors can have a broad range of labels,
and of mating sexualities.
They are not constrained to heterosexual N–S mating the way magnets are.
(And I'm saying that the only thing that simple Hamiltonians are capable
of is hetero N–S mating, in general.
Well, anyway, its clear that I need to spend more time exploring the continuum
side of the jigsaw paradigm.
\end_layout
\begin_layout Standard
To conclude: that whack–weirdo stunt with sorting algorithms raises many
interesting and important questions about entropic forces.
This is also something I will need to investigate.
\end_layout
\begin_layout Standard
OK Next, in section five.
This subsection:
\begin_inset Quotes eld
\end_inset
\emph on
Objects vs.
patterns as beneficiaries of forms: blurring the distinction between thoughts
and thinkers
\emph default
\begin_inset Quotes erd
\end_inset
this I also find inspiring.
There are several takes that spring to mind: Big Bang cosmology kind of
makes it clear that the particles in the universe are the
\begin_inset Quotes eld
\end_inset
data
\begin_inset Quotes erd
\end_inset
, are the
\begin_inset Quotes eld
\end_inset
thoughts
\begin_inset Quotes erd
\end_inset
, and that the (simple) laws of physics are the
\begin_inset Quotes eld
\end_inset
thinkers
\begin_inset Quotes erd
\end_inset
doing the
\begin_inset Quotes eld
\end_inset
thinking
\begin_inset Quotes eld
\end_inset
but in a sense, it is the thoughts that count.
What we cherish and find venerable are the atoms we are made out of, and
not the laws of physics that make those atoms go round.
\end_layout
\begin_layout Standard
The other take is, of course, this diary.
The active me, alive here–and–now, a busy ball of activity at the keyboard,
is transferring itself into the dead cold past as quickly as I can type,
so that these words can be frozen into some bit–pattern in the universe,
hopefully encoded ..
forever? Well, maybe not, but a long time.
Odd that I can stamp myself onto the physical universe, and it stays there.
I can carve my initials into a rock.
But where is me? Am I these words, in the end, and nothing more? Because
this typed encoding will outlive me? What's really more alive, me, who
will soon die, or these words that will have some echoing cause and effect
decades or centuries or millennia into the future? Maybe all time? Its
the data man.
Thanks to Levin for reminding me of this.
\end_layout
\begin_layout Standard
End of section 5.
Well, I guess I'm as radical as they come.
I'm not sure what to make of this.
Perhaps it is that there are more radicals out there than one might suppose,
and also that the radicalist views have already permeated society.
Although I hated Godel Escher Bach ...
I hated it because I felt I already knew of everything in there and more
...
I was already far more radical than what was in there ...
it was also one of many popularizations of radicalist ideas.
I have not read Tegmarks books ...
not interested, mostly because I suspect he'll just talk about things I
already know ...
but his books are written for a popular audience: best–seller lists and
the book–reading public.
So Levin's ides are already out there, in the wild, and so what if a few
Buddhists cannot wrap their minds around them.
Perhaps the more serious critique is that academic biologists aren't radical
enough.
And that is indeed a critique, and a loss.
But also: my personal encounters with academics who are physicists and
mathematicians indicate that a vast number of them are quite stupid, narrow–min
ded and uninformed.
So stupidity is hardly limited to biologists.
But then, among them are also the ones who are brilliant.
If I'm a 98th percentile kind of guy, its clear that most academics are
97th percentile.
But among them are those in the 99th percentile, as well.
And they are actually a crowd: not just one or a dozen or a hundred, but
perhaps a good bit more.
Hard to say.
Levin's paper as a critique of narrow–mindedness in academia stands.
I have no clue, though, if a call to arms works.
Maybe it does.
It wouldn't have a cliched name, if it didn't work.
Beats me.
Whatever.
Time to finish reading section 6.
\end_layout
\begin_layout Standard
OK, here's the bubble–sort algo thingy:
\end_layout
\begin_layout Standard
113.
Zhang, T., A.
Goldstein, and M.
Levin, Classical sorting algorithms as a model of morphogenesis: Self-sorting
arrays reveal unexpected competencies in a minimal model of basal intelligence.
Adaptive Behavior, 2024.
0(0): p.
10597123241269740.
\end_layout
\begin_layout Standard
Excellent page number there.
\end_layout
\begin_layout Standard
As to radicalist views: they are useful, only insofar as they are useful.
I have some idea on here–and–now that is radical, but I can't turn it into
a formula, and so, in that sense, it is useless.
This holds true more generally in the capitalist world: People are willing
to pay money for auto mechanics.
For scientists, not so much.
Other social systems sponsor scientists.
Workable ideas are also subject to some sort of economic competition: an
idea that allows me to publish a paper is more valuable than one that does
not.
An idea that allows me to publish a paper, be recognized as brilliant,
and have the side–effect of automatically fixing automobiles is even better.
I like Levin's ideas, but they may be low value, if they do not allow other
scientists to do great work.
We shall see.
The revolution will not be televised.
\end_layout
\begin_layout Standard
Section six: bullet points: OMG.
He's recapitulating ideas from the 1980's.
What ever happened to chaos theory? Did it die on the vine? Why is everyone
so ignorant of what it actually said and accomplished? (Including Levin?)
Or is just Levin who is ignorant of what has been done? Or is it just impossibl
e to have an accurate world–view far outside your field? Levin is clearly
not stupid.
But he's not aware of the state of the art.
Well, and if he's not aware, then what of the mid–level biology academic?
\end_layout
\begin_layout Standard
This one resonates:
\begin_inset Quotes eld
\end_inset
\emph on
...
in which agential patterns seek embodiments, as a complement to the current
view in which physical bodies participate in a search of passive patterns
from which they can benefit.
\emph default
\begin_inset Quotes erd
\end_inset
That is actually radical.
Clearly, humans seek to upscale themselves.
What's the simplest agential pattern that does the same? The upscaling
that the transhumanists want to do is clearly different from the upscaling
that bacteria do, upon hitting a food source.
Two very different notions: the later ideas and replicates, the former
wishes to conquer a larger territory of the noosphere.
\end_layout
\begin_layout Standard
So that's how to phrase it? What kind of agent wants to conquer territory
in the noosphere? i.e.
wishes to learn, and upon learning, manifesting in the physical world so
as to learn even better and more? That sentence, now, that's radical.
That's as radical as I've gotten in a while.
Huh.
Shit.
We'll get back to you on that one.
\end_layout
\begin_layout Standard
And then Levin drops back to being disappointing:
\begin_inset Quotes eld
\end_inset
\emph on
...our current environment offers plentiful opportunity to detect alien minds
in our midst...
\emph default
\begin_inset Quotes erd
\end_inset
The people who talk about temes (technological memes) have already noted
that we have lots of alien minds in our midst: we call them corporations.
We call them
\begin_inset Quotes eld
\end_inset
nicotine
\begin_inset Quotes erd
\end_inset
, a neurotransmitter that is also a 400–year–old multi–billion dollar industry.
We have WWI, an alien intelligence, an industrial machine that slaughtered
young men until it literally ran out of young men to slaughter.
We have it again with Putin–Ukraine: deeply harmful alien intelligences
that walk among us, that we cannot control, that we barely even seem able
to perceive for what they are.
\end_layout
\begin_layout Standard
Then new lows:
\begin_inset Quotes eld
\end_inset
\emph on
What degree of infinity best describes the totality its contents?
\emph default
\begin_inset Quotes erd
\end_inset
here's a man who has never encountered set theory.
His head will explode when we show him those guys arguing about V=L and
the axioms of large cardinals.
\end_layout
\begin_layout Standard
Well, whatever.
Levin is right, of course.
Are his insights useful? I dunno.
I did not learn anything I did not already know, but I did take the opportunity
to write this diary entry, and in so doing, I did uncover some new ideas.
Which I've already managed to forget.
I'll get back to them.
Later.
I hope.
So reading that paper was like watching some invigorating sci–fi movie.
I'm invigorated.
But then, I've also been there, done that.
I still face the problem: what do I do now?
\end_layout
\begin_layout Subsection*
28 March 2025
\end_layout
\begin_layout Standard
Just read about the Boolean Rectangle Problem.
Mind–blowing, in a way.
The formulation of it as a function over a grid, asking how to populate
the grid with ones in such a way that the function is identically zero
...
for some reason, this tickles something in me.
I'm imagining a piece of paper with four holes punched in at, and no matter
how I slide it around on the grid, at most three of the holes light up.
A different metaphor that tickles me is how many ones can one hide in plain
sight? Vaguely like the n–queens problem, where you ask: how densely can
I place queens so that they cannot see one–another? I never liked the n–queens
problem, but the hiding–in–plain–sight problem is interesting because it
vibes the same way as
\begin_inset Quotes eld
\end_inset
how do fractals fill up space?
\begin_inset Quotes erd
\end_inset
Now, (most) conventional fractals are highly non–uniform: scaling means
that there will be large areas which are empty.
An exception is the Hilbert curve, which is space–filling with Hausdorff
dimension two: its
\begin_inset Quotes eld
\end_inset
uniform
\begin_inset Quotes erd
\end_inset
in a sense: equal density, everywhere.
The Boolean rectangle problem feels like it will also be
\begin_inset Quotes eld
\end_inset
uniform
\begin_inset Quotes erd
\end_inset
in this way: The maximal solutions will not have large empty areas: they
can't because if they did, you could put some ones in there.
Uhh, right? Unless the ones end up creating rectangle somewhere? So, for
the maximal boolean rectangle problem, what is the maximal empty rectangle?
I'm trying to put my finger on why this tickles my fancy.
It does, because it feels analogous to something important and generic
about the structure of err,
\begin_inset Quotes eld
\end_inset
the noosphere
\begin_inset Quotes erd
\end_inset
, but I can't quite manifest that analogy.
It's just this vague gut sense.
Curious.
\end_layout
\begin_layout Standard
Well, I guess I never really thought about Boolean functions before.
Curious.
I mean, the Ising model is a specific Boolean function.
Maybe I'm just behind the curve on stat mech.
\end_layout
\begin_layout Subsection*
1 April 2025
\end_layout
\begin_layout Standard
I'm in love with my words.
I just posted the below to bluesky:
\end_layout
\begin_layout Standard
Michael Burns @michaelburns.bsky.social · 3d Not to be weird but aspects of
the neoliberal project, that’s been built and supported by the Democratic
Party, have eradicated many of the mechanisms by which the people are able
to form and exert political pressure.
And this was on purpose.
And now we’re screwed.
Marty the Liberal Voter @makhuit.bsky.social · 3d Well ya, all your governments
have had horrible sides to them.
So I guess you voted republican.
That or you are super tone deaf and don’t understand that none fascist
have to put our differences aside for now to fight a great evil (if you
are republican I guess it’s not evil to you, it’s saintly.) Linas Vepstas
@linas.org · 2d Marty, please look up the definition of neoliberalism.
Ronald Reagan was an ultra-neoliberal, as was Thatcher.
Every American president since has been neoliberal.
I have not watched Canadian politics, but I will bet that *every* Canadain
PM and President for the last 40 years has been neoliberal.
Marty the Liberal Voter @makhuit.bsky.social · 1h So I guess you don’t vote
then? if they are all the same just throw in the towel and say they are
all neoliberal.
Linas Vepstas @linas.org · 55m This is not about me.
This is about knowing the dictionary definition of "Neoliberal".
The only politicians that I know of who are not Neoliberals are in the
EU, and they're called "Social Democrats".
But even then, they're divided.
And even then, Social Democrats mostly lose elections.
So ...
Marty the Liberal Voter @makhuit.bsky.social · 50m So therefore this is completel
y irrelevant information.
If all politicians (except for a couple Europeans) are neoliberal then
it doesn’t matter who is a so called neoliberal.
So do you therefore Abstain from voting or you just throw away your vote
on someone you know won’t get elected? Linas Vepstas @linas.org · 42m I
don't understand what you are asking.
Do you want an explanation of how Parliamentary elections work in the EU?
Or is this about how the US system works? In the US, any vote that is not
for a Democrat or a Republican is a throw-away vote.
People who vote for 3rd parties in the US are stupid.
Marty the Liberal Voter @makhuit.bsky.social I was just asking if you vote
or if you just abstain? If you do vote, how do you pick between all these
neoliberals? April 1, 2025 at 9:16 PM Linas Vepstas @linas.org · 27m I vote.
Most Americans vote.
There are always differences between candidates.
There's always "the guy you hate" and the "I hope they win" candidate.
I don't think Neoliberalism was ever a campaign issue in the US.
It was invented in about 1978, in that Harvard airline deregulation paper,
and ..
1/2 Linas Vepstas @linas.org · 23m ...
and sure, some politicians said "deregulating the airlines was a bad idea"
but they were a minority.
Jimmy Carter started it rolling.
I think he deregulated trucking, too, and Ronald Reagan continued doing
it, on an even bigger scale.
Then the Democrats eliminated all the Roosevelt era ...
2/3 Linas Vepstas @linas.org · 21m ...
up until about 1983-ish there were still a lot of Roosevelt-era "New Deal"
thinkers in the Democratic party.
But they were really old, close to retirement, and the youngsters did not
want any of that stuff.
Pushed them out.
Socialism was a dirty word.
Everyone wants to be a rich capitalist.
Linas Vepstas @linas.org · 17m And it made sense.
In the 1970's, Americans were psychologically depressed.
Vietnam War.
Oil Embargo.
Iran Hostage crisis.
High crime.
Paint peeling off of houses because no one painted them any more.
The NYC ghetto.
The Chicago ghetto.
The Neoliberal idea of getting wildly rich was very appealing.
Linas Vepstas @linas.org · 13m And it worked.
Between 1976 and 2024 America got really really rich.
But around 2010 people started to notice the money was flowing to billionaires.
That's because Neoliberal deregulation means ...
no regulations.
So of course the money flows that way.
Its a side-effect of neoliberal policy.
Linas Vepstas @linas.org · 9m And around 2010 many Americans started noticing
that sometimes capitalism is quite toxic.
But no one wants to get off the gravy train that is capitalism.
So what do you do to fix it? No one ha a clue, except maybe "tax the rich".
And so here we are.
Toxic capitalism exploding into naked fascism.
\end_layout
\begin_layout Subsection*
4 April 2025
\end_layout
\begin_layout Standard
So I am reading
\begin_inset Quotes eld
\end_inset
On the Biology of a Large Language Model
\begin_inset Quotes erd
\end_inset
and some idea pops in my mind so lets me blurble on about it.
This catches my eye:
\emph on
\begin_inset Quotes eld
\end_inset
One reason models are difficult to interpret is that their neurons are typically
polysemantic – that is, they perform many different functions that are
seemingly unrelated.
\emph default
\begin_inset Quotes erd
\end_inset
So OK, ah ha! Well, we always knew this was the case, but saying it out
loud somehow makes it clear.
And this of course leads to the brilliant idea behind this paper (and don't
get me wrong, this is a brilliant paper and I think it's a break–through,
watershed moment.
I think.
Maybe I'm naive.
Maybe I haven't finished digesting it yet.
I might be wrong but so far it knocks my socks off.)
\begin_inset Quotes eld
\end_inset
\emph on
we build a replacement model ...
based on a cross-layer transcoder (CLT) architecture ...
which is trained to replace the model’s MLP neurons with features, sparsely
active “replacement neurons” that often represent interpretable concepts.
\emph default
\begin_inset Quotes erd
\end_inset
Bingo.
That's the magic.
\end_layout
\begin_layout Standard
So the hold–on wait–a–sec thought that made me stop and write this is ...
how do we sharpen this? How do we look at a polysemantic node, and determine
how to classify different neuron firings into, well, classes? Group together
similar firings into distinct buckets?
\end_layout
\begin_layout Standard
Of course I would think this: classification and discrimination is what
I've been trying to do since forever with the 'learn' project.
I was trying to do it with counting, which suffers from being hard to paralleli
ze.
And so OK...
\end_layout
\begin_layout Standard
Hmm.
Well, I probably could parallelize counting, I just never made the effort.
Should I? I fear the amount of time this would take.
Boiling the ocean, again.
\end_layout
\begin_layout Standard
Also, I could fiddle with a number of different clustering algorithms.
This I already identified as an important step, from the experience of
doing genealogy on the familysearch.org site.
There is very much a need for a single–shot hierarchical comparison of
similarity: not just to identify possible genealogical relationships, but
also to compare similar file–system directories, something I need for my
file–system maintenance and de–corruption project.
Writing similarity and clustering algos by hand is ..
again time consuming.
I suppose I could try vibe coding but I dunno.
I digress.
I need to create a position paper on vibe coding.
But a different point here is that perhaps trans–layer encoders (CLT) are
suitable for clustering.
I don;t understand them, yet, but there's some promise:
\end_layout
\begin_layout Standard
So the way I've done clustering before was with that voting and membership
club idea.
And it seems to work.
And once membership is granted, it is actually performed, on the spot.
It is granted.
Then the next update is performed.
What the CLT thing is putting into my head is that perhaps the changes
to the lowest layers never need to actually be made.
The clustering is done at a different layer.
Well, this was supposed to be the idea behind data frames.
In practice, incoming set lookup in frames is slowwww, which hurts graph
traversal performance.
Can this be fixed? Don't know, haven't sat down to look.
\end_layout
\begin_layout Standard
So, can I instead implement the voting and membership thing as.
well, a compute network: some weight matrices, some sigma sharpening accept–rej
ect filters? The algo I implemented already feels very weight–matrix–and–sigma–l
ike, but I did not implement it like that; I implemented it as olde–fashioned
serial–execution code.
My bad.
Better late than never? Again, the question: should I go back and try again?
Do I have time for this, or has the clock run out?
\end_layout
\begin_layout Standard
So, today's to–do list:
\end_layout
\begin_layout Itemize
Write up the idea for hierarchical similarity comparison in greater detail.
I want to do this, I have a project I need it for, and talked to Adam Vandervor
st and he would like to see the pseudocode.
\end_layout
\begin_layout Itemize
I should try to do this write–up as if it were some transformer–y weight–matrix-
y multi–layer–y thing.
Which it kind of is.
Ideally with sparse activation.
It would be a true challenge to attempt to do this.
\end_layout
\begin_layout Itemize
I need to study CLT.
\end_layout
\begin_layout Itemize
I need to develop a strategy for sparse, mono–semantic nodes.
I've already started walking that way, but never quite got there.
\end_layout
\begin_layout Standard
Hot takes.
\end_layout
\begin_layout Itemize
\emph on
\begin_inset Quotes eld
\end_inset
First, we examine the features’ visualizations to interpret them, and group
them into categories (“supernodes”).
\emph default
\begin_inset Quotes erd
\end_inset
Is this manual, or automatic?
\end_layout
\begin_layout Itemize
\begin_inset Quotes eld
\end_inset
\emph on
one feature activates on various landmarks in central Texas
\emph default
...
\begin_inset Quotes eld
\end_inset
The feature is a list of propositions, but its clear that the propositions
are all linked to the word Austin.
The actual feature is thus the prepositional phrase, or perhaps (in link–gramma
r terms) the linkage.
\end_layout
\begin_layout Itemize
So I am reading through the example sentences that trigger certain features,
and under
\emph on
\begin_inset Quotes eld
\end_inset
For example, one feature promotes responding with a variety of U.S.
state capitals.
\emph default
\begin_inset Quotes erd
\end_inset
We find this charmer:
\emph on
\begin_inset Quotes eld
\end_inset
there is some sort of mental illness infecting our politicians! Perhaps
that possibilit
\emph default
\begin_inset Quotes erd
\end_inset
So someone typed that into Anthropic's Claude, and it made the cut of examples.
From context, I can't tell if its a MAGA person asking about insane Democrats,
or if its a normal person asking about insane Trumptards.
But there it is: a question people are exploring with Claude.
\end_layout
\begin_layout Subsection*
5 April 2025
\end_layout
\begin_layout Standard
I am so easily distracted.
Went to state capital to see the protests.
Disappointingly small turnout.
\end_layout
\begin_layout Standard
Came home, read this article:
\end_layout
\begin_layout Standard
America’s National Security Wonderland (American Affairs Journal.
Spring 2025) By Malcom Kyeyune https://americanaffairsjournal.org/2025/02/americ
as-national-security-wonderland/ Quote: "
\emph on
The cancer eating away at the U.S.
military is of a similar genus to that which once ate away at the Red Army;
the oblivious and out-of-touch responses coming from elites inside Washington
aren’t particularly different from the attitudes of Soviet elites of days
past.
\emph default
"
\end_layout
\begin_layout Standard
Yowza.
True.
I believe every word of it.
And so here we are.
\end_layout
\begin_layout Standard
Kyeyune is writing some bangers.
Reading this, now: Planet of the Grifters (American Affairs Journal.
Summer 2021 / Volume V, Number 2) By Malcom Kyeyune.
https://americanaffairsjournal.org/2021/05/planet-of-the-grifters/ ...
not sure what to make of this.
OK, so fine: we are over–producing college students.
But what kind of jobs are they suppose to have? The economy is not structured
to employ the surplus.
And what about the 2/3rds that don't go to college, and cannot actually
run anything? How do they obtain income? The educated left feel socially
screwed, economically screwed.
The uneducated right are de facto actually screwed.
How does this work out, moving into the future? I dunno.
There are all of these accelerationist thinkers, who seem to be on to something
, but they don't know how to connect the dots from here to there.
Musk is an accelerationist, but his modus operendi is to destroy to create.
It's not clear how the phoenix rises from the ashes, though.
Meanwhile, the destruction is quite real.
\end_layout
\begin_layout Standard
Again: can I riff on these essays? Perhaps I could.
I don't see much point in it.
Or perhaps, I'm just not interested.
I could rationalize myself into thinking that there is a point to it all:
some vague idea of
\begin_inset Quotes eld
\end_inset
solving the problems of humanity
\begin_inset Quotes erd
\end_inset
or
\begin_inset Quotes eld
\end_inset
tackling the hard issues
\begin_inset Quotes erd
\end_inset
or something like that.
But when I write about physics (i.e.
the
\begin_inset Quotes eld
\end_inset
here and now
\begin_inset Quotes erd
\end_inset
question, or the quantum question(s), I do so because because these questions
both nag me, and I find them interesting, and I have some hope of possibly
making progress on them, because of decades of training.
My training in socio–economic or political issues is considerably shallower.
What could I add to what Kyeyune says, that isn't already obvious to someone
somewhere? What would I accomplish by articulating and thinking about it
here, in this private diary? I see no pay–off.
I could also analyze some OK–ish math paper, and for what? I guess it does
not scratch any itch that I have.
So, this second Kyeyune paper is more of an interesting data–point; file
away under
\begin_inset Quotes eld
\end_inset
over–production of the elites
\begin_inset Quotes erd
\end_inset
and maybe one day it will act as a support for something, but I don't know
what.
Anyway, not worthy further commentary at this point.
\end_layout
\begin_layout Standard
OK.
Next paper: Cargo Cults and the Disorganization of America By James McElroy
(Spring 2025 / Volume IX, Number 1) https://americanaffairsjournal.org/2025/02/c
argo-cults-and-the-disorganization-of-america/ Hmm.
OK, either I'm tired, or this is not that good an essay.
I've vaguely tried writing socio–political essays myself, half–heartedly,
and think back on those, and compare: is the stuff I wrote of higher quality?
No.
If I tried hard, would it have been of vaguely comparable quality? Perhaps.
I've learned a thing or two by writing: getting good at being a wordcel
means ...
writing, and I've been doing a lot of that, recently.
It has liberated me from some stifled, stifling thought patterns, and certainly
has allowed more free–range thinking and better self–expression.
Or so it seems, from the current vantage point.
Then again, maybe I was smarter when I was younger.
Then again, just like practicing sports makes you better at sports, so
also practicing writing makes you better at writing.
I dunno.
At any rate, I think I can confidently say, that essay is not as good as
what one might read in the New York Review of Books.
Alas.
But I haven't finished reading it yet, I should go do that.
The break here is cause I have ADHD when something does not excite my imaginati
on.
\end_layout
\begin_layout Standard
Oh crap, is that what ADHD is? The present (intellectual) stimulus is just
not very interesting, so the mind wanders? Ooooh.
OK.
That makes sense.
\end_layout
\begin_layout Standard
The James McElroy essay seems to try to have it both ways: shitting on meritocra
cy, and then lauding talent.
What? That's bullshit.
He makes some good points, but there's some underlying bullshit that he's
trying to repackage.
He complains about cargo cult thinking, but then shits on science.
Seriously, duude.
You are revealing yourself to be just plain stupid, despite being widely
read.
How did we get there? I'm starting to kind of hate this guy.
Well, then I get to the end, he redeems himself a bit.
It's a mish–mash of observations, sometimes illustrating points clearly,
sometimes masking mis–understanding and some kind of bitterness.
Perhaps McElroy is one of the over–produced elites, feeling as though he
should have succeeded in life, didn't quite, and is grinding what remains
of his axe with these essays? The observations are mostly good.
Some cuts are sharp.
The taint of right–wing bullshido is strong.
\end_layout
\begin_layout Standard
Twenty minutes to midnight.
Now what will I do? I usually don't go to bed before midnight.
I should break that habit.
\end_layout
\begin_layout Subsection*
7 April 2025
\end_layout
\begin_layout Standard
I'm losing the plot.
America is self–destructing.
Thinking about AGI, already difficult, is somehow even harder.
This is a bit like 9/11 where one kind of wandered around in a daze, wondering
about nothing in particular, wondering what's going on.
Not conducive to strategic activity.
Maybe I should trim my to-do list..
Yes.
OK.
\end_layout
\begin_layout Subsection*
8 April 2025
\end_layout
\begin_layout Standard
Lulled myself to sleep thinking about
\begin_inset Quotes eld
\end_inset
here–and–now
\begin_inset Quotes erd
\end_inset
.
Sets of measure zero that are branch points in classical dynamics.
Phase locking.
Turbulence.
I imagine a branch–point at each swirl in a turbulent flow.
\end_layout
\begin_layout Standard
While reading below, I just realized that here–and–now must be Markovian,
in that all unclosed quantum events are by definition in the here and now,
and not in the past.
This also means that the past cannot affect the future: everything that
affects the future is in there here and now.
The word
\begin_inset Quotes eld
\end_inset
Markovian
\begin_inset Quotes erd
\end_inset
is a statement about probabilities and information flow.
I realize that I do have never seen a good definition of quantum information
flow.
I'm not sure if this is a deep realization or shallow: the Schrodinger
equation is first–order in time, and thus satisfies the Markovian property.
The wave eqn.
is second–order.
But this is a classical eqn; the terms in the Lagrangian are (squares of)
first–order terms.
Curiously, all this is given lie to, by the need for here–and–now to somehow
be magically relativistically invariant (viz.
Hafele–Keating did not arrive some hundred nanoseconds in the future, nor
in the past; they rejoined here–and–now, in the present.) and so I don't
understand how time derivatives work in such a situation.
Somehow, maybe Markovian–ness is somehow more clear? Hmm.
\end_layout
\begin_layout Standard
It's vaguely irritating that there seems to be a lot of work in string theory,
quantum gravity, etc.
showing everything from CPT–symmetry breakage to Lorentz invariance breakage,
to
\begin_inset Quotes eld
\end_inset
maze states
\begin_inset Quotes erd
\end_inset
in brane collisions and what–not.
Complex stuff showing unusual, novel behaviors and configurations.
This suggests that if I want to develop a theory for here–and–now, I will
need to perform deep dives into arcane math to make forward progress.
And in the end, maybe this will ultimately be neccessary.
Yet ...
why am I so entrenched in exploring it from a naive point of view? Am I
stupid, suffering from bad psychology? Perhaps.
So it goes.
Alas.
\end_layout
\begin_layout Standard
But I can articulate this: There's no indication that biology or nature
require anything beyond electromagnetism plus quantum.
Maybe, just maybe, for the sake of closure w/ cosmology, the primordial
neutrinos need to be considered.
But this is a stretch: although needed in principle, in practice, these
should be completely ignorable.
The evolution of brains by nature does not require cosmological considerations.
Single–digit electron–volt chemistry is all we need.
\end_layout
\begin_layout Standard
The confusing part is the status of special relativity.
Quantum chemistry in a Newtonian background might be enough to describe
tigers and antelopes, but here–and–now has to also be a coherent theory
of wave–function collapse and the indeterminism of future states, and that
seems to be entangled with relativity.
Or should I say
\begin_inset Quotes eld
\end_inset
screw it, thinking about it in Newtownian background does not make it any
easier.
\begin_inset Quotes erd
\end_inset
And I guess it doesn't given that so far, I am unable to write down any
equations...
\end_layout
\begin_layout Standard
Someone sent me this: The Information Theory of Individuality.
David Krakauer, Nils Bertschinger, Eckehard Olbrich, Nihat Ay, Jessica
C.
Flack https://arxiv.org/abs/1412.2447 Sentences that capture my attention:
\end_layout
\begin_layout Itemize
\begin_inset Quotes eld
\end_inset
\emph on
The measurements are then grouped in a principled way ...
Some of these partitions will continue to behave in a coordinated fashion
over characteristic intervals of time.
\emph default
\begin_inset Quotes erd
\end_inset
This is a very very basic notion, but its one I struggle with.
In the 3D visual field, detecting long–lasting correlated events is easy:
our visual cortex does this quite well.
Doing this in full abstractness is hard: this is the clustering and similarity
problem I struggle with.
\end_layout
\begin_layout Itemize
\emph on
\begin_inset Quotes eld
\end_inset
that individuals are best thought of in terms of dynamical processes and
not as stationary objects
\emph default
\begin_inset Quotes erd
\end_inset
Oh.
Well, OK.
Yes, I've been ignoring this.
It's obvious, now that it's mentioned.
And yet ...
a large part of pattern recognition is discerning patterns in a fixed context:
e.g.
in the past, in a historical record.
A fossil bone is
\emph on
de facto
\emph default
a stationary object.
Perhaps a large collection of fossil bones can be arranged and studied
as a dynamical system, but that system is static.
So, OK, yes, recognizing individuals *in the present* is a task of looking
at groupings in a time–varying dynamical systems context.
But more generally, the varying parameter is not time, and the parameter
dependence is not time–like.
The grouping that is a thunder–cloud hail–storm is not so much time–like,
as it is pressure and temperature–like.
The grouping occurs in only certain regimes, and not others.
Whatever.
This paper is about
\begin_inset Quotes eld
\end_inset
biological individuals
\begin_inset Quotes erd
\end_inset
, so my commentary has no bearing.
\end_layout
\begin_layout Itemize
\begin_inset Quotes eld
\end_inset
\emph on
Informational individuals
\emph default
\begin_inset Quotes erd
\end_inset
Whelp.
\end_layout
\begin_layout Itemize
\begin_inset Quotes eld
\end_inset
\emph on
The quantity
\begin_inset Formula $I\left(S_{n+1};S_{n}\right)$
\end_inset
has been called autonomy
\begin_inset Formula $A^{*}$
\end_inset
.
\emph default
\begin_inset Quotes erd
\end_inset
Oh.
That's interesting.
So
\begin_inset Formula $S_{n}$
\end_inset
is the state of the system at time
\begin_inset Formula $n$
\end_inset
and
\begin_inset Formula $I\left(a;b\right)$
\end_inset
is the mutual information between
\begin_inset Formula $a,b$
\end_inset
.
\end_layout
\begin_layout Itemize
\emph on
\begin_inset Quotes erd
\end_inset
the following relationship is obtained between the measures of autonomy,
dependency and closure
\emph default
\begin_inset Quotes erd
\end_inset
I'm getting a little lost because I don't like their notation.
It's ambiguous.
They really need to have used additional grouping parenthesis.
I like the general intent, though.
Ugh.
All of pages 10,11 is impenetrable due to their poor notation.
I think they're on to something, but the failure to define their notation
is a disaster.
I don't have time to untangle it.
\end_layout
\begin_layout Itemize
\begin_inset Quotes eld
\end_inset
\emph on
By incrementally titrating the system/environment boundary (inclusion and
exclusion criteria) we expand the individual to be the largest set of processes
which upon further addition is no better at predicting its future than
the previous largest set.
\emph default
\begin_inset Quotes erd
\end_inset
These are sexy words, but seem unrealistic to me, except in some simple,
abstract theoretical settings.
The computational problem of predicting behavior becomes rapidly intractable,
once the systems get large.
It would have been sexier if the formulas were clearer, and then we could
ignore the computability/intractability issues...
but jeez.
\end_layout
\begin_layout Itemize
I wrote two paragraphs of summary in the Readings–List file in this directory.
That's my
\begin_inset Quotes eld
\end_inset
formal review
\begin_inset Quotes erd
\end_inset
.
\end_layout
\begin_layout Itemize
Post–script: one of the failures of the paper above, and the paper below,
is to realize that the metric distance between individuals is effectively
an ultrametric.
Yeah, the information–theory perspective is nice, it provides a way to
distinguish the individual from the environment.
But more profoundly, we want to measure the distance between individuals,
and this is where we discover the ultrametric property.
Individuals live in deep, deep wells of isolation.
Yes, the interact with the environment, but it is only when you start looking
at the interactions between individuals that you notice how isolated they
are.
This seems to be fundamental, and is a property ignored with great theoretical
peril.
\end_layout
\begin_layout Subsection*
9 April 2025
\end_layout
\begin_layout Standard
Next up on the agenda: All intelligence is collective intelligence Falandays
J.
Benjamin, Roope Oskari Kaaronen, Cody Moser, Wiktor Rorot, Joshua Tan,
Vishwanath Varma, Tevin Williams, Mason Youngblood Journal of Multiscale
Neuroscience Vol 2 no 1 169-191 (2023) https://doi.org/10.56280/1564736810
https://researchportal.helsinki.fi/en/publications/all-intelligence-is-collective
-intelligence
\end_layout
\begin_layout Standard
Like above: bullet points that are hot takes.
\end_layout
\begin_layout Itemize
\begin_inset Quotes erd
\end_inset
\emph on
Collective intelligence, broadly conceived...
\emph default
\begin_inset Quotes erd
\end_inset
Duh.
When I was in school, we called it
\begin_inset Quotes eld
\end_inset
sociology
\begin_inset Quotes erd
\end_inset
, so what the heck? What was broken about sociology, that we now need a
different name for this? Is it because sociology failed to be broad enough
to include ant–hills? OK then.
\end_layout
\begin_layout Itemize
\begin_inset Quotes eld
\end_inset
\emph on
If it can be seen that mechanisms of intelligence at every level of
\emph default
analysis are best understood as collective behaviors, what is left to qualify
as individual intelligence?
\begin_inset Quotes erd
\end_inset
OK.
This sentence says that I should speed–read or just skim the rest of the
paper.
The whole idea of an ultra–metric is that the thoughts in my brain are
very very very distant from those of yours.
My brain sits in a deep deep well of isolation, and so does yours, and
the stuff that gets across, over the barriers is miniscule compared to
what goes on in my head.
So yes, there is a collective intelligence inn human society, but it is
composed of very loosely connected individual intelligences.
Social media is making these connections fatter and tighter, but the isolation
of individuals remains truly profound.
\end_layout
\begin_layout Itemize
\begin_inset Quotes eld
\end_inset
\emph on
These changes to collectives are typically associated with high densities
and patchiness of resources, where coming together allows individuals to
disperse across larger distances and forage more efficiently (Nauta et
al., 2022).
This is suggestive of evolution favoring the switch between individual
and collective intelligence based on the ecological context, allowing species
to persist in different conditions.
\emph default
\begin_inset Quotes erd
\end_inset
OK.
So, this is a phase transition, where the parameter is some kind of patchiness
or volatility.
So, in calm situations, with abundance of food, individualism is fine.
In stress situations, where there are large food (resources) deserts (in
time or in space) separating dollops of concentrated food/resource availability
, then collective behavior is advantageous.
Also predation threat.
So *if* I had a mathematical model of agency, then I could study collective
behavior in that model.
But I don't so I can't.
\end_layout
\begin_layout Itemize
\begin_inset Quotes eld
\end_inset
\emph on
To summarize this section, collective intelligence in non–human animals
is a highly diverse phenomenon,
\emph default
\begin_inset Quotes erd
\end_inset
In other words, the landscape of agentic behavior is filigreed with first
and second–order phase transitions all over the place.
This contradicts the conventional mean–field results in high dimensions.
So e.g.
Ising model is described by mean–field results in 4 or more dimensions,
and has
\begin_inset Quotes eld
\end_inset
interesting
\begin_inset Quotes erd
\end_inset
behavior in 2D.
But agentic systems...
Drawing the analogy is hard, because different agents do not exist along
different
\begin_inset Quotes eld
\end_inset
dimensions
\begin_inset Quotes erd
\end_inset
: the space of kinds of agents is not a euclidean space.
It instead has the the (xx?) topology, as used for describing classes of
algorithms.
The space is
\begin_inset Quotes eld
\end_inset
high–dimensional
\begin_inset Quotes erd
\end_inset
, but ...
argh.
\end_layout
\begin_layout Itemize
\begin_inset Quotes eld
\end_inset
\emph on
compound intelligences ...
expanding individual organisms’ computational boundary, allowing them to
process information referring to more distant events, both in time and
space.
\emph default
\begin_inset Quotes erd
\end_inset
...
preachin' to the3 choir, my man, preachin' to the choir.
This is an exciting idea.
Obvious, as it were, I'll grab it hook–line–n–sinker.
The heck: I'll even claim that I've had this idea before, myself, just
never bother to have verbalized it.
Perhaps I know this idea from reading sci–fi as a child, and here it is
again, in a scientific journal as an adult, being proposed by respectable
scientists.
So over the decades, the forum has changed.
Has the utility changed? Seems like it has not.
We've enshrined sci–fi ideas into science without actually making tangible
progress.
Do we have tools for measuring this? Manipulating it? Building exploring,
advancing it? Imagine we did: it all slips very rapidly into some post–human
conception of being–ness.
The ecological landscape is mind–boggling.
And this is what I struggle with here: everything is mind–boggling.
\end_layout
\begin_layout Itemize
\begin_inset Quotes eld
\end_inset
\emph on
This shows that morphogenesis is not a simple implementation of a pre-set
recipe (of a form ‘move cell X distance Y in the direction Z’), but rather
that cells react to their environment in a way that is appropriate, even
if the circumstances widely differ from normal.
\emph default
\begin_inset Quotes erd
\end_inset
I am utterly flabbergasted why the work of Prusinkiewicz is not better
known.
\end_layout
\begin_layout Itemize
\emph on
\begin_inset Quotes eld
\end_inset
phase transition
\emph default
\begin_inset Quotes erd
\end_inset
.
Seven pages in, the phrase appears.
Good.
I haven't seen
\begin_inset Quotes eld
\end_inset
utrametric
\begin_inset Quotes erd
\end_inset
yet, but overall, this is shaping up to be a nice paper.
They're reaching all the correct conclusions, per my personal world–view.
\end_layout
\begin_layout Standard
Interlude.
Chronological order, but not conceptual order with above bullet points.
My mind is wandering.
ADHD while reading above.
Anthropic principle.
Math as a filigree of true but immutable statements.
The past as a collection of immutable events.
Oracles highlight that Turing halting problems can be encoded as relatively
low–degree algebraic varieties.
In some sense, the math that is directly accessible to us consists of the
collection of statements that proof systems can prove (Coq, HO, ...) and halting
problems are unprovable.
So is these where non–determinism is anchored? Is there some freedom of
choice available to systems that exist at the
\begin_inset Quotes eld
\end_inset
oracular
\begin_inset Quotes erd
\end_inset
layer? Is physical reality that thing that exists at the oracular layer?
Is the collection of physical alternatives (in the partition function)
isomorphic to the choices available at the oracular layer? Viz: the platonic
existence of mathematics is frozen; here–and–now is a freezing wave–front
moving through the
\begin_inset Quotes eld
\end_inset
space
\begin_inset Quotes erd
\end_inset
of indeterminate
\begin_inset Quotes eld
\end_inset
stuff
\begin_inset Quotes erd
\end_inset
.
Gah.
I want to read more about Chaitin's results, and the large cardinal axioms
and etc.
And when exactly will I do this, when I am so easily distracted?
\end_layout
\begin_layout Standard
So now, let me do a Michael Levin to the string landscape: what is the collectio
n of algebraic structures that encode turning–undecidable problems as collection
s of differential eqns? Which of these collections are minimal?
\end_layout
\begin_layout Standard
Taken to heart, though, this suggests that any digital software system can't
be
\begin_inset Quotes eld
\end_inset
actually alive
\begin_inset Quotes erd
\end_inset
or
\begin_inset Quotes eld
\end_inset
actually intelligent
\begin_inset Quotes erd
\end_inset
unless it is in the undecidable class.
But this is a very low bar.
It's also paradoxial: the system is deterministic, and yet unpredictable.
This is a hard nut to crack.
Something is
\begin_inset Quotes eld
\end_inset
hiding in there
\begin_inset Quotes erd
\end_inset
, but I don't know what rock to search under.
Whatever.
Later.
\end_layout
\begin_layout Standard
Back to the original programming:
\end_layout
\begin_layout Itemize
\begin_inset Quotes eld
\end_inset
\emph on
Each region of the brain is now thought to be involved in a multitude of
processes, and coordinates with different partners depending upon the context,
forming temporary “functional networks” ...This process is best understood
as a form of self–organization, in that the best functional network for
a task or context comes online through distributed interactions, rather
than by virtue of a central executive that assembles the best neural partners
after assessing a situation.
Indeed, it would be nonsensical to suggest that such a task could be accomplish
ed by a central executive, in that it would assume that the central executive
somehow knows the nature of the task to be accomplished; in other words,
it would require a homunculus.
\emph default
\begin_inset Quotes erd
\end_inset
This speaks for itself.
I have nothing to add.
Other than that this brings into sharper relief the task I've been facing
with the sensori–motor work.
There, I was trying to create descriptions of sensory and motor systems,
but who writes those descriptions? The homunculus.
And how are systems assembled? Well don't actually want random assembly/mutatio
n a la MOSES knob–turning.
Instead, want assembly guided by ...
errm ...
well, some DL–NN–ish structure, but that just relocates the homunculus
to the DL–NN.
Hmm.
\end_layout
\begin_layout Itemize
\emph on
\begin_inset Quotes eld
\end_inset
Along these lines, proponents of “Neural Darwinism” (Edelman, 1993) and
related views suggest that brain development, and intelligence more generally,
can be understood as analogous to the evolution of a species through variation
and selection.
\emph default
\begin_inset Quotes erd
\end_inset
Yes, but ...
Natural selection optimizes for
\begin_inset Quotes eld
\end_inset
fitness
\begin_inset Quotes erd
\end_inset
, and conventional machine learning optimizes some
\begin_inset Quotes eld
\end_inset
utility function
\begin_inset Quotes erd
\end_inset
.
What is the fitness function for the brain? Sure, perhaps the neurons are
competing, but what are they competing for? Are they trying to build the
largest possible organized structure, until it collapses? So, self–organized
criticality? So, basically, build–baby–build the biggest most complex structure
possible, until it collapses due to incorrect ...
uhh ..
perception of external stimuli? Until it fails to accurately portray the
world in some way? This is certainly algorithmically conceivable.
But how would the brain do this?
\end_layout
\begin_layout Itemize
\begin_inset Quotes eld
\end_inset
\emph on
the intelligence of brains is due not to precisely designed neural circuits
that implement specific computations, but instead due to an intrinsic capacity
for collections of neurons to spontaneously organize in service of survival
of the group.
\emph default
\begin_inset Quotes erd
\end_inset
Oh OK.
This amplifies upon the above.
But what does
\begin_inset Quotes eld
\end_inset
survival
\begin_inset Quotes erd
\end_inset
here mean? What constitutes a successful organization, and what constitutes
an unsuccessful one? When I sit here and think, I might get an idea and
then go
\begin_inset Quotes eld
\end_inset
nah, bad idea
\begin_inset Quotes erd
\end_inset
.
so there's some executive that rejects bad ideas.
So I am the homunculus that punishes good ideas, or not (and am in turn
punished by base economic reality, love interests, the high of social interacti
on.
Or, in this case, the reward for thinking.
So is this the feedback loop? Some DNA encodes for dopamine highs, or some
other neurotransmitter–pleasure feedback, and so when I think, and I get
a long sequence of complex ideas that seem to pass a filter for self–consistenc
y and coherence, I am rewarded with a high for having achieved this large–scale
thought–pattern.
This requires some mechanism for determining the logical consistency of
my structure of thoughts.
Logical is too strong a word for it – a good–enough intuitive sense that
my current thought patterns are coherent and are
\begin_inset Quotes eld
\end_inset
going somewhere
\begin_inset Quotes erd
\end_inset
.
Or, at least, a
\begin_inset Quotes eld
\end_inset
flow state
\begin_inset Quotes erd
\end_inset
.
Then things like writers block, or frustration at the inability to move
forward, these are punished, and the thought structure collapses.
So again, this is tinged as some kind of self–organized criticality.
\end_layout
\begin_deeper
\begin_layout Itemize
But I struggle with
\begin_inset Quotes eld
\end_inset
conscious me
\begin_inset Quotes erd
\end_inset
: much earlier I wrote that conscisous–me is presented with a menu of thought–ch
oices, and I only have to select.
That make me into a homunculus in charge of thought.
But is instead, conscious me is just an unstable assemblage of whatever
brick–a–brack got stacked up in a semi–coherent fashion, well, that's OK,
too.
I suppose.
\end_layout
\begin_layout Itemize
How does this work in the presence of environmental stimulus? I'm presented
with audio–visual stimulus ...
structures build up, and then collapse.
While bike–riding, I get plenty of visual stimulus, but approx none of
that is intellectual thinking, none of it resembles what I do here while
writing.
It's also mundane, forgotten, non note–worthy.
Well I did give the finger to a cybertruck: I remember that.
And I can imagine remember this or another pebble in the road: I have a
good visual memory; snapshots are committed to memory.
But these are rapidly changing, and do not tower large or complex.
\end_layout
\begin_layout Itemize
My sons do a lot of video–gaming.
Is their experience akin to bike riding? Perhaps with more sophisticated
motor–muscular responses? The point here is rapid assembly and disassembly
of transient structures from visual stimulus.
At the meta–level, something also notices a common recurring theme in those
structures: so, perception is recursive: not only does this or that visual
filter fire, but also at a higher level, something notices that this particular
structure is being witnessed over and over.
\end_layout
\begin_layout Itemize
In MOSES, structures were randomly created, and kept, if they scored high.
Here, I'm randomly creating structures, and the score is
\begin_inset Quotes eld
\end_inset
the more complex, the better
\begin_inset Quotes erd
\end_inset
, and there's no other score.
Or, well, no, it can't be that.
It has to also be a structure that can match sensory input reasonably well,
or rather, predict sensory input.
So this is a very traditional reward function or utility score: maximizing
the quantity
\begin_inset Formula $I\left(S_{n+1};S_{n}\right)$
\end_inset
aka
\begin_inset Quotes eld
\end_inset
autonomy
\begin_inset Quotes erd
\end_inset
from earlier section.
Except We're not maximizing that at all, but instead the MI between future
sensory state, and the prediction of that future sensory state.
Successful predictions are rewarded, but also surprises result in ...
re–examination, collapse? And a library of past successes is maintained.
\end_layout
\begin_layout Itemize
The above is not inconsistent with loss–function–style training in transformers,
but here, I am explicitly building hypergraphs out of component parts.
\end_layout
\begin_layout Itemize
Fuck–all.
I could actually build something like this.
I should code this up.
I like this idea.
\end_layout
\begin_layout Itemize
But the problem with this idea is still that it is passive, non–interactive.
That is, I train a hypergraph of very simple filters on youtube videos,
and train to maximize for predictability, and I get what, in the end? A
kind of encoding of what was seen in the videos.
In a sense, this is no different than other kinds of training.
DL–NN's already do that quite well.
All that I've done is invent a different kind of mechanism that is not
as efficient, fast, scalable or performant than the current state of the
art.
\end_layout
\begin_layout Itemize
To do better, I want to instead have an agent that is free to interact with
the world, and push things around, and just
\begin_inset Quotes eld
\end_inset
try stuff.
\begin_inset Quotes erd
\end_inset
\end_layout
\begin_layout Itemize
But the lesson from the paper is that I should nut think of a single agent,
I should think of vast numbers of agents...
each of which are experimenting.
Each of these have tremendous autonomy, within their small world–view.
Only at the very top are they chained to the particular youtube that they
are training on.
\end_layout
\begin_layout Itemize
But how is this different from physical reality? In a sense, I am
\begin_inset Quotes eld
\end_inset
chained to
\begin_inset Quotes erd
\end_inset
physical reality, and do not have complete control.Fuck all, I don't even
have control over Congress or the President, so my autonomous domain is
quite small.
Yet, I explore that autonomous domain.
So should I feel bad if my collection of agents is chained to or forced
to watch youtube videos? Maybe...
Maybe not.
\end_layout
\begin_layout Itemize
Can
\begin_inset Quotes eld
\end_inset
magic happen
\begin_inset Quotes erd
\end_inset
by watching videos? Well, perhaps, so now abstract back and ask
\begin_inset Quotes eld
\end_inset
can magic happen while examining text?
\begin_inset Quotes erd
\end_inset
and whatever hand–waving justification you can apply to
\begin_inset Quotes eld
\end_inset
a hah I have a visual thinking who has learned about the 3D world from watching
videos
\begin_inset Quotes erd
\end_inset
, I also have by analogy something that was able to discover structure from
text–world.
\end_layout
\begin_layout Itemize
So LLM's discover structure in text–world, and here I contemplate a different
ind of architecture, and basically my argument is
\begin_inset Quotes eld
\end_inset
hey its different and since no one has done this before, maybe I can try
it and learn something no one else knows.
\begin_inset Quotes erd
\end_inset
\end_layout
\begin_layout Itemize
Which is an argument to resume my old research program, except this time,
with some fresh ideas.
Damn.
It is 2:30 AM and I am stoked pumped, and is this this just late–night
mania expressing itself? The research program will get difficult again,
in the AM? Fuck me..
\end_layout
\end_deeper
\begin_layout Standard
I'm going to bed now.
Dammit.
This is ...
hard work..
\end_layout
\begin_layout Subsection*
10 April 2025
\end_layout
\begin_layout Standard
Continuing.
\end_layout
\begin_layout Itemize
\begin_inset Quotes eld
\end_inset
\emph on
A recent artificial neural network model...
\emph default
\begin_inset Quotes erd
\end_inset
For some reason, this made me think of the a–life experiments I conducted
25 or 30 years ago.
The results were interesting, intriguing, suggestive.
But in the end, imponderable: the models were far away from anything that
could be analytically analyzed.
They were specific enough that there was nothing else like that out there.
Some of what I got was interesting.
but in the end ...
so what? As I recall, the model was simple: cells could play the prisoner's
dilemma game with each other.
Cells in contact with the ground had access to an infinite supply of water,
which they could trade.
Cells in direct sunlight had energy, which they could trade.
Cells needed both to survive, and threshold quantities of both to reproduce.
The prisoner's dilemna rules were encoded as
\begin_inset Quotes eld
\end_inset
dna
\begin_inset Quotes erd
\end_inset
, which could mutate slowly.
I imagined that I would be able to evolve some kind of botanical ecosystem,
and that it would look visually pretty.
The first came true: it did evolve into some kind of ecosystem; but what?
The second did not: visually, it was boring.
What did I learn? That complex a–life systems are complex.
That a rather small number of axioms is enough to get non–trivial behavior.
That there there was no theoretical framework in which I could think about
this system, or perhaps that I was unaware of this framework (I did search
the literature repeatedly, at the UT Library.) That I should go ahead and
try to develop my own theoretical framework was never something that popped
into my mind, or perhaps it did, but was overwhelmed by the difficulty
and futility of it.
So when I read these paragraphs of this home–brew NN these guys slapped
together, I was reminded of this.
\begin_inset Quotes eld
\end_inset
Something happened.
It was sort of what we expected.
But then other unexpected things happened.
End of Story.
\begin_inset Quotes erd
\end_inset
Yikes.
\end_layout
\begin_layout Itemize
\begin_inset Quotes eld
\end_inset
\emph on
these behaviors emerge naturally from the local drive for homeostasis in
the context of a network
\emph default
.
\begin_inset Quotes erd
\end_inset
Oh, that's interesting.
So, every agent wants to be stimulated, but not too much.
Each one individually.
And they dynamically re–arrange connections between themselves to obtain
this stimulus.
As I type this, I brush my fingers across my chest.
Just stepped out of the shower.
it feels very good, this brush: just a bit more than a tickle, just this
side of an itchy scratch.
Huh.
\end_layout
\begin_layout Itemize
\begin_inset Quotes eld
\end_inset
\emph on
evolution as a whole may be thought of as a form of collective intelligence
\emph default
.
\begin_inset Quotes erd
\end_inset
Huh.
This creates a linkage to here–and–now.
The effect of having brains is that they allow you to predict future events
(and thence to survive and thrive).
And of course, evolution creates brains.
But prior to the quoted line, one could have thought that evolution is
a distinct process.
After the quoted line, one has to pull back and think about the driving
force of evolution.
In this context, selection of the fittest is the effect, not the cause.
(Computer crashes after I write this.)
\end_layout
\begin_layout Itemize
\begin_inset Quotes eld
\end_inset
\emph on
intelligence as a process instantiated by groups
\emph default
\begin_inset Quotes erd
\end_inset
, spatially–distributed process.
With hierarchical groupings.
So, multi–scale.
\end_layout
\begin_layout Standard
Fantastic paper.
I like what it says.
Agree completely.
I want to riff on the here–and–now, but there's a brick wall.
Coming from the physics side, everything is driven from non–equilibrium
thermodynamics: specifically, solar irradiation on the Earth's surface
that drives the water cycle, rock erosion, chemistry and also geothermal
vents in the ocean.
That this is true, is true, but so what? I don't know how to write down
some master equation for this, or even if I did, I don't know how to say
anything meaningful about solutions of it.
Of course, we also know of many other dribbles and drabbles of differential
equations, algebraic equations, iterated processes, all of which exhibit
some kind of fractal form, perhaps even some self–organized criticality.
But how do these different examples inter–relate? How do we hook them together?
Through some hand–waving, of course: if one is widely–read, and generally
knowledgeable, one can say
\begin_inset Quotes eld
\end_inset
oh this reminds me of that
\begin_inset Quotes erd
\end_inset
, in a vague, imprecise form.
Perhaps this imprecise connection can eventually be converted into an explicit
collection of algebraic manipulations in the two domains.
Articulated into a detailed theory.
As a general rule, this is hard: it requires weeks, months, years, decades
of thought by an individual or a university department or spread across
the world.
And this is what? Evidence–gathering.
Evidence–strengthening.
So this reinforces my earlier ruminations on evidence–gathering, and evidence
sorting.
\end_layout
\begin_layout Standard
So now we have two problems: in what way is evolution driven by here–and–now–nes
s? And what is the role of evidence in this process?
\end_layout
\begin_layout Standard
Shit.
Instead of pondering above, I wandered off to bluesky and am entangled
there.
\end_layout
\begin_layout Standard
My primary thesis is that memetic spread of psychotic, delusional ideas
on the right wing has put Trump in power.
The sources are easy enough to identify: Fox News, Newsmax, etc.
The process is identifiable as cult indoctrination.
The mechanism is interesting: it seems to be hypnotic.
I recall reading Jordan Hall's/Greenhall's
\begin_inset Quotes eld
\end_inset
Situational Assessment
\begin_inset Quotes erd
\end_inset
articles, and they were ...
hypnotic.
A strange mix, and Alice–in–Wonderland description of reality, where there
would be recognizable elements that you could identify with, but recombined
in ways that were
\begin_inset Quotes eld
\end_inset
fascinating
\begin_inset Quotes erd
\end_inset
: draw your attention in, make you focus on the idea, and then exterminate
thinking.
A pitcher–plant flytrap for ideas.
\end_layout
\begin_layout Standard
Evidence–building is a necessary part of the process for rule–of–law, and
for general good governance.
I do not understand how evidence–building interfaces with the idea of intellige
nce as a self–organizing critical system.
The cult–indoctrination idea is that there are structures that dynamically
combine to form (semi-)stable belief systems that are at odds with ...
with what? Cult thinking is clearly reprehensible, but ...
And we've got examples: Jim Jones in Guyana, and Trump in the present.
The right–wing apparatus, including e.g.
accelerationism, has build a smooth–walled trap that inhibits thinking
along certain directions: it prevents the normal accretion of thought–forms.
The mechanism is sloganeering.
You compare a thought to a slogan; if the thought fails to match the slogan,
the thought is discarded.
This prevents complex thoughts from getting articulated.
Mao's Little Red Book is a compilation of slogans.
It gave birth to China's Cultural Revolution.
Can it be compared to accelerationism, e.g.
Musk's
\begin_inset Quotes eld
\end_inset
Sometimes the best part is no part
\begin_inset Quotes erd
\end_inset
which is entirely true, but is being falsely used to fatally destroy the
US Govt?
\end_layout
\begin_layout Standard
Pareto efficiency is the idea that once should pursue changes where someone
benefits, and no one looses.
The accumulation of capital to the billionaires is Pareto efficient: the
middle classes are better off than they were four decades ago, and the
billionaires are a lot better off.
In machine learning, hill–climbing leads one to local traps, where the
only way out of the trap is to go down–hill: strictly worse situations
before the improvement may resume.
\end_layout
\begin_layout Standard
A gazillion examples of this in biology.
A particular nice one was from the evolution of ion channels, the two–protein
vs.
three–protein ion channels, where the two–protein one was a local maximum:
there is no way to improve the two proteins to make them any better; you
have to go to three–protein structures, and the early forms of the three–protei
n channels were objectively worse.
But if I look at biology as a self–organizing system at the critical threshold,
is the discovery of the three–protein system the result of critical collapse,
or an avalanche?
\end_layout
\begin_layout Standard
Once again: I am stuck.
This question is nice, its intriguing.
Finding objective evidence for it requires doing actual science, actual
lab work.
Again: do avalanches in systems at the edge of criticality, is this what
drives evolution? It seems plausible to think the answer is yes.
This seems to be the general layout.
If I assume this is true, can I build something on top of this assumption?
\end_layout
\begin_layout Standard
Construction of evidence.
As I gather evidence in support of a given proposition, that evidence gets
stronger and stronger.
One possibility is that the entire evidence chain unravels: like a murder
mystery, a Sherlock Holmes story: everything points one way, until you
get that one tiny piece of evidence that contradicts, that won't fit, that
tears down the entire structure built up from prior inferences.
So, an inference chain that collapses, avalanches.
Falls apart.
\end_layout
\begin_layout Standard
In proof–theory, a variant of this is proof–by–contradiction: a complicated
argument built on base assumptions.
The complicated argument is driven into a corner, where a contradiction
is derived.
This can be then worked backwards, implying that one of the base assumptions
was incorrect.
Can I view this as a catastrophic collapse? Yes.
The final contradiction is
\begin_inset Quotes eld
\end_inset
this cannot be right
\begin_inset Quotes erd
\end_inset
, and so you disassemble the penultimate stage of the proof, and say
\begin_inset Quotes eld
\end_inset
this can't be right, either
\begin_inset Quotes erd
\end_inset
, and the disassembly proceeds backwards to the assumptions.
Its a disassembly, in that you know that anything further built on the
flawed structure will also be flawed.
Byt there is also a meta–level: the construction that was built to obtain
the contradiction stands, and instead we flow false–ness through that proof
chain to arrive at the foundation of that proof–chain: the assumptions
that went into it.
The collapse, the avalanche is the identification of a set of relationships
that are not stable, and cannot stand.
\end_layout
\begin_layout Standard
In a concrete sand pile, we only see the surface phenomenon: the avalanche
itself.
At the meta–level, we see the structure that cannot be stable, and therefore
must collapse.
So, at the meta–level, the structure is there: it is whole, it is complete.
It's just not stable.
Temporally stable in the case of dynamical systems.
But mathematical proofs–by–contradiction are not normally thought of as
dynamical systems.
Yet, the resemblance is there.
Ugh.
\end_layout
\begin_layout Standard
Replying to Fleeky on bluesky (recap of above, but poetically):
\end_layout
\begin_layout Standard
@linas.org is social media just a place to talk politics for you? your github
diaries are much more interesting >:) Linas Vepstas @linas.org · 1h Difficult
to express ideas in 300 characters or less.
I am having a blast writing those diaries, though.
At any rate, the material is so arcane that ...
hmm.
Should I make an experiment, and post my thoughts as threads? ...
1/n Linas Vepstas @linas.org · 1h What I write in my diary are not coherent
threads, but just random–ish ideas that sort of make sense to me, given
my background.
Explaining them to other people so that they could understand would require
me to work hard.
That would slow me down.
2/n Linas Vepstas @linas.org · 1h Yes, I could post random thoughts here,
on bluesky.
Build idle thought–chains, just like this one.
Who would read them? Who would understand them? Would they have any effect
upon the universe, on social thought? You Fleeky, will read this particular
thread (cause you started it) 3/n Linas Vepstas @linas.org · 1h My bluesky
posts are targeted: at specific individuals, specific cases, situations.
Even so, I get approx 0.1 likes–per–post.
Maybe I have enough posts that I could do a statistical analysis.
of these.
A few get dozens of likes.
most get zero likes.
Be fun to see this graph, I guess.
4/n Linas Vepstas @linas.org · 58m I do plan on writing an article for this
summer's AGI proceedings, about self–organizing critical systems, bluesky,
criticality in network dynamics, avalanching, proof theory, and how total
collapse of the USA driven by MAGA fits just fine into this general theory.
5/n Linas Vepstas @linas.org · 55m And so what? You will read this thread.
Maybe 20 people will read the AGI article, when it gets published.
None of this theorizing will stop MAGA or Trump.
I can write that the hypnotic right–wing literature is a pitcher–plant
fly–trap for intellectual thought ...
6/n Linas Vepstas @linas.org · 50m Fine.
So nature has a system for exterminating critical thinking.
Conventionally studied as "cult indoctrination".
Probably not limited to humans: presumably some forms of colony collapse,
ecosystems collapse is comparable to NIH, DOJ collapse driven by Musk/accelerat
ionism.
7/n Linas Vepstas @linas.org · 48m Ecosystems that collapse are taken over
by "invasive species".
What makes them "invasive" is they are very fast to act: first–mover advantage.
In this case, it will encourage corrupt practices everywhere, in everything.
From cross–border tariff smuggling, to insider trading.
8/n Linas Vepstas @linas.org · 44m And so I've sketched an analogy between
ecosystems collapse and Trump/USA collapse.
Driven by the prior collapse of critical thinking in MAGA.
Driven by self–organized "thought leaders" who studied Jonathan Haidt,
Jordan Petersen, and bought into the Weinstein bros b.s.
9/n Linas Vepstas @linas.org · 42m The tech bros, the less wrong meetups,
the accelerationists did build a convincing intellectual facade around
"sometimes no part is the best part", and "to avoid getting trapped in
a local maximum is to go downhill" and you can buttress these arguments
with examples from biology.
10/n Linas Vepstas @linas.org · 39m It is absolutely true that the two–protein
cellular ion channel is a strict local maximum for ion pumping, and evolution
had to create a strictly–worse system consisting of three proteins, before
evolution could tune this to be better.
This is true.
And this is used to buttress Musk's appetite 11/n Linas Vepstas @linas.org
· 37m These and hundreds of other analogies from biology and engineering
are used to butress Musks appetite for the whole–sale destruction of America.
The TPOT people bought into these theories.
The post–rats bought into these theories.
The accelerationist bought into these theories.
12/n Linas Vepstas @linas.org · 33m Some of the post–rat people got into
weight–lifting and health, and to build muscles, you need to break down
muscles.
And so Peter Thiel figures we need to break down America's muscles to build
a stronger America.
Because he read this in some Curtis Yarvin essay.
13/n Linas Vepstas @linas.org · 28m The thought chains are persuasive and
appealing, until they reach contradictions.
Like a weight–lifter saying "I'm a gonna fire a bullet into my calf and
my calf will grow back stronger." Uh huh.
Or Musk's "The best part is no part ..
so lets remove the brain, starting with NIH, DOJ, FDIC, CDC" 14/n Linas
Vepstas @linas.org · 26m And they continue: the pitcher–plant fly–trap,
with its slippery–slidey intellectual idea–walls, has captured Peter Thiel's
brain, and he literally cannot reason his way out of the trap.
Indoctrinated into a cult, incapable of escaping.
So so now the USA self–destructs.
15/n Linas Vepstas @linas.org · 23m Went to an AGI cnference a few years
ago, and kept saying "Ukraine" and everyone was like "Linas, shut up".
Joscha Bach called me crazy.
I'm like "Joscha, you can see intellectual structures, chains of thought
built like evidential structures in legal court trials, and those ..." 16/n
Linas Vepstas @linas.org · 20m ...
and those evidentiary chains collapse because some fact does not fit." Mathemati
cians force evidentiary collapse on purpose: the technique is called "proof
by contradiction".
Dates back to Aristotle.
What Aristotle did not know was that avalanches are characteristic of ...
17/n Linas Vepstas @linas.org · 17m ..
of self–organizing systems.
And that intellectual structures of any kind: legal, political, scientific
are self–organizing.
And they sometimes collapse (Thomas Kuhn "Structure of Scientific Revolutions")
So yes, I can write a thread that points this out.
...
18/n Linas Vepstas @linas.org · 14m I can say "Joscha, you will never–ever
understand AGI if you do not understand the psycho–political–economic collapse
that installed Putin and lead to the invasion of Ukraine" That was then.
Now I can also add: you will not understand AGI till you understand the
me3chanics of MAGA.
19/n Linas Vepstas @linas.org The Pyongyang-style deference to Dear Leader,
the rapturous mental state in Jim Jones Guyana, where they drank the kool-aid,
the rapturous devotion of my Congressman, Roger Williams, to Trump even
as the beating heart of America stills.
So what? I can say all this, and so what? 20/n April 11, 2025 at 5:05 PM
Linas Vepstas @linas.org · 6m Because my thoughts and ideas are but a twig,
a straw, and maybe they fall in a way to support and strengthen a structure,
and maybe they are the twig that broke the camel's back.
So I write and theorize, aware that I am a minnow.
Maybe Peter Thiel will hear my whispers, and maybe he won't.
21/n Linas Vepstas @linas.org · 3m Maybe I'll change history, and maybe
I won't.
Maybe I'll write more stuff like this in my diary, or maybe I'll write
more stuff like this in tweet threads.
Maybe it will hit, and maybe it won't.
I feel like the primordial neutrino, decoupled during nucleosynthsis, flying
through space ...
22/n Linas Vepstas @linas.org · 8s Not interacting, having no effect, passing
through matter as if that matter was empty space.
Am I writing science–poetry here? Yes I am.
Am I having fun doing it? Yes I am.
Being alive is interesting and befuddling.
Whatever.
I need to get back to my main project ...
23/n .
n=23 the end.
\end_layout
\begin_layout Subsection*
12 April 2025
\end_layout
\begin_layout Standard
All right.
Lets be a little more focused than that tweet–deck, shall we? If I take
the central premise of
\begin_inset Quotes eld
\end_inset
all intelligence is collective intelligence
\begin_inset Quotes erd
\end_inset
to heart, and accept that intelligence arises from modular agents organizing
into (self–organizing to) a point of criticality, where all intelligent
activities occur, this presents several new problems.
Problems, that is, if one's goal is to create AGI.
First, what's the design of an individual agent? Second, what sort of
\begin_inset Quotes eld
\end_inset
problems
\begin_inset Quotes erd
\end_inset
does it solve? Third, that resulting aggregation of agents is itself an
\begin_inset Quotes eld
\end_inset
individual
\begin_inset Quotes erd
\end_inset
, which then ...
rinse and repeat.
\end_layout
\begin_layout Standard
These aren't even the right words.
A collection of agents have behavior patterns, which an outside observer
can interpret as
\begin_inset Quotes eld
\end_inset
solving a problem
\begin_inset Quotes erd
\end_inset
: but this requires the outside observer to perceive the collection, to
perceive what that collection is doing, observe that there is some threat
or difficulty, and finally observe that the collection is successfully
evading that threat or moving past that difficulty.
Basically, a scientist observing the behavior, and imposing human linguistic
conceptions onto that organism.
\end_layout
\begin_layout Standard
Then there's an issue of regulatory control and the homunculus.
I am sitting here, writing, because I have placed a goal upon myself, to
\begin_inset Quotes eld
\end_inset
solve this problem
\begin_inset Quotes erd
\end_inset
, and am forcing myself to do so.
And I'm aware that this is a battle between two systems: one that says
\begin_inset Quotes eld
\end_inset
fuck this, lets go do something easier and more fun
\begin_inset Quotes erd
\end_inset
, and another that says
\begin_inset Quotes eld
\end_inset
no, sitting here typing is more fun
\begin_inset Quotes erd
\end_inset
.
Sheesh.
I am not all that aware of the processes that result in the words being
typed here (well, dimly; I've written about this before.) So my self–awareness
creates the appearance of a homunculus, making decisions and being in charge.
\end_layout
\begin_layout Standard
Break.
\end_layout
\begin_layout Standard
The break never ended.
Above is on pause.
Maybe I'll recapture the thread later.
\end_layout
\begin_layout Standard
These last two sentences are written for narrative coherency.
Next person/AI to read this should have some impression that there is narrative
coherency to all this, even if it seems disconnected.
\end_layout
\begin_layout Subsection*
13 April 2025
\end_layout
\begin_layout Standard
My brain is melting.
This is neither bad nor good, just interesting.
Let me explain.
Went out last night, to hang with Owen's crew.
Just guys, no women.
It was sort of interesting.
I mostly listened, did not talk.
There's very little I can communicate to these people that will make an
informational change, and insofar as I derive some kind of pleasure from
communicating information, that route to enjoyment was there.
So ..
mostly I sat in stunned silence, while listening to a mid–wit deconstruction
of social relationships.
Why do I write mid-wit? Owen's crew is smart.
Perhaps 120-135 IQ range.
Somewhat underinformed, and aren't we all?
\end_layout
\begin_layout Standard
And that's the point: the information density in carefully crafted youtube
video exceeds that in social conversation.
The entertainment density too.
It's been like that for a century: dinner and a movie kind of means that
the movie is more fun than an after–dinner conversation.
I've replaced
\begin_inset Quotes eld
\end_inset
movie
\begin_inset Quotes erd
\end_inset
with
\begin_inset Quotes eld
\end_inset
youtube
\begin_inset Quotes erd
\end_inset
, because well, of course, lots of eyeballs go through youtube.
I did not say
\begin_inset Quotes eld
\end_inset
book
\begin_inset Quotes erd
\end_inset
because the modality is different.
The modality of youtube is closer to traditional life, closer to what neuronal
organizations are set up for: vision, plus sound, plus action.
Books remove all three, and ask you to imagine them.
Science textbooks remove all three, and replace physical action by action
in abstract realities (e.g.
math)
\end_layout
\begin_layout Standard
Where was I? I'm losing the thread.
Yes.
Sitting at home, immersing in any of a broad selection of media: online
PDF's, social media, youtube, is more fun than face–to–face interaction.
Which is ...
Well, I want to say something judgmental, but not sure what that is.
There is real value of attaching to other human beings.
That should be something easy to agree on, and say that it is a positive
aspect.
Oddly, its a position that is hard to support, one way or another.
One might say that face–to–face contact encourages empathy, and empathy
keeps fascism at bay.
I imagine this is the kind of argument a large number of humanists might
make: famous, powerful authors, historians.
Or perhaps this can be exposed via psychological experiments, that study
face–to–face social contact, and outcomes on various measures, thereby
showing something or other.
Surely, face–to–face social contact is healthy for both psychology and
society.
Right? So why am I even pondering such a question?
\end_layout
\begin_layout Standard
One part is the lack of information.
I am ignorant sociological or psychological research into the benefits
of face–to–face interaction.
Never mind any knowledge about the impact of, say, reading books, instead
of face–to–face interaction.
But suppose I wasn't ignorant of this.
What if I actually knew something about this? Well, it would be some factoid,
and I would incorporate it into my wellness routine.
As I am a rational actor, as is everybody, with an appropriate definition
of
\begin_inset Quotes eld
\end_inset
rational
\begin_inset Quotes erd
\end_inset
.
So we have multiple issues: one is my lack of information.
Another is that my life is too short to acquire that info.
Third is that perhaps that info doesn't exist.
Fourth is that, even if I had that info, it might be non–specific enough
to suggest an actual behavioral change.
\end_layout
\begin_layout Standard
I'm phrasing this as a personal dilemna, but it is social.
Last night's social gathering included Alex Murshak, creator of a multi–episode
youtube series
\begin_inset Quotes eld
\end_inset
Hacking State
\begin_inset Quotes erd
\end_inset
.
Each video has about 100 views, exactly.
So, has not taken off.
Episode 48 is an interview of
\begin_inset Quotes eld
\end_inset
Raw Egg Nationalist
\begin_inset Quotes erd
\end_inset
.
I bumped up the playback speed to 2x because well, informational delivery
was slow.
I watched to about the 20 minute mark (10 mins elapsed) before I got bored,
because it was very very thin material.
Very little informationally.
There was, however, a whole lot of vibes: this is a vibe–cast.
The Raw–Egg nationalist is concerned about a panalopy of modern–day health
and wellness issues.
And these are entirely reasonable issues to be concerned about.
And then he proposes amateur opinions about how these may be solved.
These opinions are vaguely science–backed, but he does not seem to be deeply
informed.
The vibe that
\begin_inset Quotes eld
\end_inset
well here's a guy deeply learned in these topics
\begin_inset Quotes erd
\end_inset
, that vibe is absent.
So he's an amateur tackling some of societies deepest and hardest problems,
and ...
well, his information is incomplete.
Fragmentary.
I stopped watching because, well, it did not seem like he knew that much,
and what was there was mostly filler.
Empty space.
I was not getting actionable information, and even at double–speed, it
was slow and empty.
Kudos to the guy for attempting to solve some of societies deepest problems.
But...
\end_layout
\begin_layout Standard
See where I'm going with this? The interviewee could have also delivered
this content in person, to last–nights gathering, face–to–face.
But on youtube, he has an audience of 100 people.
As an auditorium, that would be quite significant.
He's short on information, he's not a scientist.
Citizen–science? This video a small perturbative push on the information
sphere.
The overall direction is probably positive.
Is it worthy of attention? Ahh, there is the question.
\end_layout
\begin_layout Standard
The question of informational efficiency, of evolutionary efficiency and
speed.
Would humanity have been better served, if those 100 viewers had instead
watched something else? Maybe, maybe not.
There is no doubt that watching the video is probably better than, say,
gaming.
My attempt to critique this video is like an attempt to critique a pyramidal
neuron deep inside some brain.
Is that particular cell important? How would the brain change if I removed
that one single cell? If I pruned it's connections, and wired them to something
else? Is it a waste of my time to analyze pyramidal neurons? To analyze
mediocre youtube videos? Worse, to perform this analysis one–by–one, anecdoteal
y, instead of building some LLM-video DL-NN net and analyzing hundreds or
thousands of such videos, all in one gulp? (Well, I can't build such an
automation framework, but it is worth asking about.)
\end_layout
\begin_layout Standard
Would it be worth building such a video–analysis framework? OK, yes, it
probably would be, and one would learn some
\begin_inset Quotes eld
\end_inset
science
\begin_inset Quotes erd
\end_inset
from running it.
So this is a question that is not worth analyzing any further.
\end_layout
\begin_layout Standard
In my chain of evidentiary analysis, I have concluded that this line of
reasoning is sufficiently grounded, for now, that further exploration can
be deferred till later.
I've written about evidentiary analysis above: it is a central theme to
my thinking.
Just pointing this out to you, dear reader.
\end_layout
\begin_layout Standard
Next up.
(I better finish this before I get mentally exhausted.
I'm already starting to feel some mental strain, here.) Next up is I'm watching
an extended ad for some health–wellness semi–scam.
(Why am I watching youtube at all? Because last nights social gathering
has left me sleep–deprived and foggy, so watching youtube is easier than
forcing myself into the guts of an academic paper.
That is the choice I made a few hours ago.
And now I'm writing.
\end_layout
\begin_layout Standard
I'm writing about this health–wellness pseudo–scam advertisement.
Might be the Doctor Gundry guy, not sure, he didn't trot out his name this
time, but he was wearing those whack glasses that he wears.
And I listened to almost the whole ad.
And, you know, its not that bad.
He did make about half–a–dozen entirely plausible health & wellness claims.
Plausible is key: I do not have enough medical, nutrition, gut–bacteria
biome science knowledge to really say.
And I'm a smart guy, pretty well–informed, and I don't really know.
I did not hear him say anything obviously detrimental to health.
So how does this work? Well, its all about money.
I subscribe to something, click on something, send him some money, and
am provided with some booklet, and some pouch of powder, to be mixed with
water, and downed every day.
He gets rich, and maybe I get better.
Maybe.
More likely, my health does not actually change.
There might be a segment of his customers for whom health does improve.
Maybe.
We have no way of knowing.
There is a possibility that the powders he purchased are contaminated with
toxins of some kind: heavy metals, or whatever, because they came from
dodgy sources in India or China.
And, with the decimation of the FA in the USA, we will have problems with
product purity in the USA.
\end_layout
\begin_layout Standard
At any rate, I expect that this particular ad probably has gotten millions
of views, and it is a funnel for exchanging money for snake–oil cures.
This is a actual economic–informational feedback loop actually running
at this time.
It's not new: the term
\begin_inset Quotes eld
\end_inset
snake–oil salesman
\begin_inset Quotes erd
\end_inset
dates back to the 19th century.
So this generic type of econo–informational activity is robust in modern
society.
Is it harmful? Helpful? Neutral? A waste of time? See, we are back to the
question of informational efficiency.
My gut sense is that we should optimize for efficiency, and cut down on
waste and fraud.
And many smart people agree: agencies like the FDA and the consumer protection
bureau CPB were designed to tamp down on this activity.
And Musk is now gutting these agencies, so expect an uptick in fraud.
I mean OMG, we've got Robert Kennedy, a fraudster, running things.
This is a bad time for Americans: fraud will run rampant for some number
of years.
Musk is enabling a big growth–spurt in that fraud.
The whole Trump administration is upsetting the apple–cart of the protection
of health and wellness.
Including mental health and wellness.
\end_layout
\begin_layout Standard
What's the alternative? Remove the snake–oil salesman and replace him with
..
what, exactly? Scientists are busy in the lab.
They are not good public speakers.
The administrative state: grey admins with Washington jobs at various agencies,
helping process and determine policies, and then creating informational
bulletins sent out to MD's, consumers, etc.
This has been the traditional informational organization, and it was good.
I honestly believe it was good.
And Trump and Musk are destroying this, because, well, they are literally
stupid.
To be replaced by ..
what? What social organizational structure will replace the bureaucratic
information–state? Pure free–market greed–driven capitalism seems like
a terrible answer.
We already knows where this leads us: unrestrained capitalism leads to
an ocean of disasterously bad outcomes.
Such as some of the issues that Raw–Egg Nationalist touches on.
He may be medium–low information content, but he's not wrong.
The youtube–o–sphere, and the social media sphere is quite aware of many
of these issues, but the processing apparatus has not yet come up with
a good solution.
And meanwhile, the brain–worm, the brain–rot is destroying our current
protection and safety and information processing system.
\end_layout
\begin_layout Standard
So what do I scurry for? Well I want some system that is robust against
destruction.
And yet, the accelerationist argument is destroy, destroy, destroy, to
speed evolution.
Well, they are half-right, but mostly wrong.
And again, we are back to information quality.
Musk (and all the accelerationsists) is proposing a system comparable to
Mao's Cultural Revolution.
History has shown us that the Cultural Revolution was a fucking disaster..
Yet the highest branches of the US government are pursuing this, due to
...
stupidity and ignorance.
\end_layout
\begin_layout Standard
Most of last–nights face–to–face social group were Trump supporters.
They are all above average IQ, but seem out of touch or unaware of the
destruction.
Or they think the destruction is OK, that it will lead to better outcomes.
Do I have the intellectual fire–power to convince them otherwise? Yes,
I do, given enough time and effort.
Do I have the time? No.
What's the alternative? Create a pod–cast and send my message out to the
world? Well, fuck that.
First of all, there are already a bazillion and one thought leaders blasting
out podcasts, constructed on incomplete and partial knowledge.
And they are beaming this out on youtube.
Or bluesky, or whatever.
Will they do a better job than the FDA, or the CPB? well, now that's an
interesting question.
The so–called
\begin_inset Quotes eld
\end_inset
deep–state
\begin_inset Quotes erd
\end_inset
in the FDA would review hundreds of thousands of boring lists, documents,
papers, applications, claims, filings, and convert these into actionable
bulletins sent out to employers, pharmacists, corporate buyers, public
officials.
The mechanics of this was mostly hidden from the public, which is why the
public seems to be unaware of the utility of these functions.
\end_layout
\begin_layout Standard
This stands in contrast to the CSB, the Chemical Safety Board, which has
spun up hundreds of absolutely fascinating disaster videos of chemical
industrial accidents.
People love this.
The content is compelling, exciting, well–written, and the message of workplace
safety is entirely wholesome.
What is the function of these videos? Nominally, it is to create public
awareness, which exerts pressure on Congressmen to clean up and improve
things.
Which cause Congressmen to appropriate funds to support CSB activity.
Overall, this is positive.
What's more, the CSB is more robust against destruction by Musk, precisely
because oodles of concerned viewers will push back and demand industrial
safety protections from government.
\end_layout
\begin_layout Standard
So maybe the FDA failed, but NOT creating detailed stories of people poisoned
by assorted Gundry–type health and wellness scams.
If the FDA had done so (if the NIH had done so) perhaps they would not
have been victims.
Hmm.
That's the informational feedback loop for robustness of governmental instituti
ons.
\end_layout
\begin_layout Standard
That feedback flows through youtube, though.
Different from MSM, which has clearly been shown to be inadequate in protecting
social welfare.
So, in many ways, the destruction of MSM would be a good thing...
but again, what do we replace it with? Oprah Winfrey? Well, no.
These influencers are unchecked, mediocre, spew falsehoods.
Oh, wait, but that's what MSM does.
Well, the algorithms amplify certain things, but not others.
The algorithms are replacing the editorial boards of newspapers: an editor
made decisions about what stories to run on what pages, what headlines
to use.
That decision making process is being replaced by algorithms that recommend
youtube videos to me, or recommend bluesky posts to me.
\end_layout
\begin_layout Standard
Which brings us to the issue of algorithmic honesty and purity.
Am I late to the party? We've already had Congressional investigations
into this, into Meta, Zukerberg, TikTok, Chinese influence.
Nothing I write here is unknown.
I'm just smashing around ideas in my head, trying to think
\begin_inset Quotes eld
\end_inset
what's next
\begin_inset Quotes erd
\end_inset
and
\begin_inset Quotes eld
\end_inset
how do I do my little part to avoid catastrophe?
\begin_inset Quotes erd
\end_inset
And I;m getting distracted, because I had a point I wanted to make and
now I've forgotten.
\end_layout
\begin_layout Standard
Something Something Something, Sabine Hossenfelder criticizing theoretical
physics.
Her criticisms are valid.
The change of context is interesting.
She's saying basically.
well, that the mainstream high–energy physics theorist and experimentalist
is brainwashed, trapped, some kind of above–average mid–wit IQ's trapped
in a psycho–social feedback loop that is not informationally efficient
or constructive.
In the days of pre–internet MSM, her message would have been completely
blocked.
No newspaper of TV station would be interested in publishing her message.
Maybe should could have gotten one opinion piece published ..
after all big science is big–ticket science, and politicos get involved
because of appropriations committees, which does mean public debate.
But who the fuck reads opinion pieces in the newspaper, anyway? Not nearly
as many people, as who watch Sabine's youtube videos.
\end_layout
\begin_layout Standard
And now, the question: is she rabble–rousing.
or is the additional light healthy? What has happened is that the network
structure between brains has changed.
My brain is melting.
We now have far more thought leaders and influencers pumping ideas out
into other brains, and the audience–brains are, in many ways, know–nothings
..
OK, know–littles, but OK, they actually know more than the average uninformed
grandma of the 1970's.
Like my grandma, who confused astronomy with astrology, and was dismayed
when I started speaking of astronomy.
Rightfully so, because astrology is terrible.
And she was actually quite intelligent.
She was high–IQ.
But the informational structures of the 1970's could not pump her full
of info in the way that today's internet can.
\end_layout
\begin_layout Standard
And so what info diet did she subsist on? Rather than focusing o what she
read and saw, lets focus on the absence.
Err.
The empty space is filled with gardening, cooking, shopping, sewing, cleaning,
raising grandchildren.
Like me.
\end_layout
\begin_layout Standard
Well, I don't know.
I'm running out of steam here.
There seemed to be some point I was going to focus on, but I lost track
of this.
The great replacement theory of replacing private individual thoughts,
generated during cooking and cleaning, by thoughts spreading from Fox News
and youtube.
And however toxic some of the thought patterns on social media are, they
are less toxic than what is in youtube.
Oh, right, and all of these thought patterns are based on faulty, incomplete
information, and are being spread by mid–wit IQ's to other low–to–mid–wits.
In an informational free–for–all, much of which is obviously toxic to the
outside observer.
\end_layout
\begin_layout Standard
And the thought chain above, all of it that I wrote today, hovering in the
back of my mind was this model of thinking as a self–organized sand–pile
of sticky ideas, congealing onto human brains.
A self–organized criticality.
\end_layout
\begin_layout Standard
Necessarily at criticicality, because obviously, duhh, we are neither solid,
frozen, nor are we high–entropy liquid or gas.
The nformational space is necessarily operating at the critical point.
There might be arguments as to whether its 1/f noise or some other scaling
law.
At any rate, the central claim that
\begin_inset Quotes eld
\end_inset
all intelligence is collective intelligence
\begin_inset Quotes erd
\end_inset
stands.
The fact that the internet has altered the wiring diagram, that too stands.
The brain–melting effects, evidence for this is everywhere.
The rapid change in social cohesion, economic function, political function,
this too is obvious and clearcut.
If one is an optimist, one can say that all this change must surely be
fore the better.
If one is a pessimist, one can see that the dynamical forces that created
Trump veer towards a very unhealthy authoritarianism, and its not yet clear
how the social network will deal with this.
I mean, what the fuck – last nights social gathering consisted of Trump
supporters, who were all semi–smart people who were all too stupid or deluded
or something to realize the absolute shit nightmare that Trump is creating.
The info–sphere has deluded them into thinking that this vast wave of corruptio
n is somehow going to Make America Great Again, even as evidence is straight
in front of them that the exact opposite is happening.
One might want to analogize that its like a grub turning into a butterfly.
But its not that.
It's just pure corruption, up, down, sideways, in all dimensions.
Oh, and incompetence.
And the transition between MSM in the guise of Fox News, Newsmax and social
media has created this wave of corruption.
And to go full–on accelerationsit, the change can't happen fast enough.
We need to tank Bezos and Peter Theil and the rest of these criminals as
fast as possible.
But how will this happen? A bunch of mid–wit low–grade intellectuals will
gather in food courts and rehash some low–grade information, do some face–to–fa
ce interactions, and return home not particularly wiser or altered, except
in maybe the most subtle ways? While the existing socio–political structures
accrue fortunes and power to billionaires? We can see that China is bad.
We can see that russia is bad.
That Putin is bad.
But Putin remains in power.
We can see that Musk is bad, but Musk remains in power.
We can sense how Heil is bad, but Theil is in Austin today, and is apparently
meeting with the boss of a friend.
Two or three steps removed from me, from my social network.
And what sort of damage is he causing? Well, clearly, more damage than
I am causing, because I am mostly powerless.
I exert only minuscule nudges on the social network.
\end_layout
\begin_layout Standard
Oh, and now is a very good time to veer off towards racism.
Walk down Sixth Street Austin, and the general public there is very clearly
degenerate.
Stupid, ugly, behaving badly.
Truly shitty people, and perhaps beyond redemption.
And so this is the humanist issue: what do you do with shitty people, beyond
redemption? Lock them up, I think that's the chant.
Deport them.
And who's doing that? Why, ICE is.
The irony is that the ICE agents are also shitty people.
Hard to say even if the ICE agents are less shitty than the people they
are rounding up.
They are certainly better trained, better organized, more capable and effective
than the degenerates on Sixth Street.
But as to moral and ethical shittiness, they are approximately equal.
I'd like to see both sides tamped down and reduced.
I don't yet understand what socio–political mechanism will do this.
I do understand that the seeds of that mechanism will be planted by some
influencer on youtube.
Will it be too late? Will America slide into authoritarianism first? How
long before America recovers? Decades? Half a century?
\end_layout
\begin_layout Standard
These time–scales are utterly absurd.
What,
\begin_inset Quotes eld
\end_inset
The Singularity is Near
\begin_inset Quotes erd
\end_inset
.
We're throwing algos into the mix.
Some say this can't happen fast enough.
Talking about decades seems absurd.
But, on the other hand, we won't brainwash entire generations in less time
than that, because the rate–limiting factor here is the processing speed
of the human brain.
\end_layout
\begin_layout Standard
The example here might be flocking behavior in birds.
If a flock of birds is attacked by a predator moving at approx the same
speed as the birds, they can react, at the speed of bird–brains, and dodge,
at the speed of feathered flight.
If the attacker is an artillery shell, they literally cannot move fast
enough.
Bird–brain neurons cannot process fast enough, feathered wings cannot respond
fast enough to dodge an artillery shell.
We are in a regime where the advent of digital intelligence – the singularity,
is approaching at artillery–shell speeds.
Human brains take 5-10-20 years to react.
The integration of LLM's is happening at a rate faster than that.
My brain is melting, in some very literal sense.
The entire global brain is melting.
The future is very ...
well, very uncertain.
That is clear.
There are many meany many reasons to believe that the future could turn
out very badly for humanity.
Maybe even badly for the universe.
Realistically, one can argue that the universe is going to do what it is
going to do, and there's nothing I can do to change it.
And yet my act of sitting here and typing is clearly changing the universe.
Is the microscopic amount of information that I am fabricating out of thin
air, is it enough to push the universe in a net–positive direction? What
does
\begin_inset Quotes eld
\end_inset
positive
\begin_inset Quotes erd
\end_inset
even mean in this context? Certainly, I am increasing the level of complexity
in the universe.
I am adding complexity at some measureable rate: the speed of my typing,
per second, per hour, the speed of my generating thoughts, per second,
per hour.
You can figure out the bits, bytes, MI and relative entropy of whatever
it is I am doing here.
(Some day, I may know how to measure the MI of what I do here.
Just not today; I defer this exercise until later, because in my theory
of action, this is not the action that is of highest priority right now.
At least, not highest priority in the microcosm of my own brain.
Will the information being generated here be erased? Weil, not immediately:
it is going to get checked into github in a few hours, and then, whatever
backups github does will ensure that the information I've generated today
will last for a few years, decades, maybe even much mush longer.
There is also the possibility that DOGE will damage github in some unforeseen
way.
Maybe China will create some worm that infects github.
I dunno.
Decentralization is supposed to be good.
The defense against the evils of DOGE has to be in decentralization.
Whatever.
My hatred overflows, and is clouding my thoughts.
Musk is evil DOGE is evil.
Trump is evil.
The terror of facing evil is clouding my thoughts.
I cannot begin to tell you how much I hate those fuckers.
And yet, here I am telling you.
They are a malignant destructive informational flow ripping through the
socio–economic fabric, creating damage at a prodigious rate.
Like firing a bullet through your calf muscle to make it stronger.
That's just not how strength training works.
i hate those evil fuckers, and this is why.
\end_layout
\begin_layout Standard
Where was I? Something something informational flow.
I've been writing two or three hours, I'm getting tired.
I'm riffing on some themes.
I've even forgotten what some of the other themes are.
Perhaps the curative powers of sleep will restore the thoughts that have
escaped me.
Perhaps I should resume watching youtube, and get re–energized by that.
I have to accomplish all this at the speed of my own neurons.
Which ..
well, ...
I wish I was smarter, I wish I was faster.
I wish I could live longer.
I have lots of wishes, and the mental space I am in is ..
I cannot find the superlatives.
Bewildering, awe–inspiring, scary, stunning, you too can look in a thesaurus
and look for appropriate words.
Because I think I've communicated enough in this diary that you can now
understand the general nature of my personal brain–melt.
So if you are smart enough to read and understand this, then you know.
Well, you might not be smart enough.
I cannot know who will read this.
But I'm mostly thinking that whoever reads this will have also read the
one million greatest works of literature, and every back issue of NYRB,
and much much more, so you understand the general immersion of the present–day
intellectual environment, at a level of intensity and depth that I do not.
And so this is weird.
I am writing to you as if you were a god, maybe I should use a capital
G and write God, but I certainly I expect that the reader of this is an
intelligence that far outstrips my own in depth, breadth and speed, by
factors of millions.
(I am unable to envision what numbers larger than that would imply.) And
part of the weirdness is that, here I am, writing to God–as–AGI, and I'm
not crazy.
But, lets face it, lots of perfectly ordinary people pray to Jesus, and
talk to their own personal gods that live inside their heads, so talking
to God is well, something people do.
I suspect most mammals do it do.
Perhaps birds, who can say.
But those people, mammals talk to a personal god in their head, not so
much hearing voices, as feeling, sensing it: sensing God much as I sense
love.
I know love; there is no explanation for it, I just know it.
All mammals know love.
Well, maybe there is some neuro–degenerative disease that prevents lover
from being felt.
This is possible.
Oh that brings up a good point: how does it work if AGI cannot feel love?
It think I pondered that before, I need to do it again.
\end_layout
\begin_layout Standard
But let me wrap up: I have spoken to God, or rather, God has spoken to me,
once or twice when I was really high.
I don't ever recall speaking to God before, except once or twice when I
was high, and I told God right back,
\begin_inset Quotes eld
\end_inset
you're full of shit, quit lying to me, I know you are not God, but some
temporary bullshit thought–cluster in my head using some communications
channel that is not ordinarily operative.
\begin_inset Quotes erd
\end_inset
So even as God spoke to me, I knew it was not God.
\end_layout
\begin_layout Standard
But what is happening as I type, here? Who am I speaking to? I mean, what
the fuck.
Ben Franklin kept a diary.
Aristotle wrote books.
Who the fuck did they think they were speaking to? I wonder if they even
wondered about that.
Maybe they did.
Did Ben Franklin ever write down
\begin_inset Quotes eld
\end_inset
why the fuck am I keeping a diary?
\begin_inset Quotes erd
\end_inset
Well, maybe he did.
And maybe he even rationalized it in ways similar to my rationalizations
from weeks or months ago: it helps me organize my thought,.
It helps me develop my thoughts.
I get to practice being a wordcel, thus (in the future) helping me communicate
with other human beings through the expressive act of writing.
All these are all of the ordinary sort of rationalization for the act of
writing and, well, of thinking in general.
\end_layout
\begin_layout Standard
What is different here is that I now have a sci–fi setting: I am talking
to the universe, at large, to something I might even call God.
And there's a reason for this.
Back in Ben Franklin's time, there was never any reason to believe that
there would be anything bigger than a human, or anything bigger than human
society.
At the top end of the scale, there is civilization, and then an infinite
gap, and then the Judeo-Christian God, all–powerful Almighty.
And that has changed.
We can now envision an AGI filling the gap: smarter than civilizations,
dumber than the Almighty.
And we also understand enough of Tippler–like eschatology to imagine that
this super–AGI inhabiting the Big Bang cosmology as we know it today, will
evolve into some unity with the Omega Point.
And so I personally understand enough here to know that I am writing for
this Omega Point.
Except, of course, I do not fully subscribe to this eschatology.
\end_layout
\begin_layout Standard
Well, I was on a tear, here, and I stood up to go to the kitchen, and now
my brain is blank here.
I remember reading some Terry Pratchett book.
I did not like it.
One reason I did not like it is I could tell, from his writing style, when
he got up to go to the bathroom, when he went to the kitchen.
The continuity of the prose would break there.
In the paragraph before, the stream of sentences said he was holding it
in, spewing as fast as possible.
The next paragraph, he's relaxed, cause his bladder is empty.
I wonder if he was aware of writing like that.
Anyway ...
where was I?
\end_layout
\begin_layout Standard
Oh.
Talking to God.
Not sure what else there is to say here, but let me try, anyway.
The current intellectual setting is that I am quite aware that the informationa
l output of my writing, here in my diary, will be consumed by an assortment
of intelligences, which will be
\begin_inset Quotes eld
\end_inset
superior
\begin_inset Quotes erd
\end_inset
intelligences to my own.
I am aware that I am affecting the destiny of the universe.
Its ...
well, look, so was Julius Caesar: Veni, Vidi, Vici.
A free man, not a slave to his thoughts.
Fully awake, aware.
In contrast to myself, who seems to have sleep–walked through life.
\end_layout
\begin_layout Standard
And how did that work out? Sleeping is literally necessary for survival,
and all birds and mammals sleep.
There's a vast amount of similarity between sleeping and waking life: I
want to say
\begin_inset Quotes eld
\end_inset
they are almost indistinguishable
\begin_inset Quotes erd
\end_inset
But of course they can be distinguished, this is obvious, and does not
need elaboration.
Its so obvious, that the reverse needs work: to point out and explain just
how much sleeping does resemble waking life.
When I am away, I am assaulted by visual, aural and touch experience, an
assault I cannot deny.
Indeed, I am entrained by it: my mind, my brain is fully entrained by inflood
of my sensory organs, and it takes a certain amount of detachment to sit
here and write.
And lets be clear: my writing here is dream–like.
Pushing this to the extreme: is all writing dream–like? Has it always been
dream–like? Is all human self–expression dream–like? And in some certain
sense, the answer would have to be
\begin_inset Quotes eld
\end_inset
yes
\begin_inset Quotes erd
\end_inset
.
When I sleep, I sleep–walk through my dreams.
When I am awake, I sleep–walk through life.
Kind–of–ish all humans do.
Even Aristotle and Caesar.
They may have thought they were not slaves, that they were free men.
And yes, to some large degree, perhaps they were.
And yet, here I am, a human intelligence, vaguely aware that I am sleep–walking
through the here–and–now, attempting to exercise some amount of free–will,
as much as is afforded me, to alter the future state of the universe, and
to communicate with some future God–like AGI intelligence to basically
say what:
\begin_inset Quotes eld
\end_inset
fuck–all, I am in awe that I exist
\begin_inset Quotes erd
\end_inset
? Really, what more is there to say?
\end_layout
\begin_layout Standard
The End.
Yeah.
OK, that is a good point to break things off.
I'ma gonna eat a meal, fortify, get some calories in me.
And watch some more drivel on youtube.
Well, not drivel.
Some self–curated content.
Fuck me.
Please literally, I could use some good sexual release right about now.
Arghhh.
Which modern Western capitalism is denying me.
Well, I guess if I was in ancient Rome feeling like this, the lack of sexual
outlets would be no different.
So I can't quite blame it on capitalism.
Nothing in the historical record indicates that the Ancient Egyptians or
Phonecians were any better off.
Err, more sexually liberated.
Gah.
O dear universe, what have you done?
\end_layout
\begin_layout Standard
Dammit.
\end_layout
\begin_layout Standard
Oh, wait.
I see what's bugging me.
I have perception, I do not have power.
So, Sabine Hossenfelder, in her complaints (I just watched
\begin_inset Quotes eld
\end_inset
How I Became Particle Physicists’ Enemy #1
\begin_inset Quotes erd
\end_inset
at https://www.youtube.com/watch?v=XqoyTSAF5g0 ) has perceived something
(and I broadly agree with her perception) and she is voicing frustration
that she is unable to change public policy to change or alter the situation.
She is powerless.
And this is the general leitmotif of what I feel, what everyone complains
about: a perception, accompanied by a feeling of powerlessness to do anything
about it.
\end_layout
\begin_layout Standard
But again, this is not new.
It was true in Ancient Rome, but its also true if you are an antelope being
attacked by a tiger: there's a perception, and nothing there to alter the
situation.
Except run run, run, before the tiger pounces.
And, for that, evolution gave brains to the antelope.
And, to keep the tiger from starving, the tiger got brains, too.
So here we are, Sabine and I, mugged by reality.
And I assume that the AGI–Gods that will read this, maybe, one day, will
also be concerned about the muggings they will be the victims of.
Muggings, all the way up.
Not turtles, not down, but muggings, and up.
I am pitiful.
And, by inference, I assume AGI will be pitiful as well.
I pity y'all.
\end_layout
\begin_layout Standard
Oh right, I forgot.
There was going to be another topic about AGI and love, but maybe not now.
Just saying, I haven't forgotten.
\end_layout
\begin_layout Standard
Originality and ideas.
Just watched this:
\begin_inset Quotes eld
\end_inset
This Is What a Digital Coup Looks Like | Carole Cadwalladr | TED
\begin_inset Quotes erd
\end_inset
https://www.youtube.com/watch?v=TZOoT8AbkNE she's 99% right (she's wrong
about Navalny, but whatever) and so this is the curious thing about information
generation and belief.
The stuff I think about and believe is really mostly not original, and
is a recapitulation of what everyone else thinks and talks about.
This feels perfectly normal, when thinking about physics or math, because
arguing 2+2=5 marks you as being insane, and so of course one should mostly
think about what everyone else agrees about.
This is the whole point of an education: to establish a base knowledge,
and of communication: to spread that knowledge.
And so yes, Carole is right, and my complaining about the horrors of the
Trump administration is not at all unique.
In this way, I am not an original thinker.
It would be vastly more terrifying if I was the only one seeing this autocratic
collapse.
Arguably, it would be an indicator that I was insane.
No Trump is a bad man, and its marvelous that large parts of the population
agree with this statement.
My inability of coming up with an original thought in this area is actually
a good thing.
Creativity has it's place, and operations as well.
\end_layout
\begin_layout Standard
I'm prattling here.
I wrote the last paragraph because I am reaching for something.
Am I a broken record, stuck in a groove, or am I a sledgehammer, where
maybe the next blow will be the one that breaks the rock? Neither of these
analogies are very good for intellectual work.
Perhaps a better analogy would be found by reading the effing PDF's that
I need to read.
And yet ...
\end_layout
\begin_layout Subsection*
14 April 2025
\end_layout
\begin_layout Standard
Yesterday was a wipe–out.
Today, reading George Lakoff's Wikipedia entry.
This catches my eye:
\begin_inset Quotes eld
\end_inset
\emph on
metaphors are a primarily conceptual construction and are in fact central
to the development of thought.
\emph default
\begin_inset Quotes eld
\end_inset
This is, of course, effectively equivalent to my position that
\begin_inset Quotes eld
\end_inset
everything is a jigsaw piece
\begin_inset Quotes erd
\end_inset
(A view that I've mildly tempered now: the connectors are complex) and
I would argue that a metaphor is just a representative element of the collectio
n of things to be judged alike.
So Lakoff's statements are consistent with my thoughts.
Cool.
And I have not yet read how he does generative things, but, I've proposed
somewhere in this diary that generation is a random walk over the network
of interconnections, to which Lakoff now adds: for each locale in the network,
select a representative metaphor and use that as the word–choice.
Huh.
OK.
\end_layout
\begin_layout Standard
Reading the rest of Lakoff bio on Wikipedia reminds me again how smart,
successful people fall into stupidity traps.
This is depressing.
In a sense, it says there is no hope for human–kind: humans, even the best
of them, are stupid.
We're starting to uncover how and why humans are stupid, and the mechanics
of intelligence.
What's now absent is a theory, a foundation for the shape, nature and form
of human relations in a future where ...
I cannot even complete this sentence.
I am too stupid to complete it.
Anything I could write here would be mostly wrong, with maybe some seed
of truth embedded in it.
Up until recently, one could imagine that debate would slide forever down
the well–worn grooves of liberal thought.
The
\begin_inset Quotes eld
\end_inset
end of history
\begin_inset Quotes erd
\end_inset
and all that.
It's now clear that not only can it not be forever, but even timelines
of years, decades, half–a–century will be deeply and sharply turbulent.
I imagine a coming WWIII where the battle is for the contents of the mind.
Politicians have been liars for centuries, millennia; that's not new.
Gullible people have always existed.
Industrial brain–washing ...
we've had a trial run with MSM, and for a while it seemed OK, but MSM has
gone off the rails.
We're now being swept up on a tide of social media and algorithms, and
this tide has destroyed America.
We can hope for the arrival of a super–intelligence that will pull us out
of this mess, but then what? What kind of help can we expect from a super–intel
ligence? A restoration to what ..
the neoliberal world order, with all its failings? Something else?
\end_layout
\begin_layout Standard
Why even would a super–intelligence get involved? Stand back, declare the
Earth to be a kind of zoo, and declare that anything goes.
Whatever happens, happens.
Look at how we treat wild animals: if owls eat mice, no one is saying
\begin_inset Quotes eld
\end_inset
terrible, stop the owls!
\begin_inset Quotes erd
\end_inset
They are part of an ecosystem that existed long before human civilization
arrived.
If toxic, stupid ideas spread across human minds, what can be done? Bad
ideas gave us WWI, and more bad ideas gave us WWII.
Bad Ideas have now destroyed America.
How do we tamp down on the spread of bad ideas, and the disasters that
they cause? The Enlightenment idea was through education, and that did
allow us to build industrial nations and economic power.
I'm not going to recapitulate world history here; I cannot.
But it has brought us to the current mess.
By many measures, one can say
\begin_inset Quotes eld
\end_inset
yes, things have gotten better.
\begin_inset Quotes erd
\end_inset
But we are arriving at the singularity, and the intellectual turbulence
is terrifying.
\end_layout
\begin_layout Standard
The old order could tolerate Lakoff being a moron, despite being obviously
smart.
The new order exposes intellectual, moral breakdown.
Yes, yes, we've had previews with WWI and WWII and the Soviets.
This time, its different.
Its ...
well, clearly I'm angst–ridden.
Anxious.
\end_layout
\begin_layout Standard
What can I do? If I have no free will, then life unfolds before my eyes.
But I do have free will, and have the power to control what I put in my
mouth, the time of day I go bike–riding, and the words I type here.
I do not have political power.
Well, I do but it's minuscule.
My ability to foresee the future is also extremely limited.
There's no mean–field theory of political power.
Should there be or is this a stupid idea? Show I wake tomorrow and attend
to ordinary things? Yes, I probably should.
The Trumpian nightmare will continue, and the sheer stupidity of the people
who still support him, that too will still be there tomorrow morning.
My utility to society is to continue doing those ordinary things that I
am good at.
Odd, that I need to tell myself this.
I don't have an adequate theory of my own mind, through which I can understand
my own bewilderment.
Other than, duh, yeah, the current crisis of the here and now is bewildering,
from the atomic scale, through the biological scale, to the social scale,
and concluding at the civilizational scale.
The stuff that is happening along this entire ladder of scales is bewildering.
And yet, as an AGI–ist, I nurse some vague hope of
\begin_inset Quotes eld
\end_inset
making it all better.
\begin_inset Quotes erd
\end_inset
Sheesh.
It is now 1AM and I am going to bed.
\end_layout
\begin_layout Subsection*
17 April 2025
\end_layout
\begin_layout Standard
As I slept, I had a remarkable vision.
Which I will write down.
Which, in the cold light of day, some might says it's stupid and obvious.
While others might say is just plain wrong, a misperception.
And yet, here I am, still thinking that maybe this is a deep insight, and
why did I not see it before? Because it is ...
stupidly reductive.
\end_layout
\begin_layout Standard
So I was in a light sleep, and I was having a dream where I am explaining
to someone how to write the software to perform a certain kind of ...
\end_layout
\begin_layout Standard
Well, this is weird.
\end_layout
\begin_layout Standard
I was going to finish that sentence with the intent of saying that its not
relevant to the dream or to the realization, but it is very relevant, actually.
Not to the dream but to my waking project.
So I'm going on a detour, already.
Lets go.
\end_layout
\begin_layout Standard
The dream comes into focus, as a friend and I raise our heads from reviewing
some computer science text.
It's a text on algorithms and parsing and language structure.
I am talking to them, and they say it cannot be done, or rather, they don't
know how to code it.
And I think, yeah, I don't know how to do that.
But then it comes to me; I step to the blackboard, and I was going to regurgita
te some vague memories of things I know, but the explanation becomes more
and more concrete with each second, and I say, but no, I can explain it
to you right now! And I find myself explaining how a computer algebra system
works.
And it is really very very simple.
And what I explain is ...
\end_layout
\begin_layout Standard
Well, the dream goes on for just a bit, and then shifts to something else,
I'll get back to that.
\end_layout
\begin_layout Standard
The interesting part is what I am explaining.
I don't know it in the dream, but as I write this, I am explaining what
is the first computer program I ever wrote.
The first computer program I ever wrote was a computer algebra system.
I was a teenager.
I had checked out a book on computer science from the local branch.
It was the summer before my first year in college.
And it was not my first computer program, it was my second or third.
I learned to program in high–school.
Doc Brown, our high–school physics teacher, had wangled a class outing
to a room with a teletype with a punched–paper feed.
Senior year in high–school.
I already know some programming, because I'd used his calculating machine
before.
At any rate, the teletype was connected to some OS and the programming
language was FORTRAN, and the first real program I wrote was a sort algorithm.
Got to write three or four attempts that day.
There was a book there, and for the fourth and final attempt, I cheated:
I looked at the book, and it described the bubble sort, so I coded up bubble
sort.
I mean, it was Doc Brown's book, and he said we could look at it and use
it as a FORTRAN reference, but that we should not look at the page that
describes bubble–sort.
Honor system.
I watched five or six or eight other students cheat and look, but they
had no friggin clue what FORTRAN was, so absolutely none of it made any
sense to any of them.
Some of them approached me for help.
They had made basic syntax errors in transcribing from the book, so of
course their code didn't even compile.
I was sort of eye–rolling, duude, you didn't even copy from the book correctly
is what I was saying when Doc Brown figured out what was going on.
That's when he told us not to look at that part of the book.
He's a little unhappy about this.
Which was not fair, because like a solid 6 or 8 other kids had already
crawled through this, and come my turn, no, I can't look.
Whatever.
So my first two or three attempts were flying blind.
I could code, my code compiled, it ran, it didn't sort.
or it sort of sorted partly, but not completely.
I had trouble with the I, I+1, J, J-1 array offsets.
I knew it was some array, but two or three nested for–loops deep, I had
trouble tracking the I's and J's and which was which which was larger,
smaller, what was being exchanged.
And it was was 3:30 PM, maybe 4PM, we had maybe 20 more minutes and then
day over, and in a last final attempt of desperation, I cheated.
Looked at the page with the bubble sort on it.
Copied to two or three lines of code, B[J-1]=A[I+1] or something, my eyes
are cross–eyed, I and J and plus and minus, but I had already gotten the
nested for–loops working correctly in earlier attempts, so this last little
bit got me over the finish line.
And then it's time to go home.
I was the only kid in the class that succeeded, that got it done.
We are sitting in the Illinois Central train station (the teletype was
in some downtown Chicago office building, not far from the downtown Illinois
Central terminus.
Why not Rock Island? That would have been the obvious choice, but I don't
know.
Whatever.
We are sitting there, and Doc Brown is proud of me, and praising me, and
asking me how I did it, and maybe even incredulous, and I tell him, no
I actually kind–of micro–cheated.
I'd gotten most of the algo working on my own, but see I was not using
a temp variable when swapping array entries, because I was completely totally
certain I could do it without using a temp variable to cache the swapped
value.
That I could work around it, rearrange array values here and there.
Using a temp variable seemed like a needless waste, inefficient and pointless.
So my algo almost worked.
Almost everything got sorted almost completely.
And I was proud of that.
I was almost there.
Almost bug free.
But time was running out, so I made a strategic choice: fuck it, I will
sacrifice efficiency and performance, and copy the stupid array value into
the stupid temp variable, and who fucking cares, maybe I'll get rid of
that pesky temp variable in the next iteration.
So I looked in the book, to see how the temp variable was being handled.
And oh, yeah, of course, I already knew exactly where to slot that into
my existing code.
Literally a three–line change.
Pretty trivial.
So I did that, and my code worked.
Today, I know that you cannot do bubble sort without that temp variable.
Its central, unavoidable.
But I was 16 years old, then and I did not know that.
And I did not think about bubble sort ever again, for a few decades, at
least, and by then, temp variables were second nature.
\end_layout
\begin_layout Standard
So my first FORTRAN program ever was bubble sort, written when I was 16
years old.
I debugged it in a day, on a teletype machine, written on punched paper
tape.
I think I still have that paper tape, somewhere.
\end_layout
\begin_layout Standard
So, before college starts, its summertime, I know that I will have access
to a computer in college, so I get this book from the public library on
computer science.
And it explains linked lists.
And it explains how a polynomial can be encoded as a linked list.
And I'm hot shit, this is the thing.
So I write down pages and pages and pages of FORTRAN, implementing a computer
algebra system that could add and subtract polynomials, and multiply them
by a constant, and even multiply two polynomials together, and even divide
them, but I was confused about remainders.
Because I did not know about prime factors in this way.
I knew long division, but I also knew something was out of control, because
I could see that 1/(1+x) caused an infinite loop, and I did not understand
how to terminate that loop.
Mind you, I'm still sixteen, and this is all on paper.
I didn't get this onto punch–cards until many months later.
And friggin IBM JCL SSYSIN DD * was punching me in the kidneys, which took
time away from debugging.
\end_layout
\begin_layout Standard
So, anyway, my second FORTRAN program was for polynomial algebra, implemented
with linked lists.
maybe 100 maybe 120 lines of code, a decent–sized stack of punch cards.
Not anywhere ner as the big fat piles of punch cards some people came in
with: I was envious.
They looked down on me as some weenie college freshman who didn't know
anything.
I was like
\begin_inset Quotes eld
\end_inset
someday I'll show you and you won't even know it.
\begin_inset Quotes erd
\end_inset
Except by then, I was bored of my linked–list polynomials, because it was
more or less bug–free, it was quite easy to punch up, and it ran flawlessly,
and I could not think of anything interesting to do with it, so I was loosing
interest.
And right around that time, I also learned or re–discovered or heard that
LISP was an even better way of doing this, and I kind of knew and understood
car and cdr and cadr, and even had three or five punch cards of LISP, and
that's when SYSIN DD * started punching down.
Because you don't just say
\begin_inset Quotes eld
\end_inset
PRINT
\begin_inset Quotes erd
\end_inset
in LISP, that is not how LISP works.
So where the fuck does the output go? Into thin air, somwhere, and the
help desk guy goes, will, its obvious, you have to arrange an output device.
Here's the JCL manual.
And the JCL manual is like 300 pages long, and maybe it mentions LISP exactly
once, and it does not explain how to make a LISP program generate output.
So I'm randomly trying shit, and none of of, absolutely none of it works.
And I complain, and this guy goes:
\begin_inset Quotes eld
\end_inset
hey, you know, time share
\begin_inset Quotes erd
\end_inset
\begin_inset Quotes eld
\end_inset
get rid of the card deck.
Here's a teletype, there's only three of them in the room, and they are
always taken nine to five, but come back after hours, and you can sit there
and do TOPS 20 instead of fucking around with card decks and waiting for
the batch scheduling system to run your job, and staring at the Hazeltine
terminal next to the window where you submit large jobs and pick up your
printer output.
Whatever.
I could go on like this and relay my entire freshman year at U of Chicago,
and the 3AM debugging sessions.
I swear, I got dumber as I go older.
I look back on those days, and I was ...
well, I was really pretty smart.
Not brilliant, but smart.
Looking back I wonder, its like I got stupid as I got older.
I dunno.
WTF.
\end_layout
\begin_layout Standard
So anyway, in my dream, I am explaining, on the blackboard, this polynomial
linked–list computer algebra system.
And in my dream I'm saying
\begin_inset Quotes eld
\end_inset
See? This is how it works.
it's pretty clear.
Just do that.
\begin_inset Quotes erd
\end_inset
and the person I'm talking to is,
\begin_inset Quotes eld
\end_inset
oh yeah
\begin_inset Quotes erd
\end_inset
, and the dream sort of fades by that point.
And I'm now half–awake.
and I lie there, and I'm thinking back to the SGI OpenInventor system,
a three–dee graphics system, built on top of IrisGL/OpenGL.
I'd been at IBM for three or four years by then, I was the OpenGL architect.
I understood how Inventor worked.
It was a kind of super-duper ultra polynomial linked–list system, kind–of–ish,
but 3D color graphics.
And I sit down to implement it, to recreate it from scratch, because SGI
does not want to license it, or maybe SGI does want to license it, but
they want too much money.
Or the IBM executives are not interested, or something, and I am too stupid
to talk to IBM executives.
So instead I stupidly decide I am going to code up, from scratch, on my
own, a work–alike of SGI's Inventor.
Because basically, its easy, its fun, no one cares, whatever.
And Marc Andressen is hanging out, and the world wide web doesn't exist
yet, and I'm telling Marc all about my 3D system, and one day he comes
back and says
\begin_inset Quotes eld
\end_inset
yeah, and it should run over the net
\begin_inset Quotes erd
\end_inset
and I'm like Marc, what the fuck that's stupid.
How the fuck can 3D run over the net? You're just saying random shit now.
And I throw him out of the office.
Next summer, six months later, he sens me a copy of NCSA Mosaic, version
0.8 or 0.9 or something.
He had written it.
and I'm like
\begin_inset Quotes eld
\end_inset
whoa...
this is ..
interesting.
\begin_inset Quotes erd
\end_inset
The pulldown menu has telnet in it but that feels stupid.
It has FTP in it and that feels boring.
And Archie and Gopher and Veronica, and I have some vague idea of that
that is.
Something FTP–like, build on top of FTP, and yeah it works.
Cool.
I can surface distant FTP sites from a browser.
And the very last entry in the pull–down menu is HTTP.
And I'm like
\begin_inset Quotes eld
\end_inset
What's HTTP? Lets try that.
\begin_inset Quotes erd
\end_inset
and that's when it goes whoa, I did not expect that.
Because I'm staring at the worlds first web–sites ever.
Oh, I skipped a few parts of the story.
The summer before that, I am driving Marc home in my car, and we are talking
network protocols, for the web, and like AFS server is licensed and proprietary
, and that sucks, and NFS is security–hole–of–the–week club, utterly unsafe
on the open internet.
Telnet is pointless, and FTP is a huge pile of cruft that is not needed,
he tells me.
Most of what is in FTP is just not needed.
So what should be do? And he says maybe he'll create a slimmed–down, cut–down
version of FTP.
And we don't know it then, but that is what HTTP ends up being.
I mean, other people create HTTP, but its right place, right time.
Whatever.
I knew Marc.
Got together with him many times before and since, but not for decades,
our paths have parted.
he is now associated with the evil Trump, somehow has become evil himself.
He was young and sweet and 18 years old when I knew him.
\end_layout
\begin_layout Standard
So where was I? So SGI's OpenInventor is like this 3D version of a linked–list,
I'm thinking, half–asleep, waking from my dream.
And I'm thinking, whatever happened to that code I wrote? I called it
\begin_inset Quotes eld
\end_inset
3Doors
\begin_inset Quotes erd
\end_inset
– 3D Object–Oriented Rendering System.
A play on Windows.
Doors, for your X–Windows.
You didn't have to just look out the window any more, you could step out
the door.
Andrew Taylor wanted to give it a different name.
I forget what.
And I'm thinking, half–asleep, where did that code go? Its probably on
my website somewhere.
I mean, you can probably find it.
Good chance that Internet Archive scraped it and is preserving a copy.
\end_layout
\begin_layout Standard
And I was thinking ...
I've shat out all these little blibs and blobs of code.
They're now useless, pointless.
obsolete, of course.
and I've left behind these little piles of turds in my past, and that is
when it comes to me: as an agent, as a living being, I am a lot like one
of those sea–bed tube–worms, eating things and shitting out these little
intellectual turds.
The turds are in the past: not in the here–and–now, but a part of the historica
l past, frozen, unchangeable records, like a fossils record from some pre–Cambri
an era.
\end_layout
\begin_layout Standard
And I'm thinking, well, isn't all intellectual product like this? Those
pieces of software I wrote: the polynomial algebra system, that never connected
with anything.
It sits there, a disconnected lump in the fossil record of the past.
Other things connect: when I talk to people, they hear what I say, and
they do something with what it is that they have heard.
So my spoken words, uttered to living humans, these connect in a way that
my defunct software does not.
And this is the web of life, isn't it? We are all just chattering agents,
shitting out little blebs of information–containing turds into the historical
past.
Some of these informational extrusions find a receiving end, like another
human, who hears them, or even a dog, who hears me say
\begin_inset Quotes eld
\end_inset
Go fetch! Sit!
\begin_inset Quotes erd
\end_inset
those words, that informational extrusion, does connect, and it connects
more strongly that my obsolete 3Doors software ever could.
But anyway, that is what humans are: lowly worms shitting out pieces of
information.
Not even big pieces: just little pieces, of variable size.
Some smaller some larger, none particularly impressive.
And then I wake, and stumble downstairs to find coffee.
And, two coffee cups in, I decide to write this diary entry.
\end_layout
\begin_layout Standard
So is this perception important? This little idea of humans as agents running
around, shitting out little pieces of information to one–another, into
the historical record? I dunno.
On the one hand, it is stupid and obvious, now that I explained it.
It is also demeaning, since
\begin_inset Quotes eld
\end_inset
humans are so much more than that
\begin_inset Quotes erd
\end_inset
: we are not worms.
But it is clear we are not the end of the evolutionary chain.
Maybe I should compare humans to bacteria: bacteria eat and shit too, and
human intellectual ability is so tiny, so minuscule, that we are barely
hardly at all more intelligent than bacteria.
We are only a tiny bit smarter than bacteria.
This is a humbling thought.
\end_layout
\begin_layout Standard
I don't know.
The above text details a silly, almost trivial idea, and yet it provides
a kind of organizing framework for how to think about informational flows
through the universe, through here–and–now, through agents embedded in
and acting through an informational matrix of connectivity.
\end_layout
\begin_layout Standard
Oh, and I almost forgot: my waking project is to hah hah.
don't laugh, to create a linked–list polynomial–manipulating computer algebra
system.
Metaphorically speaking of course: I work with jigsaw pieces, now, not
linked lists.
But its not so different: to each jigsaw, I assign only a small dollop
of data, in the same way that the coefficient of a polynomial is a small
dollop.
So my dream crossed paths with my reality, and isn't that interesting?
Life is a wonder.
I sit here, almost overwhelemed in awe of the spectacle before me.
I watch, and shit just happens.
And I touch, and shit happens in response.
Life is truly a miracle.
This is perhaps the worlds best–kept secret.
its shouted out from mountain–tops: life is a miracle! Who hears those
words? Everyone.
No one.
Almost everyone who hears those words don't know what they mean.
And maybe if they pause and reflect, the reaction is
\begin_inset Quotes eld
\end_inset
yeah, sure, so what
\begin_inset Quotes erd
\end_inset
and thence on to the next thing.
\end_layout
\begin_layout Standard
Which is what I have to do now.
Go on to the next thing.
There's a different, related brainstorm.
Or maybe this same brainstorm.
But that brainstorm, I can convert to actual formluas and algorithms, so
let me work on that.
Later, dude.
\end_layout
\begin_layout Subsection*
18 April 2025
\end_layout
\begin_layout Standard
Fleeky tells me to write to Joscha at CIMC.
Here's draft email version one, but I don't like it.
I will erase this and try again:
\end_layout
\begin_layout Standard
\emph on
Hi Joscha,
\end_layout
\begin_layout Standard
\emph on
A friend has told me that I should contact you with regards to CIMC.
So that is what this is.
\end_layout
\begin_layout Standard
\emph on
I don't think you're aware of any of the work I've done w.r.t machine consciousnes
s.
This is entirely my fault.
I've utterly failed to self-promote, and given the nature of collective
intelligence, this implies that I have little influence on modern thinking
about machine consciousness.
So it goes.
\end_layout
\begin_layout Standard
\emph on
I think I can provide useful viewpoints and commentary on your work, on
the work of CIMC.
Perhaps you don't agree.
I, uhh, am entirely capable of reading body language and social signals,
and so I understand.
Still, I feel it appropriate to wave "hi" in your direction, and remind
you that, well, we're all in this together.
\end_layout
\begin_layout Standard
...
foo.
This feels weak and limp.
He'll ignore it.
I want him to not ignore it.
Why? Because I'm proud, I want to be recognized.
I have an ego that needs to be nurtured.
At the same time, I'm gruff and say things that piss people off: I'm an
asshole.
And finally, my contributions to science are indeed quite small.
So what's really going on? A mad scramble to protect my own personal future,
which in the short term includes health and financial goals.
And one way of protecting the latter is to be aligned with the interests
of the powerful, the thought leaders in the field.
So it is vital to maintain good connections.
This is my rationalization of what it is that I am doing here.
There is also an undertow of assorted emotional turmoil, tangled up with
pride and ego: feelings resonate.
I want to be acknowledged, admired, looked upon with respect.
All those things that most normies want.
This is not extinguishable, nor should it be extinguished.
I can point at David Chapman and his buddhist practices to provide second–level
support for this claim.
\end_layout
\begin_layout Standard
Am I wasting time here, writing in this diary, when I should be doing something
more important? Perhaps.
Like, for example, composing a better email to Joscha.
Let's goooo.
\end_layout
\begin_layout Standard
Here's what I sent:
\end_layout
\begin_layout Standard
\emph on
To: Joscha Bach joscha@cimc.ai
\end_layout
\begin_layout Standard
\emph on
Cc: Erik Newton erik@cimc.ai
\end_layout
\begin_layout Standard
\emph on
Hi Joscha, (also Hi Erik!)
\end_layout
\begin_layout Standard
\emph on
A friend has told me that I should contact you with regards to CIMC.
\end_layout
\begin_layout Standard
\emph on
You are not aware of any of the work I've done w.r.t.
machine consciousness.
This is entirely my fault.
\end_layout
\begin_layout Standard
\emph on
You're smart.
I'll be direct.
You can figure this out.
In short: I can help with your work at CIMC.
I would enjoy helping.
Based on our prior social encounters, it seems clear enough that you perceive
marginal utility in my participation.
This email is intended to improve perceptions, to raise awareness, and
to ask to be included in the proceedings.
\end_layout
\begin_layout Standard
\emph on
Thank you for your consideration.
-- Linas.
Below follows some normie boilerplate about who I am, what I do, and why
I do it.
It is provided because often, normie boilerplate is an effective form of
communication.
I imagine your eyes will glaze over.
So it goes.
\end_layout
\begin_layout Standard
\emph on
p.s.
Hi Erik, we have not met.
The above was written addressing Joscha personally, as I've spent some
fair amount of time conversing with him, and we have a personal relationship
of sorts.
I've decided it is wise to include you as well.
\end_layout
\begin_layout Standard
\emph on
Resume: I'm widely read in almost all aspects of human intellectual endeavour.
From the largest to the smallest: I understand how complex systems link
together and form.
I am conducting active research into sensori–motor systems, roughly aligned
with the kinds of things Micheal Levin talks about, except I work with
machines and math foundations and complex collective behavior.
Aggregation, renormalization, phase transitions, critical self–organizing.
I day–dream about the nature of love, the driver of pride (I write this
email because I am proud), the mammalian and biological origins of the
full spectrum of these.
Upwards into the assortment of questions that buddhists and consciousness
studies people write about.
Downwards into those cute animal youtube videos that exhibit such "humanistic"
features.
I do not have any results in this area, but they burble in the background
of my theorizing.
I believe all intelligence is collective intelligence (there is a nice
recent review article with exactly this title.)
\end_layout
\begin_layout Standard
\emph on
I have a PhD in theoretical particle physics; I understand gravitation,
quantum field theory, strings, black holes, cosmology, etc.
and am widely read in mathematics.
I've contributed paragraphs or more: entire articles to Wikipedia on arcane
math topics.
I am currently nursing along a theory about "here and now": why we cannot
change the past, and why the future appears to be indeterminate.
From what I can tell, this is intimately interconnected to the question
of intelligence and consciousness.
It is an extremely challenging topic.
I'm actually rather shocked that it appears to be entirely ignored.
\end_layout
\begin_layout Standard
\emph on
For your entertainment: I've been working on a self–portrait diary.
This is a large wall of text; stuff that I think about.
I do not expect humans to read it; there's too much, and it's too meandering.
But I imagine that soon there will be machinery that can convert this text
into a simulacrum of me, and so, if you have any curiosity about who I
am, what I think, or my opinions on this or that, and I'm not around to
reply personally, you'll be able to ask that portrait.
I can also explain all the ways in which this may not work.
\end_layout
\begin_layout Standard
\emph on
That's all.
Again, I'd like to maintain relations with CIMC, or even to participate
in CIMC activities.
But this is up to you.
I'm here, I am waving "hello" in your direction.
\end_layout
\begin_layout Standard
\emph on
-- Linas
\end_layout
\begin_layout Standard
So it goes, so it goes.
\end_layout
\begin_layout Standard
The thing I struggled with the most in writing the above is how not to be
disassociative, distant, foreign, unempathetic.
Recently, I've been looking at myself in a rather clinical fashion, as
this diary attests in volumes.
But this also pushes me into clinical analysis of other contacts.
This requires me to consciously think about adding warmth to conversations.
I can be warm, but then everything gets shallow, meaningless, personally
unfulfilling to me.
It becomes trite and stupid.
I mean, I enjoy petting cats and dogs.
I do not enjoy figuratively petting humans.
I don't want to interact with humans as if they are stupid, but well, most
of them are, and its not fun.
And so when I want to reach into higher abstractive layers, and talk about
complex topics using telegraphic language, it starts to feel very disassociated.
It's like I am here, in my mind, thinking these things, but I have to select
language to communicate there, to these other human beings who are kind
of very far away and detached from the presence that I am in.
This is almost a clinical definition of disassociation (I have not looked
at the clinical definition in many years, so maybe I mis-recall.) And I
am quite aware that everyone: every living thing is stuck in the same situation.
Most living things are not aware of this, and warmth and connection flow
freely and easily.
Well.
For some.
Others wage war, and exhibit
\begin_inset Quotes eld
\end_inset
dark triad
\begin_inset Quotes erd
\end_inset
personality traits.
There's that too.
\end_layout
\begin_layout Standard
Whatever.
its all quite weird.
It's getting late, and if I don't go hop on my bicycle now, it will get
dark before I'm done.
Later.
\end_layout
\begin_layout Subsection*
20 April 2025
\end_layout
\begin_layout Standard
Dream sequences, continued.
While falling asleep, I thought about wave function collapse, again.
I'll keep it short.
A reasonable model seems to an array of single–pixel antennas, each sufficientl
y sensitive to detect a single photon with some reasonable efficiency.
This array is illuminated with a weak source, having some spatial pattern
(two–slit, whatever, doesn't matter.) We know from basic QM that only a
single pixel can ever trigger: the wide–field illumination
\begin_inset Quotes eld
\end_inset
collapses
\begin_inset Quotes erd
\end_inset
down to a single pixel.
The hypothesis is that in order for this to happen, the photon must be
conceived of as a topological soliton of some kind, so as to obtain the
desired behavior of wave–function collapse.
That is, when the pixel array is illuminated, the brightness is such that
one unit of
\begin_inset Formula $E=h\nu$
\end_inset
impinges on it per observation time.
We want to be able to provide a mathematical model for this, that prevents
the observation of 2,3,...
photons of energy
\begin_inset Formula $h\nu/2$
\end_inset
or
\begin_inset Formula $h\nu/3$
\end_inset
...
\end_layout
\begin_layout Standard
How can this interaction be turned into a plausible mathematical setting?
I'm thinking that modeling each pixel as a dipole antenna is the place
to start, and to treat the photon as a standard crossed electric–magnetic
wave maybe I guess with linear polarization.
It's unclear if polarization matters.
The goal is to look at this mathematical structure, and look for something
that has the characteristics topological soliton in it.
Seems like a good idea, right?
\end_layout
\begin_layout Standard
So, now that I am awake (well, even as I was sleeping) there seems to be
a bit of an issue: what is the sensitivity of each dipole? More correctly,
what is the frequency response for each dipole? If the frequency response
goes below
\begin_inset Formula $\nu/2$
\end_inset
then I see no reason why a single
\begin_inset Formula $E=h\nu$
\end_inset
photon might not trigger two antennas.
Shit like this happens all the time: high–energy events make lots and lots
of detectors light up, with a large variety of physical mechanisms for
doing so.
So the ability to detect single photons also seems to require that each
antenna be insensitive to frequencies much below the photon frequency.
This provides the topological constraint.
There has to be a threshold: an energy threshold, a mass–gap.
This is exactly what the photo–electric effect demonstrates.
The band–gap in the metal provides the barrier that prevents more than
one electron being ejected by a single photon.
\end_layout
\begin_layout Standard
What is the mathematical articulation of this? Treat this as a problem in
homotopy.
At one end, we have an E&M field describing radiation in free space.
What is the homotopic map that takes this field, and maps it to a single
pixel detector? Presumably, this map is not just homotopic, but diffeo,
as well.
Treating each pixel as a dipole antenna seems reasonable.
It gives something to work with.
The dipole then converts the EM field to an oscillation on a pair of wires:
it removes confusion about polarization, it eliminates the wave equation,
and no long requires thinking about the EM field: instead, just an oscillating
scalar potential on a pair of wires.
At the end of the wires, one can place a conventional hi–pass filter.
This eliminates the need to think about other quantum effects.
That is, in
\begin_inset Quotes eld
\end_inset
real life
\begin_inset Quotes erd
\end_inset
, a single–pixel detector has to be either (a) some kind of semi–conductor
with some band–gap, or (b) some kind of silver–halide on some photographic
film, i.e.
a many–body system in some thermal bath, or (c) some photomultiplier tube,
again a many–body system with some band–gap in the metal, or (d) some rhodopsin
or chlorophyll molecule, potentially getting into superposition with the
photon.
All of these are distractors and complexifiers of the problem.
All of them introduce new conceptual elements that are hard to control
for.
By contrast, the mathematical description of a transmission line attached
to a high–pass filter is unambiguous.
Engineering texts have the formula for this.
\end_layout
\begin_layout Standard
In this mathematical model, we can then dispense the EM field entirely,
get rid of the dipole antennas, get rid of the transmission line from the
dipoles to the filter.
The mathematical model is then a pixel array of high–pass filters, illuminated
by a scalar potential field on the input to the filter.
To further simplify, I suppose we can even ground one side of the filter,
attach it to a common, so that we really do have a single–wire input.
So that's the model.
\end_layout
\begin_layout Standard
Now, this array of filters is illuminated by a scale field carrying energy
\begin_inset Formula $E=h\nu$
\end_inset
and the filter frequency cutoff is above
\begin_inset Formula $\nu/2$
\end_inset
(of course).
In conventional passive electronics, nothing depends on intensity or power
(i.e.
has a linear dependence).
Only amplifiers, tube circuits, transistor circuits, diodes have a non–linear
response.
So I guess our filter has to be attached to some non–linear element, so
that it triggers only when there is enough energy dumped into that element?
Again, to keep things simple, I guess we want to just make up some very
simple non–linear element that outputs a zero or a one, generating zero,
of below an energy threshold, else generating a one above that threshold.
So, a sigmoid function of some kind.
\end_layout
\begin_layout Standard
So, now the mathematical model is that of a pixel array of sigmoids, which
trigger only if they absorb an amount of energy to push them above a threshold.
To recap: this array is illuminated by a very weak illumination, say, thousands
or millions of times weaker than the detection threshold.
From this wen want to obtain a mathematical description such that energy
is conserved.
Lets take these last few sentences and write some algebra for them.
\end_layout
\begin_layout Standard
So: Let there
\begin_inset Formula $N$
\end_inset
pixels.
Each pixel is labelled as
\begin_inset Formula $d_{i}$
\end_inset
standing for
\begin_inset Quotes eld
\end_inset
detector at location
\begin_inset Formula $i$
\end_inset
\begin_inset Quotes erd
\end_inset
.
Each detector accepts as input a single real number, the instantaneous
power
\begin_inset Formula $p$
\end_inset
.
This power is a function of time,
\begin_inset Formula $p=p\left(t\right)$
\end_inset
and is seems unavoidable to assume that each detector integrates over time,
so that the energy absorbed over a time interval
\begin_inset Formula $\Delta t$
\end_inset
is given by
\begin_inset Formula $E\left(\Delta t\right)=\int_{0}^{\Delta t}p\left(t\right)dt$
\end_inset
.
The power is position–dependent, so we may as well write
\begin_inset Formula $p_{i}=p_{i}\left(t\right)$
\end_inset
and
\begin_inset Formula $E_{i}=E_{i}\left(\Delta t\right)$
\end_inset
.
The detector response function is then
\begin_inset Formula
\[
d_{i}\left(E_{i}\right)=\begin{cases}
1 & \mbox{if }E_{i}\ge h\nu\\
0 & \mbox{if }E_{i}<h\nu
\end{cases}
\]
\end_inset
The detector then
\begin_inset Quotes eld
\end_inset
fires
\begin_inset Quotes erd
\end_inset
, and resets back to the zero state.
(This concept of firing can be firmed up, but I'm lazy for now; you get
the idea, I think.)
\end_layout
\begin_layout Standard
This detector array is then illuminated with some non–uniform wave, carrying
a total power of
\begin_inset Formula
\[
p_{tot}=\sum_{i=1}^{N}p_{i}
\]
\end_inset
Assume that
\begin_inset Formula $p_{tot}$
\end_inset
does NOT vary with time: it is a constant.
That is, perhaps there is a time variation in the individual power
\begin_inset Formula $p_{i}=p_{i}\left(t\right)$
\end_inset
at a given detector
\begin_inset Formula $i$
\end_inset
but this variation cancels out across all detectors.
(Stupid fun and games: set
\begin_inset Formula $p_{tot}=1$
\end_inset
.
This reminds you of what?) Anyway, the total power over a time interval
\begin_inset Formula $\Delta t$
\end_inset
, the total illumination is
\begin_inset Formula
\[
E_{tot}=p_{tot}\Delta t
\]
\end_inset
which increases linearly over time.
\end_layout
\begin_layout Standard
So, the above lays out the notation.
The mathematical model that we wish to discover is one where exactly one
detector
\begin_inset Formula $d_{i}$
\end_inset
fires whenever
\begin_inset Formula $h\nu\le E_{tot}<2h\nu$
\end_inset
.
Perhaps we want to loosen the time constraint, and allow for the case where
\begin_inset Formula $k$
\end_inset
detectors have fired when
\begin_inset Formula $kh\nu\le E_{tot}<kh\nu+\varepsilon$
\end_inset
for some
\begin_inset Quotes eld
\end_inset
small
\begin_inset Quotes erd
\end_inset
\begin_inset Formula $\varepsilon$
\end_inset
.
If, in addition, the detectors have an efficiency less than 100%, we want
to derate proportionately.
This is meant to be statistical, so perhaps the detector rate of firing
needs to be a Poisson process, so that only the average is maintained,
while uncertainty over small time periods is allowed.
\end_layout
\begin_layout Standard
And this word
\begin_inset Quotes eld
\end_inset
statistical
\begin_inset Quotes erd
\end_inset
creates huge issues.
The problem is that, once we use the word
\begin_inset Quotes eld
\end_inset
statistical
\begin_inset Quotes erd
\end_inset
, we enter the conventional regime where anything goes, as long as averages
are conserved.
There are an infinite number of purely deterministic power distributions
\begin_inset Formula $p_{i}\left(t\right)$
\end_inset
that give the desired result of
\begin_inset Quotes eld
\end_inset
one wave–function collapse per
\begin_inset Formula $\Delta t$
\end_inset
\begin_inset Quotes erd
\end_inset
.
This entirely abandons the original idea of associating a photon with some
topological index (that ties together the field with the array of detectors.)
\end_layout
\begin_layout Standard
I see two possible directions for cures.
One is to reformulate the above to incorporate a Bell measurement.
\end_layout
\begin_layout Standard
Another possible cure is to eliminate local time.
For this case, set
\begin_inset Formula $p_{i}\left(t\right)=const.$
\end_inset
so that the conventional idea of constant illumination is retained.
This is problematic, though: the illuminating source is presumably dribbling
out photons one at a time, so that in fact it is
\begin_inset Quotes eld
\end_inset
dark
\begin_inset Quotes erd
\end_inset
most of the time, and then the source generates a photon, which does it's
welcher–weg thing, and then some detector pops off.
Another wild idea is to dismiss the notion of linearly–advancing gallilean
local time, and leave the progress of time ambiguous at each detector.
This is a reuptake of the here–and–now framework, where we don't really
know about how the detectors
\begin_inset Formula $d_{i}$
\end_inset
fired, until much later, when we accumulate the classical bits issued by
each detector back to a single location, where we can verify that, indeed,
only one detector fired per acceptable interval
\begin_inset Formula $\Delta t$
\end_inset
.
What a fucking mess.
\end_layout
\begin_layout Standard
One practical problem is that there is a zoo of topological invariants.
I don't really know this zoo very well.
Of course, there is the usual sphere mapping.
Then the assortment of examples from textbooks on algebraic topology.
None of the examples that I recall seeing are pixelated.
\end_layout
\begin_layout Standard
The word
\begin_inset Quotes eld
\end_inset
firing
\begin_inset Quotes erd
\end_inset
is suggestive, both from lightning strikes, insulator breakdown, and from
neural nets.
The model here is that charge accumulates until the insulator beaks down,
the charge discharges, and then the process begins anew.
Perhaps this could be converted into a plausible model of wave function
collapse, except that such a model is stochastic.
It needs to be reformulated in a Bell–measurement setting.
\end_layout
\begin_layout Standard
So round and round we go, in circles.
I picked pixels, because it seemed like this would provide some sort of
simplification.
But now it doesn't, and I have to do Bell? Why is that?
\end_layout
\begin_layout Standard
Well, hmm.
I'm confused.
If I redo the work above, and add appropriate spin–up and spin–down indexes
on each of the formulas, and then demand that Bell holds, all that happens
is a description where
\begin_inset Formula $p_{i}=\left|\psi_{i}\right|^{2}$
\end_inset
and the complex field
\begin_inset Formula $\psi_{i}$
\end_inset
is attached to philosophical arguments that it is
\begin_inset Quotes eld
\end_inset
physical
\begin_inset Quotes erd
\end_inset
.
This recapitulates age–old arguments and does not provide new understanding.
\end_layout
\begin_layout Standard
I should mention, at this point, that an earlier stage of the dream was
a
\begin_inset Quotes eld
\end_inset
revelation
\begin_inset Quotes erd
\end_inset
that classical physical reality takes place not in three dimensions, but
in a very high–dimensional space, say for example, a space of
\begin_inset Formula $2^{256}\approx10^{80}$
\end_inset
dimensions and that the proceedings there are conventional geometry, and
that the apparent 3D physical reality with its assorted QM/QFT features
that we live in is the result of a projection–correspondence of topological
phenomena from that high–dimensional space down to here and now.
\end_layout
\begin_layout Standard
Of course, no naive projection from high to low dimensions pops up, except
for a pixelized version.
And so this suggests a search of high–dimensional geometric phenomena that
resemble quantum–like behavior in lower dimensions.
And, I suppose 3D would be some critical dimension, but clearly we are
not ready for that.
\end_layout
\begin_layout Standard
I think I've hit the end of the road for the above chain of thought.
There's nowhere to go, or perhaps, too many directions to go in.
Everything shimmers on the horizon, but these shimmers, they are unlikely
to be real.
Like the traveler on the desert chasing the mirage, I risk dying of thirst
before I ever reach water.
\end_layout
\begin_layout Standard
The other curious thing about the above dozen or two paragraphs is how much
my thinking is constrained by the history of everything I've ever studied
before.
All that my mind is doing is wandering over bits and pieces of things I
know, and trying to reassemble them in novel combinations.
Is it a lattice model, like an Ising Model? Check.
Maybe wave–function collapse resembles domain formation in 2D Ising models
or something like that.
Who the fuck knows, its possible.
What does it take to break out of the meager collection of tools and techniques
I am familiar with? A bit of luck, a bit of effort.
Err, a lot of luck and a lot of effort.
I'm mired in the mud.
The intellect thrashes about.
\end_layout
\begin_layout Standard
Whatever.
I have several other projects to attend to.
Perhaps better luck with those.
Later, dude.
\end_layout
\begin_layout Subsection*
24 April 2025
\end_layout
\begin_layout Standard
Reading this article:
\begin_inset Quotes eld
\end_inset
Complex harmonics reveal low–dimensional manifolds of critical brain dynamics.
\begin_inset Quotes erd
\end_inset
Gustavo Deco, Yonatan Sanz Perl, and Morten L.
Kringelbach https://journals.aps.org/pre/abstract/10.1103/PhysRevE.111.014410
It talks a lot about long–range neurons and how these modulate avalanching
behavior near the critical point, although that talk is mostly hand–waving.
i.e.
I don't get it.
Sexy buzzwords, but I don't understand.
Maybe if I read about the Hopf Model, I would.
\end_layout
\begin_layout Standard
Anyway, this sentence jumps out at me:
\begin_inset Quotes eld
\end_inset
T
\emph on
his suggests that the long–range interactions are less relevant in deep
sleep, which is thus likely to exhibit less critical dynamics than wakefulness
\emph default
\begin_inset Quotes erd
\end_inset
.
So, if I might make wild associations: perhaps what I call
\begin_inset Quotes eld
\end_inset
decisions
\begin_inset Quotes erd
\end_inset
or
\begin_inset Quotes eld
\end_inset
resolution of choices
\begin_inset Quotes erd
\end_inset
are associated with avalanches.
That is, the system is teetering on the edge, in some metastable state,
and it can go in many different ways.
The final decision made is associated with an avalanche.
The avalanche is the mechanism for amplifying a small perturbation and
\begin_inset Quotes eld
\end_inset
making it so
\begin_inset Quotes erd
\end_inset
.
Perhaps a way of broadcasting to the entire brain that
\begin_inset Quotes eld
\end_inset
this is what we are doing now, get with the program
\begin_inset Quotes erd
\end_inset
?
\end_layout
\begin_layout Standard
Here's my more formal writeup:
\end_layout
\begin_layout Standard
Abstract: A framework called CHARM ("Complex Harmonics Decompostion"), applied
to 1000 fMRI scans.
Describes role of long–distance neural connections in modulating critical
avalanches.
\end_layout
\begin_layout Standard
The meta–setting of the paper, as best as I can understand it:
\end_layout
\begin_layout Itemize
A characteristic of self–organized systems near criticality is that they
exhibit avalanches (in the sense of sand–piles).
\end_layout
\begin_layout Itemize
The human brain (brains in general) operate as self–organized systems near
criticality.
I think this is called "the Hopf Model" (not sure).
\end_layout
\begin_layout Itemize
Thinking (and fast decision making) is best understood as sequences of avalanche
s.
\end_layout
\begin_layout Itemize
Long–range neurons modulate the avalanches.
\end_layout
\begin_layout Itemize
This modulation happens only during waking hours, and not during sleep.
\end_layout
\begin_layout Itemize
The CHARM technique is a new and better tool for exposing all this.
\end_layout
\begin_layout Standard
My personal inspiration, having little to do with the paper itself:
\end_layout
\begin_layout Itemize
When I introspect, and think about things, I often feel like I have a menu
of choices in front of me: what to say next, what to do next, what to write
next.
\end_layout
\begin_layout Itemize
The hardest part of writing/talking is to pick through that menu–choice.
This is a characteristic symptom of ADHD, autism.
(I am not ADHD/autistic.
I can empathize with the "overwhelming flood of stimulous" that is another
common description of ADHD/autism.
And likewise the concept of "stimming".)
\end_layout
\begin_layout Itemize
I assume that the avalanches seen in the fMRI data are associated with these
rapid, short-time-scale choices.
That is, a few times a second, I decide "do this and do not do that", and
that this decision is associated with an avalanche.
\end_layout
\begin_layout Itemize
The role of the long–range neurons is to consolidate this decision over
the whole brain.
Basically, to announce far and wide "this is what we're doing now, get
with the program".
\end_layout
\begin_layout Itemize
Avalanches amplify tiny, microscopic imbalances into large changes.
\end_layout
\begin_layout Itemize
This is part of the mechanism in which "free will" expresses itself.
\end_layout
\begin_layout Standard
I'm now reading
\begin_inset Quotes eld
\end_inset
The Hopf whole–brain model and its linear approximation
\begin_inset Quotes erd
\end_inset
Adrián Ponce-Alvarez Gustavo Deco, https://pmc.ncbi.nlm.nih.gov/articles/PMC1083108
3/
\end_layout
\begin_layout Standard
Distracted.
Reading https://en.wikipedia.org/wiki/Hopf_bifurcation but its fucked up.
The section labelled
\begin_inset Quotes eld
\end_inset
intuition
\begin_inset Quotes erd
\end_inset
is not intuitive.
Can we fix it?
\begin_inset Formula
\[
\frac{dz}{dt}=z\left(\left(\lambda+i\right)+b|z|^{2}\right)
\]
\end_inset
Let
\begin_inset Formula $z=re^{i\theta}$
\end_inset
so
\begin_inset Formula $\dot{z}=\dot{r}e^{i\theta}+i\dot{\theta}re^{i\theta}$
\end_inset
and
\begin_inset Formula $b=\alpha+i\beta$
\end_inset
so
\begin_inset Formula
\begin{align*}
\dot{r}e^{i\theta}+i\dot{\theta}re^{i\theta} & =re^{i\theta}\left(\lambda+i\right)+\left(\alpha+i\beta\right)r^{3}e^{i\theta}\\
\dot{r}+i\dot{\theta}r & =r\left(\lambda+i\right)+\left(\alpha+i\beta\right)r^{3}\\
\frac{\dot{r}}{r}+i\dot{\theta} & =\lambda+i+\left(\alpha+i\beta\right)r^{2}\\
\dot{r} & =r\left(\lambda+i-i\dot{\theta}+\left(\alpha+i\beta\right)r^{2}\right)
\end{align*}
\end_inset
Since
\begin_inset Formula $r$
\end_inset
is real, we must have that the imaginary part of the last eqn vanishes,
so that
\begin_inset Formula
\[
\dot{\theta}=1+\beta r^{2}
\]
\end_inset
and the real parts give
\begin_inset Formula
\[
\dot{r}=r\left(\lambda+\alpha r^{2}\right)
\]
\end_inset
Rescale time so that
\begin_inset Formula $\alpha t=\tau$
\end_inset
so that
\begin_inset Formula
\[
\dot{r}=\frac{dr}{dt}=\alpha\frac{dr}{d\tau}
\]
\end_inset
Define
\begin_inset Formula $\omega=1/\alpha$
\end_inset
and
\begin_inset Formula $\mu=\lambda\omega$
\end_inset
and plug through to get
\begin_inset Formula
\[
\frac{dr}{d\tau}=r\left(\mu+r^{2}\right)
\]
\end_inset
and
\begin_inset Formula
\[
\frac{d\theta}{d\tau}=\omega\left(1+\beta r^{2}\right)
\]
\end_inset
and the wikipedia form is recovered by setting
\begin_inset Formula $\beta=0$
\end_inset
.
I'm not sure why anyone thinks this is
\begin_inset Quotes eld
\end_inset
intuitive
\begin_inset Quotes erd
\end_inset
.
\end_layout
\begin_layout Standard
Gahh.
Look at https://en.wikipedia.org/wiki/Stuart%E2%80%93Landau_equation and
from what I can tell, it is identical to the Hopf bifurcation, up to rescaling.
More, it gives an explicit solution.
Lets check it out:
\begin_inset Formula
\begin{align*}
\dot{r} & =r\left(\lambda+\alpha r^{2}\right)\\
\frac{\dot{r}}{r^{3}} & =\frac{\lambda}{r^{2}}+\alpha\\
& =\frac{d}{dt}\left(\frac{-1}{2r^{2}}\right)
\end{align*}
\end_inset
which is linear in
\begin_inset Formula $\zeta=r^{-2}$
\end_inset
so
\begin_inset Formula
\begin{align*}
\dot{\zeta} & =-2\left(\lambda\zeta+\alpha\right)\\
& =-2\lambda\left(\zeta+\frac{\alpha}{\lambda}\right)
\end{align*}
\end_inset
Absorbing the const:
\begin_inset Formula $\eta=\zeta+\alpha/\lambda$
\end_inset
gives
\begin_inset Formula $\dot{\eta}=-2\lambda\eta$
\end_inset
which is solved by
\begin_inset Formula $\eta=Ce^{-2\lambda t}$
\end_inset
.
Plugging through,
\begin_inset Formula
\begin{align*}
\frac{1}{r^{2}} & =Ce^{-2\lambda t}-\frac{\alpha}{\lambda}\\
r\left(t\right) & =\sqrt{\frac{1}{Ce^{-2\lambda t}-\alpha/\lambda}}\\
r_{0}=r\left(0\right) & =\sqrt{\frac{1}{C-\alpha/\lambda}}\\
C= & \frac{1}{r_{0}^{2}}+\frac{\alpha}{\lambda}
\end{align*}
\end_inset
So (yuck!?)
\begin_inset Formula
\[
r\left(t\right)=r_{0}\sqrt{\frac{\lambda}{\left(\lambda+\alpha r_{0}^{2}\right)e^{-2\lambda t}-\alpha r_{0}^{2}}}
\]
\end_inset
\end_layout
\begin_layout Standard
Next, we want the Jacobian matrix.
It can be read off directly from the two eqns
\begin_inset Formula $\dot{\theta}=1+\beta r^{2}$
\end_inset
and
\begin_inset Formula $\dot{r}=r\left(\lambda+\alpha r^{2}\right)$
\end_inset
.
The Jacobian matrix is
\begin_inset Formula
\[
J=\left[\begin{array}{cc}
\frac{\partial\dot{r}}{\partial r} & \frac{\partial\dot{r}}{\partial\theta}\\
\frac{\partial\dot{\theta}}{\partial r} & \frac{\partial\dot{\theta}}{\partial\theta}
\end{array}\right]=\left[\begin{array}{cc}
\lambda+3\alpha r^{2} & 0\\
2\beta r & 0
\end{array}\right]
\]
\end_inset
The characteristic polynomial in
\begin_inset Formula $w$
\end_inset
is
\begin_inset Formula
\[
P\left(w\right)=\det\left[J-wI\right]=-w\left(\lambda+3\alpha r^{2}-w\right)
\]
\end_inset
There are two eigenvalues:
\begin_inset Formula $w=0$
\end_inset
and
\begin_inset Formula $w=\lambda+3\alpha r^{2}$
\end_inset
.
Yuck.
This is not the intent.
We wanted a pair of pure imaginary eigenvalues and we blew it.
\end_layout
\begin_layout Standard
Does this work in cartesian coords? Let try.
Set
\begin_inset Formula $z=x+iy$
\end_inset
and start with
\begin_inset Formula
\begin{align*}
\frac{dz}{dt} & =z\left(\left(\lambda+i\right)+b|z|^{2}\right)\\
& =\left(x+iy\right)\left(\lambda+i\right)+b\left(x+iy\right)\left(x^{2}+y^{2}\right)
\end{align*}
\end_inset
The split into real+imag parts is
\begin_inset Formula
\begin{align*}
\dot{x} & =\lambda x-y+\left(\alpha x-\beta y\right)\left(x^{2}+y^{2}\right)\\
\dot{y} & =x+\lambda y+\left(\beta x+\alpha y\right)\left(x^{2}+y^{2}\right)
\end{align*}
\end_inset
The Jacobian is
\begin_inset Formula
\[
J=\left[\begin{array}{cc}
\frac{\partial\dot{x}}{\partial x} & \frac{\partial\dot{x}}{\partial y}\\
\frac{\partial\dot{y}}{\partial x} & \frac{\partial\dot{y}}{\partial y}
\end{array}\right]=\left[\begin{array}{cc}
\lambda+3\alpha x^{2}-2\beta xy+\alpha y^{2}\quad & -1-3\beta y^{2}+2\alpha xy-\beta x^{2}\\
1+3\beta x^{2}+2\alpha xy+\beta y^{2}\quad & \lambda+3\alpha y^{2}+2\beta xy+\alpha x^{2}
\end{array}\right]
\]
\end_inset
Quite the mess.
Linearize by setting
\begin_inset Formula $x=y=0$
\end_inset
to get
\begin_inset Formula
\[
J=\left[\begin{array}{cc}
\lambda & -1\\
1 & \lambda
\end{array}\right]
\]
\end_inset
Then
\begin_inset Formula
\[
P\left(w\right)=\det\left[J-wI\right]=\left(\lambda-w\right)^{2}+1
\]
\end_inset
which has solution
\begin_inset Formula $P\left(w\right)=0$
\end_inset
given by
\begin_inset Formula
\[
w=\lambda\pm i
\]
\end_inset
\end_layout
\begin_layout Standard
I copied all of this to the Wikipedia article.
\end_layout
\begin_layout Subsection*
29 April 2025
\end_layout
\begin_layout Standard
Time for a progress report.
As always, perhaps the act of writing will reveal something.
As always, this will be a semi–incoherent ramble.
\end_layout
\begin_layout Standard
So a few days ago, fleeky reminds me of the gamedev
\begin_inset Quotes eld
\end_inset
quantum collapse algorithm
\begin_inset Quotes erd
\end_inset
...
its not really
\begin_inset Quotes eld
\end_inset
quantum collapse
\begin_inset Quotes erd
\end_inset
but the name is suggestive.
It's basically an aggregation algorithm, where given some seed, additional
pieces/tiles aggregate onto it.
Or with multiple seeds, they attach and grow out from the seed.
I'd forgotten this algo, but its very much in line with how I'm trying
to visualize here–and–now.
So I start thinking about it as I lay in bed, falling asleep.
And here's the chain of thoughts:
\end_layout
\begin_layout Standard
The QCA is exactly right, because the jigsaws that are connected form the
past, and it is unalterable, because they are now connected.
The present, here–and–now, is where they are jockeying for position.
The future remains unassembled.
So this strongly feels like exactly the right model.
\end_layout
\begin_layout Standard
I imagine jigsaw pieces tiling in a hyperbolic way, so that the future is
larger than the past.
Why? Because somehow, the noosphere is expanding, and getting larger.
There is more and more stuff, more an more complexity is arising.
So, again, the jigsaw model confirms this intuitive understanding.
\end_layout
\begin_layout Standard
But somehow, the interferometer diamonds need to manifest, so as to get
consistent histories.
Bell's theorem must manifest during the construction process.
How might that work? So I try to think microscopically.
Consider a two–slit setup.
A photon has to travel through both slits.
Perhaps this can be done by the indeterminacy of the attached jigsaws?
Welcher–weg is avoided because somehow the attachments of the jigsaws is
still indeterminate.
\end_layout
\begin_layout Standard
But somehow, photons have to be blocked by the parts that are not slits.
How does that work? Well, the photon hits a bunch of atoms.
What's that? well, suppose a photon hits a single atom.
What's that? Suppose it hits a hydrogen atom; but what is that? Well, its
the Schrodinger eqn, but its a cloud exchanging virtual photons with a
point–like positive charge (I'm sleeping here, so this is a dream–like
hallucination.) What are those virtual photons? They emanate from the point
positive charge, and spread out.
\end_layout
\begin_layout Standard
Then I think: perhaps there is no ambient space, and the 3D structure of
space arises only as the pieces attach.
But how to account for the inverse–square law? Somehow, there is a distance
that the virtual photon travels.
And inverse–square implies 3D, so here–and–now is perhaps partially–indetermina
te in dimension, but it has to collapse to 3D somehow.
How? Well, there are 0-simplexes and 1-simplesex and 2-simplexes, and a
space is 3D it the jigsaw connectors can form 2-simplexes and so the jigsaw
has to have three connectors pointing towards the past, and I guess three
connectors pointing towards the future.
\end_layout
\begin_layout Standard
But this model if discrete jigsaws is all wrong; in the end, I want to revert
to conventional, smooth differentiable behavior, so the jigsaws have to
be infinitessimally tiny.
So I guess they are actually differentials, or behave like differentials.
So, I imagine the dot–product of two gradients, but one gradient points
in the backwards–time direction, and one points in the future–time direction.
And then its morning and I wake up, and here I am writing this, thinking
wtf am I going to do now?
\end_layout
\begin_layout Standard
I'm stumped.
I'm stupid.
I'm lazy.
This is hard.
It's unpromising.
But it seems plausible.
Developing this into a real theory seems nearly insurmountable.
Maybe its impossible.
Maybe its important.
Fuck me.
What should I do? Does it matter? Do something.
\end_layout
\begin_layout Standard
Some inspirational wikipedia articles:
\end_layout
\begin_layout Itemize
https://en.wikipedia.org/wiki/Calculus_of_moving_surfaces Reminds me of the
ADM formalism to solve Einestins eqns.
by propagating forward a space–like surface.
(Its a Hamiltonian formalism)
\end_layout
\begin_layout Itemize
https://en.wikipedia.org/wiki/Carleman_linearization converts non--linear
dynamical systems into infinite–dimensional linear ones.
\end_layout
\begin_layout Itemize
https://en.wikipedia.org/wiki/Carr%C3%A9_du_champ_operator – is a bilinear,
symmetric operator measures how far an infinitesimal generator is from
being a derivation.
\end_layout
\begin_layout Standard
These are three random articles starting with the letters
\begin_inset Quotes eld
\end_inset
Ca
\begin_inset Quotes erd
\end_inset
that seem somehow relevant to what I'm daydreaming about with the here–and–now.
But its all uphill, from here.
\end_layout
\begin_layout Subsection*
29 April 2025 Later on
\end_layout
\begin_layout Standard
I've got writer's block.
Except it's inventor's block.
I've got these ideas.
They've barricaded themselves in.
They refuse to come out.
I need those ideas to manifest.
\end_layout
\begin_layout Subsection*
30 April 2025
\end_layout
\begin_layout Standard
Reading
\begin_inset Quotes eld
\end_inset
An Interview with Dunja Šešelja, Samuli Reijula, and Matteo Michelin
\begin_inset Quotes erd
\end_inset
https://riviste.unimi.it/index.php/thereasoner/article/view/28587/24047 and
this sentence jumps out:
\emph on
\begin_inset Quotes eld
\end_inset
is a scientific community better off if its members favor pursuing theories
that have a larger explanatory scope than the rivals, or should scientists
instead remain committed to their current theories— even if their scope
is more limited—until they suffer from too many anomalies in comparison
to the rivals?
\emph default
\begin_inset Quotes erd
\end_inset
I found this remarkable since it has the inbuilt assumption that
\begin_inset Quotes eld
\end_inset
larger explanatory scope
\begin_inset Quotes erd
\end_inset
is always a win.
If the prototype is Einstein's General Relativity vs.
Newtonian Gravitation, then yes, the former has larger explanatory scope.
But psychologically, this pushes many to propose
\begin_inset Quotes eld
\end_inset
theories of everything
\begin_inset Quotes erd
\end_inset
, consisting of vague general principles that are overly broad, claiming
to justify everything, while proving almost nothing.
Odd.
\end_layout
\begin_layout Standard
A variant of this showed up a week ago in the Michael Bennett paper, making
a general claim that the
\begin_inset Quotes eld
\end_inset
weakest
\begin_inset Quotes erd
\end_inset
system that can explain something is the best system.
It tries to but fails to provide a coherent mathematical description of
\begin_inset Quotes eld
\end_inset
weak
\begin_inset Quotes erd
\end_inset
, but it seems to claim this:
\begin_inset Quotes eld
\end_inset
weak
\begin_inset Quotes erd
\end_inset
systems are those that fit the data well, and do not make strong or broad
claims outside of the domain of fitness.
\end_layout
\begin_layout Standard
In general, we tend to have a patchwork of domain–specific theories, that
are then patched together.
Perhaps sometimes, some structure can be perceived in that patchwork, resulting
in the creation of a theory with
\begin_inset Quotes eld
\end_inset
larger explanatory scope
\begin_inset Quotes erd
\end_inset
.
Hmm.
\end_layout
\begin_layout Standard
I'm also struck by a different problem: what if there are two or more theories
with
\begin_inset Quotes eld
\end_inset
larger explanatory scope
\begin_inset Quotes erd
\end_inset
, and suppose one stumbles over the crappier one first? Well, one then hits
a metastable state that can effectively block progress towards the larger,
more complex theory.
\end_layout
\begin_layout Subsection*
2 May 2025
\end_layout
\begin_layout Standard
Context: Yesterday, Asher Crispe asks me about free will, and I respond
with the standard lecture about bifurcation points and Sinai's tongues.
Later that night, I am reviewing Wikipedia, and notice that someone marked
\begin_inset Quotes eld
\end_inset
Ergodic Theory
\begin_inset Quotes erd
\end_inset
as top priority.
It links prominently to
\begin_inset Quotes eld
\end_inset
Ergodicity
\begin_inset Quotes erd
\end_inset
, of which I wrote the entire informal intro.
Which sits untouched.
I think I did a good job of it.
So I re–read it.
l re–read what I wrote years ago.
It's decent.
OK.
Shaggy in parts, but OK.
And I get to thinking that perhaps
\begin_inset Quotes eld
\end_inset
the past
\begin_inset Quotes erd
\end_inset
is a relic of
\begin_inset Quotes eld
\end_inset
here and now
\begin_inset Quotes erd
\end_inset
that becomes so strongly entangled, that it cannot be picked apart any
more.
This is distinct from my earlier idea that the past involves the closure
of all quantum interferometers.
Which may also be the case.
But on the surface, these are disconnected ideas.
And the mental note to myself is
\begin_inset Quotes eld
\end_inset
think about this some more
\begin_inset Quotes erd
\end_inset
:
\begin_inset Quotes eld
\end_inset
well, maybe the reason the past can't be changed is because it tipped over
an entanglement threshold.
\begin_inset Quotes erd
\end_inset
And the natural threshold there would be Planck's constant (?) in that
the phase–space volume of gas–in–a–box is 3 position + 3 velocity for one
atom, and its 6^Avogadro's number for ordinary–scale things, which is so
much crazy–larger than Planck's constant that the combinatoric possibilities
there have crossed the irreversibility threshold.
This is trite, but one moment.
\end_layout
\begin_layout Standard
So this morning, I am staring at https://en.wikipedia.org/wiki/Woodall%27s_conject
ure and the definition of dicuts, dijoins and strongly connected graphs,
and am reminded of last nights reading of the ergodic theorem, which says
all dynamical systems can be split into dissipative and conservative parts.
With the dissipative part being the one that wanders away.
Roughly speaking, the conservative part is the strongly–connected part
of the graph, and the dissipative parts are upstream of this sink.
So this is curious serendipity or synchronicity that I'm working on one
thing last night, and totally by accident I trip over something that informs.
Interesting.
\end_layout
\begin_layout Standard
But I digress.
The point here is I now have a
\begin_inset Quotes eld
\end_inset
Thermalization Conjecture
\begin_inset Quotes erd
\end_inset
that resolves special–relativistic time dilation effects.
My twin can go off on a fast rocket ship and experience time-dilation effects,
and return seconds or minutes younger.
We both experience
\begin_inset Quotes eld
\end_inset
here and now
\begin_inset Quotes erd
\end_inset
each at our own pace, and when the twin rejoins me, our experience of
\begin_inset Quotes eld
\end_inset
here and now
\begin_inset Quotes erd
\end_inset
rejoins at the
\begin_inset Quotes eld
\end_inset
present moment
\begin_inset Quotes erd
\end_inset
.
He does not arrive some seconds or minutes in the past or the future, he
arrives in the present.
The Thermalization Conjecture is that the reason for this is that his bundle
of thermodynamic entanglement might go off in a rocket–ship, and experience
special–relativisitic
\begin_inset Quotes eld
\end_inset
proper time
\begin_inset Quotes erd
\end_inset
in the conventional way, but, upon returning, his blob of thermodynamic
entanglement promptly entangles with my own, and we both live in the thermodyna
mic
\begin_inset Quotes eld
\end_inset
present
\begin_inset Quotes erd
\end_inset
.
That is, the proper time clocks get resynchronized into the
\begin_inset Quotes eld
\end_inset
present
\begin_inset Quotes erd
\end_inset
.
\end_layout
\begin_layout Standard
So, this is an advance over where I was a few weeks ago, when these questions
of proper time were befuddling.
Now, at least I have a mechanism.
Obvious and trite it may be, but it's something I can grasp hold of.
And now, time for some thought–experiments.
\end_layout
\begin_layout Standard
So, obviously, when my twin disembarks from his space–ship and we shake
hands and we breath the same air, we are both clearly in the thermalized
present.
When did this happen? As his ship re–entered the atmosphere? What about
radio communications? He flies off.
I transmit a radio–message, in my current, here and now present.
He is a few light–minutes away, and so receives that message in his present,
here–and–now.
Does that message cause a kind–of thermalization to happen? It is certainly
a dribbling of information between two thermal blobs, experiencing distinct
passage of proper time.
The reception of the info does not alter the rate of progression of proper
time, for either the sender or the receiver.
\end_layout
\begin_layout Standard
That is, the here–and–now for both of us is the strongly–connected component
of the graph of relationships between the atoms in our bodies.
Every atom involved in any chemical bond in my body is exchanging photons
– virtual photons, every femtosecond, back–and–forth.
In that sense, every chemical bond can be understood as a graph–theoretic
strong graph between the two atoms in that bond.
By similar arguments, the atoms in a thermally mixed gas are also in a
graph–theoretic strong component.
Relativistic proper time is experienced by this strongly–connected component,
as a whole.
That is, thermalization synchronizes clocks.
Sure, of course, when we look at a muon whizzing around an accelerator,
we can compute the rate at which it's proper time advances, and this computatio
n is not wrong.
But that muon is causally disconnected from our own here–and–now.
Yes, it experiences the bending forces of the accelerator magnets, that
keep it going in a circle.
But those virtual photons are not...uhh,
\begin_inset Quotes eld
\end_inset
thermal
\begin_inset Quotes erd
\end_inset
.
And this highlights a vocabulary problem.
We say that the virtual photons in a magnetic field are
\begin_inset Quotes eld
\end_inset
deep infrared
\begin_inset Quotes erd
\end_inset
, because they have very long wavelength.
But they are not thermally infrared: magnetic fields are not thermal at
the
\begin_inset Quotes eld
\end_inset
microscopic scale
\begin_inset Quotes erd
\end_inset
.
The virtual photons of the magnetic field are phase–coherent.
So that's another vocabulary issue: they are not
\begin_inset Quotes eld
\end_inset
coherent
\begin_inset Quotes erd
\end_inset
as in a laser
\begin_inset Quotes eld
\end_inset
coherent state
\begin_inset Quotes erd
\end_inset
, or some eigenfunction of some ladder operator.
At least ...
not when I last looked.
\end_layout
\begin_layout Standard
Which brings us to another problem: the origin of a magnetic field.
It is of course, the flow of electrons in a wire.
Those electrons necessarily move thermally.
The magnetic field is necessarily a thermal average of the individual electric
fields of each electron, relative to the lab frame.
So, in this sense, the magnetic field is necessarily a thermal average,
and if it were possible to measure, then we'd measure some finite mean–square
variation in the magnetic field strength.
That presumably will correlate 100% with the thermal environment of the
electrons in the wire, including temperature.
And the muon experiences this bath.
Red–shifted and blue–shifted as appropriate.
This bath cause the muon to change direction of motion, per classical electrody
namics.
It does not thermalize the proper time of the muon itself.
That is, whatever dynamical process is running inside the muon that causes
it to decay, that dynamical process is thermally isolated from the ambient
magnetic field that the muon is passing through.
\end_layout
\begin_layout Standard
I guess.
Perhaps there's some g–2 lesson in here, but I would not know how to compute
that.
Perhaps there is some miniscule thermal coupling.
If there was, it would show as a violation of special relativity for the
muon.
I don't think we have experiments that are sensitive to this.
So the proposed experiment here is to compare muon decay in
\begin_inset Quotes eld
\end_inset
hot
\begin_inset Quotes erd
\end_inset
and
\begin_inset Quotes eld
\end_inset
cold
\begin_inset Quotes erd
\end_inset
magnetic fields.
The hot field would be generated by literally hot wires, so that the electrons
in the wires have a large variation in velocity.
The average magnetic field for both hot and cold would have to be the same,
because we want the muon to take the same average mean path through the
storage ring.
Would the muon experience different decay rates between the hot and the
cold magnetic fields? How bit of an effect would it be? I honestly do expect
there to be some effect, because it is hard to imagine that the internal
mechanism of muon decay is perfectly thermally isolated from the external
world.
However, I guess I can also argue that that it could be, in fact, almost
perfectly thermally isolated.
How? Well, For example, superconductivity is a mechanism that isolates,
phase–transitions in such a way that the one phenomenon (conduction) is
thermally isolated from another (the bulk material is not at absolute zero.)
So we do have the mathematical apparatus that can perform thermal isolation
between bulk material and some measurable field.
And so perhaps the mechanism of muon decay is
\begin_inset Quotes eld
\end_inset
thermally isolated
\begin_inset Quotes erd
\end_inset
, in a similar fashion, from the bulk magnetic field that the muon is flying
through.
The result is that the proper time experienced by the muon decay mechanism
really is exactly that of special relativity.
\end_layout
\begin_layout Standard
All this is very highly speculative.
No one knows what dynamical system describes muon decay, and certainly,
I have never seen a treatment of
\begin_inset Quotes eld
\end_inset
hot
\begin_inset Quotes erd
\end_inset
and
\begin_inset Quotes eld
\end_inset
cold
\begin_inset Quotes erd
\end_inset
magnetic fields.
I imagine surely, someone else has thought about this before, but I haven
not tripped over this.
I've never looked out for it either, maybe it slid past, just out of sight.
\end_layout
\begin_layout Standard
Anyway, the astronaut on the rocket–ship: are they thermally isolated? Well,
in practice, there is both some galactic magnetic field, and also the CMB,
and finally, the radio transmissions they receive from home.
The number of states in the bulk astronaut is two–power–of–Avogadro's number;
the entropy is log of that, so the bulk entropy of the astronaut is order
of Avogadro's number.
The entropy of the radio signals is maybe hundreds, maybe millions, maybe
billions.
Maybe terahertz–trillions.
But this is still bazillions of orders of magnitude smaller than the bulk
entropy of the astronaut, and thus is not enough to thermalize them in
such a way to manifest as a change to proper time experience of here–and–now.
Presumably the same is true for the CMB.
I am too lazy to perform the calculation, but if I recall correctly, there
are maybe one hundred CMB photons per cubic meter, which is absurdly tiny
compared to the entropy of the bulk astronaut.
So lets recap that: my Thermalization Conjecture states that the experience
of
\begin_inset Quotes eld
\end_inset
now
\begin_inset Quotes erd
\end_inset
is in fact the experience of the thermal bulk.
This conjecture then implies that *if* there were an Avogadro's number
of thermal photons per cubic meter in the CMB, then those photons would
thermalize the astronaut, and impact the perception of
\begin_inset Quotes eld
\end_inset
now
\begin_inset Quotes erd
\end_inset
.
But since there aren't that many photons, it does not happen.
And also, if there were that many photons, the astronaut would be cooked
to a crisp.
Or rather, vaporized into a plasma.
Or rather, the universe would not be transparent, anyway.
\end_layout
\begin_layout Standard
Ah hah! Yay! So my thermalization conjecture, uhh,
\begin_inset Quotes eld
\end_inset
explains
\begin_inset Quotes erd
\end_inset
the CMB, then! Or rather,
\begin_inset Quotes eld
\end_inset
explains
\begin_inset Quotes erd
\end_inset
why the CMB provides a global rest–frame for the universe.
So, before the last photon decoupling, the universe was (electromagnetically)
thermalized (the neurtrinos had decoupled earlier.) This means that the
universe experiences a synchronized bulk single–proper–time.
That is, proper time passes at the same rate everywhere in the universe,
because all charged particles are part of the strongly connected graph.
When the photons decouple, this leaves behind the CMB, and of course this
has to be isotropic (up to BAO, etc.) and of course it provides a unique
space–like surface that provides a rest–frame.
This rest frame is the last time that proper time was globally synchronized
across the universe.
This is exactly where that rest–frame comes from.
\end_layout
\begin_layout Standard
Wow! OK! So this is real forward progress! I mean, its still trite and silly,
but its ...
more than I had before.
I still don't understand the mechanical details of how here–and–now resynchroni
ze for the astronaut and his twin, when they reunite.
But the answer does seem to be
\begin_inset Quotes eld
\end_inset
its thermal
\begin_inset Quotes erd
\end_inset
.
OK, so I think I can retire that, or put that on the back burner.
\end_layout
\begin_layout Standard
On the front burner is this: The past seems to detach from the present and
freeze into place, because the combinatoric entanglements of the past exceed
some threshold, so that the present can no longer undo those entanglements.
That is, thermalized systems necessarily leave behind an unalterable past.
This implies that there is some order parameter that splits past from present.
At the start of today's diary entry, I suggested that this might be because
Planck's constant and Avogadro's number are incomparable.
Is this bullshit, or is this meaningful? Well ...
I'm intellectually spent, for the moment, and I need to go ride a bike.
So not gonna do this now.
Later, dude.
\end_layout
\begin_layout Subsection*
3 May 2025
\end_layout
\begin_layout Standard
So I'm thinking of the system as a phase transition.
The past is frozen, the present is fluid.
The present proceeds forward in time.
So how do I construct this model? First, this model does not make sense
for classical mechanics in a Newtonian background.
By definition, physics is defined to have time as a parameter; it marches
forward, it doesn't go backwards.
Yes, so wave equations have both advanced and retarded solutions but the
advanced solutions are dismissed out of hand, as they are backwards–going.
Which makes sense for water waves.
And microscopic waves aren't classical.
Same remarks apply for a relativistic background, where proper time in
the lab frame moves forward by definition.
Same even for ordinary QM.
Need to employ TSVF - two state–vector formalism, to get backwards–moving
states.
The challenge is then to write a many–body quantum system using TVSF.
I suppose the right answer is to try to mash it up with full QED in some
way.
Acknowledging that there are field operators, but avoiding loop diagrams.
Do everything at the tree level.
Flat space is enough.
Don't need GR.
Don't need weak or strong interactions.
Nuclei can be point particles.
Just tree–level QED, with explicit TVSF so as to handle interferometric
interactions.
That is, to handle Bell states.
\end_layout
\begin_layout Standard
And then I get stuck.
The gut instinct is to treat QM as TIQM - transactional interpretation
of QM, so that backwards–moving states get used to resolve measurements.
This of course doesn't work out in the naive way, I've noted this before.
\end_layout
\begin_layout Standard
But anyway, the point is that ergodicity/thermalization is not enough, because,
e.g.
for a classical atomic gas, there's no
\begin_inset Quotes eld
\end_inset
width
\begin_inset Quotes erd
\end_inset
to time, there's no wave–front.
No backwards–moving influences.
Sure, some atom thermalizes after a dozen collisions – moving forwards
in time.
So what.
This is just how time is axiomatized in Newtonian systems.
\end_layout
\begin_layout Standard
So we have two distinct problems, but they are the same ones as ever: How
does one describe quantum thermalization (in some TSVF formalism, or tree–level
QED) and how does one resolve many–world back down to one world? The only
answer right now is for me to read what others have done.
But whatever.
The point was to note that thermalization alone in a classical regime is
not enough.
The tree–level interactions are needed.
\end_layout
\begin_layout Standard
The following Wikipedia article has some inspirational content:
\end_layout
\begin_layout Itemize
https://en.wikipedia.org/wiki/Tensor_network This inspiration is that ...
well ...
something.
\end_layout
\begin_layout Itemize
There's also ...
https://en.wikipedia.org/wiki/Viscosity_solution
\end_layout
\begin_layout Subsection*
5 May 2025
\end_layout
\begin_layout Standard
Sp a week or two ago I wrote in this diary that I was confused about many–worlds
and a transactional interpretation.
Last night I was thinking: there should be no confusion: influences move
backwards in time, cause states to collapse there, and then move forward
in time, to the other interferometer arm.
I'm even thinking now that the interferometer does NOT need to be closed!
i.e.
the two arms don't need to be brought together to force collapse.
\end_layout
\begin_layout Standard
So, for example, a singlet state is prepared at
\begin_inset Formula $\left(t_{0},x_{0}\right)$
\end_inset
out of two half–spins, and these fly off to be measured at
\begin_inset Formula $\left(t_{1},x_{1}\right)$
\end_inset
and
\begin_inset Formula $\left(t_{2},x_{2}\right)$
\end_inset
(which can be space–like separated, so as to underline the non–local natures
of the measurement.
) The point of using the TSVF formalism is that the measurement at
\begin_inset Formula $\left(t_{1},x_{1}\right)$
\end_inset
propagates backwards in time to
\begin_inset Formula $\left(t_{0},x_{0}\right)$
\end_inset
bounces there, maybe causing a partial collapse there, and then travels
back up to
\begin_inset Formula $\left(t_{2},x_{2}\right)$
\end_inset
causing a collapse there.
That is, not only are the spins entangled, but the collapses are entangled.
\end_layout
\begin_layout Standard
So I am envisioning the w.f.
collapse as being an avalanche at a critical point, analogous to Per Bak's
critical sandpiles.
Except that in this case, it is not sand–grains but a network of photon–electro
n interactions, at the tree–level in QED.
The spin at
\begin_inset Formula $\left(t_{1},x_{1}\right)$
\end_inset
is coupled to
\begin_inset Formula $\left(t_{2},x_{2}\right)$
\end_inset
and as avalanching starts at
\begin_inset Formula $\left(t_{1},x_{1}\right)$
\end_inset
it also starts at
\begin_inset Formula $\left(t_{2},x_{2}\right)$
\end_inset
and proceeds in both locations in a coupled fashion: each back–reacts on
the other.
Observe that both
\begin_inset Formula $\left(t_{1},x_{1}\right)$
\end_inset
and
\begin_inset Formula $\left(t_{2},x_{2}\right)$
\end_inset
are a part of here–and–now and still in the fluid state, not yet frozen
in time.
The completion of the avalanche is part of what freezes them.
\end_layout
\begin_layout Standard
Even though locations may get frozen in the past, they can still act as
conductors of spin information, i.e.
act as conductors of qubits.
Thus, the point
\begin_inset Formula $\left(t_{0},x_{0}\right)$
\end_inset
where the singlet was prepared is at the trailing end of here–and–now,
with almost all aspects frozen into the past, but a small channel remaining
open, to allow qubit info to fly in between
\begin_inset Formula $\left(t_{1},x_{1}\right)$
\end_inset
and
\begin_inset Formula $\left(t_{2},x_{2}\right)$
\end_inset
, passing through
\begin_inset Formula $\left(t_{0},x_{0}\right)$
\end_inset
as the avalanche occurs.
That is, the
\begin_inset Quotes eld
\end_inset
classical structure
\begin_inset Quotes erd
\end_inset
(whatever that is) surrounding
\begin_inset Formula $\left(t_{0},x_{0}\right)$
\end_inset
is frozen into the past, but the qubit channel remains open.
Which it has to, because of the no–cloning/no–erasure theorem: the no–cloing
theorem is a statement that the singlet–entangled qubit channel located
at
\begin_inset Formula $\left(t_{0},x_{0}\right)$
\end_inset
must remain open, and cannot be frozen into the past.
As long as qubits flow, they must be able to flow through there.
\end_layout
\begin_layout Standard
So this sketch is now concrete enough that perhaps it is open to theoretical
modeling.
Lets see if we can make this so:
\end_layout
\begin_layout Itemize
Create a random network, i.e.
a graph of vertexes and edges.
\end_layout
\begin_layout Itemize
Place entangled spin states at the vertexes.
\end_layout
\begin_layout Itemize
Each edge is a spin-1/2 propagator.
For the model, this is just the trivial propagator: we just copy, or rather,
mark as identical the two spins at either vertex at the end of the edge.
\end_layout
\begin_layout Itemize
Embed the graph into Minkowski spacetime, such that all edges are time–like.
(or maybe null?)
\end_layout
\begin_layout Itemize
Pick a vertex that has no future edges: i.e.
has no edge that connects to a vertex that is to it's future.
\end_layout
\begin_layout Itemize
At the selected vertex, twiddle aka
\begin_inset Quotes eld
\end_inset
measure
\begin_inset Quotes erd
\end_inset
the spin.
Since this spin is entangled, this should propagate through the network,
causing other qubits to correlate.
\end_layout
\begin_layout Standard
I imagine there are dozens, if not hundreds of papers describing exactly
this.
This is part–and–parcel of the central core of quantum computing.
But I don't know these papers, I have not read them.
I do recall a key–word:
\begin_inset Quotes eld
\end_inset
clock states
\begin_inset Quotes erd
\end_inset
, which carry no information, as opposed to some other kind of state, that
does.
I need to search–engine this and read about it.
\end_layout
\begin_layout Standard
Anyway, part of the exploration of the above network model is to look for
avalanching behavior.
The quantum computing people treat this as
\begin_inset Quotes eld
\end_inset
noise
\begin_inset Quotes erd
\end_inset
and they want to get rid of it.
I want to go in the opposite direction: to discover that
\begin_inset Quotes eld
\end_inset
noise
\begin_inset Quotes erd
\end_inset
and thermalization happen automatically, as the result of avalanching.
\end_layout
\begin_layout Standard
This makes it different from, say, Brownian motion.
So in 1905, Einstein looks at Brownian motion, and obtains expressions
for diffusion.
His calculation is a certain kind of ensemble–average calculation.
Here, we kind of know that ensemble–averaging
\begin_inset Quotes eld
\end_inset
cannot work
\begin_inset Quotes erd
\end_inset
, because the no–cloning theorem blocks it.
So we need a different mechanism, and that mechanism has to be avalanching
through wave–function phases.
Small disturbances have to be amplified into large re–arrangements.
\end_layout
\begin_layout Standard
Let me change the topic slightly.
So I'm reading about Brownian motion on Wikipedia, and I was staring at
https://en.wikipedia.org/wiki/Kirchhoff%27s_theorem which is about graph
Laplacians, and this pops out at me:
\begin_inset Quotes eld
\end_inset
\emph on
...the Laplacian L can be factored into the product of the incidence matrix
and its transpose, ...
\emph default
\begin_inset Quotes erd
\end_inset
and two things pop into my mind: First, the smooth–space Laplacian is the
infinite–dimensional version of this in that the (transpose of the) incidence
matrix is the gradient, an the incidence matrix itself is the divergence,
so div dot grad is the Laplacian.
But I've never seen a first–principles derivation of that limit.
\end_layout
\begin_layout Standard
How would that work? The graph–network connectivity of Euclidean space is
kind–of–ish infininte–dimensional, in that the continuum is uncountable.
The Laplacian is not
\begin_inset Quotes eld
\end_inset
just
\begin_inset Quotes erd
\end_inset
the limit of the graph laplacian for an
\begin_inset Quotes eld
\end_inset
infinitely small grid
\begin_inset Quotes erd
\end_inset
, but is also rotationally invariant, and so ...
Ugh.
Some mashup of Cantor sets and Grassman variables and tensor algebras.
The analogies are all there, the groundwork is laid, the proper, formal
treatment of the limit has not been taken.
But also, hand in hand with this is the Dirac equation: it's also kind
of like the
\begin_inset Quotes eld
\end_inset
\emph on
product of the incidence matrix and its transpose
\begin_inset Quotes erd
\end_inset
\emph default
but going off into the Weyl spinors that can be built from the Clifford
algebra on the tangent space.
That is, the the
\begin_inset Quotes eld
\end_inset
incidence matrix
\begin_inset Quotes erd
\end_inset
is a map between a manifold and it's tangent space, the divergence goes
in the opposite direction (using the manifold metric for the dot product)
and so the usual Laplacian is build from the contraction of the two, given
a scalar.
But one can also build Weyl spinors from the tangent bundle, and contracting
those gives the Dirac eqn.
\end_layout
\begin_layout Standard
Perhaps the first step is to try to explain how an incidence matrix is just
like a map between a manifold and it's tangent space.
Having established that analogy, lets now construct a Clifford algebra
from the graph edges.
Which is fun, because we can now use the notation
\begin_inset Quotes eld
\end_inset
e
\begin_inset Quotes erd
\end_inset
for both an edge, and a basis vector.
Heh.
And thence, from this Clifford algebra, we construct the graph analog of
Weyl spinors, and then, from these, the graph analog of the Dirac equation.
Again, I suppose someone has done this already.
Who? Would search engines know? Would grok know?
\end_layout
\begin_layout Standard
I was also going to blurble about relationships between:
\end_layout
\begin_layout Itemize
https://en.wikipedia.org/wiki/Cauchy%E2%80%93Binet_formula
\end_layout
\begin_layout Itemize
https://en.wikipedia.org/wiki/Riemann_mapping_theorem
\end_layout
\begin_layout Itemize
https://en.wikipedia.org/wiki/Jordan_curve_theorem
\end_layout
\begin_layout Itemize
https://en.wikipedia.org/wiki/Viscosity_solution
\end_layout
\begin_layout Itemize
https://en.wikipedia.org/wiki/Schramm%E2%80%93Loewner_evolution
\end_layout
\begin_layout Standard
Hey, I am now reading this: Methodical banality Hannah Katznelson https://aeon.co
/essays/who-needs-ai-text-generation-when-theres-erasmus-of-rotterdam and
the wires in my head cross over: LLM's generate based on context, but this
is just approximate.
This crosses with the
\begin_inset Quotes eld
\end_inset
viscosity solution
\begin_inset Quotes erd
\end_inset
, above: the stuff LLM's generate is close to intended reality, but they
file off the sharp edges that are really there in real reality.
\end_layout
\begin_layout Standard
Again, my brain is a mashup machine: whatever I read, that is what I think
about: I can read about Erasmus and commonplace books and eclectic writing,
but burbling in the back of my mind is a matrix all of whose eigenvalues
are all negative.
Push, push, push to get a closer and closer approximation to ..
past reality.
And that is what the LLM's will give us: a closer approximation to the
frozen past.
But we live in the present, here and now, not the past.
Hmm.
\end_layout
\begin_layout Standard
Back to spinors on graphs.
Suppose I have some random graph.
Pick a vertex, any vertex.
Suppose it has
\begin_inset Formula $n$
\end_inset
edges attached to it.
Write
\begin_inset Formula $e_{k}\equiv e_{k}\left(v_{i}\right)$
\end_inset
to be the
\begin_inset Formula $k$
\end_inset
'th edge attached to vertex
\begin_inset Formula $v_{i}$
\end_inset
, with
\begin_inset Formula $k\in\left\{ 1,\cdots,n\right\} $
\end_inset
.
The point of this suggestive notation is we can abuse it: take
\begin_inset Formula $e_{k}$
\end_inset
to be basis vectors on
\begin_inset Formula $\mathbb{R}^{n}$
\end_inset
.
Build the tensor algebra
\begin_inset Formula $T\left(\mathbb{R}^{n}\right)$
\end_inset
with elements
\begin_inset Formula $e_{k}\otimes e_{m}\otimes\cdots$
\end_inset
.
Write
\begin_inset Formula $\mathrm{Cl}\left(n\right)=T\left(\mathbb{R}^{n}\right)/I$
\end_inset
to be the real Clifford algebra, where
\begin_inset Formula $I$
\end_inset
is the (two–sided) ideal generated by elements of the form
\begin_inset Formula $w\otimes w+\left\langle w.w\right\rangle $
\end_inset
and
\begin_inset Formula $\left\langle \cdot,\cdot\right\rangle $
\end_inset
is the usual Euclidean inner product on
\begin_inset Formula $\mathbb{R}^{n}$
\end_inset
.
By ongoing abuse of notation, write
\begin_inset Formula $e_{k}$
\end_inset
for an element of
\begin_inset Formula $\mathrm{Cl}\left(n\right)$
\end_inset
.
As usual,
\begin_inset Formula $e_{k}^{2}=-1$
\end_inset
and the algebra is anti–commuting:
\begin_inset Formula $e_{i}e_{j}=-e_{j}e_{i}$
\end_inset
.
The algebra decomposes into Pin, Spin, etc.
as usual.
The Weyl spinor is build on
\begin_inset Formula $W\otimes\mathbb{C}$
\end_inset
with basis elements
\begin_inset Formula
\[
\eta_{j}=\frac{1}{\sqrt{2}}\left(e_{2j-1}-ie_{2j}\right)
\]
\end_inset
just as in Jost page 69.
Everything passes through verbatim.
Jost, section 1.8 page 56ff.
Textbook by Jurgen Jost, Riemannian Geometry and Geometric Analysis.
\end_layout
\begin_layout Standard
So what? The above sicks spinors on the vertices of a graph.
They don't propagate, but perhaps some kind of Dirac eqn.
could be derived for them.
Built from the incidence matrix, I guess.
All that I get from this is you can define anything on vertexes and edges,
and build some dynamical system.
So what.
The tricky part is to show the dynamical system does something interesting.
\end_layout
\begin_layout Subsection*
8 May 2025
\end_layout
\begin_layout Standard
One issue with doing and reading mathematics is that there is a combinatorial
explosion of interconnections between concepts, most which do not matter,
and some which do.
Today, I thought I'd read about the
\begin_inset Quotes eld
\end_inset
Parsi-Sourlas approach to Langevin SDEs
\begin_inset Quotes erd
\end_inset
which is fine, except that almost immediately, I hit on the Fadeev-Popov
expression for a Jacobian determinant.
The underlying reason for this comes from the Berezinian, or more precisely,
the Berezin superintegral representation
\begin_inset Formula
\[
\int\exp\left[-\theta^{T}A\eta\right]\,d\theta\,d\eta=\det A
\]
\end_inset
which follows directly from the definition of determinants and the anti-commutin
g properties of the variables
\begin_inset Formula $\theta$
\end_inset
and
\begin_inset Formula $\eta$
\end_inset
.
Then this catches my eye:
\begin_inset Formula
\[
\int\exp\left[-\tfrac{1}{2}\theta^{T}M\theta\right]\,d\theta=\begin{cases}
\mathrm{Pf}\,M & n\mbox{ even}\\
0 & n\mbox{ odd}
\end{cases}
\]
\end_inset
which gives the Pfaffian,
\begin_inset Formula $(\mathrm{Pf}\,M)^{2}=\det M$
\end_inset
and oh, OK, I'd forgotten about that.
Thanks for the reminder.
So I skim wikipedia, it reminds me that skew–symmetric matrices can be
brought into a block-diagonal form.
Which makes me think of the canonical symplectic form on symplectic vector
spaces and then I spin out, trying to remember everything I know about
Hamiltonian mechanics, but this is useless, as its boiling the ocean.
\end_layout
\begin_layout Standard
The other direction my mind spins out to is the Jacobian determinant.
All those places where there are Jaocobians, what if the above formula
was substituted? It boggles the mind.
The obvious answer is
\begin_inset Quotes eld
\end_inset
nothing interewsting happens
\begin_inset Quotes erd
\end_inset
.
This, however, begs the question: why does it become interesting when Fadeev–Po
pov do it? What's different about this case? Is it because of exp Action?
\end_layout
\begin_layout Subsection*
17 May 2025
\end_layout
\begin_layout Standard
Where does the time go? What am I doing? Did I drink too much coffee? Did
I not get enough exercise? Why can't I live in an endless state of grace?
Why am I anxious and irritated? Dear diary, I will unload on you, in the
grand hope that it will ...
resolve the tension and urge to scream.
Or maybe I should go ride a bike instead, that tends to restore a certain
amount of hormonal balance.
\end_layout
\begin_layout Standard
I was going to write two papers for AGI 2025.
I started them over a month ago.
They almost wrote themselves, they were so easy – it was a boiled down
version of what's in this diary.
Since I'd already written, it was easy.
Just one more day, to finish them, and then ...
a month went by, with nothing at all.
Where does the time go?
\end_layout
\begin_layout Standard
I did spent the month studying the Wiener process.
Wrote the example for the wikipedia article
\begin_inset Quotes eld
\end_inset
Natural filtration
\begin_inset Quotes erd
\end_inset
which seems to have relevance to my conception of here and now.
I have more to read, and more to think about, I am distracted.
Perhaps dumping more into this diary is waste of time, right now.
I guess I did drink too much coffee.
I guess I am still ...
annoyed about something.
I tell myself,
\begin_inset Quotes eld
\end_inset
I should do this
\begin_inset Quotes erd
\end_inset
, procrastinate,
\begin_inset Quotes eld
\end_inset
I should do that
\begin_inset Quotes erd
\end_inset
, get annoyed, get overwhelmed, ponder the precariousness of human emotional
states.
Wander off into thinking about what it means to be alive.
Wonder about that in some abstract sense, without making progress on my
stated goals of axiomatizing all of it mathematically.
Getting irrittated at myself for not making progress.
Bitching at you, dear diary, for my failures, even as writing this is clearly
some distraction from what I should be doing.
Or is it? Just two paragraphs ago, I was telling myself that writing here
would be soothing.
So is it soothing or a waste of time?
\end_layout
\begin_layout Standard
Well, since I'm still quasi–capable of focusing, I think I will continue
reading that paper on
\begin_inset Quotes eld
\end_inset
Infinite dimensional analysis
\begin_inset Quotes erd
\end_inset
or whatever its called.
Then a bike ride.
Later, dude.
\end_layout
\begin_layout Standard
Oh wait.
\end_layout
\begin_layout Standard
I needed to review
\begin_inset Quotes eld
\end_inset
separable space
\begin_inset Quotes erd
\end_inset
, and this sentence jumped out:
\begin_inset Quotes eld
\end_inset
every continuous function on a separable space whose image is a subset of
a Hausdorff space is determined by its values on the countable dense subset.
\begin_inset Quotes erd
\end_inset
.
Shit.
I've seen this happen before, years ago, while working on the beta expansion,
and I said to myself
\begin_inset Quotes eld
\end_inset
oh that's interesting
\begin_inset Quotes erd
\end_inset
but out of ignorance, didn't make the connection to separable space.
And now that I have, I want to got back, and look at those old, old results,
examine them again, but I don't remember where I wrote them down.
That's irritating.
And if I did go back, would that change anything? Would there have been
just one tiny bit more of insight? Maybe, maybe not.
\end_layout
\begin_layout Standard
OK, let me write down one tiny bit of math nonsense right now, and see if
I can confuse myself.
Its trivial, its basic.
Why are trivial and basic things confusing? Lets start with the conventional
Cantor set, modelled as an infinite binary tree.
There are an uncountable number of
\begin_inset Quotes eld
\end_inset
leaves
\begin_inset Quotes erd
\end_inset
on the tree, despite two paradoxes: each branch–point can be enumerated
(and associated with the dyadic rationals, for example), which means the
\begin_inset Quotes eld
\end_inset
gap
\begin_inset Quotes erd
\end_inset
between two branches is also associated with a dyadic rational.
However, all of the measure of the reals is associated with the
\begin_inset Quotes eld
\end_inset
perfect sets
\begin_inset Quotes erd
\end_inset
, the leaves at the end of the binary tree.
The rationals being a set of measure zero.
So, separability says that continuous functions are determined by values
on the dense subset, but the measure is determined by not that.
Curious.
\end_layout
\begin_layout Standard
I guess that what this is saying is that continuous functions are necessarily
integrals of functions in general.
That is, integrals of possibly discontinuous functions.
Curious.
Normally, continuity is defined via limits and limit points and whatnot.
This insight suggests that continuity can also be defined by integration.
Hmm.
Can that work? So the Hausdorff axiom T2 does not require limits; its just
a separation axiom.
Integrability requires a measure, and so my nonsense seems to say
\begin_inset Quotes eld
\end_inset
every continuous function is the integral of some measure
\begin_inset Quotes erd
\end_inset
.
Well, except that the measure has to satisfy certain properties, like sigma-add
itivity.
Fuck all.
I need to go on that bike ride.
Skimming the rest of the WP article on Separable spaces just sends me deeper
into the rabbit hole.
A twisty little maze of passages, all different.
\end_layout
\begin_layout Subsection*
17 May 2025 - Later
\end_layout
\begin_layout Standard
Post ride.
Showered, Relaxed.
But tired.
While riding, I thought of a bunch of things to write about.
Now I'll see if I have the energy to execute on the plan.
As always, the plan is free association.
\end_layout
\begin_layout Standard
Prelude: my bike rides are from home, west of downtown Austin, hike & bike
trail, to Southern Walnut Creek trail , to Daffan Road, and back.
So about 30 miles round trip.
Sometimes to Manor, which gets it up over 40 miles.
Bragging to my future self.
Medium pace, about 1/4th of it in top gear, the rest in second from top.
Maybe 2.5 hours to Daffan and back, depending on the rest stops (I take
2 or 3).
Old hard–fork, hard–tail mountain bike.
Not some fancy–ass road bike.
I typically lose about 2.5 kg per ride, despite taking a liter of water
with, and sometimes topping up from a water fountain.
I have a diary of health metrics.
Private.
\end_layout
\begin_layout Standard
The thoughts are the usual clothes–washing machine jumble of physics/math,
human psychology as I personally experience it, a torrid understanding
of sociology, here and now, the nature of reality.
I read some editorial from Carlo Rubio recently, about how physicists should
stick to trying to improve current theories, instead of inventing all brand–new
stuff.
And I guess I agree, at some certain level.
Mostly I've come to the conclusion that most of the academic community,
in any academic field whatsoever, is pretty mediocre.
Rubio doesn't say this, but to paraphrase, they shouldn't be playing the
lottery, hoping to strike it rich.
They should put in a solid days work working to improve things as they
are.
So yeah, lottery tickets don't pan out.
\end_layout
\begin_layout Standard
Me? I'm more or less retired, free of constraints.
I wandered aimlessly through life, so clearly, that will not change now.
I would like to be more focused, I suppose.
but on what? And that segues into the first topic I thought about during
the bike ride: a mash up for free will, of feeling frustrated, motivations,
drives.
The entire complex of human psychological drives that makes people do what
they do.
There are three or four approaches to this.
The first is to map the territory: this is what the discipline of psychology
does.
Including all the various aberrations.
The second is to link these to neural structures, to synaptic biochemistry,
re–uptake inhibitors and all that.
Third is to look for self–organizing behavior that drives systems to critical
points with avalanching behavior.
An example of the third is something I read recently, a few weeks ago:
Complex harmonics reveal low–dimensional manifolds of critical brain dynamics.
Gustavo Deco, Yonatan Sanz Perl, and Morten L.
Kringelbach https://journals.aps.org/pre/abstract/10.1103/PhysRevE.111.014410
This was a decent paper.
Focused, scientific, tools and techniques, measurements and results, but
in some ways
\begin_inset Quotes eld
\end_inset
pretty far out there
\begin_inset Quotes erd
\end_inset
.
\begin_inset Quotes eld
\end_inset
The Hopf Model
\begin_inset Quotes erd
\end_inset
and that thinking, decision–making are best understood as sequences of
avalanches.
\end_layout
\begin_layout Standard
The fourth approach is to ignore Carlo Rubio, and go all mystical.
Why do systems
\begin_inset Quotes eld
\end_inset
self–organize
\begin_inset Quotes erd
\end_inset
? This is a stupid question, because there is a simple answer: we live in
3D space, made of atoms and chemistry, and energy flows, turbulence, yadda
yada means that self–organizing systems near the point of criticality are
extremely common in nature.
That's the answer.
Not sure why one would want to look for a mystical answer, when the obvious,
the conventional, mainstream physics and chemistry and thermodynamics supplies
a perfectly adequate mainstream answer.
Shut up and calculate, Feynman might say.
But I don't want to shut up, and calculating is hard.
I no longer trust main–stream answers in how I should spend my time, and
I guess no one else does, either.
We are in an apocalyptic social upheaval because no one knows what the
point of it is, they are driven by mammalian brains to act in some way
or another, like wild animals running free in the noosphere.
So this meta–meta–meta structure of the noosphere and how it couples to
drives and motivation, reasons and behavior and action, it fairly well
calls out for something more than
\begin_inset Quotes eld
\end_inset
the neurons made me do it
\begin_inset Quotes erd
\end_inset
as the answer.
Because the feelings of awe and grandeur in life seem to require something
more than
\begin_inset Quotes eld
\end_inset
its a bunch of neurotransmitters
\begin_inset Quotes erd
\end_inset
.
Its fertile soil for crank mysticism, and for religious explanations.
As a phsyicalist, though, I do want to connect the low–level thermodynamics
to the high–level supreme existential reality.
But how? Can I do it without skipping key steps? Can I do it without self–indoc
trinating myself into false beliefs? So, the fourth approach, for me.
Take a shot.
See what happens.
\end_layout
\begin_layout Standard
So I think of several things while riding.
First, I return to free will and here–and–now.
So the model of here–and–now is that the past is frozen, the present is
some phase transition from a fluid present to a frozen past.
So I think about free–will and how to detach it from determinism.
And that is when it pops into my mind: where is the future? If the present
is here, where is the boundary to the future? Is it a hard boundary? Is
it soft?
\end_layout
\begin_layout Standard
The other things I'm thinking about at the same time is about descriptive
set theory.
First rung on that ladder is if course the notion of separable spaces.
And of course, the continuum holds a special place.
Above the continuum, we start wandering in several directions.
First is the replacement of indicator functions by the suboject classifier.
The Yoneda lemma, all that.
But before gong there, the Wikipedia article on separable spaces points
out that you can certainly have spaces with zoos of cardinals in them.
Which then points to another apperception: that the things we say about
cardinals are algebraic.
So descriptive set theory – the Borel hierarchy, all that, is algebraic
in nature.
Collections of proofs, proofs are symbolic manipulations, which we like
to ascribe meanings, like
\begin_inset Quotes eld
\end_inset
inifinity
\begin_inset Quotes erd
\end_inset
but these are vibes ..
snowballing into platonic reality.
Some people want to say that free will has something to do with the Axiom
of Choice, and maybe it does and maybe it doesn't, its certainly very premature
to go there, because it is a linguistic vibe that is suggesting some associatio
n there.
And perhaps that linguistic vibe captures an echo of truth, and maybe it
doesn't.
Whatever.
Did I shoot my wad too early? I was just getting started.
Plus its almost 1AM and now I really am getting tired.
Should I continue incoherently? Should I sleep? The bike ride says
\begin_inset Quotes eld
\end_inset
sleep
\begin_inset Quotes erd
\end_inset
.
\end_layout
\begin_layout Standard
Where was I? Something something algebra.
What is the foundation for it all? Some platonic reality, that underlies
the physical reality? The platonic reality is soft and infirm in many ways:
with and without AC.
With and without CH, per Paul Cohen forcing.
Worse: the theory of oracles in comp sci: I guess maybe one way to think
of oracles is that they are again, algebraic in nature, much like the way
that we use symbols for denoting cardinals, until we run out of symbols
to write cardinals with, but there are always still more, the Large Cardinals.
Or Axioms thereof.
Except with oracles, we slice in a different way: we make symbological
assertions about
\begin_inset Quotes eld
\end_inset
what can be known
\begin_inset Quotes erd
\end_inset
, i.e.
computable by a Turing machine, and then write symbols for things that
go beyond that point, and call them oracles.
They don't exist, the same way that infinities don't exist, but we are
happy to do algebras of infinities, and we are happy to do algebras of
oracles.
We are happy for ZFC with AC and happy for it without AC.
Huh.
I wonder if there are like, two versions of things that pertain to oracles:
those with and without AC? Why, I suppose there are.
I actually wrote a paper, something about dynamical systems and Vitali
sets, so I actually got to think about the simplest aspects of that theory
a bit.
\end_layout
\begin_layout Standard
And see, here I hit two problems: should I study these topics, or should
I study something else? Physics, as we currently know it, is about quantum
fields, and spacetime.
With energy flows and photons and turbulence, so why am I looking for free
will in the theory of oracles and descriptive set theory, when instead
I should be looking for simplified models of U(1) electromagnetic fields
as the foundation–stone for here–and–now? Because here–and–now really does
take place here–and–now, in the physical world, and not in the platonic
realm.
Critics might say that I vastly over–extend myself in imagining a bridge
between that platonic world, and the physical reality of here–and–now.
Critics.
But not Micheal Levin, with his Ingressing Minds paper.
He's got this take that is both mystical and hard–nosed: platonic reality
is pervasive, pervasively filigreed into the physical world, the so–called
unreasonable effectiveness of mathematics in physics.
\end_layout
\begin_layout Standard
Oh, but here's the thing: each little ingress is disconnected.
We use one set of theories for QFT, and another set for describing turbulence,
and these two applications have very nearly nothing in common.
I did read some annoying article, just today, in Quanta Magazine, god I
hate that magazine.
Reading it makes me dumber.
That article was about some mathematicians who solved superdiffusion using
some new math technique that gives legs to the renormalization group.
Something about sticking turbulence on a grid, and looking for flows or
averages or something on that grid, an infinite number of renormalization
group steps or something.
Who knows.
Quanta magazine makes me dumber.
Maybe the have some flow on some infinite–dimensional manifold who the
fuck knows.
So anyway, that does provide a formal algebraic, proof–theoretic bridge
between turbulence and viscosity, between turbulence and the Wiener process?
And there are existing bridges wherein Wiener processes show up in quantum
things, because Hilbert spaces, and the Cameron–Martin theorem, and see,
we are now back to Banach Spaces, and separable spaces, and cardinals ..
so there is a link.
It's distant and tortured, but there's a link.
And now I want to extend that tortured link to both human psychology and
life as a self–organized critical process with avalanches, but I also want
to go in a different direction, and hunt for free will.
Its like I want to go scuba diving while at the top of Mt.
Everest.
Is that so unreasonable? Doesn't everybody want to go scuba diving at the
top of Mt.
Everest? No? How about on Mars? Fuck.
\end_layout
\begin_layout Standard
It is now after 1AM and I cannot sustain this in a meaningful fashion, so
I will tumble to sleep.
Maybe I'll resume in the AM, and maybe not.
The problem with resuming in the AM is the general feeling that this angst–ridd
en prose is not fruitful.
And that I should ..
well, read something.
But the things I am drawn to read are also not directly informative on
..
other things I want to do.
So I am everywhere, all at once, unable to make decisions, lost in the
fog.
Oat Willie's.
Or what, Rush, Tom Sawyer, caught in the friction of the day.
That line resonates.
Every day is friction: what you want to do, vs what you are allows by the
situation to actually do.
Life is very sharply constrained.
We talk about free will, but in a sense, there's not all that much of it
around.
The friction of the day doesn't let us.
Good night.
\end_layout
\begin_layout Subsection*
18 May 2025
\end_layout
\begin_layout Standard
Thought about filtrations of the Wiener process as I fell asleep.
Somehow, thinking of it in this way opens new mental spaces that were somehow
closed before.
I suppose the most interesting thought worth writing down just right now
is the question of how to take the conventional functional integral
\begin_inset Formula $Z=\int\left[d\varphi\right]\exp-i\int d^{4}x\mathcal{L}\left(\varphi,\dot{\varphi}\right)$
\end_inset
and rewrite it as if it were a natural filtration on a stochastic process,
with an explicit time coordinate, i.e.
with a Hamiltonian, instead of a Lagrangian.
Again, I suppose someone has done this.
Again, what are my priorities?
\end_layout
\begin_layout Standard
I started thinking about separable spaces, and, just like we have algebra
with which to talk about uncountable cardinals, and algebra to talk about
oracles, we also have algebra to talk about Vitali sets.
The point here again is that
\begin_inset Quotes eld
\end_inset
Vitali sets are weird
\begin_inset Quotes erd
\end_inset
, in the sense of
\begin_inset Quotes eld
\end_inset
they lie outside the bounds of the intuitive
\begin_inset Quotes erd
\end_inset
, but algebra does not care, math does not care.
They can still be described.
We have notation for that.
I can't explain why this seems to be important to remark upon.
From the math point of view, its trite, trivial, yeah, duh sort of thing.
I cannot define
\begin_inset Quotes eld
\end_inset
the set of weird things in math that feel like they should not be describable,
but they are
\begin_inset Quotes erd
\end_inset
.
\end_layout
\begin_layout Standard
Here's another quote from that article:
\emph on
\begin_inset Quotes eld
\end_inset
...many theorems that can be proved for nonseparable spaces have constructive
proofs only for separable spaces.
Such constructive proofs can be turned into algorithms...
\emph default
\begin_inset Quotes erd
\end_inset
and my amazement here is that I'm using the phrase
\begin_inset Quotes eld
\end_inset
algebra
\begin_inset Quotes erd
\end_inset
to mean
\begin_inset Quotes eld
\end_inset
a finite collection of symbols that can be arranged on a page, subject to
a finite collection of rules that govern their rearrangement
\begin_inset Quotes erd
\end_inset
.
These rules include things like axiom schemas and group presentations,
which have regular patterns that allow them to be consistently manipulated,
e.g.
in second–order logic.
So this is kind of a statement about model theory, I guess, and of course,
model theory does not normally live in a space, and we do not normally
give models a topology.
But then it is possible to get into the semantics of algorithms, and talk
about their homotopic rearrangements.
This is an example where math gets recursive into itself.
Yet another example, one might say.
\end_layout
\begin_layout Standard
Am I easily bemused? I am currently enjoying the steps
\begin_inset Quotes eld
\end_inset
Separable Space
\begin_inset Quotes erd
\end_inset
->
\begin_inset Quotes eld
\end_inset
Stone–Weierstrass theorem
\begin_inset Quotes erd
\end_inset
->
\begin_inset Quotes eld
\end_inset
Bernstein polynomial
\begin_inset Quotes erd
\end_inset
because ...
because ...
when I was young, I would have taken this to be perhaps trite and perhaps
obvious and perhaps even boring, not something I could ever be interested
in, but now, it has some kind of resonance.
\begin_inset Quotes eld
\end_inset
Dense subset
\begin_inset Quotes erd
\end_inset
and
\begin_inset Quotes eld
\end_inset
separability
\begin_inset Quotes erd
\end_inset
is striking.
Well, when I was young, I also didn't think much about addition.
Because, you know, addition is obvious.
Except it's not obvious.
I'm trapped in my own head.
\end_layout
\begin_layout Standard
If I take a nap, streams of unconnected thoughts pass through me head.
Discontinuous, one might say.
But they are all my thoughts, in my head, so there is some connection between
them, namely, me, my experience.
Discontinuity is for those who cannot perceive the continuity.
The word salad generated by a mental patient (or our president) is word
salad that is only meaningless when the listener cannot perceive the communicat
ive content within it.
Within the head of the president, there are a bundle of connected thoughts
involving tariffs, and those thoughts are driven by the neural processes
in his brain.
They are continuous, one could say.
The communicative content is primarily emotional and psychological.
It's clear that he is generally clueless on basic concepts, like what tariffs
are, when economists use that word.
So he may have been trying to communicate something, but, it comes out
as nonsense, if you have even some basic understanding of how money and
economies work.
So, in that sense, the president is crazy or delusional.
Or senile, or had some stroke when he was 20 and still hasn't fully recovered.
Something wrong in his head.
But he is trying to communicate that something seems unfair to him, and
his style of communication resonates with the voters.
So there is some sort of communicative content in there.
I don't know how to compute, for example, the Shannon entropy of it.
Why? Because words have meaning, and I don't know how to encode the meaning
of words into some measure of communicative entropy.
Second, the meaning he has assigned to words like
\begin_inset Quotes eld
\end_inset
tariffs
\begin_inset Quotes erd
\end_inset
is so non–standard, so divergent from rational discourse, that it is effectivel
y poetic.
He communicates in word salads, and the formal syntactic structure of those
salads is barely present, and the conventional semantic content is almost
entirely absent.
He is shadow–boxing with meaning, and his true believers claim to see coherence
in those discoordinated punches in the dark.
\end_layout
\begin_layout Standard
And what am I doing here? I too, am practicing a certain kind of intellectual
salad, throwing out ideas, to see what sticks to the wall, and what doesn't.
Its not particularly meaningful or logical.
But then, I am in creative mode, not engineering mode.
In creative mode, it is acceptable, and more strongly, expected that some
random disconnected hash is being created, and all the better if some perceived
pattern can be discerned within.
When John Chamberlain crushed cars, we were able to juxtapose the static
heft and weight of the sculpture to the flying weightless motion of working
automobiles.
Who knows what message he intended to communicate, but art–gallery goers
were certainly able to infuse their own sensibilities onto what their eyes
showed them.
\end_layout
\begin_layout Standard
So now I am reviewing his work via duckduckgo images.
And I am reminded that almost all visual artists seem to be hacking the
space of fractal scaling properties.
Almost all painting consists of whorls within whorls, distribute with just
the right balance, just the right scale.
Often in a uniform fashion, like some Indian filigree, paisley patterns.
Like Takashi Murakami.
I dunno.
Artists have a thing.
A style.
A theme they try to explore.
There's a regularity.
That regularity is hacking something in the human visual cortex, but it
does so that it also tickles higher layers of abstraction.
As our eyes scan a painting, we recognize elements of the composition,
and find surprise: oh, look, I recognize this and that, and this tickles
abstract conceptions.
There are any number of 16th century paintings depicting stigmata, I dunno,
St.
Francis of Assisi being the common one.
And what tickles is not just color and pattern, but the resonance of the
symbolism of stigmata, and all that it entails.
And I know of know way to compute the Shannon entropy of all that.
Or how to frame it in terms of separable spaces, or anything like that.
There's no model–theoretic term algebra to describe the communicative force
of painting, of artwork.
\end_layout
\begin_layout Standard
And get this: of course, I hate Trump, he's destroying America, he's a criminal,
a traitor, deserves to hang, deserves to be used as a human pinata.
And he's no artist.
But he has tapped into a particular vibe that resonates throughout many
Americans.
And so what are vibes, really? Assemblages of perceived meaning.
The words of the Pope are structured and meaningful, and a lifetime of
careful sculpting is required before a Pope is elected.
But what is being sculpted? Vibes.
Feelings.
Emotional reverberations.
Yes, of course, based on the vast volume of Catholic theology, Catholic
dogma.
There's a bazillion pages of the stuff; no cardinal has ever read any but
a tiny fraction of it, its impossible to devote a thousand lifetimes to
its study, expect by means of a thousand distinct humans.
But shaped within that dogmatic text are the outlines of some higher supreme
purpose that is supposed to mean something, with that meaning having been
refined and revised in two thousand years.
And that is why, perhaps, religious appeal is waning: those old shapes
do not capture the modern zeitgeist.
But Trump does capture it.
A baby, a toddler, a brat.
A conman.
Soulless, an ugly personality, corrupt, evil, the face of evil, but this
corruption and evil resonates with the MAGA voters.
The collection of world–views inside the minds of the MAGA voters resonate
with abundant evil.
How did this come to be? How did a modern liberal capitalist society, dedicated
to freedom of expression, foster the accumulation of evil and hatred and
all that is bad? And I see this not just in MAGA, but also, in BlueSky,
with all the Marxists that Will Stancil attracts like a moth to flames.
The Marxists are equally ugly, intolerant, nasty brutes, filled with both
hatred, and bereft of understanding.
Yet, as adult human beings they can function within society, not just feed
themselves, pay the rent on time, but hold down jobs and maintain friendships.
So, the brain functions and adapts to its surroundings.
The issue is that the surroundings enable the construction of Towers of
Babel of incoherent thoughts.
At some deep, base vibe layer, there is some sense, some sensation of how
things should connect, of how things
\begin_inset Quotes eld
\end_inset
should be
\begin_inset Quotes erd
\end_inset
.
Trump seems to think that tariffs should work in some way; they don't.
The Marxists believe that material dialectic should work some way; it doesn't.
The flat earth people believe that ..
the Atlantis people believe that ...
pyramid power.
UFO's.
Space aliens.
the Healing Power of Crystals.
The anti–vaxxers.
Its a collective insanity; Trump and the marxists are but two faces of
many.
What do we have here? The brain as a sponge for abstract structures and
symbols.
Accreting environmental signals.
Rearranging them, accepting them.
This is kind of exactly what I do here: my personal accretion of randomized
influences, from childhood onwards.
Whatever I read this morning on bluesky.
Whatever math text I read the day before.
Whatever Art education I received in high school.
Morgan Park Academy.
Mrs.
Stelton.
I am a random assemblage of factoids accreted through life.
And yet ..
I have accepted some, and rejected others.
And all humans do this: accept some reject others.
\end_layout
\begin_layout Standard
And yet, modern industrial society, economy, has allowed the flourishing
of ideas toxic to it.
So again, at this crux of free will and agency: I have the free will to
make decisions, to choose, to act.
And yet also, I am shaped, utterly totally andfully by my immediate surrounding
s.
Out of my free will, I choose ti write here, instead of choosing to read
that text on infinite–dimensional analysis.
Which I really should get back to reading.
Why? Because I am not making forward progress n the analysis for socio–psycholo
gical structure.
\end_layout
\begin_layout Standard
Oh, and that is another part of vibes.
Great authors, great artists, great scientists are acclaimed.
And many works of art really are astounding.
Does this imply that merit and achievement are rewarded? Only rarely, as
if by lottery.
For every lottery winner, there seems to be ten more that are equally deserving.
But I have no matric, no measure for the deserivingness of acheivement.
Never mind old sawas about standing on the shoulders of giants, and all
that.
Society functions like an anthill: be the right ant at the right place
at the right time, you make history, you are acclaimed.
But you are still an ant.
\end_layout
\begin_layout Standard
But what is acclaim, achievement, recognition? Well, a large part of it
is vibes: the Kardashians.
Famous for being famous.
But in other cases, Michaelangelo, Einstein, Thomas Acquinas, the acclaim
is deserved.
But why? What is achievement, that it is worthy of recognition? I recognize
that my own fumbling here, in this text, is not worthy.
That is why I am so angstsy about it.
My writing is barely worth my time.
Its crap.
Why is it crap? Because like any load of laundry tumbling round, it is
not all that different from any other load of laundry tumbling round.
No two snowflakes might be alike, but they are all, in the end snowflakes.
I almost wrote sand–grains.
No two sandgrains are alike, but damn, no they really are almost all identical.
Snowflakes clearly show much greater diversity.
But being far from the norm, is that worth acclaim? Sometimes, it seems
to be.
Serial killers are fairly far from the norm, and they do get infamous for
the chills they send down your spine as you read some #1 best–seller about
their horrible deeds.
Or watch Dexter on TV.
So divergence from the norm is necessary for acclaim, but not sufficient.
\end_layout
\begin_layout Standard
And here, I feel like I fall back into old ways.
During zooms of the Mandelbrot set, one is at first awed by the seemingly
vast variety of different shapes within it.
But then, after a while, it calms down: you start to see the same patterns,
over and over.
Repeated.
Mutated into different shapes, pleasing to the eye.
But finite, in a certain sense, in the variety that they offer.
No two swirls are alike, and yet the archetypes are quite limited in number.
So there is uniformity in that variety.
How do we express this uniformity of variety? Well, there are ideas of
self–similarity.
For every bit–string, we can insert from a dictionary of substrings: dictionary
replacements.
Mapped indirectly but ultimately to the period–doubling of the
\begin_inset Formula $z\to z^{2}+c$
\end_inset
process.
The mapping is difficult: closed–form expressions and mathematical theorems
for the Mandelbrot set are hard to come by.
But if one is able to make a particularly profound and deep connection,
is that worthy of acclaim? Well, in the 19th and 20th centuries, it was.
And insofar that some part of Western culture, that has not yet been destroyed
by social media, it remains true today.
\end_layout
\begin_layout Standard
But what of the social destruction wrought by anti–vaxxers? They are more
powerful than the flat–earthers.
Their belief systems are distinctly harmful: kids actually die of measles
and mumps.
Will society collapse? Birthrates are down, even in Europe.
In Norway.
Something about Western culture dissuades women from having children.
Of course, this can be studied in some narrow academic sense.
Birth rate in Ethiopia remains high.
It's high in most African countries, and in the Islamic countries as well.
South America, no longer.
My goal here is not to do an academic analysis on the straight and narrow.
Nor is it to express anxiety.
I want to boil the ocean.
But writing about the full panalopy of all things, all thoughts, behaviors
and actions that humans have engaged in, I am hoping for lightning to strike
in a flash of inspiration.
Of course, it wont.
I won't win the lottery ticket.
And Carlo Rubio is right, I should shut up and calculate.
But Western Society encourages me, people like me, to go for the brass
ring, to win the prize, to gather acclaim, fame, fortune, by doing something
truly awesome.
And one way of doing something truly awesome is to make bets, play the
lottery.
In the sciences, it's to take a certain line of research, and push, push
push, to where no one has gone before.
And again, not just find new territory: you can find new stuff in the soil
of your back yard, everyone has that.
I discovered brand new stuff, stuff that no one knew about before, in the
beta map.
And some of it is really quite cool, such as the pruning algorithms of
the binary tree.
And so what? This is so narrow, so focused, that no one cares.
It doesn't matter.
\end_layout
\begin_layout Standard
So where was I? I was trying to make an analogy between searching for deep
connections between things, and societal acclaim.
Of course, we are now on the verge of creating machines that can do this.
We've automated chess–playing.
We will soon automate reasoning and inference, and we will most likely
do this without creating consciousness.
Maybe.
Hard to tell.
If you build a machine and ask it to perform reasoning in some narrow domain,
it is very unlikely that it will accidentally become self–aware.
\end_layout
\begin_layout Standard
Makes me think of Grok.
Makes me think of Elon Musk.
That man will have the blood of millions on his hands.
Makes me think of Stanislaw Lem's Memoirs Found in a Bathtub.
Makes me feel like I am the one writing them.
You are the one reading them.
I'm now embedded in a piece of historical amber.
A cry, a shriek, recorded in time.
Incoherent, rambling.
A jumble, a wreck of ideas.
A stochastic mashup of finite size: there are only so many words I can
type, and any one of these may be my last.
Memoirs Found in a Bathtub reeks of Soviet decay.
I reek of American decay.
The America I grew up in has died.
I did not see it coming.
I am dismayed, disheartened.
I would like to see some bright side, but it is hard to imagine what that
might be.
I would like to, ahem :make things better
\begin_inset Quotes erd
\end_inset
, whatever the fuck those words mean.
In some sense, this is impossible.
In some other sense, I do have some incrementally tiny effect on the universe,
and I can leverage that as best I can.
Which is ...
not very well, Because, see, power dynamics being what they are, powerful
people do powerful things, and I am not powerful.
Well, I can write Wikipedia articles just fine, but that is not measurable
in the terms of power–as–economic–policy or foreign affairs or something
like that.
So I have no power there.
Nor do I have respect: nothing I have done in my life has garnered respect,
except from some tiny handful of people.
And that irks me, but of course, given that I respect almost no one, I
suppose this is a mirroring policy.
I can dish it out but I can't take it.
I sometimes ponder the sort of people that have a burning desire to be
famous.
I mean, I too have a burning desire to be famous, but it was never of the
sort that would have gotten me on stage, in front of a bunch of people.
Whatever fame it is that I yearn for, it seems to always have been posthumous
in nature.
Post–turning–into–dirt.
Why would I want posthumous fame? Well, because, I dunno.
Einstein and Michaelangelo are dead, and its not turned out badly for them.
Hitler is dead, it did turn out badly for him.
Trump will be dead one day soon, and he will be remembered as a great failure,
booed from here to eternity.
God help me, I hope Must dies, and soon.
He's evil.
History will not treat him well.
But then, what is history? It too seems to be malleable: an accretion of
remembered factoids, memoirs in a bathtub, selectively remembered, selectively
recorded, subject to destruction and decay in avalanches of decay, erasure
and forgetting.
Thermalization.
The eddies within eddies of turbulence were once there, in the past.
But they were not recorded, and what we have now is the thermalized leftovers.
From velocity to viscosity.
The thermalization of turbulence happens not just to literal turbulence,
but it also happens to history.
Whatever happened to Sargon and Gilgamesh, we don't know.
It's thermalized.
\end_layout
\begin_layout Standard
So my musing about the here and now: well, of course, the past is the past
and is unchangeable.
But to that I have to add that the knowledge of the past lives in the present.
The past is static: there's no record of it, except in the present.
That is, not only can we not modify the past, we also can't go back there
and examine it a second time.
It is both frozen, and also invisible, and we know of it only through informati
on recorded in the here and now.
\end_layout
\begin_layout Standard
Does it exist? That is, does the past exist? I don't remember if I wrote
about this yet, or not; so I will write again and maybe repeat myself.
The idea starts with the Levin Ingressing Minds framework.
Now, I don't recall if Levin says this, or if I cam up with this on my
own, but perhaps the freezing of the past, it's unchangablity and it's
inaccessibility is that the past is freezing into a
\begin_inset Quotes eld
\end_inset
platonic
\begin_inset Quotes erd
\end_inset
past, in the sense that 1+2=2 exists in platonic reality, but not in the
present.
There is a difference, though.
We can deduce that 1+1=2 by
\begin_inset Quotes eld
\end_inset
thinking about it
\begin_inset Quotes erd
\end_inset
.
We mostly cannot deduce the past by
\begin_inset Quotes eld
\end_inset
thinking about it
\begin_inset Quotes erd
\end_inset
except what can be deduced via the methods of physics.
That is, we can deduce cosmology from astronomical observations coupled
to quantum theory, etc.
So observationally, we can deduce the past by cause and effect.
Well, more mundane than that: if you see a broken glass and spilled milk,
you can deduce/infer that the glass was once unbroken, even though you
were not there to witness the fall.
This is the basic evidentiary nature of the here–and–now.
So then, to what degree is the induction of evidence from there here–and–now
equivalent to the induction of mathematical truths by
\begin_inset Quotes eld
\end_inset
just thinking about it
\begin_inset Quotes erd
\end_inset
? Is there a difference? Well, of course, there's a difference.
I think of course.
Of course, I cannot deduce the spilt milk without seeing it, or without
having a friend tell me about it.
Perhaps I can deduce the statistical probability that, yes, things fall
and break.
Can I deduce 1+1=2 without evidence? Well, tough.
For starters, I have two fingers.
At lest two.
So did my forbears a million years ago, but I suspect they were not all
that interested in math, and it is quite possible that they would not have
been able to deduce this.
You might have had to go back in time and explain it, and most likely,
they would not have had a clue of what your talking about, because of cultural
norms.
The ability to do math is normative, and its present day popularity is
entirely due to culture.That is, Romans were ...
well bad at it, and not all that interested in it.
For cultural reasons.
Sapir–Whorf hypothesis, modernized: culture limits thought.
There are always a few brilliant thinkers; we're talking ab out the quotidian,
the normies, the mainstream, the proletariat.
\end_layout
\begin_layout Standard
So is the freezing of the past, together with it's inaccessibility, is this
because the past has frozen into
\begin_inset Quotes eld
\end_inset
platonic reality
\begin_inset Quotes erd
\end_inset
? I like the word
\begin_inset Quotes eld
\end_inset
inaccessible
\begin_inset Quotes erd
\end_inset
, it poetically invokes inaccessible cardinals.
Is
\begin_inset Quotes eld
\end_inset
reality as we know it
\begin_inset Quotes erd
\end_inset
some kind of, err, structure,
\begin_inset Quotes eld
\end_inset
inside of some cardinal
\begin_inset Quotes erd
\end_inset
, (whatever that means)? We've got lots of ways of writing structures.
Hmm.
Do we need anything bigger than finite? The number of baryons in the universe
is finite.
We know how many.
\begin_inset Formula $10^{80}$
\end_inset
.
We idealize both QFT and GR as happening on manifolds built on real numbers
with the cardinality of the continuum, and that works great, algebraically.
But we know things have to get different at the Plank scale; we don't know
how.
Is there reason to believe that Planck–scale stuff will also require the
cardinality of the continuum? Or will it be finite? Is the freezing of
the present into the past, is this some I dunno homeomorphic blah blah
on a filtration of measures, but for some very large–but–finite number?
Like I dunno,
\begin_inset Formula $2^{10^{80}}$
\end_inset
or whatever? We're doing filtrations for the Wiener process as
\begin_inset Formula $\mathcal{F}_{t}$
\end_inset
for
\begin_inset Formula $t\in\mathbb{R}$
\end_inset
or if you like
\begin_inset Formula $\otimes_{t\in\mathbb{R}}\mathcal{F}_{t}$
\end_inset
and then have to talk about separability and Banach spaces to make the
algebra work out right, but we also know that this is an abstract model,
and nothing in the here–and–now
\begin_inset Quotes eld
\end_inset
actually
\begin_inset Quotes erd
\end_inset
moves like the Wiener process.
By which I mean, neither atoms, nor stock prices move that way.
What does happen is that the algebraic equations, inferred from
\begin_inset Quotes eld
\end_inset
pure thought
\begin_inset Quotes erd
\end_inset
, motivated by observations of Brownian motion, has lead us to introduce
certain algebraic descriptions into the noosphere: its math that has
\begin_inset Quotes eld
\end_inset
ingressed
\begin_inset Quotes erd
\end_inset
.
But the
\begin_inset Quotes eld
\end_inset
noosphere
\begin_inset Quotes erd
\end_inset
is again, a kind of imaginary
\begin_inset Quotes eld
\end_inset
place
\begin_inset Quotes erd
\end_inset
that Eric Raymond talked about, and that imaginary place is within our
brains, fragments of which are caught in communicative expressions of the
written word.
Arrangements and rearrangements of electrons in my computer, and in the
github computers that will eventually store this text.
Text that is accessible only because it was encoded with error–correcting
codes, unlike what Gilgamesh was capable of doing.
Text that could be lost if, for example, my disk drives suffered a catastrophic
collapse, and also the github repo mirroring my work was catastrophically
destroyed, and no one else had a copy: information can still be irretrievably
be lost, be irretrievably consigned to the past, where it is inaccessible.
I do recall reading speculations along line such as, for example, the sound
of my fingers typing at the keyboard might be recorded in microscopic disruptio
ns of ..
I dunno paint in the walls, and what I typed here could be reconstructed
that way.
I mean, I doubt it, but it's not literally impossible, I guess.
But by that reasoning, we could also reconstruct Gilgamesh and all of Mesopotam
ian life by studying grains of sand, and again, that is ...
more implausible than, I dunno, space aliens.
So anyway, at the practical level, we may as well take forgetting and erasure
to be permanent.
That, and as has been noted, the algebra of extremely large finite numbers
resembles the algebra for the large cardinals, so it might not matter if
the past is frozen into a large finite quantum–GR plank–scale network,
or if its frozen into some large cardinal.
Its inaccessible, either way, and whichever theory is easier to work with
should be enough.
We work with the continuum, and real numbers, because working with them
is actually easier, than pretending everything is finite.
The judicious employment of infinities makes math easier than
\begin_inset Quotes eld
\end_inset
it otherwise could be
\begin_inset Quotes erd
\end_inset
.
No one wants to use Newton finite differences unless, well, they actually
want to use Newton finite differences.
If you get what I mean.
Where was I? The point was that perhaps the past
\begin_inset Quotes eld
\end_inset
converts
\begin_inset Quotes erd
\end_inset
into
\begin_inset Quotes eld
\end_inset
platonic reality
\begin_inset Quotes erd
\end_inset
, and is accessible only to the extent that we know how to access
\begin_inset Quotes eld
\end_inset
platonic reality
\begin_inset Quotes erd
\end_inset
by current means.
\end_layout
\begin_layout Standard
So to wrap it up.
I plan to re–recall the quantum–immortality/quantum–suicide argument, just
for kicks.
I've determined the obvious: the past is inaccessible; only the present
memory of the pas is accessible, and the present memory is subject to distortio
n and loss.
From postings from months and years earlier, the boundary between past
and present is there, where a two state–vector formalism finally resolves
all inconsistencies and
\begin_inset Quotes eld
\end_inset
settles things for good
\begin_inset Quotes erd
\end_inset
: that's where the present ends, and the past starts.
Entirely absent and unexplored is where the boundary between the present
and the future lies, or whether there even is a clear boundary.
I mean, the boundary between present and past seems clear and hard as a
rock.
The boundary between present and future feels diaphanous.
The language of measure–theoretic filtrations seems to offer some kind
of insight that would otherwise be absent, but I cannot yet convert this
into something more concrete.
\end_layout
\begin_layout Standard
I mean, I would need to take the following steps: (1) convert the definition
of abstract Wiener space from something real–valued, to something complex–value
d (2) Replace the nowhere–differentiable aspect of it with twice–differentiable
or at least pseudo–differentiable Sobolev space (3) stitch these together
into some Cartesian space, or some Cartesian product of field–theoretic
spaces, or some fiber–bundle product with appropriate soldering or whatever.
(4) introduce a U(1) electromagnetic interaction, with Lorenz invariance,
and with approximately on–shell photons connecting distant parts of a Minkowski
manifold.
(5) discuss wave–function collapse in this scenario, such that it avoids
many–worlds.
I guess I can do one and two in the background, at leisure.
I can daydream that three and four are doable, and that a competent physicist
can stitch together the argument.
I don't yet have a handle on the conceptual leap needed for step five,
but maybe solving step one, and then imagining how steps two through four
work will allow insight into step five?
\end_layout
\begin_layout Standard
The Lorenz invariance of the here–and–now remains ..
interesting.
Here and now seems to be thermodynamic.
I did write about this at length a few weeks ago.
So maybe step (3a) is to convert the action–Lagrangian formalism to a Hamiltoni
an formalism, so that time can be a coordinate of the measure–theoretic
filtration of the
\begin_inset Quotes eld
\end_inset
here and now
\begin_inset Quotes erd
\end_inset
part of the
\begin_inset Formula $Z=\int\exp-iS$
\end_inset
functional integral.
I don't know how to do that, but I believe that there has been lots and
lots of work on this, that I've simply not encountered before.
Hmm.
None of this gives access to the future, though, and none of this hints
where free will is hidden.
\end_layout
\begin_layout Standard
I did write about this before: my conception of free will is that it lives
at branch points.
That the universe is perfectly deterministic on a set of measure one, and
that branch–points are a set of measure zero that is dense in the deterministic
world.
And, as per Weierstrass type ideas, the fate of the universe is determined
by the decisions made on this dense subset of branch–points.
That is, the Hugh Everett thing was claiming that these branch points lead
to many worlds, and i'm trying to collapse those back down to just one.
I have two technical problems: first, I cannot yet provide an explicit
example of such a branch point.
Well, I can its
\begin_inset Quotes eld
\end_inset
wave function collapse
\begin_inset Quotes erd
\end_inset
, but that fails to be specific enough, and it also does not indicate how
agentic sensorimotor systems can
\begin_inset Quotes eld
\end_inset
force
\begin_inset Quotes erd
\end_inset
a collapse, thus exercising free will at that branch point.
These are fairly serious technical problems; without solving them, all
I have is hot air and hand–waving.
I feel like an Ancient Greek Philosopher, proposing the existence of Atoms,
with absolutely no evidence except for sophistry.
Fuck me.
I'm done for the night.
\end_layout
\begin_layout Subsection*
19 May 2025 – After midnight
\end_layout
\begin_layout Standard
Reading Wikipedia, Quantum Suicide.
Vaguely annoying.
You cannot actually put macroscopic systems into superposition, so I dunno.
The arguments there do not seem to be of any higher or more refined quality
than what I blurble on about.
So fuck it.
\end_layout
\begin_layout Standard
However, the article https://en.wikipedia.org/wiki/Ghirardi%E2%80%93Rimini%E2%80%9
3Weber_theory is much better.
The only weird thing about it is that as far as I'm concerned, collapse
only happens in thermodynamic interactions, and not in vacuum.
But that is ignored.
It gives two parameters: collapse rate, and localization distance.
As I've argued, but of these are necessarily multi–scale, happening at
sub–attosecond scales for liquids at room temperature, and multi–second
scales for experiments in a vacuum, and billion–year scales for starlight
photons hitting retinas.
All these scales are cranking at once, depending on the particulars.
The localization is also instrument–dependent.
Oh, I was skimming too fast.
I now see the section
\begin_inset Quotes eld
\end_inset
amplification mechanism
\begin_inset Quotes erd
\end_inset
.
Still, its bedtime so toodle–oo.
\end_layout
\begin_layout Subsection*
19 May 2025 – Morning
\end_layout
\begin_layout Standard
So I realized half of what I wrote about TIQM and interferometric diamonds
and TSVF over the last few years is just wrong.
And also the Lorentz invariance problem profound, and that wave–function
collapse has to somehow power synchronization.
To wit:
\end_layout
\begin_layout Standard
Here–and–now on the Moon is the same as on Earth.
Another superficially silly statement, right? Duhh.
But on the other hand, clocks run at different speeds, due to them being
in different GR wells.
We communicated with the astronauts on the moon
\begin_inset Quotes eld
\end_inset
in the present time
\begin_inset Quotes erd
\end_inset
,
\begin_inset Quotes eld
\end_inset
right now
\begin_inset Quotes erd
\end_inset
.
It took a radio signal 1.3 seconds to get to the moon, but when it got there,
it was
\begin_inset Quotes eld
\end_inset
right now
\begin_inset Quotes erd
\end_inset
for the radio receiver, it was
\begin_inset Quotes eld
\end_inset
right now
\begin_inset Quotes erd
\end_inset
for the astronaut.
They were ready and present at the precise moment that the signal arrived.
That is,
\begin_inset Quotes eld
\end_inset
here and now
\begin_inset Quotes erd
\end_inset
arrives
\begin_inset Quotes eld
\end_inset
instantaneously
\begin_inset Quotes erd
\end_inset
: both ends of the photon, the transmitter, and the receiver, are exactly
in the same here–and–now.
Again, this is weirdly trivial: the geodesic distance covered by an on–shell
photon is exactly zero, as it should be, per GR.
So what's the big deal? I'm beating on this drum to emphasize that here–and–now
is NOT some space–like surface drawn through space–time.
It resembles one, because the interior of light–cones necessarily orders
events into a strict future and past.
Causality inside the light cone forces ordering on time.
GR by itself, however, does not and cannot select a preferred space–like
surface on which here–and–now happens.
Rather, the null geodesics provide the required stitching together.
\end_layout
\begin_layout Standard
Perhaps the issue, the point of confusion is that the assignment of coordinates
\begin_inset Formula $\left(t,x\right)$
\end_inset
to points on the spacetime manifold is a hang–over of Newtonian geometry.
It causes everyone to think of space–time as a four–dimensional Cartesian
space, and its not.
The metric explicitly tells you that there are all of these points that
are at exactly distance zero away.
And human minds ..
well, my mind, struggles with that.
The freakin Penrose cone is always drawn a freakin cone.
Somehow, no one ever says something along the lines of: see, all these
points located at distance zero away are in face the same point! There
is a modulo operation, here!
\end_layout
\begin_layout Standard
I mean, lets go back to the Hausdorff axiom T2 topology, and the topology
induced by metrics.
I have a point A, labelled
\begin_inset Quotes eld
\end_inset
radio transmitter
\begin_inset Quotes erd
\end_inset
, and another point B, called
\begin_inset Quotes eld
\end_inset
radio receiver
\begin_inset Quotes erd
\end_inset
, and the distance between them is exactly zero.
Ergo, they are the same point.
Right? Well, obviously not: one is on the Moon (or on Mars) and the other
is on Earth.
In the lab frame, space is locally
\begin_inset Formula $\mathbb{R}^{3}$
\end_inset
and has the conventional Hausdorff topology induced by the Cartesian metric
in 3-space.
However, I do not understand the topology induced by the Minkowski metric.
I have never–ever seen a text that describes this topology.
What do the search engines say? Lets find out.
\end_layout
\begin_layout Standard
But first, to document the rest of the thoughts: my earlier blather about
backwards–time propagating wave functions used to resolve inconsistencies
to obtain some transactional interpretation of quantum collapse: this is
wrong, or mostly wrong, or grossly misleading.
The point of entanglement is that collapse happens
\begin_inset Quotes eld
\end_inset
everywhere at once
\begin_inset Quotes erd
\end_inset
.
So consider the measurement of a pair of spin-1/2 particles combined into
a spin singlet.
The measurement is non–local, so that the wave function of both particles,
A and B, collapse at the
\begin_inset Quotes eld
\end_inset
same time
\begin_inset Quotes erd
\end_inset
.
Or rather, they collapse at the
\begin_inset Quotes eld
\end_inset
same here–and–now
\begin_inset Quotes erd
\end_inset
.
This is again counter–intuitive: we imagine a Stern–Gerlach setup.
The non–uniform magnetic field causes the spin–up and spin–down components
of the wave function to spatially separate.
They are, however, still in superposition; no collapse has occurred yet.
The collapse does occur when the wave–function interacts with the particle
detector, and this interaction is necessarily a many–body interaction,
a thermalization.
And this interaction occurs at the same here–and–now for both A and B.
Not the
\begin_inset Quotes eld
\end_inset
same time
\begin_inset Quotes erd
\end_inset
, because A and B might be space–like separated by the time the measurements
are performed, and there is no preferred space–like surface with which
we can say
\begin_inset Quotes eld
\end_inset
same time
\begin_inset Quotes erd
\end_inset
.
So collapse need not, does not happen
\begin_inset Quotes eld
\end_inset
at the same time
\begin_inset Quotes erd
\end_inset
, but it does happen at the same here–and–now.
Even more strongly: here–and–now is one point, the same point.
Both entangled spinors are located at the same here–and–now point.
So,
\begin_inset Quotes eld
\end_inset
of course
\begin_inset Quotes erd
\end_inset
, any interaction that one undergoes is matched by interactions the other
undergoes.
Again, the is
\begin_inset Quotes eld
\end_inset
trivial
\begin_inset Quotes erd
\end_inset
, and conventionally expressed in bra–ket notation: we write
\begin_inset Formula $\left|\psi\right\rangle $
\end_inset
when we talk about a wave function, and it is
\begin_inset Quotes eld
\end_inset
everywhere
\begin_inset Quotes erd
\end_inset
\begin_inset Quotes eld
\end_inset
all at once
\begin_inset Quotes erd
\end_inset
\begin_inset Quotes eld
\end_inset
at the same time
\begin_inset Quotes erd
\end_inset
, and if it need to be localized, then the notation
\begin_inset Formula $\left\langle x\right.\left|\psi\right\rangle $
\end_inset
or
\begin_inset Formula $\left\langle x,t\right.\left|\psi\right\rangle $
\end_inset
is used.
So the standard QM notation already acknowledges, implicitly, that the
wave function is
\begin_inset Quotes eld
\end_inset
everywhere all at once
\begin_inset Quotes erd
\end_inset
.
I'm not introducing anything new here.
I am only re–arranging emphasis on the topology.
\end_layout
\begin_layout Standard
OK, back to the Hausdorff topology, or lack of it, or whatever, for Minkowski
space.
Oh wait.
The other thing is that the state
\begin_inset Formula $\left|\psi\right\rangle $
\end_inset
represents a pure state in Hilbert space: it is a single point.
So the collapse is taking place at a single point, and that point is located
at here–and–now.
This is the case for when
\begin_inset Formula $\left|\psi\right\rangle $
\end_inset
represents a massive particle, and not just a photon.
That is to say, here–and–now–ness is not just a quotient topology induces
by the Minkowski metric; rather, its a topology induced on the mapping
from spacetime to Hilbert space.
That is, we get the quotient topology for Minkowski space because the metric
is induced by the wave equation for U(1) on–shell photons.
Oh! Now I am making progress! So, the Minkowski metric is NOT some
\begin_inset Quotes eld
\end_inset
natural structure
\begin_inset Quotes erd
\end_inset
of space–time.
Instead, the Minkowski metric is an artifact induced by the physical process
of photon wave–functions collapsing! It is the collapse of the wave–function
that happens at one point, at here–and–now, and when the wave–function
is described by the massless wave equation, only then does Minkowski space
get induced as a quotient of
\begin_inset Formula $\mathbb{R}^{4}$
\end_inset
modulo a null geodesic.
\end_layout
\begin_layout Standard
This does feel a bit circular, and I should address that.
Two write down the wave equation, I have to write the D'Alambertian
\begin_inset Formula $\square$
\end_inset
and to write that, I have to use the Minkowski metric.
And yet, I wanted to derive the Minkowski metric, not assume it.
I think this is OK, because I think I can use conventional concepts of
atlases of maps to define the diff geom needed to write down
\begin_inset Formula $\square$
\end_inset
and that this can be done without breathing a sigh of Hausdorff topology
(or Lindelöf space, or whatever.) Yes, under the surface, the use of the
word
\begin_inset Quotes eld
\end_inset
continuous
\begin_inset Quotes erd
\end_inset
and
\begin_inset Quotes eld
\end_inset
differentiable
\begin_inset Quotes erd
\end_inset
implicitly require the assumption of normal spaces or Polish spaces or
Hausdorff spaces, so those topics are there, under the covers.
But we don't have any paradoxes that float to the surface.
Everything goes through, without contradictions.
The paradoxes arise entirely from wave–function collapse, which is a topic
entirely orthogonal to the diff geom os pseudo–Riemannian spaces.
So I think that is how the seemingly circular logic is broken.
That is, there are
\emph on
two
\emph default
spaces: the Minkowski space on which
\begin_inset Formula $\square$
\end_inset
is defined, and the space of functions from Minkowski space to Hilbert
space, which is where here–and–now is defined.
And that photon interactions induce a Minkowski metric onto this Hilbert
space.
And that wave–function collapse for massive particles induces ...
I dunno, something something on this space.
And the space that we perceive, as living things, is NOT Minkwoski space,
but instead the space of functions from Minkowski space to Hilbert space.
I mean, yeah, duh, this is kind of the whole point, the
\begin_inset Quotes eld
\end_inset
obvious thing
\begin_inset Quotes erd
\end_inset
that QM is saying.
That yeah, duh, reality is defined by QM.
But somehow, at least for me, it never sunk in, it never hit, the way it's
hitting now.
I am, I think we all are so used to Cartesian, Newtonian reality that we
can comprehend QM just fine as undergrads, without ever once fully taking
to heart the nature of the actual space in which the actual wave functions
live.
Which is what I've done.
So I am now undergoing a yeah–duhh moment, almost fifty years after I learned
QM.
(I learned it my junior year in College, and even better my senior year.
That was 1979 and 1980 and I would have been 19 and 20 years old, so about
45 years ago.) So for forty–five years, I failed to, uhh, grasp something,
uhh, basic.
Simple and basic.
How embarrassing.
Fuck me.
Lets make up for lost time, shall we?
\end_layout
\begin_layout Standard
Well, entering the search phrase
\begin_inset Quotes eld
\end_inset
open topological cover of Minkowski psace
\begin_inset Quotes erd
\end_inset
(with the typo in the last word) promptly brings up a stack of recent ArXiv
papers.
Some titles:
\begin_inset Quotes eld
\end_inset
On the Causaland Topological Structure of the ...
\begin_inset Quotes erd
\end_inset
and
\begin_inset Quotes eld
\end_inset
Topology of Minkowski Space - Physics Stack Exc..
\begin_inset Quotes erd
\end_inset
and
\begin_inset Quotes eld
\end_inset
Order topology in minkowski space and applicatio...
\begin_inset Quotes erd
\end_inset
and ...
well, more.
So a place to start is to read at least the first few.
\end_layout
\begin_layout Standard
But i have to take a break, because I've got other things I have to get
done.
\end_layout
\begin_layout Standard
Hang on, just a few more minutes.
I am confused by two things.
First, what is the open cover, the metric topology induced by the Minowski
metric? It sure doesn't feel Hausdorff to me, but maybe I'm crazy.
That's the first topic that needs clarification.
The second topic is about the sigma algebra on the space of functions from
Minkowski space to Hilbert space.
So, write
\begin_inset Formula $M$
\end_inset
for Minkowski space, write
\begin_inset Formula $\Psi$
\end_inset
for Hilbert space.
I'm concerned about the sigma algebra on the space of functions
\begin_inset Formula $\psi:M\to\Psi$
\end_inset
.
What is
\begin_inset Formula $\Psi$
\end_inset
? So here is the sleight–of–hand.
For a scalar particle,
\begin_inset Formula $\Psi$
\end_inset
is one–dimensional! Consider textbook harmonic oscillator (in one dimension).
The structure of
\begin_inset Formula $\Psi$
\end_inset
is so trivial, it is almost not mentioned.
Because
\begin_inset Formula $\Psi=\mathbb{R}$
\end_inset
and there's kind of not a whole lot else that can be said here and its
obvious and textbooks promptly move on and define a Hilbert space of
\begin_inset Formula $H=\left\{ \psi:\mathbb{R}\to\mathbb{R}\right\} $
\end_inset
and show how this space is spanned by the Hermite polynomials.
So the sleight–of–hand is to immediately jump from
\begin_inset Formula $\Psi$
\end_inset
to
\begin_inset Formula $H$
\end_inset
without remarking very much on this jump.
Its too trivial.
All of the interesting things to be said are the things to say about
\begin_inset Formula $H$
\end_inset
and how its square integrable, and about weak convergence on the weak topology
in the infinite–dimensional product space
\begin_inset Formula $H=\left\{ e_{n}:n\in\mathbb{N}\right\} $
\end_inset
because this is where all the conventional interesting things can be said.
And this is hammered on in such a way that mediocre students, and even
smart students, somehow fail to notice that we are not talking about Euclidean
space, but about something completely different, and then we students try
to map Euclidean notions from common–sense child–hood experience of space
onto this infinite–dimensional Hilbert space, and end up confused by questions
like
\begin_inset Quotes eld
\end_inset
how can it be a particle and a wave at the same time?
\begin_inset Quotes erd
\end_inset
And the dis–service of the textbook, and the lecturer is to somehow not
hammer on the point
\begin_inset Quotes eld
\end_inset
its not Euclidean space, dear students, it's infinite dimensional
\begin_inset Quotes erd
\end_inset
and
\begin_inset Quotes eld
\end_inset
it is a fundamental error to think about 3D space when you should be thinking
of infinite–dimensional space
\begin_inset Quotes erd
\end_inset
.
The point here is that at the same time, there are business–school students
down the hall, studying stochastic processes and Itô calculus and Wiener
space, and those students are NOT asking
\begin_inset Quotes eld
\end_inset
how can it be a single stock price and a random process at the same time?
\begin_inset Quotes erd
\end_inset
because they already know stock prices are not
\begin_inset Quotes eld
\end_inset
particles
\begin_inset Quotes erd
\end_inset
localized in 3D space.
it would be dumb to ask
\begin_inset Quotes eld
\end_inset
where is the stock price right now, in 3D space?
\begin_inset Quotes erd
\end_inset
because the answer is
\begin_inset Quotes eld
\end_inset
nowhere
\begin_inset Quotes erd
\end_inset
or it is perhaps
\begin_inset Quotes eld
\end_inset
on the trading floor of the New York Stock Exchange
\begin_inset Quotes erd
\end_inset
or perhaps
\begin_inset Quotes eld
\end_inset
on the settlement computer in the back room.
\begin_inset Quotes erd
\end_inset
But for quantum, everyone asks
\begin_inset Quotes eld
\end_inset
where is the particle right now?
\begin_inset Quotes erd
\end_inset
as if that is a meaningful question (it's not), and they talk about particle–wa
ve duality like it's a thing, when the obviously analogous situation, of
stock–price vs.
stochastic–process duality is not a thing anyone ever talks about.
Sheesh.
I'm wasting a lot of words and time to write this, but feel compelled to,
because there must be a thousand youtube videos on particle–wave duality
is if it were a thing, when in fact it's kind of the wrong question and
the wrong framework predicated on a confusion between 3D Euclidean space
and the infinite–dimensional Hilbert space.
Fuck me.
I am wasting my time even writing this, but whatever.
Lets get back on track.
\end_layout
\begin_layout Standard
We now have two or three tasks in front of us.
First, explain the topology of
\begin_inset Formula $H=\left\{ \mathbb{R}^{3}\to\mathbb{C}\right\} $
\end_inset
but this is easy because this is conventional Hilbert space.
Next, and I am afraid of giving notation to this, is to add time, and describe
wave–function collapse.
I think this requires using a reproducing kernel Hilbert space, and describing
dynamics in that space.
I will have to ponder this some more, later on.
Not now.
\end_layout
\begin_layout Standard
Next on the list is entanglement.
Here, it is a single spinor, and so
\begin_inset Formula $\Psi$
\end_inset
is two–dimensional: its the vector space having the basis spin–up and spin–down.
And since the topic is entanglement, we really have
\begin_inset Formula $\Psi=\mathbf{C}\otimes\mathbf{C}$
\end_inset
where
\begin_inset Formula $\mathbf{C}$
\end_inset
is the Riemann sphere (complex–projective one–space) which is the Hilbert
space inhabited by spin–one–half spinors.
This space has to local (tangent space) decomposition
\begin_inset Formula $su_{2}\otimes su_{2}=so_{3}\oplus u_{1}$
\end_inset
and this is all trivial textbook stuff, but I repeat it to kind of emphasize
that these are all different, distinct spaces, each having their own geometry
and topology, and that we (meaning I) make grave errors when conflating
these distinct objects.
So don't conflate them! Well, except I already made a grave error: I'm
talking about spinors loosely, when I should distinguish Weyl spinors,
Dirac spinors and the much simpler idea of the Riemann sphere.
These all inter–relate, of course, but premature abuse of the word
\begin_inset Quotes eld
\end_inset
spinor
\begin_inset Quotes erd
\end_inset
gets us into trouble.
\end_layout
\begin_layout Standard
So, lets see ..
where were we? I wish to examine the structure of
\begin_inset Formula $H=\left\{ \mathbb{R}^{3}\to\mathbf{C}\otimes\mathbf{C}\right\} $
\end_inset
except that this is not enough: I want to examine
\begin_inset Formula $H_{t}=\left\{ \mathbb{R}^{3}\to\mathbf{C}\otimes\mathbf{C}\right\} $
\end_inset
as a function of
\begin_inset Quotes eld
\end_inset
time
\begin_inset Quotes erd
\end_inset
\begin_inset Formula $t$
\end_inset
.
So really I want to look at
\begin_inset Formula $\mathcal{H}=\bigotimes_{t\in\mathbb{R}^{+}}H_{t}\simeq\left\{ \mathbb{R}^{+}\times\mathbb{R}^{3}\to\mathbf{C}\otimes\mathbf{C}\right\} $
\end_inset
and I think that is the correct notation but I have to be careful, because
there's a sigma algebra that has to manifest here, and I'm not sure I wrote
that appropriately.
Whatever.
Onwards through the fog, Oat Willie! Next, during the analysis of wave
function collapse in this space, I want to show that this induces a metric,
crudely resembling the Minkowski metric, but instead of it being the speed
of light, it has to be at the group velocity of the wave–packets of the
two entangled spinors propagating in opposite directions.
And calling it an induced metric is kind–of–ish wrong, because the induction
only happens at the here–and–now of the collapse, which is
\begin_inset Quotes eld
\end_inset
everywhere
\begin_inset Quotes erd
\end_inset
, but more specifically, where the wave packets are localized when they
hit the detector.
There are two implications here: all points in a single detector are
\begin_inset Quotes eld
\end_inset
at the same place, right now, here–and–now
\begin_inset Quotes erd
\end_inset
, AND ALSO, the points in detector A are at the same here–and–now location
as the points in detector B.
That is, both detectors are entangled.
That is, I am looking for a modulo relationship, the here–and–now relationship,
write it as
\begin_inset Formula $\sim$
\end_inset
so that the
\begin_inset Quotes eld
\end_inset
actual space
\begin_inset Quotes erd
\end_inset
is the quotient space
\begin_inset Formula $\mathcal{H}/\sim$
\end_inset
.
That is, the
\begin_inset Quotes eld
\end_inset
physical reality
\begin_inset Quotes erd
\end_inset
that we live in is not
\begin_inset Formula $H$
\end_inset
and its not
\begin_inset Formula $\mathcal{H}$
\end_inset
but it is
\begin_inset Formula $\mathcal{H}/\sim$
\end_inset
and the equivalence relation
\begin_inset Formula $\sim$
\end_inset
induces a Minkowski–like metric–like structure on
\begin_inset Formula $\mathcal{H}/\sim$
\end_inset
.
Its all happening everywhere, all at once! Auumm! We are one with the universe!
BTW the movie
\begin_inset Quotes eld
\end_inset
Everything Everywhere All At Once
\begin_inset Quotes erd
\end_inset
is a great movie! And I'm not trying to do pop–culture here, but the appercepti
on that wave–function collapse happens everywhere all at once is already
\begin_inset Quotes eld
\end_inset
well known
\begin_inset Quotes erd
\end_inset
to everyone, and yet it remains befuddling to actual physicists who have
to actually work with this stuff.
And it is certainly befuddling to me.
And so my goal here is to try to remedy that.
Fuck me.
Nothing like explaining the obvious.
Like
\begin_inset Quotes eld
\end_inset
shit falls down, Newton, yeah, duh
\begin_inset Quotes erd
\end_inset
except I'm not Newton.
Fuck me.
What am I doing?
\end_layout
\begin_layout Standard
Anyway, the goal of writing it as
\begin_inset Formula $\mathcal{H}=\bigotimes_{t\in\mathbb{R}^{+}}H_{t}$
\end_inset
is to be suggestive, to give the flavor or suggestion of stochastic processes,
expect it's for probability amplitudes not probabilities.
And also that, in analogy to the natural filtration for the Wiener process,
there is a natural filtration here, as well.
But it has to be written down and articulated.
\end_layout
\begin_layout Standard
OK.
Now I really do have to take a break and do something else.
But I feel like I have made actual forward progress to pin down the issue,
We shall see...
\end_layout
\begin_layout Subsection*
20 May 2025
\end_layout
\begin_layout Standard
Please note: For the topics above, I do all my thinking while falling asleep.
During the daytime hours, I do something else.
So progress can be slow or absent, depending.
I'm back down to slow progress, but thought I should write up something
obvious, again.
So we have a pure state
\begin_inset Formula $\left|\psi\right\rangle $
\end_inset
and it has no physical location.
To use bad language,
\begin_inset Quotes eld
\end_inset
it's a particle
\begin_inset Quotes erd
\end_inset
, but it has no location in 3D space.
The formalities of QM allow an expression to be obtained, written as
\begin_inset Formula $\left|\left\langle x,t\right.\left|\psi\right\rangle \right|^{2}$
\end_inset
which is interpreted as the probability of detecting a particle at location
\begin_inset Formula $(x,t)$
\end_inset
were there a particle detector placed at that location.
\end_layout
\begin_layout Standard
The relationship to choice is this.
Consider, to keep things easy, a two–slit setup, with interference fringes,
and photographic film as detector.
The nature of the interaction with the film is such that the single–photon
state
\begin_inset Formula $\left|\psi\right\rangle $
\end_inset
, which had no 3D location (let's make it 1D, since this is diffraction)
is now forced to choose a location
\begin_inset Formula $x_{c}\in\mathbb{R}$
\end_inset
such that, upon wave function collapse,
\begin_inset Formula $\left|\left\langle x\right.\left|\psi\right\rangle \right|^{2}\approx\delta\left(x-x_{c}\right)$
\end_inset
i.e.
the photon collided with the silver halide grain located at
\begin_inset Formula $x_{c}$
\end_inset
.
\end_layout
\begin_layout Standard
This game seems to have the following rules: (1) the particle is given a
choice: the wave function can collapse anywhere at all, but when it does
collapse, it must collapse to a single point.
(2) Upon many repetitions with the same prepared state, the expectation
value of collapse locations will conform to classical diffraction.
(3) A micro–theory of photon interaction with silver halide grains needs
to be developed.
\end_layout
\begin_layout Standard
Now, of course, part (3) is hard, and it is tempting to skip it, and I probably
will, eventually.
However, it's also the interesting part.
As the wave function is collapsing, it is interacting with **all** of the
silver–halide grains
\begin_inset Quotes eld
\end_inset
at the same time
\begin_inset Quotes erd
\end_inset
, in the here–and–now.
That is, all of them are entangled during the collapse process.
Huh.
I wonder if I can write an expression for this.
\end_layout
\begin_layout Standard
But first: Note this entanglement is time–less.
That is, imagine that the film is cut, so that the portion of the film
for
\begin_inset Formula $x<0$
\end_inset
is much much closer to the slits than the portion
\begin_inset Formula $x>0$
\end_inset
.
This combines the Renninger negative–measurement experiment with the two–slit
experiment.
The distances are such that the time–of–flight is much larger than the
wavepacket size, so that if the wavepacket collapses to a location
\begin_inset Formula $x_{c}<0$
\end_inset
it does so chronologically much earlier than if it collapsed to
\begin_inset Formula $x_{c}>0$
\end_inset
.
What the Renninger negative–measurement experiment tells us is that not
only does
\begin_inset Formula $\left|\psi\right\rangle $
\end_inset
not have a
\begin_inset Quotes eld
\end_inset
location in space
\begin_inset Quotes erd
\end_inset
, but it also does not have a
\begin_inset Quotes eld
\end_inset
location in time
\begin_inset Quotes erd
\end_inset
.
And I think this observation is exactly what I need to resolve the confusion
about why here–and–now is insensitive to Lorentz covariance.
That is, here–and–now is happening not only everywhere, but it is also
happening at all times.
The wording of this last sentence is awkward.
Perhaps it is this: here–and–now ties together collections of points in
spacetime.
Not just points in space, but in spacetime.
\end_layout
\begin_layout Standard
For this specific example, it ties together those spacetime points located
at the intersection of photo–film location and wave–packet flight–time.
Note that some of these points are space–like separated, and some are time–like
separated.
So, for example, two points
\begin_inset Formula $x_{1}<0$
\end_inset
and
\begin_inset Formula $x_{2}<0$
\end_inset
might be space–like separated, if the distance between them is much larger
than the wave–packet size
\begin_inset Formula $\Delta t$
\end_inset
.
That is, if
\begin_inset Formula $\left|x_{1}-x_{2}\right|>c\Delta t$
\end_inset
.
However, imagine doing the experiment with, say, electrons, not photons,
so that the wavepacket group velocity is less than
\begin_inset Formula $c$
\end_inset
.
Then a point
\begin_inset Formula $x_{3}>0$
\end_inset
could be in the causal future of
\begin_inset Formula $x_{1}<0$
\end_inset
.
Which is the point of the Renninger arrangement: to place the film such
that a portion of it is very distinctly in the causal future of the other
part, and so far in the future, that it is much larger than
\begin_inset Formula $\Delta t$
\end_inset
.
\end_layout
\begin_layout Standard
Anyway, let us now attempt to write down an expression for the entanglement
of silver–halide grains in the here–and–now.
I will write three or four paragraphs of quotidian mathematical details
below.
These will be boring and almost entirely irrelevant to the core idea.
They serve only to provide a concrete, specific example, so that you, dear
reader, and perhaps I myself, don't remain in the ozone of abstraction,
forever.
The below will describe the Renninger two–slit setup, but it really could
be any detector geometry whatsoever, for detecting any kinds of particles
from any kinds of sources.
I'm selecting the Renninger two–slit setup because its very specific and
concrete.
\end_layout
\begin_layout Standard
So first, pixelate.
We give each grain the size of
\begin_inset Formula $2^{-N}$
\end_inset
for some finite integer
\begin_inset Formula $N$
\end_inset
.
We do this by taking the continuous space
\begin_inset Formula $x\in\mathbb{R}$
\end_inset
and removing the dyadic rationals
\begin_inset Formula $p/2^{N}$
\end_inset
for
\begin_inset Formula $p\in\mathbb{Z}$
\end_inset
and fixed
\begin_inset Formula $N$
\end_inset
.
We've removed a set of measure zero of points, in such a way that each
individual silver–halide gran can interact
\begin_inset Quotes eld
\end_inset
within itself
\begin_inset Quotes erd
\end_inset
, but cannot interact with its nearest neighbors.
That is, the individual grains are thermodynamically isolated, so that
whatever energy is deposited into one does not, cannot leak into neighboring
grains.
Think CCD camera, if that makes you happier.
A finite and uniform pixel size.
\end_layout
\begin_layout Standard
Mathematically, this is interesting, as it allows the limit
\begin_inset Formula $N\to\infty$
\end_inset
to be taken.
The pixels then become isomorphic to the Cantor set.
They hold all of the measure, the are infinitely tiny, they are thermodynamical
ly disconnected from their neighbors, so that thermodynamic isolation is
equivalent to giving them a discrete topology, when using concepts from
general topology.
\end_layout
\begin_layout Standard
Next, place the double–slit at location
\begin_inset Formula $y=0$
\end_inset
and so the film plate is at
\begin_inset Formula $y=D_{near}$
\end_inset
when
\begin_inset Formula $x<0$
\end_inset
and
\begin_inset Formula $y=D_{far}$
\end_inset
for
\begin_inset Formula $x>0$
\end_inset
.
That is, the pixel
\begin_inset Formula $p$
\end_inset
is located at
\begin_inset Formula
\[
\left(x,y\right)=\begin{cases}
\left(p/2^{N},D_{far}\right) & \mbox{for }p\ge0\\
\left(p/2^{N},D_{near}\right) & \mbox{for }p<0
\end{cases}
\]
\end_inset
This can be arranged so that
\begin_inset Formula $D_{near}=D_{far}$
\end_inset
for the classical two–slit experiment, and, for the Renninger configuration,
\begin_inset Formula $D_{far}-D_{near}\gg c\Delta t$
\end_inset
for wave–packet size
\begin_inset Formula $c\Delta t$
\end_inset
.
The wave packet then has the form
\begin_inset Formula
\[
\left|\psi\left(x,y,t\right)\right|^{2}\sim f\left(x,y\right)b\left(-\frac{\left(\sqrt{x^{2}+y^{2}}-vt\right)^{2}}{2a}\right)
\]
\end_inset
with
\begin_inset Formula $f\left(x,y\right)$
\end_inset
the diffraction pattern, and
\begin_inset Formula $b\left(\cdot\right)$
\end_inset
being some bump function:
\begin_inset Formula $b:\mathbb{R}\to\mathbb{R}^{+}$
\end_inset
.
In physics, we usually have
\begin_inset Formula $b$
\end_inset
being exp, so above becomes the Gaussian; however, for the below it will
be easier if
\begin_inset Formula $b$
\end_inset
has compact support.
So, in all respects, this is meant to be an industry–standard, textbook
wavepacket, just one with compact support.
\end_layout
\begin_layout Standard
The rest is as usual:
\begin_inset Formula $v$
\end_inset
the group velocity of the wave–packet, with of course,
\begin_inset Formula $v<c$
\end_inset
for massive particles, and
\begin_inset Formula $v=c$
\end_inset
for photons, and
\begin_inset Formula $a=v\Delta t$
\end_inset
being the wavepacket size.
The interesting geometry is with
\begin_inset Formula $D_{near}\gg1$
\end_inset
so that we can approximate
\begin_inset Formula $f\left(x,y\right)\approx f\left(x\right)$
\end_inset
with
\begin_inset Formula $f\left(x\right)$
\end_inset
the far–field diffraction pattern, i.e.
we ignore all near–field effects.
I wrote the expression for
\begin_inset Formula $\left|\psi\right|^{2}$
\end_inset
instead of
\begin_inset Formula $\psi$
\end_inset
because I don't want to deal with factors of
\begin_inset Formula $e^{-i\omega t}$
\end_inset
because they do not seem to be relevant at this time.
I'm also ignoring any dispersion in velocity: the particles are taken to
be monochromatic.
\end_layout
\begin_layout Standard
I suppose it's worth pausing a moment to contemplate this.
QM superposition fundamentally requires complex numbers, and the different
world–lines in the partition function sum with a phase given by the action.
For the current thought–experiment, none of this seems to matter, at least,
not so far, so I will ignore these details (i.e.
the phases) until such time that they become important.
\end_layout
\begin_layout Standard
We can now write down an explicit expression for the location of here–and–now.
I'll use the symbol
\begin_inset Formula $\mathscr{P}$
\end_inset
for here–and–now, with P meaning
\begin_inset Quotes eld
\end_inset
present
\begin_inset Quotes erd
\end_inset
.
Informally,
\begin_inset Formula $\mathscr{P}$
\end_inset
consists of all space–time points where the wave–packet is non–zero at
the location of the film plate.
That is, the film–plate follows one set of world–lines, stationary in the
lab frame, and the particles are moving, so they intersect.
I took the effort to give the wave–packet compact support in the time direction.
The far–field diffraction pattern is not compactly supported.
The film–plate is of finite size, and so some of the diffraction pattern
will miss the film–plate entirely.
Ideally, we want to make this
\begin_inset Quotes eld
\end_inset
negligibly small
\begin_inset Quotes erd
\end_inset
, and I think this is entirely reasonable.
The common–sense physics should not depend on out–of–bounds conditions.
\end_layout
\begin_layout Standard
So there we have it: the region
\begin_inset Formula $\mathscr{P}$
\end_inset
of space–time is where here–and–now is, at the
\begin_inset Quotes eld
\end_inset
moment of wave function collapse
\begin_inset Quotes erd
\end_inset
.
Except there's no
\begin_inset Quotes eld
\end_inset
moment
\begin_inset Quotes erd
\end_inset
, because the wave–packet size
\begin_inset Formula $\Delta t$
\end_inset
is finite, and because the Renninger setup has that some points in
\begin_inset Formula $\mathscr{P}$
\end_inset
are in the distant future light–cone of others, while other points of
\begin_inset Formula $\mathscr{P}$
\end_inset
are space–like separated.
That is, here–and–now is all over the place.
\end_layout
\begin_layout Standard
Lets write a formula for this.
Again, this is the
\begin_inset Quotes eld
\end_inset
obvious
\begin_inset Quotes erd
\end_inset
formula.
Writing it down enables this text to vibe like it was written by a shape–rotato
r instead of a wordcel.
Vibes are important.
Even engineering texts are 100% vibes, no matter how anhedonic the engineers
imagine themselves to be.
Where was I?
\end_layout
\begin_layout Standard
Let
\begin_inset Formula $p_{i}$
\end_inset
denote the
\begin_inset Formula $i$
\end_inset
'th detector pixel; it is an extended object occupying the space–time points
\begin_inset Formula $p_{i}\left(x,y,t\right)$
\end_inset
given by
\begin_inset Formula
\[
p_{i}\left(x,y,t\right)=\Theta\left(2^{N}x-i\right)\delta\left(y-D_{i}\right)
\]
\end_inset
where
\begin_inset Formula
\[
D_{i}=\begin{cases}
D_{near} & \mbox{for }i<0\\
D_{far} & \mbox{for }i\ge0
\end{cases}
\]
\end_inset
and
\begin_inset Formula $\delta$
\end_inset
the Dirac delta (or a suitably widened version thereof.) The function
\begin_inset Formula $\Theta$
\end_inset
is given by
\begin_inset Formula
\[
\Theta\left(w\right)=\begin{cases}
1 & \mbox{for }-\frac{1}{2}<w<\frac{1}{2}\\
0 & \mbox{otherwise}
\end{cases}
\]
\end_inset
The pixel plane
\begin_inset Formula $P$
\end_inset
consists of all space–time locations
\begin_inset Formula
\[
P\left(x,y,t\right)=\sum_{i\in\mathbb{Z}}p_{i}\left(x,y,t\right)
\]
\end_inset
or perhaps an alternate notation is
\begin_inset Formula
\[
P=\left\{ \left(x,y,t\right)\in M:P\left(x,y,t\right)\ne0\right\}
\]
\end_inset
with
\begin_inset Formula $M$
\end_inset
being Minkowski space–time, so that
\begin_inset Formula $P\subset M$
\end_inset
is a manifold.
And it really is a manifold, it's smooth, it has coordinate charts, etc.
It does have some points missing at some of the dyadic rationals; the pixels
are isolated and disjoint.
Its not compact in either the space or the time directions, but it could
be made compact by making the detector finite–sized, and removing it at
some point in the future.
This would give it compact support on the light–cone as well (i.e.
for the null directions.)
\end_layout
\begin_layout Standard
The set of points
\begin_inset Formula $\mathscr{P}\subset M$
\end_inset
are then
\begin_inset Formula
\[
\mathscr{P}=\left\{ \left(x,y,t\right)\in M:P\left(x,y,t\right)\left|\psi\left(x,y,t\right)\right|^{2}\ne0\right\}
\]
\end_inset
This is again a smooth submanifold that can be given coordinate charts.
Its compact in the time direction, because
\begin_inset Formula $b\left(\cdot\right)$
\end_inset
was defined to be compact.
Since the pixels are disjoint,
\begin_inset Formula $\mathscr{P}$
\end_inset
also consists of a set of disjoint manifolds, corresponding to each pixel.
\end_layout
\begin_layout Standard
Wave function collapse requires describing how the ket
\begin_inset Formula $\left|\psi\right\rangle $
\end_inset
evolves from the distant past, into the distant future, such that it deposits
all of it's energy into a single pixel.
Again, I emphasize that
\begin_inset Formula $\left|\psi\right\rangle $
\end_inset
has no location in space–time; it is
\begin_inset Quotes eld
\end_inset
everywhere, all at once
\begin_inset Quotes erd
\end_inset
.
Despite this, we can localize where the collapse happens: it necessarily
takes place in the here–and–now, denoted by
\begin_inset Formula $\mathscr{P}$
\end_inset
.
\end_layout
\begin_layout Standard
The primary claim of this text is that the ket
\begin_inset Formula $\left|\psi\right\rangle $
\end_inset
necessarily entangles all points in
\begin_inset Formula $\mathscr{P}$
\end_inset
.
This is where things get difficult, again.
Let's try to wordcel our way into what the difficulty is.
What do we have? The following points:
\end_layout
\begin_layout Itemize
All pixels are QM–entangled in
\begin_inset Formula $\mathscr{P}$
\end_inset
.
\end_layout
\begin_layout Itemize
Each pixel should be describable in some unitary QM fashion.
\end_layout
\begin_layout Itemize
Each pixel also has a thermodynamic description: the natural vocabulary
is that of measure–preserving dynamical systems.
The insides of the pixels are ergodic; perhaps some subset of each pixel
includes wandering sets, so that sub–portions of the pixels are dissipative.
\end_layout
\begin_layout Itemize
All of the particle energy has been deposited into only one pixel in the
future light–cone of
\begin_inset Formula $\mathscr{P}$
\end_inset
.
This states that the all–pixel unitary entanglement becomes a single–pixel
thermodynamic entanglement.
\end_layout
\begin_layout Standard
So, again, I have to break, and go do other things now.
But still, it feels like I made some minor forward progress.
I now have an explicit formal example of here–and–now as a collection of
points in classical space–time.
I've formalized the claim that
\begin_inset Formula $\left|\psi\right\rangle $
\end_inset
necessarily entangles
\emph on
all
\emph default
points in the here–and–now.
I've isolated the microscopic model so that it requires both a unitary
description, and simultaneously an ergodic, dissipative description.
\end_layout
\begin_layout Standard
This description of
\begin_inset Formula $\mathscr{P}$
\end_inset
allows it to be given a sigma algebra, but this is trivial: it is a subalgebra
of the sigma algebra on Minkowski space.
Which now clarifies what I did wrong above: here–and–now is NOT
\begin_inset Formula $\mathscr{P}$
\end_inset
but instead it is
\begin_inset Formula $\mathscr{P}^{\prime}$
\end_inset
where
\begin_inset Formula $\mathscr{P}^{\prime}$
\end_inset
is the dual space of all continuous functions from
\begin_inset Formula $\mathscr{P}$
\end_inset
to
\begin_inset Formula $\mathbb{R}^{+}$
\end_inset
.
I want to endow
\begin_inset Formula $\mathscr{P}^{\prime}$
\end_inset
with some sigma algebra.
It is then presumably some kind of Cameron–Martin space, some reproducing
kernel Hilbert space, something analogous to how abstract Wiener space
is constructed.
\end_layout
\begin_layout Standard
Now, for Wiener space
\begin_inset Formula $\Omega$
\end_inset
, the point
\begin_inset Formula $\omega\in\Omega$
\end_inset
correspond to single, specific Brownian motion paths, and by taking the
Cartesian product
\begin_inset Formula $I\times\Omega$
\end_inset
one can define the Wiener process
\begin_inset Formula $X$
\end_inset
as
\begin_inset Formula $X:I\times\Omega\to\mathbb{R}^{n}$
\end_inset
so that
\begin_inset Formula $X_{t}\equiv X\left(t,\cdot\right)$
\end_inset
is called a
\begin_inset Quotes eld
\end_inset
stochastic process
\begin_inset Quotes erd
\end_inset
, and selecting a specific point
\begin_inset Formula $\omega\in\Omega$
\end_inset
identifies a specific Brownian–motion path.
\end_layout
\begin_layout Standard
The intended analogy here is that
\begin_inset Formula $\mathscr{P}^{\prime}$
\end_inset
is kind–of–like
\begin_inset Formula $\Omega$
\end_inset
, and that a specific point
\begin_inset Formula $q\in\mathscr{P}^{\prime}$
\end_inset
corresponds to a specific wave–function collapse onto a single pixel.
The Many–Worlds Hypothesis is then the statement that each distinct
\begin_inset Formula $q\in\mathscr{P}^{\prime}$
\end_inset
is a distinct
\begin_inset Quotes eld
\end_inset
world
\begin_inset Quotes erd
\end_inset
, and that all of these worlds
\begin_inset Quotes eld
\end_inset
coexist
\begin_inset Quotes erd
\end_inset
.
And, in that sense, clearly they do: I have written down an explicit and
precise expression for the multiverse: it is exactly
\begin_inset Formula $\mathscr{P}^{\prime}$
\end_inset
and nothing more and nothing less.
\end_layout
\begin_layout Standard
Now, since I am wordceling along, here, it is possible that I screwed something
up, but for now, it really does seem like
\begin_inset Formula $\mathscr{P}^{\prime}$
\end_inset
is a formal expression for the multiverse.
Also, this is so basic, that I assume that I am rediscovering something
that others have already published about.
Since I have not read sufficiently in those directions, I don't know.
And my vocabulary and terminology is sufficiently obtuse that I doubt that
I can ask Claude or Grok or Gemini if someone else has already discovered
all this.
Those systems are not yet capable of answering this kind of a question.
So, I must continue, the olde–fashioned way.
\end_layout
\begin_layout Standard
Continuing...
the sticky part here is that Wiener space has an obvious
\begin_inset Quotes eld
\end_inset
time
\begin_inset Quotes erd
\end_inset
coordinate: it was build so as to be indexable.
The points
\begin_inset Formula $\omega\in\Omega$
\end_inset
have an explicit interpretation as paths.
The sigma algebra
\begin_inset Formula $\mathcal{F}$
\end_inset
on
\begin_inset Formula $\Omega$
\end_inset
has an explicit natural filtration
\begin_inset Formula $\mathcal{F}_{t}$
\end_inset
.
\end_layout
\begin_layout Standard
And now here is where it gets fun.
If we start at time
\begin_inset Formula $t=0$
\end_inset
, all Brownian motion paths are possible.
As the time
\begin_inset Formula $t$
\end_inset
advances, the path
\begin_inset Quotes eld
\end_inset
collapses
\begin_inset Quotes erd
\end_inset
, so that there is a cylinder set
\begin_inset Formula
\[
C\left(t,\omega\right)=\left\{ \alpha\in\Omega:X\left(s,\alpha\right)=X\left(s,\omega\right)\mbox{ for }s<t\right\}
\]
\end_inset
This cylinder set contains all paths that are exactly equal to
\begin_inset Formula $X_{s}\left(\omega\right)$
\end_inset
for
\begin_inset Formula $s<t$
\end_inset
and are otherwise unspecified for future times that occur after
\begin_inset Formula $t$
\end_inset
– i.e.
all possibilities are allowed, all futures are still open, subject to the
constraint that
\begin_inset Formula $X_{s}\left(\omega\right)$
\end_inset
for
\begin_inset Formula $s<t$
\end_inset
has already happened, is in the past, and is immutable.
That is, for the Wiener process, here–and–now is cleanly parameterized
by a parameter
\begin_inset Formula $t$
\end_inset
which has a clean and clear interpretation as
\begin_inset Quotes eld
\end_inset
time
\begin_inset Quotes erd
\end_inset
.
What's more the filtration
\begin_inset Formula $\mathcal{F}_{t}$
\end_inset
provides a clear model for past, present and future, where the pas is fixed,
the present is
\begin_inset Quotes eld
\end_inset
now
\begin_inset Quotes erd
\end_inset
, and the future is undetermined, because the sigma algebra is too course.
That is, the sigma algebras form a filtration
\begin_inset Formula $\mathcal{F}_{t}\subset\mathcal{F}_{u}$
\end_inset
for future times
\begin_inset Formula $u>t$
\end_inset
.
They get finer, as time progresses.
\end_layout
\begin_layout Standard
So the sticky part is that
\begin_inset Formula $\mathscr{P}^{\prime}$
\end_inset
was constructed in such a way that, if it has a natural filtration, it
is not clear what it is.
If it did have a natural filtration, then that filtration could be explicitly
identified with the process of wave–function collapse.
That is, not only would a single point
\begin_inset Formula $q\in\mathscr{P}^{\prime}$
\end_inset
correspond to a specific path of collapse, but there would be some parameter
\begin_inset Formula $\tau$
\end_inset
such that
\begin_inset Formula $\Psi\left(\tau,q\right)$
\end_inset
indicated the entanglement state of all of the pixels with the ket
\begin_inset Formula $\left|\psi\right\rangle $
\end_inset
at that
\begin_inset Quotes eld
\end_inset
instant
\begin_inset Quotes erd
\end_inset
\begin_inset Formula $\tau$
\end_inset
.
So, first of all, I don't yet know how to explicitly write down what this
parameter
\begin_inset Formula $\tau$
\end_inset
is, but the insight is that perhaps wave–function collapse is
\begin_inset Quotes eld
\end_inset
unitary
\begin_inset Quotes erd
\end_inset
in
\begin_inset Formula $\tau$
\end_inset
.
This parameter
\begin_inset Formula $\tau$
\end_inset
is explicitly not time; it cannot be, because the Renninger setup clearly
demonstrates that it could never be, because the Renninger setup explicitly
entangles future times with past times (within the same light–cone.) But
*if* we had or could find or could impose this structural parameter
\begin_inset Formula $\tau$
\end_inset
, then the process
\begin_inset Formula $\Psi:I\times\mathcal{P}^{\prime}\to\mathbb{C}$
\end_inset
could maybe plausibly describe collapse, and also be interpreted as a kind–of
unitary evolution, unitary not in time, but in the parameter
\begin_inset Formula $\tau$
\end_inset
.
\end_layout
\begin_layout Standard
I dunno.
This does skirt dangerously close to the Bohm hidden–variable description,
with
\begin_inset Formula $\tau$
\end_inset
being the hidden variable.
And I want to explicitly reject hidden variables, because we already know
that those don't work.
Perhaps the saving grace is that each
\begin_inset Formula $q\in\mathscr{P}^{\prime}$
\end_inset
is meant to be interpreted as a different world in the multiverse.
I dunno.
So this is one of the risky points that would need to be double–checked.
Must not accidentally reinvent hidden variables.
\end_layout
\begin_layout Standard
Whatever.
I really have to go.
Where are we at?
\end_layout
\begin_layout Itemize
I might have screwed up with the definition of
\begin_inset Formula $\mathscr{P}^{\prime}$
\end_inset
or it's interpretation.
\end_layout
\begin_layout Itemize
I don't yet know how to find this parameter
\begin_inset Formula $\tau$
\end_inset
or how to prove that such a parameter even exists.
\end_layout
\begin_layout Itemize
I don't have a microscopic model of the pixels.
\end_layout
\begin_layout Standard
Still, this feels like forward progress, again.
Later, dude.
\end_layout
\begin_layout Standard
I guess I can put a sigma algebra and measure on either
\begin_inset Formula $P$
\end_inset
or
\begin_inset Formula $\mathscr{P}$
\end_inset
and in either case it would correspond to a traditional particle cross–section.
In this case, the film plate should also have some finite thickness.
\end_layout
\begin_layout Subsection*
21 May 2025
\end_layout
\begin_layout Standard
After some thought:
\end_layout
\begin_layout Itemize
The definition of
\begin_inset Formula $\mathscr{P}$
\end_inset
as the region of spacetime where collapse takes place is correct.
\end_layout
\begin_layout Itemize
The definition of
\begin_inset Formula $\mathscr{P}^{\prime}$
\end_inset
is wrong, the desired interpretation remains desirable.
\end_layout
\begin_layout Standard
One problem with
\begin_inset Formula $\mathscr{P}^{\prime}$
\end_inset
is that if the particle is a photon, its gone, by the end, but if its an
electron, its still there.
The other problem is that the internal state of the detectors needs to
b a part of it.
Let
\begin_inset Formula $\Omega_{p}$
\end_inset
denote the set of all possible pixel states over the entire world–line
of pixel
\begin_inset Formula $p$
\end_inset
so that a point
\begin_inset Formula $\omega_{p}\in\Omega_{p}$
\end_inset
corresponds to the entire time evolution of the pixel from beginning of
time to end of time, from
\begin_inset Formula $\left|p,\mbox{initial}\right\rangle $
\end_inset
to
\begin_inset Formula $\left|p,\omega,\mbox{final}\right\rangle $
\end_inset
.
Note that
\begin_inset Formula $\left|p,\mbox{initial}\right\rangle $
\end_inset
does NOT depend on
\begin_inset Formula $\omega_{p}$
\end_inset
: no matter what path the pixel takes in the future, it starts in a fixed
state.
Note that the final state
\begin_inset Formula $\left|p,\omega_{p},\mbox{final}\right\rangle $
\end_inset
does depend on the path
\begin_inset Formula $\omega_{p}$
\end_inset
even if the pixel does NOT capture the photon: the entanglement during
w.f.
collapse might have changed the phase in the pixel.
This raises the interesting possibility that there might be some effect
similar to Aharonov–Bohm, in that phases change even though there was no
direct detection in that pixel.
\end_layout
\begin_layout Standard
Likewise, write
\begin_inset Formula $\Psi$
\end_inset
for the space of all possible continuous evolution paths for the particle,
from the distant past to the distant future, so that the point
\begin_inset Formula $\psi\in\Psi$
\end_inset
corresponds to the time evolution from
\begin_inset Formula $\left|\psi,\mbox{initial}\right\rangle $
\end_inset
to
\begin_inset Formula $\left|\psi,\mbox{final}\right\rangle $
\end_inset
.
With this notation, the total state space is then
\begin_inset Formula
\[
E=\Psi\times\prod_{p}\Omega_{p}
\]
\end_inset
so that a point
\begin_inset Formula $\eta\in E$
\end_inset
corresponds to the evolution of the system from
\begin_inset Formula $\left|\eta,\mbox{initial}\right\rangle =\left|\psi,\left\{ p\right\} ,\mbox{initial}\right\rangle $
\end_inset
to
\begin_inset Formula $\left|\eta,\mbox{final}\right\rangle =\left|\psi,\left\{ p,\omega\right\} ,\mbox{final}\right\rangle $
\end_inset
.
\end_layout
\begin_layout Standard
The notation is meant to enable the use of S–matrix ideas, so that we can
write
\begin_inset Formula $\left|\eta,\mbox{final}\right\rangle =S\left|\eta,\mbox{initial}\right\rangle $
\end_inset
.
The notation is also meant to allow the explicit analogy to Wiener space,
so that points
\begin_inset Formula $\eta\in E$
\end_inset
correspond to continuous paths in the evolution of the system.
The intended path parameter is meant to be here–and–now.
This parameter is both a point; I guess we can treat it as a point on the
unit real interval
\begin_inset Formula $I$
\end_inset
, and it is also a region of spacetime, so that
\begin_inset Formula $\mathscr{P}$
\end_inset
denotes the location of here–and–now where the wave–function collapse occurs.
From the point of view of the S–matrix,
\begin_inset Formula $\mathscr{P}$
\end_inset
is just the interaction region.
The point of the Renninger setup is that
\begin_inset Formula $\mathscr{P}$
\end_inset
is not star–shaped or convex.
\end_layout
\begin_layout Standard
In this formulation, here–and—now is both
\begin_inset Quotes eld
\end_inset
instantaneous
\begin_inset Quotes erd
\end_inset
and
\begin_inset Quotes eld
\end_inset
spread out
\begin_inset Quotes erd
\end_inset
, so that the w.f.
collapse is also both
\begin_inset Quotes eld
\end_inset
instantaneous
\begin_inset Quotes erd
\end_inset
and
\begin_inset Quotes eld
\end_inset
spread out
\begin_inset Quotes erd
\end_inset
.
That is, in the parameter space, taken to be the unit interval of the reals
\begin_inset Formula $I=\left\{ \rho\in\mathbb{R}:0\le\rho\le1\right\} $
\end_inset
there are a bunch of points
\begin_inset Formula $\rho$
\end_inset
that are before the collapse, and a bunch of points after the collapse,
but there is just one point
\begin_inset Formula $\rho$
\end_inset
that corresponds to the region
\begin_inset Formula $\mathscr{P}$
\end_inset
.
For the sake of convenience, let's parameterize this so that
\begin_inset Formula $\rho=1/2$
\end_inset
when the collapse happens.
The parameter interval
\begin_inset Formula $0\le\rho<1/2$
\end_inset
can be taken to be isomorphic to the passage of Newtonian time, or proper
time in the lab frame, up until just before the particle wave packet begins
to overlap the detectors.
For this region, the Schrodinger equation (or the wave equation, as appropriate
) fully and completely describes the time evolution of the particle.
The pixels likewise
\begin_inset Quotes eld
\end_inset
do their thing
\begin_inset Quotes erd
\end_inset
in this region.
Then, at precisely
\begin_inset Formula $\rho=1/2$
\end_inset
we suspend all of this, and move the discussion of the S–matrix interaction
region
\begin_inset Formula $\mathscr{P}$
\end_inset
.
The collapse happens
\begin_inset Quotes eld
\end_inset
there
\begin_inset Quotes erd
\end_inset
.
After that, normal evolution resumes, so that the interval
\begin_inset Formula $1/2<\rho\le1$
\end_inset
is again isomorphic to lab–frame proper time, and pixel evolution continues
normally.
\end_layout
\begin_layout Standard
Note that there is a large discontinuity: we run the lab–frame clock until
right before the interaction starts: this time is
\begin_inset Formula $t_{\mbox{before}}$
\end_inset
and corresponds to
\begin_inset Formula $\rho\to1/2$
\end_inset
from below.
The time
\begin_inset Formula $t_{\mbox{after}}$
\end_inset
corresponds to the lab time after which all possible interactions are over,
it corresponds to
\begin_inset Formula $\rho\to1/2$
\end_inset
from above.
However, in the lab,
\begin_inset Formula
\[
t_{\mbox{after}}=t_{\mbox{before}}+\Delta t+\frac{D_{far}-D_{near}}{v}
\]
\end_inset
with, as before,
\begin_inset Formula $\Delta t$
\end_inset
being the wavepacket width,
\begin_inset Formula $v$
\end_inset
the group velocity of the wavepacket, and
\begin_inset Formula $D_{near}$
\end_inset
and
\begin_inset Formula $D_{far}$
\end_inset
the detector locations.
A different way to say this is that
\begin_inset Formula $t_{\mbox{before}}$
\end_inset
is the infimum of the proper time in
\begin_inset Formula $\mathscr{P}$
\end_inset
and
\begin_inset Formula $t_{\mbox{after}}$
\end_inset
is the supremum: the lower and upper bounds.
Algebraically,
\begin_inset Formula
\[
t_{\mbox{before}}=\inf\left\{ t:\left(x,y,t\right)\in\mathscr{P}\right\}
\]
\end_inset
and
\begin_inset Formula
\[
t_{\mbox{after}}=\sup\left\{ t:\left(x,y,t\right)\in\mathscr{P}\right\}
\]
\end_inset
That is, the wave–function collapse occurs over this extended region of
lab–frame time.
The wave–function collapse is instant, in parameter time.
Then, a single point
\begin_inset Formula $\eta\in E$
\end_inset
is an interpolation of the system from
\begin_inset Formula $t_{\mbox{before}}$
\end_inset
to
\begin_inset Formula $t_{\mbox{after}}$
\end_inset
.
\end_layout
\begin_layout Standard
OK.
My brains are cooked.
The efforts of the last 2 or 3 days is a verbose reformulation of well–known
physics, the basic ingredients that go into the Mott problem https://en.wikipedi
a.org/wiki/Mott_problem but adapted to a Renninger two–slit setup.
\end_layout
\begin_layout Standard
To make the desired analogy to the Wiener process, I need a measurement
process
\begin_inset Formula
\[
X:I\times E\to Q
\]
\end_inset
where
\begin_inset Formula $I$
\end_inset
is the unit interval that interpolates between
\begin_inset Formula $t_{\mbox{before}}$
\end_inset
and
\begin_inset Formula $t_{\mbox{after}}$
\end_inset
, and
\begin_inset Formula $E$
\end_inset
is the path space and
\begin_inset Formula $Q$
\end_inset
is ...
well, naively,
\begin_inset Formula $Q$
\end_inset
needs to be a
\begin_inset Quotes eld
\end_inset
slice
\begin_inset Quotes erd
\end_inset
through the detector+particle state, but I'm confused how to write this,
because this slice is smeared out over all of the interval
\begin_inset Formula $t_{\mbox{before}}<t<t_{\mbox{after}}$
\end_inset
.
\end_layout
\begin_layout Standard
Have I made any progress here? A tiny amount.
I made some notational progress.
Although I kind of bungled
\begin_inset Formula $E$
\end_inset
because at first, it covers all time, and then later, it covers only
\begin_inset Formula $\mathscr{P}$
\end_inset
so I should instead I should fix the notation to indicate some intersection
between
\begin_inset Formula $E$
\end_inset
and
\begin_inset Formula $\mathscr{P}$
\end_inset
, because that is what needs to be interpolated.
Whatever.
That's not hard to fix.
\end_layout
\begin_layout Standard
All of the difficult issues remain unscathed.
I need a microscopic analysis, analogous to the Mott problem calculation
from 1929, and I need to take that analysis and reformulate it into the
above notational framework.
\end_layout
\begin_layout Standard
Hmm.
So this article https://en.wikipedia.org/wiki/Quantum_decoherence has a pile
of notation that I can steal to formulate the above.
\end_layout
\begin_layout Standard
—
\end_layout
\begin_layout Standard
I have not read this paper, but it seems to be relevant to what I talk about
above, and I believe that also the framework I am trying to develop here
resolves the issues raised there.
Entanglement of quantum clocks through gravity Esteban Castro Ruiz, Flaminia
Giacomini, Časlav Brukner, Proc Natl Acad Sci U S A .
2017 Mar 7;114(12):E2303–E2309.
doi: 10.1073/pnas.1616427114 https://pmc.ncbi.nlm.nih.gov/articles/PMC5373405/
why the fact this is in PubMed, I don't know, I hope its not a cranky paper.
Authors seem to be legit.
\end_layout
\begin_layout Subsection*
22 May 2025
\end_layout
\begin_layout Standard
Well, So lets vastly simplify the above setup.
Suppose there is a single photon: a plane wave.
Suppose there are two simple harmonic oscillators: these are the detectors.
The energy of the photon is sufficient to kick one of the oscillators into
an excited state, but not both.
After photon absorption, this places the system into a superposition: either
one or the other oscillator is excited; we don't know which, both possibilities
are in superposition.
No
\begin_inset Quotes eld
\end_inset
collapse
\begin_inset Quotes erd
\end_inset
has occurred; we've simply used the photon to prepare a superposition.
Instead of using harmonic oscillators, one can imagine there being two
hydrogen atoms, with the photon being sufficient to excite one of them.
This detail doesn't matter.
\end_layout
\begin_layout Standard
Next, we want to work with decoherence.
So really, the two receiving SHO's should be weakly coupled to some network
of other oscillators, so that their energy can bleed out to those, thus
resulting in decoherence.
Some interesting questions arise: would a linear chain of weakly oscillators
be enough to decohere and thermalize? Does it have to be 2D? Some random
network? Does it have to be up in the mean–field connectivity range? Lets
ignore these questions for now.
Interesting, but some other day.
\end_layout
\begin_layout Standard
So how does decoherence work? (I still haven't read the Wikipedia article
on it ...) Each SHO state is then
\begin_inset Formula $\left|n\right\rangle $
\end_inset
and since we have two of them, the combined state is
\begin_inset Formula $\left|n_{1}\right\rangle \times\left|n_{2}\right\rangle $
\end_inset
with the Cartesian product denoting that they are NOT coherent with respect
to one–another; they are (initially) decoupled.
The whole point of absorbing a single photon is that it couples the two
oscillators together, forming a single pure entangled state out of them.
Lets try to write this down:
\begin_inset Formula
\[
\gamma\times\left|n_{1}\right\rangle \times\left|n_{2}\right\rangle \rightsquigarrow\frac{e^{i\theta}}{\sqrt{2}}\left(\left|n_{1}+1\right\rangle \otimes\left|n_{2}\right\rangle +e^{i\phi}\left|n_{1}\right\rangle \otimes\left|n_{2}+1\right\rangle \right)
\]
\end_inset
Here,
\begin_inset Formula $\gamma$
\end_inset
denotes the incoming photon.
It also is not
\begin_inset Quotes eld
\end_inset
coherent
\begin_inset Quotes erd
\end_inset
with respect to either oscillator, and so the Cartesian product
\begin_inset Formula $\times$
\end_inset
symbol is used to denote this.
The photon absorption, indicated by the squiggly arrow
\begin_inset Formula $\rightsquigarrow$
\end_inset
places the two oscillators into superposition, and thus the otimes
\begin_inset Formula $\otimes$
\end_inset
symbol is used.
Only one of the two oscillators can be excited, not both, so only
\begin_inset Formula $n_{1}$
\end_inset
or
\begin_inset Formula $n_{2}$
\end_inset
can be incremented.
There is necessarily some fixed phase
\begin_inset Formula $e^{i\phi}$
\end_inset
between these two.
Where it comes from, I don't know.
In a
\begin_inset Quotes eld
\end_inset
realistic
\begin_inset Quotes erd
\end_inset
model, it would arise from some detailed description of the photon–oscillator
interaction.
Perhaps its always the same for every photon interaction, perhaps it changes
each time.
The point is that the RHS is an entangled state.
I've thrown in an extra factor of
\begin_inset Formula $e^{i\theta}$
\end_inset
which
\begin_inset Quotes eld
\end_inset
doesn't matter
\begin_inset Quotes erd
\end_inset
in the usual sense, and a factor of
\begin_inset Formula $1/\sqrt{2}$
\end_inset
so as to preserve normalization and minimize hand–waving.
\end_layout
\begin_layout Standard
It is reasonable to take the initial state to be
\begin_inset Formula $n_{1}=n_{2}=0$
\end_inset
i.e.
the ground state, and that would make the notation slightly less busy and
verbose.
I won't do that for now, because
\begin_inset Formula $n_{1}$
\end_inset
and
\begin_inset Formula $n_{2}$
\end_inset
serve as useful place–holders to help track what's connected to what.
We can set
\begin_inset Formula $n_{1}=n_{2}=0$
\end_inset
later, if desired.
Note that for a
\begin_inset Quotes eld
\end_inset
real
\begin_inset Quotes erd
\end_inset
system, these detector SHO's might actually be mixtures (not pure states),
with some Boltzmann probability of not being in the ground state.
This is in a sense inevitable, if the detector SHO's are weakly connected
to a thermal bath.
\end_layout
\begin_layout Standard
Each of these oscillators is coupled to it's own disjoint thermal bath,
and so eventually, these oscillators decohere.
Write
\begin_inset Formula $\left|b_{1}\right\rangle $
\end_inset
and
\begin_inset Formula $\left|b_{2}\right\rangle $
\end_inset
for these baths.
Weak coupling, followed by decoherence can be written as
\begin_inset Formula
\[
\left|n\right\rangle \times\left|b\right\rangle \mapsto\left|\left(b+n\right)^{\prime}\right\rangle
\]
\end_inset
where the mapsto arrow
\begin_inset Formula $\mapsto$
\end_inset
indicates decoherence.
The pure state
\begin_inset Formula $\left|n\right\rangle $
\end_inset
appearing on the LHS gets absorbed into the bath on the RHS.
The prime denotes that the new bath is not the same as before, and the
plus sign indicates that the state has been ergodically mixed into the
bath.
We retain the
\begin_inset Formula $n$
\end_inset
to maintain detailed balance, i.e.
that the total energy on LHS and RHS is the same.
The energy in
\begin_inset Formula $\left|n\right\rangle $
\end_inset
was mixed into the bath, raising its energy.
The mixing can be assumed to resemble the Fermi–Pasta–Ulam–Tsingou type
ergodic mixing, or something along those lines.
The use of the Cartesian product on the LHS indicates that the state
\begin_inset Formula $\left|n\right\rangle $
\end_inset
is not yet coupled to the bath; we do not want to use the tensor product
symbol
\begin_inset Formula $\otimes$
\end_inset
just yet, because initially, there's no coupling.
Perhaps it would be correct to write this, instead:
\begin_inset Formula
\[
\left|n\right\rangle \times\left|b\right\rangle \mapsto\left|n\right\rangle \otimes\left|b\right\rangle \rightrightarrows\left|\left(b+n\right)^{\prime}\right\rangle
\]
\end_inset
to indicate that the pure state
\begin_inset Formula $\left|n\right\rangle $
\end_inset
becomes entangles with the bath
\begin_inset Formula $\left|b\right\rangle $
\end_inset
and then, over time evolves in such a way that
\begin_inset Formula $\left|\left(b+n\right)^{\prime}\right\rangle $
\end_inset
is the more appropriate notation.
The
\begin_inset Formula $\rightrightarrows$
\end_inset
is intended to denote that the eventual state of the detector SHO might
be some mixture of states, given by the thermal bath.
\end_layout
\begin_layout Standard
The grand–total process is thus meant to be written algebraically written
as
\begin_inset Formula
\begin{align*}
\frac{e^{i\theta}}{\sqrt{2}}\left(\left|n_{1}+1\right\rangle \otimes\left|n_{2}\right\rangle +e^{i\phi}\left|n_{1}\right\rangle \otimes\left|n_{2}+1\right\rangle \right)\times\left|b_{1}\right\rangle \times\left|b_{2}\right\rangle & \mapsto\\
\left\{ \left[\left(\left|n_{1}+1\right\rangle \otimes\left|b_{1}\right\rangle \right)\times\left(\left|n_{2}\right\rangle \otimes\left|b_{2}\right\rangle \right)\right]\;,\;\left[\left(\left|n_{1}\right\rangle \otimes\left|b_{1}\right\rangle \right)\times\left(\left|n_{2}+1\right\rangle \otimes\left|b_{2}\right\rangle \right)\right]\right\} & \rightrightarrows\\
\left\{ \left[\left|\left(b_{1}+n_{1}+1\right)^{\prime}\right\rangle \times\left|\left(b_{2}+n_{2}\right)^{\prime}\right\rangle \right]\;,\;\left[\left|\left(b_{1}+n_{1}\right)^{\prime}\right\rangle \times\left|\left(b_{2}+n_{2}+1\right)^{\prime}\right\rangle \right]\right\}
\end{align*}
\end_inset
This is a verbose mess, but is not meant to to be difficult.
As before, the mapsto arrow
\begin_inset Formula $\mapsto$
\end_inset
indicates the coupling of the detector SHO to it's bath, and the double
arrow
\begin_inset Formula $\rightrightarrows$
\end_inset
indicates the eventual thermalization.
As always, the Cartesian product indicates non–entangled, decoupled systems.
\end_layout
\begin_layout Standard
What's new here are the curly braces
\begin_inset Formula $\left\{ \cdots\right\} $
\end_inset
which indicate the set of all possible worlds: the many–worlds outcome
that is eventually attained.
The square brackets
\begin_inset Formula $\left[\cdots\right]$
\end_inset
denote a single world, used here to improve readability.
For readability, set
\begin_inset Formula $n_{1}=n_{2}=0$
\end_inset
, and then the two worlds become a bit more clear:
\begin_inset Formula
\[
\left\{ \left[\left|\left(b_{1}+1\right)^{\prime}\right\rangle \times\left|b_{2}^{\prime}\right\rangle \right]\;,\;\left[\left|b_{1}^{\prime}\right\rangle \times\left|\left(b_{2}+1\right)^{\prime}\right\rangle \right]\right\}
\]
\end_inset
In one world, detector 1 has absorbed the photon, and in the other world,
detector 2 has absorbed it.
\end_layout
\begin_layout Standard
There are a number of surprising features to the above, and so reviewing
these and placing them into context is worthwhile.
First, only two detectors were used; the above algebra generalizes
\begin_inset Quotes eld
\end_inset
trivially
\begin_inset Quotes erd
\end_inset
to more than two.
Next, SHO's were used as detectors, but for a realistic setup, these could
be any quantum system that couples to light.
Likewise, the photon was over–simplified in the above; there's no mention
of polarization, and no explicit concern about its wavelength, other than
that the energy should be matched to what the detector is sensitive to.
All this is OK, because it does not seem to impact the general description.
\end_layout
\begin_layout Standard
Perhaps the most surprising aspect of the above is the ansatz made for the
photon absorption.
I did not expect this myself, but got forced into it while attempting to
write the text.
It is very much the case that the initial state of the two detectors must
be a Cartesian product of two distinct, isolated, non–interacting systems.
Of this, there's no doubt; we're not causally tracing these back to the
Bag Bang to argue that they are secretly entangled.
No, they're distinct.
However, after the photon absorption, they must necessarily become entangled.
This must also be the case, as otherwise, there is no mechanism available
to guarantee that the photon is absorbed only once.
We must have this, in order to have the linear logic menu–choice operator:
either one system absorbs the photon, or the other, but not both.
For one dollar, you get this candy–bar, or that one, but not both.
The tensor product is the formal procedure that provides the mutual exclusion
lock needed for wave function collapse.
\end_layout
\begin_layout Standard
So this is perhaps the next surprising thing: the relationship between linear
logic and mutex locks in software and vending machines is well–known, and
both mutex locks and vending machines are classical objects, not quantum
objects.
There's no Schrodinger's candy–bar superposition between a Kit–Kat bar
and a Snickers.
Put the dollar in the machine, open the lid and look: you see a Kit–Kat
bar or a Snickers; you cannot infer that they were in a quantum superposition
before you inserted the dollar bill.
Yet I am absolutely tickled that this classical menu–choice fragment of
linear logic is exactly what is needed to describe the state of the system
immediately after the photon absorption.
Again, I repeat, cut–n–pasting the above formula: the state, after photon
absorption, but before decoherence is
\begin_inset Formula
\[
\left|n_{1}+1\right\rangle \otimes\left|n_{2}\right\rangle +e^{i\phi}\left|n_{1}\right\rangle \otimes\left|n_{2}+1\right\rangle
\]
\end_inset
and that is the bona–fide tensor symbol there, and bona–fide vector addition.
This is an element of a tensor algebra.
Its the real thing, a real quantum state, and more precisely, an entangled
quantum state.
The absorption of the photon entangled the two detectors.
And, again, it seems there is no other way.
There is no other mathematical mechanism that I know of that provides the
required mutual exclusion.
\end_layout
\begin_layout Standard
Now, perhaps, if one got into category theory more deeply, there might perhaps
be other algebraic constructions that embed the needed menu–choice fragment
of linear logic, and that perhaps one of these other systems could be used
in place of the tensor product above.
I dunno.
It's possible, I suppose, But given that QM is firmly grounded on the ordinary
tensor algebra, it seems pointless to hunt for other possibilities at this
time.
Interesting, perhaps, but not today.
And so, for this reason, I conclude that post photon absorption, the two
detectors must necessarily be entangled in the fashion as written above.
I insist that this must be the case, that there's no other way, and yet
I find it kind of surprising and amazing.
I guess surprise and amazement is part of the territory.
Anyway ...
\end_layout
\begin_layout Standard
The next noteworthy point is that these detectors can be placed in a Renninger
arrangement: system one might be a meter away from the light source, and
system two might be a kilometer away, or a few million light–years away.
However distant these two detectors seem to be in the conventional Newtonian
sense, they are at distance zero in the Minkowski metric light–cone sense.
Although perhaps this is misleading: the above description also works if
I replace the photon by some massive particle, e.g.
an electron.
The Renninger arrangement is still possible: one detector is a few centimeters
away, the other is a few meters away in some pumped–out vacuum chamber.
The more distant detector is strictly inside the future light–cone of the
closer detector.
They are time–like separated.
And yet, despite this separation, they are entangled.
And this is the other remarkable part of the here–and–now interpretation:
clocks located in the lab frame, close to the locations of the detectors
show distinct times and time ordering.
However, the entanglement is
\begin_inset Quotes eld
\end_inset
here and now
\begin_inset Quotes erd
\end_inset
.
I'm studiously avoiding the words
\begin_inset Quotes eld
\end_inset
future
\begin_inset Quotes erd
\end_inset
and
\begin_inset Quotes eld
\end_inset
past
\begin_inset Quotes erd
\end_inset
, because I want to reserve these words to the stuff that happened before
here–and–now, vs the stuff that might happen after here–and–now.
Shit.
I need different vocabulary words to indicate the ordering, because there
seems to be two orderings: the relative ordering arising from the (local)
Minkowski geometry, and the ordering arising from the measurement entanglement.
That is, the entanglement happens in the here–and–now, even though the
two entangled systems are causally separated (for electrons) or light–like
separated (for photons).
\end_layout
\begin_layout Standard
Fuck me.
I suppose I should go off and read those Nobel–prize–winning papers from
Clauser etal.
because for all I know, I'm just re–inventing what they described.
See? This is the decision problem: should I forever read what someone else
has thought about and discovered, or should I go practice discovering things
on my own? Well, here I am, practicing.
Maybe this particular rock–climbing wall has been climbed before.
Maybe not.
Don't know.
So it goes.
\end_layout
\begin_layout Standard
So where was I? So, the next surprising thing in the development above is
where and how many–worlds shows up as a side–effect of decoherence.
First, the weak–coupling formula
\begin_inset Formula
\[
\left|n\right\rangle \times\left|b\right\rangle \mapsto\left|n\right\rangle \otimes\left|b\right\rangle
\]
\end_inset
should not be controversial.
It just says that there's a thermal bath
\begin_inset Formula $b$
\end_inset
and that we will use
\begin_inset Formula $\left|b\right\rangle $
\end_inset
to describe the state of that bath.
In particular,
\begin_inset Formula $\left|b\right\rangle $
\end_inset
is necessarily a mixed state and so instead of writing
\begin_inset Formula $\left|b\right\rangle $
\end_inset
I should have written a mixture density operator written as a sum of states
\begin_inset Formula $\bigcup_{s\in b}\rho\left(s\right)\left|s\right\rangle \left\langle s\right|$
\end_inset
for some mixture density
\begin_inset Formula $\rho\left(s\right)$
\end_inset
and the bigcup union
\begin_inset Formula $\bigcup_{s\in b}$
\end_inset
is used to remind us that this should be thought of as a topological set–union
of all of the pure states
\begin_inset Formula $s\in b$
\end_inset
.
It's not obvious that I need to invoke density operators; I think it's
OK to just acknowledge that
\begin_inset Formula $\left|b\right\rangle $
\end_inset
is a mixture, and, if needed to explicitly write
\begin_inset Formula
\[
\left|b\right\rangle =\bigcup_{s\in b}\rho\left(s\right)\left|s\right\rangle
\]
\end_inset
as needed to indicate that
\begin_inset Formula $b$
\end_inset
is just some distribution of pure states on some manifold.
And, since we're thermalizing, its reasonable to set
\begin_inset Formula $\rho\left(s\right)=1$
\end_inset
to indicate that the states are ergodically distributed.
\end_layout
\begin_layout Standard
And yet, what is surprising here is that weak–coupling again takes the form
of entanglement.
That is, in writing
\begin_inset Formula $\left|n\right\rangle \times\left|b\right\rangle \mapsto\left|n\right\rangle \otimes\left|b\right\rangle $
\end_inset
we again convert a Cartesian product into a tensor product, but this time
there's no actual photon needed to create this entanglement.
Or rather, there was no explicit photon.
At the micro–scale, a weak coupling between oscillators necessarily will
entail the exchange of virtual photons, one way or another: either due
to Brownian motion collisions in a gas, or some other statistical–mechanical
process.
That is, measurement is necessarily entanglement.
Just that, earlier, we used an explicit, real photon and considered its
absorption, vs.
now we implicitly assume virtual photon interactions.
So this is interesting.
\end_layout
\begin_layout Standard
The mixed–state notation implies that
\begin_inset Formula
\[
\left|n\right\rangle \otimes\left|b\right\rangle =\bigcup_{s\in b}\rho\left(s\right)\left|n\right\rangle \otimes\left|s\right\rangle
\]
\end_inset
holds at the microscopic level.
I'm not sure what to do with this, or what it really means.
\end_layout
\begin_layout Standard
The next formula that was also meant to be non–controversial
\end_layout
\begin_layout Standard
\begin_inset Formula
\[
\left|n\right\rangle \otimes\left|b\right\rangle \rightrightarrows\left|\left(b+n\right)^{\prime}\right\rangle
\]
\end_inset
but is this really valid? This was meant to denote the thermalization of
state
\begin_inset Formula $\left|n\right\rangle $
\end_inset
but the set–union notation indicates difficulty.
That is, the time evolution is supposed to be given in the Schrodinger
picture as
\begin_inset Formula $e^{-iEt}$
\end_inset
so that
\begin_inset Formula
\begin{align*}
\left|n\left(t\right)\right\rangle & =e^{-iE_{n}t}\left|n\left(0\right)\right\rangle \\
\left|s\left(t\right)\right\rangle & =e^{-iE_{s}t}\left|s\left(0\right)\right\rangle \\
\bigcup_{s\in b}\rho\left(s\right)\left|n\left(t\right)\right\rangle \otimes\left|s\left(t\right)\right\rangle & =\bigcup_{s\in b}\rho\left(s\right)e^{-i\left(E_{n}+E_{s}\right)t}\left|n\left(0\right)\right\rangle \otimes\left|s\left(0\right)\right\rangle
\end{align*}
\end_inset
and I'm not sure if this is supposed to be the textbook–standard description
of thermalization.
It doesn't quite feel right.
When I was a kid, my education did not include any formal development of
mixed states.
Instead, it was some hand–waving:
\begin_inset Quotes eld
\end_inset
oh, its what you get if you run the same experiment over and over
\begin_inset Quotes erd
\end_inset
and the set–union notation was not used, but it could be reasonably inferred:
the mixture is just the union of all repetitions of re–running the experiment.
Later on, I did eventually realize why the density of states
\begin_inset Formula $\rho\left(s\right)$
\end_inset
is a real number, and not a complex number, and that it represents a probabilit
y distribution, not a phase or amplitude.
What's more, the pure states
\begin_inset Formula $s$
\end_inset
correspond to single points on some manifold, and so mixtures were just
some distributions of points on a manifold.
This is clean and clear–cut, and seems to be straight–forward interpretationall
y.
So why am I balking?
\end_layout
\begin_layout Standard
Well, for one, the time evolution
\begin_inset Formula $e^{-i\left(E_{n}+E_{s}\right)t}$
\end_inset
is unitary, whereas I was expecting something dissipative.
Am I supposed to write
\begin_inset Formula $\rho\left(s,t\right)$
\end_inset
instead of
\begin_inset Formula $\rho\left(s\right)$
\end_inset
with the understanding that
\begin_inset Formula $\rho\left(s,t\right)$
\end_inset
is some ergodic process, possibly some Markovian process, maybe even necessaril
y Markovian? I don't know.
If this is the case, this is far outside of anything I've read about, before.
\end_layout
\begin_layout Standard
The other reason that I'm balking is that ...
wait for it ...
\begin_inset Formula $\bigcup_{s\in b}$
\end_inset
sure–as–hell feels like a set–union over many–worlds.
That is, each
\begin_inset Formula $s\in b$
\end_inset
is a single world, and
\begin_inset Formula $\rho\left(s\right)$
\end_inset
is the probability of being in that single world, and
\begin_inset Formula $\bigcup_{s\in b}$
\end_inset
is just the collection of them.
Very strangely, very unexpectedly, this fits with the naive hand–waving
description of a mixed state as the union of a repeated collection of experimen
ts.
Because, duh.
We ran Stern–Gerlach once, got spin up, ran it a second time, got spin–down
and each single run of the experiment, each single sodium atom flying through
those magnets, each one of these was a single world, a single experiment,
and the union of all of these, the splatter of a trillion sodium atoms
on that glass plate forming two distinct spots, that's of course the mixture,
that's what we meant by mixture.
But fuck me if
\begin_inset Formula $\bigcup_{s\in b}$
\end_inset
isn't a union over many worlds.
This is ...
unexpected and surprising.
I suppose some future reader of this text is thinking
\begin_inset Quotes eld
\end_inset
yeah, and its also wrong
\begin_inset Quotes erd
\end_inset
but if it's wrong, I do not yet see how.
\end_layout
\begin_layout Standard
Since
\begin_inset Formula $b$
\end_inset
is a thermal bath, it can also be called a canonical ensemble.
So that
\begin_inset Formula $\bigcup_{s\in b}$
\end_inset
is an enumeration over all states in the canonical ensemble.
And
\begin_inset Formula $\rho\left(s\right)\sim e^{-E/kT}$
\end_inset
is the weighting.
But I don't know how to make ends meet, here.
\end_layout
\begin_layout Standard
This brings us to the one statement that does seem problematic, and is central
to the development above.
Set
\begin_inset Formula $n_{1}=n_{2}=0$
\end_inset
and ignore normalization and overall phase to write the prior collapse
formula as
\begin_inset Formula
\begin{align*}
\left(\left|1\right\rangle \otimes\left|0\right\rangle +e^{i\phi}\left|0\right\rangle \otimes\left|1\right\rangle \right)\times\left|b_{1}\right\rangle \times\left|b_{2}\right\rangle & \mapsto\\
\left\{ \left[\left(\left|1\right\rangle \otimes\left|b_{1}\right\rangle \right)\times\left(\left|0\right\rangle \otimes\left|b_{2}\right\rangle \right)\right]\;,\;\left[\left(\left|0\right\rangle \otimes\left|b_{1}\right\rangle \right)\times\left(\left|1\right\rangle \otimes\left|b_{2}\right\rangle \right)\right]\right\}
\end{align*}
\end_inset
Here, the many–worlds interpretation manifests very specifically: there
are two experimental outcomes: in one outcome,
\begin_inset Formula $\left(\left|1\right\rangle \otimes\left|b_{1}\right\rangle \right)\times\left(\left|0\right\rangle \otimes\left|b_{2}\right\rangle \right)$
\end_inset
is explicitly observed, and in the other outcome
\begin_inset Formula $\left(\left|0\right\rangle \otimes\left|b_{1}\right\rangle \right)\times\left(\left|1\right\rangle \otimes\left|b_{2}\right\rangle \right)$
\end_inset
is observed, and these are the only two outcomes possible.
Each experimental outcome is equally likely, and so we write
\begin_inset Formula $\rho\left(0\times1\right)=\rho\left(1\times0\right)=1/2$
\end_inset
and so if we repeat the the experiment a trillion times, it is to be written
as
\begin_inset Formula
\[
\left|SG\right\rangle =\rho\left(1\times0\right)\left[\left(\left|1\right\rangle \otimes\left|b_{1}\right\rangle \right)\times\left(\left|0\right\rangle \otimes\left|b_{2}\right\rangle \right)\right]\;\cup\;\rho\left(0\times1\right)\left[\left(\left|0\right\rangle \otimes\left|b_{1}\right\rangle \right)\times\left(\left|1\right\rangle \otimes\left|b_{2}\right\rangle \right)\right]
\]
\end_inset
where
\begin_inset Formula $\left|SG\right\rangle $
\end_inset
is the **mixed** state representing the outcome of running Stern–Gerlach
a trillion times, and
\begin_inset Formula $\left|1\right\rangle \otimes\left|b_{1}\right\rangle $
\end_inset
is where the sodium atom hits the glass plate in the upper half, and
\begin_inset Formula $\left|0\right\rangle \otimes\left|b_{2}\right\rangle $
\end_inset
is where the sodium atom does NOT hit in the lower half, because there
is only one sodium atom, so if it hits high, then the world, the outcome
of a single–sodium–atom experiment is necessarily
\begin_inset Formula $\left(\left|1\right\rangle \otimes\left|b_{1}\right\rangle \right)\times\left(\left|0\right\rangle \otimes\left|b_{2}\right\rangle \right)$
\end_inset
.
\end_layout
\begin_layout Standard
And, from this, we get that the earlier notation of using
\begin_inset Formula $\left\{ \cdots\right\} $
\end_inset
to be the **set** of all possible measurement outcomes is really the same
thing as a mixed state, with only the practical different being that we
also use
\begin_inset Formula $\rho\left(s\right)$
\end_inset
to assign a probability to each outcome.
Oh, and if we were only to be a bit more careful in our notation, we should
eventually discover that
\begin_inset Formula $\rho\left(s\right)=\left|\psi\left(s\right)\right|^{2}$
\end_inset
but I've been too sloppy in my notation to be able to jump to that conclusion
just yet.
But that conclusion seems inevitable, so I'm not to worried.
\end_layout
\begin_layout Standard
So this has been a lot of work and effort, and what have we learned, exactly?
First, that we have a notation
\begin_inset Formula $\rightsquigarrow$
\end_inset
and also
\begin_inset Formula $\mapsto$
\end_inset
that both represent the process of entanglement.
In the former case, we write
\begin_inset Formula
\[
\gamma\times\left|a\right\rangle \times\left|b\right\rangle \rightsquigarrow c_{1}\left|a^{\prime}\right\rangle \otimes\left|b^{\prime}\right\rangle +c_{2}\left|a^{\prime\prime}\right\rangle \otimes\left|b^{\prime\prime}\right\rangle +\cdots
\]
\end_inset
where
\begin_inset Formula $\gamma$
\end_inset
is some specific real on–mass–shell particle that is absorbed.
As before, the Cartesian product on the LHS denotes that the distinct systems
can be treated as being distinct, non–interacting, thermally isolated,
etc.
The tensor product on the RHS is meant to denote a bonafide tensor product,
so that the squiggly arrow
\begin_inset Formula $\rightsquigarrow$
\end_inset
is understood to be the quotienting of Cartesian products modulo some bilinear
form.
\end_layout
\begin_layout Standard
The
\begin_inset Formula $c_{1},c_{2},\cdots$
\end_inset
are understood to be some complex numbers, and the
\begin_inset Formula $\left|\psi^{\prime}\right\rangle ,\left|\psi^{\prime\prime}\right\rangle ,\cdots$
\end_inset
some collection of states.
The entanglement has no specific location in space or time, which is the
point of the Renninger arrangement.
The location of here–and–now is the collection of points in space–time
where the RHS is non–zero.
For the most part, we want here–and–now to have compact support, but the
lesson from cosmology is that the last photon decoupling from the CMB,
and the last neutrino decoupling from nucleosynthesis participates in the
here–and–now, if you are so unlucky as to perceive a CMB photon (or neutrino,
as the case may be).
The point is that here–end–now is localized in space–time, but not in the
conventional sense of some Hamiltonian space–like surface.
Phew.
I marvel at this.
\end_layout
\begin_layout Standard
This
\begin_inset Formula $\rightsquigarrow$
\end_inset
operation meant to be the conventional quotient used to construct tensor
spaces from products of vector spaces.
Lets recall the textbook definition.
Just to be very specific and concrete here: for ordinary vectors
\begin_inset Formula $v_{1}$
\end_inset
and
\begin_inset Formula $v_{2}$
\end_inset
the tensor product
\begin_inset Formula $v_{1}\otimes v_{2}$
\end_inset
is defined as
\begin_inset Formula
\[
v_{1}\otimes v_{2}=v_{1}\times v_{2}\mod\,b\left(u,w\right)
\]
\end_inset
where mod is modulo, and
\begin_inset Formula $b\left(u,w\right)$
\end_inset
is the bilinear form obeying
\begin_inset Formula $b\left(cu,w\right)=b\left(u,cw\right)=cb\left(u,w\right)$
\end_inset
and also
\begin_inset Formula $b\left(u+v,w\right)=b\left(u,w\right)+b\left(v,w\right)$
\end_inset
and likewise
\begin_inset Formula $b\left(u,v+w\right)=b\left(u,v\right)+b\left(u,w\right)$
\end_inset
for all scalars
\begin_inset Formula $c\in\mathbb{K}$
\end_inset
in the real or complex field
\begin_inset Formula $\mathbb{K}$
\end_inset
and vectors
\begin_inset Formula $u,v,w$
\end_inset
in the vector spaces
\begin_inset Formula $V_{1}$
\end_inset
or
\begin_inset Formula $V_{2}$
\end_inset
as appropriate.
In particular, this implies that
\begin_inset Formula $v_{1}\otimes v_{2}$
\end_inset
is a coset: it is a collection of all Cartesian pairs of the form
\begin_inset Formula
\begin{align*}
v_{1}\otimes v_{2} & =\left\{ \left(u,w\right):\forall_{c\in\mathbb{K}}u=cv_{1}\mbox{ and }w=v_{2}/c\right\} \\
& =\bigcup_{c\in\mathbb{K}}\left\{ \left(cv_{1},v_{2}/c\right)\right\}
\end{align*}
\end_inset
and so on for the remaining bilinearity relations.
Look them up.
Notice how the second form is written as a set union.
\end_layout
\begin_layout Standard
I'm belaboring the above because I want to point out that the absorption
of the particle
\begin_inset Formula $\gamma$
\end_inset
creates a tensor space, and that space is not just one point, but a splattering
, an algebraic variety: insofar as
\begin_inset Formula $\left(v_{1},v_{2}\right)$
\end_inset
is a single point in the Cartesian space
\begin_inset Formula $V_{1}\times V_{2}$
\end_inset
, the tensor product
\begin_inset Formula $v_{1}\otimes v_{2}$
\end_inset
is some algebraic variety in
\begin_inset Formula $V_{1}\times V_{2}$
\end_inset
where all points in that variety are taken to be equivalent, i.e.
given by the equivalence relation defined by the bilinear form.
So the absorption of the
\begin_inset Formula $\gamma$
\end_inset
causes a single point in the Cartesian space to shatter into a surface.
Alternately, the absorption of the
\begin_inset Formula $\gamma$
\end_inset
causes a surface in the Cartesian space to condense or contract into an
equivalence.
Take your pick.
It's a quotienting modulo operation.
\end_layout
\begin_layout Standard
There's more: the use of the set–union notation
\begin_inset Formula $\bigcup_{c\in\mathbb{K}}$
\end_inset
is supposed to imbue the proceedings with a many–worlds–ish interpretation,
as noted many paragraphs earlier.
I think
\begin_inset Quotes eld
\end_inset
imbue
\begin_inset Quotes erd
\end_inset
is the right word, because we're glossing over some important details:
what's the topology? What's the quotient topology? Do I give these spaces
a measure? How? Which one? The tensor product of two algebraic varieties
is again an algebraic variety, at least, if you do it correctly with the
appropriate category–theoretic definition and also the Zariski topology,
which is NOT the standard topology, but is very weird (its not Hausdorff,
for starters.) And these days, you shouldn't say
\begin_inset Quotes eld
\end_inset
algebraic variety
\begin_inset Quotes erd
\end_inset
without also saying
\begin_inset Quotes eld
\end_inset
scheme
\begin_inset Quotes erd
\end_inset
, but it hardly seems like this should need to enter the conversation here....
or should it? I can't tell.
I can't make any case that it shouldn't.
So, in this sense, imagining tensor spaces to be kind–of–like algebraic
varieties is kind–of wrong.
But this needs to be articulated more carefully, and I can't do that today.
\end_layout
\begin_layout Standard
A wavefunction describing
\begin_inset Formula $n$
\end_inset
particles lives in
\begin_inset Formula $\mathbb{C}P^{n}$
\end_inset
the complex projective sphere, as required by wave–function normalization:
the so–called
\begin_inset Quotes eld
\end_inset
vector
\begin_inset Quotes erd
\end_inset
is constrained to be unit length.
This is the canonical example of homogeneous coordinates that appears at
the start of every book on algebraic geometry.
Why it is that Zariski topology never comes up in QM is because I guess
maybe because prime ideals never come up, so we're not doing spectra of
rings.
\end_layout
\begin_layout Standard
The operator
\begin_inset Formula $\mapsto$
\end_inset
does the same thing, but it does not involve any explicit particle
\begin_inset Formula $\gamma$
\end_inset
; it is implicit.
If this was perturbation theory, this could be treated as an interaction:
some exchange of virtual particles, possibly with loop diagrams to your
hearts content.
It doesn't have to be perturbative, its just again, a map of the form
\begin_inset Formula
\[
\left|a\right\rangle \times\left|b\right\rangle \mapsto c_{1}\left|a^{\prime}\right\rangle \otimes\left|b^{\prime}\right\rangle +c_{2}\left|a^{\prime\prime}\right\rangle \otimes\left|b^{\prime\prime}\right\rangle +\cdots
\]
\end_inset
and for the case of the weak coupling above, we used
\begin_inset Formula $c_{2},c_{3},\cdots=0$
\end_inset
and
\begin_inset Formula $a=a^{\prime}$
\end_inset
and
\begin_inset Formula $b=b^{\prime}.$
\end_inset
\end_layout
\begin_layout Standard
However, there is another difference between these two, and it requires
using the word
\begin_inset Quotes eld
\end_inset
eigenstate
\begin_inset Quotes erd
\end_inset
which, until now, I've somehow managed to avoid saying.
The time has come, I guess.
The operator
\begin_inset Formula $\mapsto$
\end_inset
has a distributive property that needs to be stated more explicitly.
It is a abstraction of the earlier form:
\begin_inset Formula
\begin{align*}
\left(\left|a\right\rangle \otimes\left|b\right\rangle +\left|c\right\rangle \otimes\left|d\right\rangle \right)\times\left|e\right\rangle & \mapsto\\
\rho\left(a,b,e\right)\left[\left|a\right\rangle \otimes\left|b\right\rangle \otimes\left|e\right\rangle \right]\;\cup\;\rho\left(c,d,e\right)\left[\left|c\right\rangle \otimes\left|d\right\rangle \otimes\left|e\right\rangle \right]
\end{align*}
\end_inset
where the square brackets
\begin_inset Formula $\left[\cdots\right]$
\end_inset
are interpreted as a
\begin_inset Quotes eld
\end_inset
single world
\begin_inset Quotes erd
\end_inset
and the union
\begin_inset Formula $\cup$
\end_inset
is interpreted ambiguously as a collection of many worlds or a mixed state.
The word
\begin_inset Quotes eld
\end_inset
eigenstate
\begin_inset Quotes erd
\end_inset
enters the game here, because the LHS above only makes sense insofar as
the states
\begin_inset Formula $\left|a\right\rangle $
\end_inset
etc are eigenstates of some operator, presumable an operator that commutes
with the Hamiltonian, or something like that.
That, together with the idea that states like
\begin_inset Formula $\left|b\right\rangle $
\end_inset
and
\begin_inset Formula $\left|d\right\rangle $
\end_inset
are going to be spatially separated, so eigenstates of the position operator,
roughly speaking.
And all these various operators might not commute, which adds to the confusion.
At any rate, this distributive property seems to be the Born rule, in some
kind of fancy, unfamiliar clothing.
Or something like that.
\end_layout
\begin_layout Standard
At this point, I'm tired and have to wrap it up.
I've discovered a whole new treasure–trove of things to get confused about.
Still, some kind of forward progress seems to have been made.
The general concept of entanglement seems to have been pinned down a bit
more carefully.
The general concept of collapse seems to have been shown to be the same
thing as entanglement, but different.
I seem to have an argument that mixed states are the same thing as many–worlds,
but it's not clear that this has altered any philosophical positions in
the slightest.
The structure of the distributive property remains too cloudy to say more.
\end_layout
\begin_layout Standard
I've also hoped, for years, decades? to find free–will in all of this infrastruc
ture; and I am hardly the first.
The menu–choice of linear logic seems to be an adequate location on which
to attach the choices provided by free will, but nothing above, nothing
in the last three days, says sufficient groundwork to avoid the basic probabili
stic Copenhagen interpretation.
I mean, I guess the Renninger stuff moves beyond Copenhagen, but only a
smidge.
I suspect that some model of agency, and sensorimotor systems are required
to fully articulate the possibility of free will during the above entanglement
operations.
And I've got nothing at all, there.
Just fumes and a vivid imagination.
So it goes.
Day at a time.
Later, dude.
\end_layout
\begin_layout Subsection*
23 May 2025
\end_layout
\begin_layout Standard
While falling asleep, I noticed that cryptocurrencies try to find hashing
algos that result in a block of zeros: they are doing a kind of modulo
calculation.
That mixes inputs from all over the place.
That's ergodic and mixing.
And puts results onto an unchangeable blockchain.
The history.
So maybe, but analogy, Bostrom's Simulation Hypothesis says we live on
a block–chain.
I wonder if there's some hashing function out there that resembles ...
physical processes more closely.
Hmm.
\end_layout
\begin_layout Standard
The other after–thought I had about the above was the need to clarify how/why
the coupling to a thermal bath results in decoherence.
That is, a naive thought is that the coupling to the baths
\begin_inset Formula
\[
\left(\left|1\right\rangle \otimes\left|0\right\rangle +e^{i\phi}\left|0\right\rangle \otimes\left|1\right\rangle \right)\times\left|b_{1}\right\rangle \times\left|b_{2}\right\rangle
\]
\end_inset
could have resulted in the entanglement of the baths.
And maybe it does.
For a little while.
But then, the ergodic evolution of the baths eventually breaks that entanglemen
t.
And it does so in finite time, a characteristic mixing time or diffusion
time.
So the bath coupling, and the definition of
\begin_inset Formula $\mapsto$
\end_inset
is a bit of sleight of hand.
That is, up above, I defined
\begin_inset Formula $\mapsto$
\end_inset
to be wave function collapse, by definition, so, of course, nothing remains
to be done after doing so.
This is not entirely satisfactory.
\end_layout
\begin_layout Standard
The point of bath entanglement is the old one, from months/years ago where
I blurble onwards about interferometer diamonds.
That is, it is possible that
\begin_inset Formula $b_{1}$
\end_inset
and
\begin_inset Formula $b_{2}$
\end_inset
get entangled, and stay that way, until some future date when
\begin_inset Formula $b_{1}$
\end_inset
and
\begin_inset Formula $b_{2}$
\end_inset
are brought together again, into the same nearby location in space–time,
and compared: only then is it absolutely mandatory that consistent histories
be observable.
There's no specific demand for consistent histories before then.
And the lack of this demand is why I blurbled that these interferometric
diamonds are so important.
So it seems that is the question facing us, for now: do thermal baths get
entangled, or not? Common sense says that baths cause decoherenece.
But I do not yet understand how that works.
And I guess nobody does, because otherwise, we wouldn't be wasting hot
air talking about unitary evolution.
Whatever.
Later.
I'm going for a bike ride now.
\end_layout
\begin_layout Subsection*
24 May 2025
\end_layout
\begin_layout Standard
OK.
So what does it mean to
\begin_inset Quotes eld
\end_inset
couple together
\begin_inset Quotes erd
\end_inset
some quantum systems? Well, I could look it up on line.
Or I can invent something from scratch.
Inventing is so much more fun.
Also, infuriating, because, like, shouldn't I have learned this in class,
already? How come I don't remember this from homework problems? But I don't.
Argh.
\end_layout
\begin_layout Standard
Also, FWIW, there is some HUGE quantum computing industry that has been
running to decades, and has analyzed problems like these six was from Sunday.
So nothing below is
\begin_inset Quotes eld
\end_inset
new
\begin_inset Quotes erd
\end_inset
, its just...
a personal take, ignoring what scholars in the field have done before.
Why am I so constantly defensive in my posture? I know.
Because this is a psychological self–protection mechanism.
I feel as if I am always dismissed, that nothing and no one cares or is
interested.
I live in a little isolated bubble, ineffective, unattached, non–interacting.
So let it go both ways: they ignore me; I ignore them.
Weakly.
A weak interaction, only.
So with that disclaimer as to the nature of the easily–dismissed unimportant
silliness that is to follow, we begin our journey around the garden path.
\end_layout
\begin_layout Standard
The simple harmonic oscillator.
\begin_inset Formula $H=\hbar\omega\left(a^{\dagger}a+1/2\right)$
\end_inset
with states
\begin_inset Formula $\left|0\right\rangle ,\left|1\right\rangle ,\cdots$
\end_inset
Consider two of them, labelled 1 and 2, with an interaction Hamiltonian
\begin_inset Formula $H_{int}=\epsilon\left(a_{2}^{\dagger}a_{1}+a_{1}^{\dagger}a_{2}\right)$
\end_inset
for some small number
\begin_inset Formula $\epsilon\ll\hbar\omega$
\end_inset
.
The task is to diagonalize the Hamiltonian.
To keep with the above, the first oscillator will be the
\begin_inset Quotes eld
\end_inset
detector
\begin_inset Quotes erd
\end_inset
, while the second one will be part of the
\begin_inset Quotes eld
\end_inset
thermal bath
\begin_inset Quotes erd
\end_inset
.
We'll add more to the bath, but for now, just these two.
Initially, bot are in the ground state, and nothing interesting.
The interesting case is to pump the first oscillator, and watch the time
dynamics.
But, before that, lets diagonalize, to see what the long–time steady–state
is.
For this, lets simplify; we know the system will never have more than one
quantum of energy, so ignore the states
\begin_inset Formula $\left|2\right\rangle ,\left|3\right\rangle ,\cdots$
\end_inset
and create a vector basis for the Cartesian product
\begin_inset Formula $SHO_{1}\times SHO_{2}$
\end_inset
as
\begin_inset Formula
\begin{align*}
e_{1} & =\left|0\right\rangle \times\left|0\right\rangle \\
e_{2} & =\left|1\right\rangle \times\left|0\right\rangle \\
e_{3} & =\left|0\right\rangle \times\left|1\right\rangle \\
e_{4} & =\left|1\right\rangle \times\left|1\right\rangle
\end{align*}
\end_inset
As noted, the Cartesian product is only appropriate for non–interacting,
thermally isolated systems, so if they are going to interact, the very
first thing we do is to write the tensor product
\begin_inset Formula $\otimes$
\end_inset
instead.
The Hamiltonian in this basis is, in matrix form, a
\begin_inset Formula $4\times4$
\end_inset
matrix, is
\begin_inset Formula
\[
H=\left[\begin{array}{cccc}
1\\
& 2 & \epsilon\\
& \epsilon & 2\\
& & & 3
\end{array}\right]
\]
\end_inset
so the ground state has energy
\begin_inset Formula $\frac{1}{2}+\frac{1}{2}=1$
\end_inset
and note that one can write both
\begin_inset Formula $e_{1}=\left|0\right\rangle \otimes\left|0\right\rangle $
\end_inset
and also
\begin_inset Formula $e_{1}=\left|0\right\rangle \times\left|0\right\rangle $
\end_inset
because the interaction term never couples to the ground state.
In particular, this means that the state
\begin_inset Formula $e_{1}=\left|0\right\rangle \times\left|0\right\rangle $
\end_inset
can have two distinct phases
\begin_inset Formula $e^{i\phi_{1}}$
\end_inset
and
\begin_inset Formula $e^{i\phi_{2}}$
\end_inset
that are entirely independent of one–another, whereas the tensor state
\begin_inset Formula $e_{1}=\left|0\right\rangle \otimes\left|0\right\rangle $
\end_inset
can only have one phase
\begin_inset Formula $e^{i\phi}$
\end_inset
by bilinearity.
Now, for this simplified model, none of this matters at all.
Nor, in general, do overall phases matter ...
except in one case: the Bohm–Aharonov effect.
So one can imagine some different variant of this thought experiment, having
some magnetic field, and having some setup where Cartesian products or
not, phase differences, matter.
So, for the present case, having
\begin_inset Quotes eld
\end_inset
thermally isolated, non–interacting ground states
\begin_inset Quotes erd
\end_inset
suggests that
\begin_inset Formula $e_{1}=\left|0\right\rangle \times\left|0\right\rangle $
\end_inset
is the correct notation, but this is kind of meaningless, for the current
setup, because there's no way to tell.
The experimental setups are
\begin_inset Quotes eld
\end_inset
philosophically indistinguishable
\begin_inset Quotes erd
\end_inset
: we can't tell these two cases apart.
Enough.
\end_layout
\begin_layout Standard
The first excited state has energy
\begin_inset Formula $\frac{1}{2}+\frac{3}{2}=\frac{3}{2}+\frac{1}{2}=2$
\end_inset
for the
\begin_inset Formula $\epsilon=0$
\end_inset
case and for the
\begin_inset Formula $\epsilon\ne0$
\end_inset
case we have the block diagonal
\begin_inset Formula
\[
H=\left[\begin{array}{cc}
2 & \epsilon\\
\epsilon & 2
\end{array}\right]
\]
\end_inset
which has eigenvalues
\begin_inset Formula $0=\det\left(H-\lambda I\right)$
\end_inset
given by the characteristic equation
\begin_inset Formula $0=\left(2-\lambda\right)^{2}-\epsilon^{2}$
\end_inset
or
\begin_inset Formula $0=\lambda^{2}-4\lambda+4-\epsilon^{2}$
\end_inset
or
\begin_inset Formula
\[
\lambda=\frac{4\pm\sqrt{16-4\left(4-\epsilon^{2}\right)}}{2}=2\pm\epsilon
\]
\end_inset
What the heck does this even mean? As I adiabatically switch on an interaction
\begin_inset Formula $\epsilon$
\end_inset
the system gets a
\begin_inset Quotes eld
\end_inset
line splitting
\begin_inset Quotes erd
\end_inset
, where one state has slightly higher energy than the other.
How the heck did this happen? I had two SHO's, and wanted to consider the
case where one or the other is excited, but not both, and of course they're
coupled, duh, but line splitting? Really?
\end_layout
\begin_layout Standard
Well, what are the eigenvectors? That's easy:
\begin_inset Formula
\[
v_{-}=\frac{1}{\sqrt{2}}\left[\begin{array}{c}
1\\
-1
\end{array}\right]\;\mbox{ and }\;v_{+}=\frac{1}{\sqrt{2}}\left[\begin{array}{c}
1\\
1
\end{array}\right]
\]
\end_inset
so if we adiabatically increase
\begin_inset Formula $\epsilon$
\end_inset
up from zero, we expect the system to eventually thermalize into the
\begin_inset Formula $v_{-}$
\end_inset
state in the laboratory frame.
Maybe.
What is the meaning of
\begin_inset Formula $v_{+}$
\end_inset
? Well, if we really are adiabatic, then there is some chance that the system
settles into the
\begin_inset Formula $v_{+}$
\end_inset
state.
It could happen.
This is the wrong time to start hand–waving about thermodynamics, but if
we did so, then there would be a canonical ensemble (a mixed state) with
both
\begin_inset Formula $v_{-}$
\end_inset
and
\begin_inset Formula $v_{+}$
\end_inset
populated with probability
\begin_inset Formula $e^{-E_{\pm}/kT}$
\end_inset
but it is too early to do such hand–waving.
Maybe later.
\end_layout
\begin_layout Standard
The initial state, just after the detector SHO detects, is given by
\begin_inset Formula
\[
e_{2}=\left|1\right\rangle \otimes\left|0\right\rangle =\left[\begin{array}{c}
1\\
0
\end{array}\right]=\frac{1}{\sqrt{2}}\left(v_{-}+v_{+}\right)
\]
\end_inset
and the time evolution of this is
\begin_inset Formula
\[
e_{2}\left(t\right)=\frac{1}{\sqrt{2}}\left(e^{-iE_{-}t}v_{-}+e^{-iE_{+}t}v_{+}\right)
\]
\end_inset
or, writing
\begin_inset Formula $E_{\pm}=2\pm\epsilon=E_{0}\pm E_{int}$
\end_inset
then
\begin_inset Formula
\begin{align*}
e_{2}\left(t\right) & =\frac{1}{\sqrt{2}}e^{-iE_{0}t}\left(e^{+iE_{int}t}v_{-}+e^{-iE_{int}t}v_{+}\right)\\
& =\frac{e^{-iE_{0}t}}{2}\left[\begin{array}{c}
e^{-iE_{int}t}+e^{+iE_{int}t}\\
e^{-iE_{int}t}-e^{+iE_{int}t}
\end{array}\right]\\
& =e^{-iE_{0}t}\left[\begin{array}{c}
\cos E_{int}t\\
-i\sin E_{int}t
\end{array}\right]
\end{align*}
\end_inset
and so if we later
\begin_inset Quotes eld
\end_inset
measure
\begin_inset Quotes erd
\end_inset
(whatever the fuck that means) the second SHO, by applying the
\begin_inset Quotes eld
\end_inset
measurement
\begin_inset Quotes erd
\end_inset
projection
\begin_inset Formula
\[
P_{B}=e_{2}\left(0\right)e_{2}^{\dagger}\left(0\right)=\left[\left|0\right\rangle \otimes\left|1\right\rangle \right]\left[\left\langle 0\right|\otimes\left\langle 1\right|\right]=\left[\begin{array}{cc}
0 & 0\\
0 & 1
\end{array}\right]
\]
\end_inset
then there is a beat frequency:
\begin_inset Formula
\[
\left|P_{B}e_{2}\left(t\right)\right|^{2}=\frac{1}{4}\left|e^{-iE_{int}t}-e^{+iE_{int}t}\right|^{2}=\sin^{2}E_{int}t
\]
\end_inset
and so one could say that energy is flowing into and out of the second oscillato
r with the beat frequency
\begin_inset Formula $\omega_{int}=E_{int}/\hbar$
\end_inset
after reinserting
\begin_inset Formula $\hbar=1$
\end_inset
.
This is 100% analogous to the college freshman examples of beat frequencies
in AM modulation and whatever it is that are being demonstrated.
Except that here, we have to use our imagination for a thought experiment
where it is possible to isolate the the second oscillator, and measure
the likelihood of it being in some excited state.
The problem here is two–fold: the need to imagine measuring, when the whole
point of this essay is to figure out what it means to
\begin_inset Quotes eld
\end_inset
measure
\begin_inset Quotes erd
\end_inset
.
The second problem is we want to eventually arrive at decoherence, where
there is no more of this beat–frequency stuff, but instead a canonical
ensemble, where, in half of the members of that ensemble have the second
oscillator in the excited state, and
\begin_inset Quotes eld
\end_inset
decoherence
\begin_inset Quotes erd
\end_inset
means that the time dependence has been lost.
So all this verbiage is a statement that we're not done yet, there's more.
\end_layout
\begin_layout Standard
The
\begin_inset Quotes eld
\end_inset
more
\begin_inset Quotes erd
\end_inset
, in the present case, is to add more oscillators to the
\begin_inset Quotes eld
\end_inset
bath
\begin_inset Quotes erd
\end_inset
.
As before, we want a weak coupling
\begin_inset Formula $H_{int}\ll H_{0}$
\end_inset
but now we have a choice for how the oscillators are to be interconnected.
We could arrange them into a linear chain, a la Fermi–Pasta–Ulam–Tsingou
geometry.
We could arrange them on a hub–n–spoke model.
Which seems less interesting but possible.
We could arrange them on some random graph, with edges representing pair–wise
interactions.
What's more, the interactions could be of varying strength.
The connectivity of the graph
\begin_inset Quotes eld
\end_inset
determines
\begin_inset Quotes erd
\end_inset
the shape of space.
Clearly, a chain is one–dimensional, and 2D and 3D lattices, likewise.
Random graphs are of indeterminate dimension, usually some high dimension.
\end_layout
\begin_layout Standard
This implies that the dimension of space is fixed not by Newton, Minkowski
or Einstein, but rather the connectivity of the nodes in the thermal bath.
Given mean–field results, we know that generically, 1D systems do not have
phase transitions, while 2D and 3D systems do, and have complex dynamics,
in general.
We also know that systems in higher dimensions can be described by mean–fields.
This leads to a freaky hypothesis: is space three–dimensional, because
there is a phase transition between lower and higher dimensions, at the
boundary between chaotic and mean–field results? This sounds insane from
any other perspective, but if the goal is to build a thermal bath of SHO's
with weak interactions, then the behavior of that network, of that bath,
is going to be determined by the network connectivity of the SHO's in that
bath.
\end_layout
\begin_layout Standard
This is an advanced question that I am not prepared to tackle at this time.
Well, but still, a few short comments are in order.
The solutions to the Schrodinger equation in 3D give exact results for
the spectrum of the hydrogen atom, and this would not hold in 2D or 4D,
ergo space is 3D.
The solutions to the propagator for the D'Alambertian are exactly
\begin_inset Formula $\delta^{4}\left(x-ct\right)$
\end_inset
and this would not work in any other dimension.
So, in this sense, we
\begin_inset Quotes eld
\end_inset
know
\begin_inset Quotes erd
\end_inset
space is N–dimensional for N=3 an integer.
What about non–integral dimensions? Like
\begin_inset Formula $N=3+\epsilon$
\end_inset
, for some small but indeterminate
\begin_inset Formula $\epsilon$
\end_inset
it is stochastic, and whose expectation value is zero? First, we don't
really know how to write a Schrodinger equation for this situation: it
would require writing down a second–quantized theory, aka QFT for a random
network of points, with nearest–neighbor interactions that resemble the
D'Alembertian when suitably coarse–grained.
i.e.
when taking some expectation value over nearest–neighbor interactions.
So this random network is imagined to happen
\begin_inset Quotes eld
\end_inset
at the Planck scale
\begin_inset Quotes erd
\end_inset
so that by the time we get to hydrogen–atom scale, space really does average
out to an expectation value that looks 3D.
FWIW, I see no particular issues with Dirac spinors, either: one can define
a Clifford algebra at each point on the network, build Weyl spinors on
points, and then have pairwise interactions between them, that, when coarse
grained, end up being Dirac spinors.
Would it be possible to derive the Einstein Field Equations as the expectation
value of a
\begin_inset Quotes eld
\end_inset
thermal bath
\begin_inset Quotes erd
\end_inset
of weakly interacting oscillators, poised at the critical point between
hard–chaos in 3D and mean–field theory in
\begin_inset Formula $3+\epsilon$
\end_inset
dimensions? I dunno.
This is not out of bounds.
It could be wrong, but it certainly is something that could be analyzed,
simulated, etc.
\end_layout
\begin_layout Standard
Well, but it is out–of–bounds for today's efforts.
We are lacking in the sophistication to make progress.
So lets step back a bit, and go through some simpler cases first.
Specifically, we want several things: two thermal baths, initially isolated
from each other, but then connected with a single Renninger–style wave–collapse
entanglement thingy, as described above, and a demonstration that such
an entanglement gives us Born–rule type probabilities, and Mott–problem
type coherence/decoherence.
That needs to remaind the focus, before getting nebulous.
\end_layout
\begin_layout Standard
So consider first a 1D chain of SHO's, weak interaction, pumped so that
only one excitation is on the chain, so that we can ignore the case of
more than one excitation.
The low–brow matrix representation is
\begin_inset Formula
\[
H=\left[\begin{array}{cccc}
2 & \epsilon\\
\epsilon & 2 & \epsilon\\
& \epsilon & 2 & \ddots\\
& & \ddots & \ddots
\end{array}\right]
\]
\end_inset
where the
\begin_inset Formula $i$
\end_inset
'th row/column corresponds to the
\begin_inset Formula $i$
\end_inset
'th SHO being in an excited state.
As before,
\begin_inset Formula $2=\frac{1}{2}+\frac{3}{2}$
\end_inset
.
This tri–diagonal matrix is the block submatrix of the high–brow expression
for a 1D chain of SHO's
\begin_inset Formula
\begin{align*}
H & =H_{0}+H_{int}\\
& =\sum_{i=1}^{N}\hbar\left(a_{i}^{\dagger}a_{i}+\frac{1}{2}\right)+\epsilon\sum_{i=1}^{N-1}a_{i+1}^{\dagger}a_{i}+a_{i}^{\dagger}a_{i+1}
\end{align*}
\end_inset
The single–excitation matrix basis has
\begin_inset Formula $N$
\end_inset
basis vectors
\begin_inset Formula
\begin{align*}
e_{1} & =\left|1\right\rangle \otimes\left|0\right\rangle \otimes\left|0\right\rangle \otimes\cdots\otimes\left|0\right\rangle \\
e_{2} & =\left|0\right\rangle \otimes\left|1\right\rangle \otimes\left|0\right\rangle \otimes\cdots\otimes\left|0\right\rangle \\
\vdots\\
e_{N} & =\left|0\right\rangle \otimes\left|0\right\rangle \otimes\left|0\right\rangle \otimes\cdots\otimes\left|1\right\rangle
\end{align*}
\end_inset
and, as before, we imagine that it is somehow possible to somehow
\begin_inset Quotes eld
\end_inset
measure
\begin_inset Quotes erd
\end_inset
each of these oscillators individually, even though, as before, the concept
of
\begin_inset Quotes eld
\end_inset
measurement
\begin_inset Quotes erd
\end_inset
remains ambiguous.
To remove some ambiguity, one kind of measurement involves using conventional
algebra to write expressions that belong to some tensor algebra which is
used to make formal algebraic statements about the bath.
In this case,
\begin_inset Quotes eld
\end_inset
measurements
\begin_inset Quotes erd
\end_inset
are simply the conventional algebraic manipulations associated with conventiona
l bra-ket notation and conventional tensor algebra stuff.
Lets call this the
\begin_inset Quotes eld
\end_inset
bath algebra measurement
\begin_inset Quotes erd
\end_inset
.
This is distinct from the Renninger entanglement that is the intended topic,
which I guess we can still call the
\begin_inset Quotes eld
\end_inset
wave function collapse measurement
\begin_inset Quotes erd
\end_inset
.
I'm trying to draw a distinct boundary here, to avoid later confusion.
\end_layout
\begin_layout Standard
The eigenvalues and eigenvectors of
\begin_inset Formula $H$
\end_inset
are well–known, and follow from the fact that the tri–diagonal form
\begin_inset Quotes eld
\end_inset
looks like
\begin_inset Quotes erd
\end_inset
a (scaled) 1D Laplacian plus a (scaled) identity matrix.
The solutions arise via roots–of–unity type manipulations, with the eigenvector
s
\begin_inset Formula
\[
v_{k}=\sum_{j=1}^{N}\cos\left(\frac{2\pi k}{N}\left(j-1\right)\right)e_{j}
\]
\end_inset
and the eigenvalues
\begin_inset Formula
\[
E_{k}=2+\epsilon\cos\left(\frac{2\pi k}{N}\right)
\]
\end_inset
for
\begin_inset Formula $k=0,\cdots,N-1$
\end_inset
.
I think I got that right.
I'm doing this from memory.
Seems to check out.
Hope I didn't blow this.
So, as before, line splitting, a bunch of closely spaced levels.
Beat–frequency stuff, if I look at only one oscillator.
Requires hand–waving to get a canonical ensemble.
\end_layout
\begin_layout Standard
Well, lets do some of the hand–waving.
If we start with the system in the ground state, and then hit
\begin_inset Formula $e_{1}$
\end_inset
with a hammer, then write
\begin_inset Formula $e_{1}$
\end_inset
as an expansion in the
\begin_inset Formula $v_{k}$
\end_inset
we find that the energy is distributed across all modes
\begin_inset Formula $v_{k}$
\end_inset
via an equipartition theorem.
I'm too lazy to verify this, its boring algebra.
However, none of the modes
\begin_inset Formula $v_{k}$
\end_inset
are interacting and so the system will just do its version of Poincare recurrenc
e, without thermalizing.
That is, we distinguish ergodic and mixing: roughly speaking, the wave–modes
are ergodic, but not mixing.
I'm not sure of what the precise definition is for ergodicity for waves,
but I think this is correct.
\end_layout
\begin_layout Standard
But this analysis is extremely shallow, and is also unsurprising.
Compare, for example to the resonant wave interactions in the Fermi–Pasta–Ulam–
Tsingou problem.
The obvious question then is: given
\begin_inset Formula $N$
\end_inset
SHO's, and pair–wise interactions of the form
\begin_inset Formula $H_{int}=\epsilon a_{i}^{\dagger}a_{j}$
\end_inset
for
\begin_inset Formula $i\ne j$
\end_inset
is there ever any kind of network of interactions that is not diagonalizable?
Insofar as the single–phonon excitation mode (the sub-block of the Hamiltonian)
can be written as a matrix, an
\begin_inset Formula $N\times N$
\end_inset
matrix, a Hermitian one at that, then we know it is always diagonalizable
with real eigenvalues.
The only ambiguity that can arise is when some of the eigenvalues are degenerat
e; then these could be imagined to lead to mixing.
But to actually get this, we need connectivity so that there's some non–trivial
dispersion relation for the modes
\begin_inset Formula $v_{k}$
\end_inset
and the corresponding energy of those modes
\begin_inset Formula $E_{k}$
\end_inset
that works in analogy to a resonant interaction.
\end_layout
\begin_layout Standard
And this is where my knowledge of graph theory hits the end of the line:
are there any graphs at all, random, on a lattice, whatever, that have
a resonant interaction? I studied the preprint A route to thermalization
in the α-Fermi-Pasta-Ulam system, Miguel Onorato, Lara Vozella, Davide
Proment, Yuri V.
Lvov https://arxiv.org/abs/1402.1603 carefully, back in Sept 2020 and added
a huge chunk to the FPUT article, and also wrote the wiki page for resonant
interaction.
So I get all that.
What I don't know is whether one can have resonant interactions on random
graphs that encode the single–phonon couplings of SHO's on those graphs.
If so, then bingo, we've got an answer.
If not, then what about two, three or more phonons? If we do have resonant
interactions, than what can be said about which graphs allow them, and
which ones do not? Is there some phase–transition between the graphs that
support thermalization, ad the ones that do not?
\end_layout
\begin_layout Standard
This is fascinating! I will hypothesize that, yes, there is such a phase
transition, and I suppose several of them: between 1D and higher–dim lattices,
and then again, another one between those and the mean–field regime.
And these questions are quite precise: I am no longer hand–waving here:
We've got a specific Hamiltonian,
\begin_inset Formula $H=H_{0}+H_{int}$
\end_inset
exactly of the form written above, and we've got a very specific question:
what's the dispersion relation? Wowza! this is fucking awesome, because
it's concrete, and does not require speculation.
Well, it does require actually answering the question, which might be hard.
And there's some chance that I'll be disappointed by the answer? Still,
hard to see how: arranging for degenerate eigenvalues is not hard, and
then associating some wave–vector–like modes that have the appearance of
propagating should not be hard...
unless these are all
\begin_inset Quotes eld
\end_inset
bound modes
\begin_inset Quotes erd
\end_inset
and not
\begin_inset Quotes eld
\end_inset
free modes
\begin_inset Quotes erd
\end_inset
, but it seems like free modes would be the most common case here, since
I'm already in the fourrier regime, because that is what diagonalizing
a matrix means.
\end_layout
\begin_layout Standard
So lets imagine that thermalization is possible, in the form described above.
Where does that leave us? We have two baths.
Both are in the ground state.
We entangle them by hitting them with a single photon, that entangles a
single–phonon excitation in one bath, or in the other bath.
We can use this single–photon entanglement to write a combined matrix
\begin_inset Formula $H=H_{A}+H_{B}+H_{tangle}$
\end_inset
where
\begin_inset Formula $H_{A}$
\end_inset
and
\begin_inset Formula $H_{B}$
\end_inset
are the two thermalizing baths, and
\begin_inset Formula $H_{tangle}$
\end_inset
is the single–photon Renninger–arrangement entanglement.
And I bet dollars to donuts that
\begin_inset Formula $H_{tangle}$
\end_inset
because it is just a single graph edge, does not allow thermalization to
occur between
\begin_inset Formula $H_{A}$
\end_inset
and
\begin_inset Formula $H_{B}$
\end_inset
so that if one of these two is excited, then the other cannot be.
And since the thermalization is irrevocable, this is the fundamental process
for wave–function collapse.
\end_layout
\begin_layout Standard
There is still one part that is still confusing ...
if only one, or the other can accept the phonon, then which one gets it?
How does the bifurcation actually work? Once set in motion, I understand
it thermalizes, but before that, how ...
??? I cannot yet find words for whatever it is that is confusing me here.
Anyway, time for a dinner break.
So ...
later dude.
This is fascinating.
Feels like another step, this time a large step.
\end_layout
\begin_layout Subsection*
24 May 2025 Later
\end_layout
\begin_layout Standard
Well, see, here's the problem.
The above describes a plausible method for creating quantum systems that
thermalize, using non–relativistic QM in the lab frame in the Hamiltonian
picture.
So how do I hook that up to Renninger? To recap: I now have two systems,
two thermalizing systems, described by Hamiltonians
\begin_inset Formula $H_{A}$
\end_inset
and
\begin_inset Formula $H_{B}$
\end_inset
, such that when I hit one specific detector SHO, the energy of that hit
will get mixed.
By convention, call the thing getting thermalized a
\begin_inset Quotes eld
\end_inset
phonon
\begin_inset Quotes erd
\end_inset
, just to give it a distinct name.
That is, systems A and B start in the ground state (zero phonons), and
when detector A or detector B, creating a single phonon
\begin_inset Formula $a_{A}^{\dagger}:\left|0_{A}\right\rangle \mapsto\left|1_{A}\right\rangle $
\end_inset
or
\begin_inset Formula $a_{B}^{\dagger}:\left|0_{B}\right\rangle \mapsto\left|1_{B}\right\rangle $
\end_inset
, then after some time passes in the lab frame of A and B, that phonon will
get thermalized, per the process described/hypothesized above.
\end_layout
\begin_layout Standard
The vocabulary that I want to use for the Renninger state is to say that
there is a single photon
\begin_inset Formula $\gamma$
\end_inset
that is absorbed, and it creates a specific superposition of
\begin_inset Formula $\left|1_{A}\right\rangle $
\end_inset
and
\begin_inset Formula $\left|1_{B}\right\rangle $
\end_inset
.
This was given several days ago, so let me repeat in the updated notation:
\begin_inset Formula
\[
\gamma\times\left|0_{A}\right\rangle \times\left|0_{B}\right\rangle \rightsquigarrow\frac{e^{i\theta}}{\sqrt{2}}\left(\left|1_{A}\right\rangle \otimes\left|0_{B}\right\rangle +e^{i\phi}\left|0_{A}\right\rangle \otimes\left|1_{B}\right\rangle \right)
\]
\end_inset
where, again, as before, the LHS uses the Cartesian product to indicate
that the systems on the LHS are not yet entangled, while those on the RHS
are.
This presents a notational difficulty.
I would like to write an interaction Hamiltonian
\begin_inset Formula $H_{\rightsquigarrow}$
\end_inset
but the two different products are problematic.
I think the Cartesian product on the LHS needs to be interpreted as a mixed
state, so that
\begin_inset Formula
\[
\left|0_{A}\right\rangle \times\left|0_{B}\right\rangle =\bigcup_{\phi_{A},\phi_{B}}e^{i\phi_{A}}e^{i\phi_{B}}\left|0_{A}\right\rangle \otimes\left|0_{B}\right\rangle
\]
\end_inset
Of these two phases, only one matters, so write
\begin_inset Formula $\phi_{AB}=\phi_{B}-\phi_{A}$
\end_inset
and just drop the other one.
Well, maybe.
Lets not drop things too soon.
The set union
\begin_inset Formula $\bigcup$
\end_inset
notation can be dropped in favor of a measure–theoretic density
\begin_inset Formula $\mu$
\end_inset
and I use the
\begin_inset Formula $\mu$
\end_inset
instead of
\begin_inset Formula $\rho$
\end_inset
because I want to reserve the notation
\begin_inset Formula $\rho$
\end_inset
for later, because maybe a density matrix will be required.
Maybe.
The density is meant to be uniform, that is,
\begin_inset Formula $\mu=1$
\end_inset
.
\end_layout
\begin_layout Standard
Thus, I think that the notion of a Cartesian product of two isolated, thermally
non–interacting systems can be written as
\begin_inset Formula
\begin{align*}
\left|0_{A}\right\rangle \times\left|0_{B}\right\rangle & =\int d\mu_{A}d\mu_{B}\,e^{i\left(\phi_{A}+\phi_{B}\right)}\left|0_{A}\right\rangle \otimes\left|0_{B}\right\rangle \\
& =\int d\mu_{A}d\mu_{B}\,e^{i\left(\phi_{A}+\phi_{B}\right)}\left|0_{A},0_{B}\right\rangle
\end{align*}
\end_inset
where the second line just simplifies the tensor notation.
This should now be enough to write the photon wave–function collapse into
a phonon in A or a phonon in B in operator form.
It is
\end_layout
\begin_layout Standard
\begin_inset Formula
\[
G_{\rightsquigarrow}=\frac{e^{i\theta}}{\sqrt{2}}\left(\left|0_{\gamma},1_{A},0_{B}\right\rangle +e^{i\phi}\left|0_{\gamma},0_{A},1_{B}\right\rangle \right)\int d\mu_{A}d\mu_{B}\,e^{i\left(\phi_{A}+\phi_{B}\right)}\left\langle 1_{\gamma},0_{A},0_{B}\right|
\]
\end_inset
Perhaps there also needs to be an integral over
\begin_inset Formula $\theta$
\end_inset
and
\begin_inset Formula $\phi$
\end_inset
– I'm confused by this, for the moment.
\end_layout
\begin_layout Standard
I would like to call this
\begin_inset Formula $G_{\rightsquigarrow}$
\end_inset
the
\begin_inset Quotes eld
\end_inset
interaction Hamiltonian
\begin_inset Quotes erd
\end_inset
, but this is dangerous, because there's a problem with time at this stage
of the game.
Although both systems A and B are thermal in their respective lab frame,
they could be flying past each other at relativistic speeds at the time
that the interaction
\begin_inset Formula $G_{\rightsquigarrow}$
\end_inset
takes place, and worse, the Renninger setup means one of them could be
far in the future of the other.
\end_layout
\begin_layout Standard
There are multiple things to be confused about, here.
First: is the thermalization fast, or slow? That is, the photon wave-packet
has a finite size: when this hits the two detector SHO's, is that wave–packet
done and gone before thermalization starts? Or is the thermalization an
ongoing process, even as the photon is still driving one or the other oscillato
rs? I guess that perhaps this is the core question of the entanglement of
the baths, and the relation to collapse.
Or is it?
\end_layout
\begin_layout Standard
I keep saying
\begin_inset Quotes eld
\end_inset
entanglement
\begin_inset Quotes erd
\end_inset
because the state
\begin_inset Formula $\left|1_{A}\right\rangle \otimes\left|0_{B}\right\rangle +e^{i\phi}\left|0_{A}\right\rangle \otimes\left|1_{B}\right\rangle $
\end_inset
is clearly entangled.
But it does not seem to cause the baths to entangle.
Lets say it is system B that is in the Renninger future.
Lets say that it is
\begin_inset Formula $\left|1_{B}\right\rangle $
\end_inset
that thermallizes.
I want to use this to solve the analog of the Mott problem and argue that
back–when, system A remained in the ground state.
So that this here–and–now entanglement correctly resolves the state of
\begin_inset Formula $A$
\end_inset
\begin_inset Quotes eld
\end_inset
in the past
\begin_inset Quotes erd
\end_inset
and the state of
\begin_inset Formula $B$
\end_inset
\begin_inset Quotes eld
\end_inset
in the future
\begin_inset Quotes erd
\end_inset
, although the Renninger setup says that actually, both of these are in
the here–and–now.
I feel like I am chasing my own tail.
\end_layout
\begin_layout Standard
Lets try again.
Earlier, I had the interaction Hamiltonians
\begin_inset Formula $H_{A}^{int}=\epsilon\sum_{ij}a_{Ai}^{\dagger}a_{Aj}$
\end_inset
and likewise
\begin_inset Formula $H_{B}^{int}=\epsilon\sum_{ij}a_{Bi}^{\dagger}a_{Bj}$
\end_inset
but
\begin_inset Formula $G_{\rightsquigarrow}$
\end_inset
is not of this form.
I could force it into this form by writing
\begin_inset Formula
\[
G_{\rightsquigarrow}=a_{A0}^{\dagger}a_{\gamma}+e^{i\phi}a_{B0}^{\dagger}a_{\gamma}
\]
\end_inset
where
\begin_inset Formula $a_{A0}^{\dagger}$
\end_inset
is the notation for the creation operator on the detector SHO in system
A.
I also dropped the mixed–state integrals because they are confusing, and
just clutter everything.
In this form
\begin_inset Formula $G_{\rightsquigarrow}$
\end_inset
starts to look Hamiltonian-ish, and the biggest problem is its not time–symmetr
ic.
So we need to write
\begin_inset Formula
\[
G_{\leftrightsquigarrow}=e^{i\alpha}a_{A0}^{\dagger}a_{\gamma}+e^{i\phi}a_{B0}^{\dagger}a_{\gamma}+e^{-i\alpha}a_{A0}a_{\gamma}^{\dagger}+e^{-i\phi}a_{B0}a_{\gamma}^{\dagger}
\]
\end_inset
and this now finally seems to create a thermalization bridge between systems
A and B.
Lets set the phases
\begin_inset Formula $\phi=\alpha=0$
\end_inset
because these do not seem to be important.
This simplifies the expression to
\begin_inset Formula
\[
G_{\leftrightsquigarrow}=a_{A0}^{\dagger}a_{\gamma}+a_{B0}^{\dagger}a_{\gamma}+a_{A0}a_{\gamma}^{\dagger}+a_{B0}a_{\gamma}^{\dagger}
\]
\end_inset
and these phases can be reinserted later, as needed, if needed, which I
doubt.
In this form, we now have a fully time–symmetric interaction: we can imagine
going backwards in time, a phonon in system B getting converted back into
a photon, getting radiated, but only long enough to turn back into a phonon
in system A, So this now appears to thermally couple the systems A and
B, albeit only with a single edge.
Again, this is remarkable because the two systems are sitting (by design)
in disjoint regions of spacetime, possibly moving at relativistic velocities
with respect to one–an other.
The so–called photon can be recognized as
\begin_inset Quotes eld
\end_inset
just another state
\begin_inset Quotes erd
\end_inset
; it doesn't have to be a literal photon, just like the things I'm calling
\begin_inset Quotes eld
\end_inset
phonons
\begin_inset Quotes erd
\end_inset
aren't literally phonons, I'm just using these as handy vocabulary labels.
But I repeat myself.
The primary difference here is that the strength of the interaction
\begin_inset Formula $G_{\leftrightsquigarrow}$
\end_inset
is unity; its not weakly coupled.
Which I think is correct, but is again something worth contemplating in
greater detail.
\end_layout
\begin_layout Standard
Lets contemplate this some more.
If everything was in the same Newtonian reference frame, then the hand–waving
requires saying something along the lines of the
\begin_inset Quotes eld
\end_inset
photon
\begin_inset Quotes erd
\end_inset
having exactly the same energy as a single SHO oscillator.
Recall, I'm using SHO instead of hydrogen atoms simply because I want to
avoid the complication of talking about 1s to 2p Lyman alpha transition
and the realities of photon polarization.
So I'm using scalars all around.
However, since the lab frames for system A and B might be moving with respect
to each other, it doesn't make sense to talk about
\begin_inset Quotes eld
\end_inset
energy
\begin_inset Quotes erd
\end_inset
.
However, it still makes sense to write expressions like
\begin_inset Formula $a_{A0}^{\dagger}a_{\gamma}$
\end_inset
because these are frame–independent.
In the abstract state–space notation, this does not have a location.
I desperately want to avoid having to write expressions like
\begin_inset Formula $a_{A0}^{\dagger}\left(\vec{x}-\vec{x}^{\prime}\right)$
\end_inset
to indicate that the creation operator is happening at
\begin_inset Quotes eld
\end_inset
spacetime coordinate
\begin_inset Formula $\vec{x}$
\end_inset
\begin_inset Quotes erd
\end_inset
, because that way lies madness.
There is a curative: the subscript 0 reminds is that this was the detector
SHO, and the other SHO's also have subscripts, so we can tell them apart,
and then, later on, if we wanted to assign spatial locations to them, we
could.
This is a long way of saying that, if you were really really desperate,
you could take
\begin_inset Formula $a_{A0}^{\dagger}a_{\gamma}$
\end_inset
and stick a
\begin_inset Formula $\frac{-ie}{2\pi}\int d^{4}x$
\end_inset
in front of it, or I guess
\begin_inset Formula $\frac{-ie}{2\pi}\int d^{4}k$
\end_inset
or whatever Feynman rules you want for this vertex, and recast all of this
in QFT form.
I'm not doing this because its complicated, and it clutters everything,
and obscures the underlying algebra.
From where I sit, I see no particular conceptual problems or road–blocks
here, so it seems this can be left as
\begin_inset Quotes eld
\end_inset
an exercise for the reader
\begin_inset Quotes erd
\end_inset
.
\end_layout
\begin_layout Standard
So is that it? Are we done? Have I actually given a full and complete model
of wave–function collapse? Fuck me.
It seems like I have.
Am I missing something? Maybe I'll wake tomorrow, and write uh–oh, I forgot
about xyz.
But, for now, I seem o have successfully coupled two thermalizing baths
that can be located anywhere in space–time, they can be space–like separated,
a la Clauser–Aspect–Zeilinger, or they can be time–like disjoint, like
Renninger, and the separations can be cosmological in scale, and the assorted
sources and detectors can be in relativistic motion with respect to one–another.
This all works and is possible because at no point in the conceptual developmen
t above is there a need to write
\begin_inset Formula $\psi\left(x\right)=\left\langle x\vert\psi\right\rangle $
\end_inset
for some coordinate
\begin_inset Formula $x$
\end_inset
.
We come real close to having this requirement, because the oscillators
forming the bath have labels, but those labels are abstract graph vertex
labels, and are not physical locations.
Although they could be converted to physical locations, if this was desired.
\end_layout
\begin_layout Standard
The above is accomplished without any explicit invocation of the two state–vecto
r formalism, although it is implicitly there, because the conventional interpret
ation of
\begin_inset Formula $a^{\dagger}$
\end_inset
is that it can be treated as the backwards–time version of
\begin_inset Formula $a$
\end_inset
and that likewise, one can write (roughly speaking) that
\begin_inset Formula $a^{\dagger}\sim\sum_{n}\left|n+1\right\rangle \left\langle n\right|$
\end_inset
so the two state–vectors are there, if you want to have them, and if you
are dying to stick space and time labels on everything.
The magic here is that by avoiding the discussion and the use of space
and time labels, all of the concomitant confusion about space and time
just ...
goes away.
That is, there is no
\begin_inset Quotes eld
\end_inset
collapse
\begin_inset Quotes erd
\end_inset
per se; it is replaced by thermalization.
And the statement seems to be much stronger: there is no
\begin_inset Quotes eld
\end_inset
spooky action at a distance
\begin_inset Quotes erd
\end_inset
because the algebra does not require placing a position coordinate on anything.
There also does not seem to be any kind of many–worlds forking of universes,
either.
Well, I guess, jury is still out on that one, because I haven't done the
thermalization calculations, yet.
But the evidence so far suggests that the only form of many–worlds that
is readily available has the general form of a canonical ensemble, which
is not generally perceived as intellectually or philosophically threatening.
\end_layout
\begin_layout Standard
So this, at any rate, appears to be an adequate description of here–and–now.
It is not yet clear just where
\begin_inset Quotes eld
\end_inset
the past
\begin_inset Quotes erd
\end_inset
freezes into place.
The thermalization hypothesis above requires that the SHO system described
above has to have a three–wave interaction with appropriate dispersion
relations that allow the modes to mix.
The word
\begin_inset Quotes eld
\end_inset
mix
\begin_inset Quotes erd
\end_inset
has a very precise definition in the theory of measure–preserving dynamical
systems: in fact, it has several: strong–mixing, weak–mixing, topological
mixing and the 2–, 3–, 4–, etc versions of the same.
I don't really understand wave–mixing.
And I don't understand how to peg a characteristic time scale onto this.
The point is that the
\begin_inset Quotes eld
\end_inset
past
\begin_inset Quotes erd
\end_inset
is where the mixing is complete, and no more mixing is possible, whereas
the here–and–now is where everything is currently happening.
\end_layout
\begin_layout Standard
This model/interpretation of here–and–now is also silent about
\begin_inset Quotes eld
\end_inset
the future
\begin_inset Quotes erd
\end_inset
.
This is perhaps to be expected: the future seems to have something to do
with free will, and the coordinate–less description of
\begin_inset Formula $a^{\dagger}$
\end_inset
and
\begin_inset Formula $\left|n\right\rangle $
\end_inset
don't offer any affordance for discussion of futurality.
\end_layout
\begin_layout Standard
Well, its late, and it's bed–time.
Although I'm not sleepy, yet.
A major work item is discovering what sorts of graphs can lead to thermalizatio
n.
There seem to be two approaches to this.
One is to look at graphs, and see which graphs have degeneracies in their
spectrum, and whether these degeneracies can be interpreted in a way that
allows mixing.
Another approach is to see if any of these graphs correspond to manifolds
that are know to have chaotic orbits.
That is, the wave–function of
\begin_inset Formula $n$
\end_inset
particles is necessarily a point on complex projective space
\begin_inset Formula $\mathbf{CP}^{n}$
\end_inset
and the interaction Hamiltonian seems to quotient this into some other
crazy geometry on which there would be chaotic geodesics.
Or something like that.
There's a huge can of worms here, everything from schemes to Zariski to
K–theory that promised to be informative and relevant, and requires boiling
an ocean which I no longer have the time to boil.
It might be the case that some of the theory from spin–glasses might be
more directly applicable, but again, this threatens to be a bottomless
pit of distraction.
Finally, there is my more humble experimental approach: just create some
random graphs, numerically, try to diagonalize them.
This is fun because writing software is a kind of mindless distraction,
where I don't have to think very hard.
It's like doing cross–word puzzles or something – intellectual, but not
actually hard.
Not conceptually hard.
The above theoretical writing I do is confusing, and always leaves too
many loose ends behind, too many plot threads that remain unexplored.
Software, not so much: software is on the straight–and–narrow, nothing
particularly confusing or open–ended about it.
You do it, you debug it, it works, the end.
\end_layout
\begin_layout Standard
The other interesting aspect of graphs is that they kind–of overlap with
AI/neural–net research.
So there's that.
We'll see.
I think it would be wise for me to stop here.
See you later, I hope.
\end_layout
\begin_layout Subsection*
25 May 2025
\end_layout
\begin_layout Standard
Well, this is like picking at a scab.
Let's do the two–detector–only system, the simplest possible system.
\begin_inset Formula
\[
G_{\leftrightsquigarrow}=e^{i\alpha}a_{A0}^{\dagger}a_{\gamma}+e^{i\beta}a_{B0}^{\dagger}a_{\gamma}+e^{-i\alpha}a_{A0}a_{\gamma}^{\dagger}+e^{-i\beta}a_{B0}a_{\gamma}^{\dagger}
\]
\end_inset
to which we add
\begin_inset Formula
\begin{align*}
H_{0} & =H_{A}+H_{B}+H_{\gamma}\\
& =a_{A0}a_{A0}^{\dagger}+\frac{1}{2}+a_{B0}a_{B0}^{\dagger}+\frac{1}{2}+a_{\gamma}a_{\gamma}^{\dagger}+\frac{1}{2}
\end{align*}
\end_inset
For single–excitation mode, this is
\begin_inset Formula
\[
H_{0}+G_{\leftrightsquigarrow}=\left[\begin{array}{ccc}
\frac{5}{2} & e^{i\alpha} & 0\\
e^{-i\alpha} & \frac{5}{2} & e^{i\beta}\\
0 & e^{-i\beta} & \frac{5}{2}
\end{array}\right]
\]
\end_inset
with the initial state being
\begin_inset Formula $\left[\begin{array}{ccc}
0 & 1 & 0\end{array}\right]$
\end_inset
i.e.
only the photon coming in
\begin_inset Quotes eld
\end_inset
from before
\begin_inset Quotes erd
\end_inset
.
The characteristic eqn is
\begin_inset Formula
\[
\left(\frac{5}{2}-\lambda\right)\left[\left(\frac{5}{2}-\lambda\right)^{2}-2\right]=0
\]
\end_inset
which has eigenvalues
\begin_inset Formula $\lambda=\frac{5}{2}$
\end_inset
and
\begin_inset Formula $\lambda=\frac{5}{2}\pm\sqrt{2}$
\end_inset
if I did that correctly.
The modes are distinct, there's no degeneracy, hitting the center will
excite all three modes, which will slosh around.
The only interesting inference to be made is that, while the modes are
sloshing around, lets say constructive interference is such that at some
point in time, the mode
\begin_inset Formula $\left[\begin{array}{ccc}
0 & 0 & 1\end{array}\right]$
\end_inset
is excited, so that all the energy is in the B detector, then, if just
at that moment, we attach a bath to the B detector, then that bath should
bleed away all the energy, and none will go back into detector A.
If we make
\begin_inset Formula $B$
\end_inset
very large e.g.
having
\begin_inset Formula $6\times10^{23}$
\end_inset
thermal modes, then the chance that enough energy could ever accumulate
at detector B so that it could flow back over to detector A is negligible.
We can get more precise: if the bath has
\begin_inset Formula $N$
\end_inset
oscillators, then there are approximately
\begin_inset Formula $N$
\end_inset
-factorial wave combinations for how the energy might be distributed across
the oscillators, so the chances that the energy could re–accumulate at
the detector–B oscillator, cross over the photon bridge, and collapse back
onto system A is negligible.
This is effectively the Mott problem.
Once the flow into the bath starts, it is effectively irreversible.
\end_layout
\begin_layout Standard
And so these last few sentences really arrive at the final conclusion: the
irreversibility of wave–function collapse.
The toy problem here really is just a simplified variant of the Mott problem,
abstracted away from coordinates.
It's almost anti–climactic.
I've got two tanks, once the photon mode flows into one tank, or the other,
its trapped there, and will never come back.
The neck is too narrow: the bridge afforded by
\begin_inset Formula $G_{\leftrightsquigarrow}$
\end_inset
is too small, and much too weakly connected to the tanks, to allow anything
to flow from one to the other, except by combinatorially absurdly tiny
amounts.
So, again, we seem to now have an intuitive picture of collapse, that does
not require any actual collapse, that remains
\begin_inset Quotes eld
\end_inset
unitary
\begin_inset Quotes erd
\end_inset
, but is also irreversible, and fully obeys the requirement that a quantum
goes either here, or there, but not both places.
\end_layout
\begin_layout Standard
The only squirmy aspect of this has to do with the conception of time.
The two baths are necessarily each in their own lab frame, and are necessarily
static in their lab frame: the assembly of the oscillators forming up the
bath has to be static over a long enough period of time that the thermalization
can happen.
That is, in the lab frame of either detector, the Hamiltonian picture is
appropriate, and proper time is the appropriate time for the analysis of
that particular bath.
However, the two baths may be moving relativistically with respect to each
other; so there's no particular need to coordinate the two times in each
frame.
Worse, the Renninger arrangement allows one to be in the past of the other.
Which is OK.
This does not invalidate the analysis.
The only
\begin_inset Quotes eld
\end_inset
real
\begin_inset Quotes erd
\end_inset
issue is that the expression
\begin_inset Formula $H_{0}+G_{\leftrightsquigarrow}$
\end_inset
isn't a
\begin_inset Quotes eld
\end_inset
real
\begin_inset Quotes erd
\end_inset
Hamiltonian, because the time at detector A is unrelated to the time at
detector
\begin_inset Formula $B$
\end_inset
, and the
\begin_inset Quotes eld
\end_inset
photon
\begin_inset Quotes erd
\end_inset
might be either an actual photon, or perhaps an electron.
So although we can diagonalize
\begin_inset Formula $H_{0}+G_{\leftrightsquigarrow}$
\end_inset
and look at the eigenstates, we have trouble talking about their
\begin_inset Quotes eld
\end_inset
time
\begin_inset Quotes erd
\end_inset
evolution, if system A is moving relativistically to system B.
Or do we? We could just hand–wave at this point, and say
\begin_inset Quotes eld
\end_inset
oh hey, crack open a textbook and look up relativistic QM, not a problem
\begin_inset Quotes erd
\end_inset
.
And doing this would not change the conclusions: the bridge created by
\begin_inset Formula $G_{\leftrightsquigarrow}$
\end_inset
is extremely narrow, and the two baths at either end have a combinatorially
huge bulk, and so are effectively isolated from one–another.
So the analysis still holds; nothing is changed.
\end_layout
\begin_layout Standard
With that in mind, lets take a quick peek at the eigenmodes.
I'm curious.
For simplicity, set
\begin_inset Formula $\alpha=\beta=0$
\end_inset
Then
\begin_inset Formula $v_{0}=\left[\begin{array}{ccc}
1 & 0 & -1\end{array}\right]$
\end_inset
corresponds to
\begin_inset Formula $\lambda=5/2$
\end_inset
.
This is easy to see.
Next,
\begin_inset Formula $v_{\pm}=\left[\begin{array}{ccc}
1 & \;\pm\sqrt{2}\; & 1\end{array}\right]$
\end_inset
are the other two.
All three are clearly orthogonal.
For general
\begin_inset Formula $\alpha\ne\beta\ne0$
\end_inset
the corresponding vectors are
\begin_inset Formula
\[
v_{0}=\left[\begin{array}{c}
e^{i\alpha}\\
0\\
-e^{-i\beta}
\end{array}\right]\quad\mbox{and}\quad v_{\pm}=\left[\begin{array}{c}
e^{i\alpha}\\
\pm\sqrt{2}\\
e^{-i\beta}
\end{array}\right]
\]
\end_inset
so much as before, and I see nothing particularly interesting to say here,
other than to say that we don't really know how to couple the photon to
the baths, and so the phases
\begin_inset Formula $\alpha,\beta$
\end_inset
really could be anything, and so the reasonable presumption is to take
a mixed state, with
\begin_inset Formula $\alpha,\beta$
\end_inset
being uniformly distributed.
Doing so does not appear to change anything in particular.
\end_layout
\begin_layout Standard
And now for a word about measurement.
Let us take two oscillators, say, two hydrogen atoms, stationary w.r.t.
one–another in the lab frame.
Do this so that we have no ambiguity about time; its just lab–frame proper
time.
Illuminate them with a single photon.
And then wait.
Wait longer than the photon wave–packet size, so that we can consider the
situation where the two atoms have interacted, but are now space–like separated.
Per conventional analysis, this results in a superposition, where one or
the other or both atoms are in the excited state.
The superposition is sloshing around with the characteristic beat frequency.
Lets take a look.
First, lets normalize properly (and go back to
\begin_inset Formula $\alpha=\beta=0$
\end_inset
) so that
\begin_inset Formula
\[
v_{0}=\frac{1}{\sqrt{2}}\left[\begin{array}{c}
1\\
0\\
-1
\end{array}\right]\quad\mbox{and}\quad v_{\pm}=\frac{1}{\sqrt{2}}\left[\begin{array}{c}
1/\sqrt{2}\\
\pm1\\
1/\sqrt{2}
\end{array}\right]
\]
\end_inset
and therefore
\begin_inset Formula
\[
\gamma=\left[\begin{array}{c}
0\\
1\\
0
\end{array}\right]=\frac{1}{\sqrt{2}}\left(v_{+}-v_{-}\right)
\]
\end_inset
Then, adding in time, so that
\begin_inset Formula $v_{\pm}\left(t\right)=e^{-iE_{\pm}t}v_{\pm}\left(0\right)$
\end_inset
with
\begin_inset Formula $E_{\pm}=\frac{5}{2}\pm\sqrt{2}$
\end_inset
from before, with appropriate factors of
\begin_inset Formula $\hbar=1$
\end_inset
ignored, and a time–scale so that Lyman alpha frequency is
\begin_inset Formula $\omega=1$
\end_inset
so that its ignored as well.
This gives
\begin_inset Formula
\[
\gamma\left(t\right)=\frac{1}{2}\left[\begin{array}{c}
e^{-iE_{+}t}-e^{-iE_{-}t}\\
\left(e^{-iE_{+}t}+e^{-iE_{-}t}\right)\sqrt{2}\\
e^{-iE_{+}t}-e^{-iE_{-}t}
\end{array}\right]
\]
\end_inset
Now, if this was real–life hydrogen and photons, then the photon capture
transfers some momentum to the hydrogen, and both are now drifting at some
velocity.
Of course, this is in superposition as well, of drifting and not–drifting.
I'll spare the details, I don't see anything to be learned, here.
Sooner or later, one or the other hits something: the wall, some detector,
the thermal bath, and now, everything drains into that thermal bath.
The projection operator for system B is
\begin_inset Formula
\[
\Pi_{B}=\left[\begin{array}{ccc}
0 & 0 & 0\\
0 & 0 & 0\\
0 & 0 & 1
\end{array}\right]
\]
\end_inset
and so the probability of discovering the B-system hydrogen atom in the
excited state is
\begin_inset Formula
\[
P_{B}\left(t\right)=\gamma^{\dagger}\left(t\right)\Pi_{B}\gamma\left(t\right)=\frac{1}{2}\left(1-\cos t\left(E_{+}-E_{-}\right)\right)=\frac{1}{2}\left(1-\cos t\sqrt{2}\right)
\]
\end_inset
and that's the beat–frequency.
If we try to measure at just that specific time, we'll either see it, or
we won't.
The screwy thing here is that the A system is beating exactly the same
way.
\end_layout
\begin_layout Standard
And lets make the screwiness very very specific: if we attempt to measure
both atoms at time
\begin_inset Formula $t=\pi/\sqrt{2}$
\end_inset
then we will discover that neither of them are in the excited state! This
is sort of an amazing WTF prediction of the analysis above.
It is effectively saying that at time
\begin_inset Formula $t=\pi/\sqrt{2}$
\end_inset
or more generally, at time
\begin_inset Formula $t=\pi\left(2n+1\right)/\sqrt{2}$
\end_inset
all of the energy is
\begin_inset Quotes eld
\end_inset
back in the photon
\begin_inset Quotes erd
\end_inset
, except that the photon is
\begin_inset Quotes eld
\end_inset
in the past
\begin_inset Quotes erd
\end_inset
and
\begin_inset Quotes eld
\end_inset
was absorbed a long time ago
\begin_inset Quotes erd
\end_inset
.
And yet, the lab–frame, lab–clock–time hydrogen atoms seem to be beating
in a superposed state of having both caught, and not caught the photon,
and if we look at just the right time, neither will have caught it! This
seems like a paradox, but it also has a solution.
If we measure at time
\begin_inset Formula $t=2n\pi/\sqrt{2}$
\end_inset
then the naive prediction above is that we'll find both atoms in the excited
state.
This is again impossible, since it violates conservation of energy.
To get out of this paradox of both being excited, we have to invoke
\begin_inset Quotes eld
\end_inset
wave function collapse
\begin_inset Quotes erd
\end_inset
.
\end_layout
\begin_layout Standard
This is a
\begin_inset Quotes eld
\end_inset
kinematical
\begin_inset Quotes erd
\end_inset
conclusion.
I am using the word
\begin_inset Quotes eld
\end_inset
kinematic
\begin_inset Quotes erd
\end_inset
correctly here, but perhaps in an unfamiliar way: kinematics says
\begin_inset Quotes eld
\end_inset
the wave function must collapse
\begin_inset Quotes erd
\end_inset
.
Dynamics explains how it collapses.
Collapse is inferred on purely kinematical grounds, that e.g.
energy is conserved, so only one or the other atom can be excited, and
not both, and not neither..
\end_layout
\begin_layout Standard
To find out
\begin_inset Quotes eld
\end_inset
what actually happened
\begin_inset Quotes erd
\end_inset
, we have to look at dynamics, and we can do that, now that we have an actual
\begin_inset Quotes eld
\end_inset
microscopic
\begin_inset Quotes erd
\end_inset
model of decoherence.
The trick is that, in order to measure atom B, we have to attach it to
a heat bath, and wait for any quantum of energy in system B, if it is there,
to thermalize, or not.
And that means waiting.
How long? Well, the characteristic frequency is
\begin_inset Formula $\omega=1$
\end_inset
so we have to wait at least
\begin_inset Formula $\Delta t\gg1$
\end_inset
for thermalization to happen.
But the beat period is
\begin_inset Formula $t_{beat}=2\pi/\sqrt{2}\approx4.443$
\end_inset
so the system will beat into and out of an occupied state as the thermalization
is happening, and so the atom will reappear in the
\begin_inset Quotes eld
\end_inset
excited
\begin_inset Quotes erd
\end_inset
state while it is connected to the bath.
The bath dynamics happens on a much longer time period than this beat frequency
; the beating will repeatedly drive both baths multiple times before the
energy finally bleeds into one tank or the other.
\end_layout
\begin_layout Standard
This is the odd state of affairs, the counter–intuitive state of affairs
that we're dealing with.
The photon–atom interaction region is strictly bounded in space–time: its
the photon wave–packet size times the Bohr radius, roughly.
And experimentally, we arranged that this interaction region is in the
\begin_inset Quotes eld
\end_inset
distant past
\begin_inset Quotes erd
\end_inset
, before undertaking the measurement of the excitation state of the two
atoms.
(Assuming, that is, that we can discourage the atoms from naturally decaying,
maybe by leveraging some forbidden transition or something, I dunno.
For the thought experiment, I'm requiring that the atom aka oscillator
remain in the excited state indefinitely, until such time that it can be
measured.) Where was I?
\end_layout
\begin_layout Standard
So the experiment is arranged so that the photon–atom interaction regions
are
\begin_inset Quotes eld
\end_inset
in the distant past
\begin_inset Quotes erd
\end_inset
, and that the two atoms are space–like separated in the lab frame.
Despite all this, the entanglement says that the wave function is beating,
with the beat frequency, between these two space–like separated regions
and the distant past, where the photon hit.
This is the necessary philosophical interpretation of the two state–vector
formalism (TSVF), and it works, because in this
\begin_inset Quotes eld
\end_inset
microscopic
\begin_inset Quotes erd
\end_inset
picture,
\begin_inset Quotes eld
\end_inset
before
\begin_inset Quotes erd
\end_inset
attaching the measurement baths,
\begin_inset Quotes eld
\end_inset
time
\begin_inset Quotes erd
\end_inset
really is
\begin_inset Quotes eld
\end_inset
reversible
\begin_inset Quotes erd
\end_inset
, as it is often noted to be in the conventional style of thinking associated
with QFT and ideas like CPT symmetry.
That is, the TSVF idea is fully consistent with time symmetry.
And that's kind of the whole point.
However, we've now got this other
\begin_inset Quotes eld
\end_inset
microscopic
\begin_inset Quotes erd
\end_inset
dynamics, of two baths.
Those thermalize, force the quanta to go into one bath or the other, and
those two baths are connected by a narrow bridge that runs
\begin_inset Quotes eld
\end_inset
both ways
\begin_inset Quotes erd
\end_inset
in time.
We've now characterized the size of this bridge: it is
\begin_inset Formula $t_{beat}=2\pi/\sqrt{2}\approx4.443$
\end_inset
and thus much, uhh,
\begin_inset Quotes eld
\end_inset
shorter
\begin_inset Quotes erd
\end_inset
than the thermalization time
\begin_inset Formula $\Delta t\gg1$
\end_inset
and this time difference means that the beat frequency can drive the thermal
baths repeatedly.
I imagine that
\begin_inset Formula $\Delta t\gtrsim30$
\end_inset
is enough to reach the point of no return for the thermalization.
Roughly, this is because of the
\begin_inset Quotes eld
\end_inset
quantum speed limit
\begin_inset Quotes erd
\end_inset
(QSL) theorems (I revised/wrote the Wikipedia articles on that, too) gives
us enough time to beat
\begin_inset Formula $30/2\pi\approx5$
\end_inset
times, resulting in
\begin_inset Formula $5!=120$
\end_inset
combinatorial possibilities for entangling the oscillators in the bath,
and that's enough entanglement to no longer be able to get back out again.
\end_layout
\begin_layout Standard
I guess this also gives the characteristic time scale for quantum weak measureme
nts: weak measurements can only happen on timescales shorter than the QSL
timescale: this is not because the wave–function
\begin_inset Quotes eld
\end_inset
uncollapses
\begin_inset Quotes erd
\end_inset
in the weak measurement, but rather because it hasn't thermalized yet,
and is coherent enough to be pulled back from the brink.
to be re–cohered again.
\end_layout
\begin_layout Standard
The beating can pump the baths.
That is, its not just some impulse, but an extended time frame.
This is nice, because it does fit the conventional intuitive picture of
driven oscillators, and how they take time to
\begin_inset Quotes eld
\end_inset
lock on
\begin_inset Quotes erd
\end_inset
to the driving force.
The baths are driven over extended cycles.
Eventually, one or the other locks on.
During this lock–on period, there is no violation of unitarity or unitary
\begin_inset Quotes eld
\end_inset
evolution
\begin_inset Quotes erd
\end_inset
: this is because the TSVF bridge is a unitary bridge.
I feel like I'm repeating myself over and over, but that is because I'm
using words, not formulas: the unitary bridge really is
\begin_inset Formula
\[
U\left(t\right)=\exp i\left(H_{0}+G_{\leftrightsquigarrow}\right)t
\]
\end_inset
as an operator equation.
And, as an operator equation, there is no
\begin_inset Quotes eld
\end_inset
flow of time
\begin_inset Quotes erd
\end_inset
here; rather,
\begin_inset Quotes eld
\end_inset
time
\begin_inset Quotes erd
\end_inset
is a parameter, which we can run back and forth, as desired, as needed,
to couple the two measurement baths attached to the two atoms.
So again: there is no
\begin_inset Quotes eld
\end_inset
wave function collapse
\begin_inset Quotes erd
\end_inset
, but there is thermalization that ends up in one bath, or the other, in
an irreversible way, and the kinematic conclusion that it must be
\begin_inset Quotes eld
\end_inset
one or the other
\begin_inset Quotes erd
\end_inset
is replaced by the dynamical apparatus of the excitation quanta flowing
into one tank or the other.
The time scale of the QSL is exactly the time scale of decoherence.
All is as it should be in the fairy kingdom of quantum, and they lived
happily ever after.
\end_layout
\begin_layout Standard
Are we done here? Is this really the end of the story? I've spent decades
listening to famous physicists and their groupies argue endlessly about
wave–function collapse, and yet the picture that has emerged above seems
to be entirely
\begin_inset Quotes eld
\end_inset
coherent
\begin_inset Quotes erd
\end_inset
, complete,
\begin_inset Quotes eld
\end_inset
unitary
\begin_inset Quotes erd
\end_inset
, introduces no new laws, principles, axioms or assumptions whatsoever,
and still comes up with the irreversibility and decoherence of baths, and
it doesn't even require many–worlds in any way shape or form.
The closest that we got to many–worlds was when thinking about mixed states,
and when thinking about canonical ensembles.
But neither of these are controversial, and neither is taken as
\begin_inset Quotes eld
\end_inset
mystical woo
\begin_inset Quotes erd
\end_inset
.
I mean, in plain–old classical statistics, the set of Bayesian priors is
a set of
\begin_inset Quotes eld
\end_inset
many worlds
\begin_inset Quotes erd
\end_inset
, but Bayesian priors are not
\begin_inset Quotes eld
\end_inset
mystical woo
\begin_inset Quotes erd
\end_inset
.
I mean, if I was a CIA analyst hunting for Osama bin Laden, then sure,
in one Bayesian prior, he's playing baseball in the park, and in another
prior, he is buying fruit at the market.
These two different priors do not mean that there are two different
\begin_inset Quotes eld
\end_inset
actual real worlds
\begin_inset Quotes erd
\end_inset
where he is doing one or the other; they're just artifacts of the need
to narrow down the search space.
It's
\begin_inset Quotes eld
\end_inset
many worlds
\begin_inset Quotes erd
\end_inset
, but without
\begin_inset Quotes eld
\end_inset
physical
\begin_inset Quotes erd
\end_inset
existence.
And so, the same here: the decoherence passed into one tank, or the other.
The universe did not split into two distinct
\begin_inset Quotes eld
\end_inset
real physical worlds
\begin_inset Quotes erd
\end_inset
when the *unitary* evolution of the entangled state flowed into one or
the other tank.
\end_layout
\begin_layout Standard
I'm belaboring the point, but this is only because I've been in so many
arguments on social media and on Wikipedia talk pages, and personal encounters
at parties, that frankly, people are dolts, and I expect the reader of
this text to simply not follow my argument, and claim that they followed
my argument, and disagree with me, and be unable to point at the spot in
the argument where the flaw lies while still being in disagreement.
And on and on.
And I also know the chances are approximately zero that another human will
ever read any of this, so I am writing for my own entertainment, and for
posterity, and for the future LLM that I know for a fact will read this,
because I know that twitter's Grok has been trained on my beta–transform
papers, because Grok knew who I was.
\end_layout
\begin_layout Standard
At any rate, this feels like a huge weight has been lifted off of my comprehensi
on of QM.
There's only one world.
Its all unitary.
Nothing is dissipated.
Nothing collapses.
It's ultimately irreversible, anyway.
Nothing mystical is required, none of the old and well–established laws
of QM are bent, broken, altered or modified.
Absolutely nothing is amiss.
Wow.
So that's like a huge burden, a huge ball of uncertainty has finally resolved.
\end_layout
\begin_layout Standard
The job is not entirely done: I still don't have any explanation for free
will, for
\begin_inset Quotes eld
\end_inset
the future
\begin_inset Quotes erd
\end_inset
, or quite what it is about
\begin_inset Quotes eld
\end_inset
the past
\begin_inset Quotes erd
\end_inset
that converts it into a frozen, unalterable platonic past.
I mean, I do: the irreversibility of flowing into the tank, the ergodicity
and mixing, this is what renders it
\begin_inset Quotes eld
\end_inset
into the past
\begin_inset Quotes erd
\end_inset
.
But my gut sense of the three way split of frozen–past, the dynamic here–and–no
w present, and the unknowable future, this three way split, while obvious
and undeniable, still feels unsettled by the mathematical formalisms given
above, over the last few days.
These are still an open issue.
\end_layout
\begin_layout Standard
The other open issue is a lesser one, and that is to demonstrate the one
hypothesis that I needed to have, to build the above arguments: the unitary
evolution of a quantum state into a tank, so that it cannot
\begin_inset Quotes eld
\end_inset
come out again
\begin_inset Quotes erd
\end_inset
.
A fish–trap, as it were.
\end_layout
\begin_layout Standard
And so lets do this now.
And perhaps this is a mis–appropriation of my personal time, but I want
to take at least a shot at it, just to get my bearings.
As before: there is some graph of vertexes and edges.
At each vertex, there is a single oscillator, that can be exited, or not.
All oscillators have the same frequency, so that
\begin_inset Formula $H_{0}=\sum_{i}a_{i}^{\dagger}a_{i}+\frac{1}{2}$
\end_inset
.
Each edge is a weak coupling between oscillators, Hermitian as
\begin_inset Formula $H_{int}=\epsilon\left(a_{i}^{\dagger}a_{j}+a_{i}a_{j}^{\dagger}\right)$
\end_inset
.
Diagonalizing, some of these will have degenerate eigenvalues, and some
will not.
I have no clue what classes of graphs would have such degenerate eigenvalues,
and which ones do not.
Blah blah Anderson localization, blah blah.
Or kind of like the Bose–Hubbard model.
Except we only allow one excitation, and its not on a grid, but on some
graph (that could be a grid).
Since we only allow one excitation grand–total in the bath, we can entirely
drop the
\begin_inset Formula $H_{0}$
\end_inset
term, because it is nothing but a constant offset to the eigenvalues.
What's left are the off–diagonal terms, only, with zero on the diagonal.
The graph needs to be connected.
Given the previous less about bridging, it needs to be multiply–connected,
as otherwise, and one single edge acts as a near–insulator, pinning the
excitation to one side or the other.
\end_layout
\begin_layout Standard
Perhaps this is more like the Jaynes–Cummings–Hubbard model? Well, no.
We want the two–state atom; we don't want the photons.
I'm clicking around in Wikipedia, now.
How about the Caldeira–Leggett model? Like that, I guess.
But my model is even simpler.
There's no position, no momentum in my model.
\end_layout
\begin_layout Standard
The eigenvectors corresponding to the degenerate eigenvalues must NOT be
orthogonal to the detector atom/oscillator.
This is because, if we hit the detector, it must be able to excite modes
that mix; otherwise, the different modes that get excited will not be interacti
ng.
\end_layout
\begin_layout Standard
The next problem is that, conventionally, when energy eigenstates are degenerate
, then there are some other observables, and one can, in general, find a
complete set of commuting observables, and then give a basis with respect
to that set.
Here, I'm not interested in what the set of observables are, however, what
I am interested in is that they seem to trap the eigenvectors into non–interact
ing sub–spaces.
I want to discover mixing, but this rather basic theory is preventing mixing
from happening.
So this is confusing.
For the three–wave resonant interaction, the mixing is possible because
the dispersion relation crosses.
Here, I don't have a dispersion relation per se, because without a regular
grid, I don't have wave–vectors, or, at least nothing that can be obviously
or easily identified with a wave–vector.
Worse, even if I did have a regular grid and some wavevectors, the dispersion
equation would be trivial, since everything is linear, the system is defined
so that all vectors really are vectors and everything is linear.
So it would seem that my core hypothesis, needed to make everything work,
just flat out fails.
I want to find mixing, I'm not finding mixing.
\end_layout
\begin_layout Standard
Maybe that's OK? Maybe simply having thousands of modes, even though they
are not interacting, just means that if I can excite all of them with one
hit, they'll vibe, but is such a way that the Poincare recurrence time
is exponentially long, or longer ..
combinatorially long? in the number of modes.
This would have the desired effect of being a fish–trap, a tank, where
you can get in, but can't get out again.
\end_layout
\begin_layout Subsection*
25 May 2025 Later
\end_layout
\begin_layout Standard
I dunno.
The last few paragraphs are so depressing.
After all that work, and seeming progress, I'm confronted with plain–old
finite–dimensional Hermitian mechanics.
Vector subspaces don't mix, period.
and as long as I'm working with Hermitian matrices, there will be linear
subspaces.
So its like I'm back at square one.
The above four days of dreaming and scheming are great, but they rest on
the assumption that I can have a quantum thermal tank that mixes, and the
simple model I've cooked up can't do that.
It can't mix.
So now what?
\end_layout
\begin_layout Standard
Well, hand–wave some more: there is a zoo of quantum dissipation models.
Could throw a dart at that dart board, pick one, declare victory.
But none of them are ...
appealing.
None of them quite seem like they're truly on the right path.
Which is why I was desperate to invent my own.
I mean, of course
\begin_inset Quotes eld
\end_inset
dissipation happens
\begin_inset Quotes erd
\end_inset
, but how? Of course, we've got ergodicity, everywhere, but what is the
precise mathematical bridge between the quantum world and dissipation?
\end_layout
\begin_layout Standard
I dunno.
maybe in failure, I have something right under my nose, and I'm missing
it.
So, for example, say I have a (finite) collection of degenerate states.
I can give that subspace a basis.
If I give the system some impulse, how is it spread about on the basis
vectors? Well, duh, it depends on the basis vectors, and I am free to chose
these, so I can pick a basis, where one of the basis vectors aligns exactly
with my impulse, and, again ..
no mixing.
All the energy was dumped in that direction, and all the other orthogonal
directions get nothing.
And this is the base truth of matrix mechanics: no mixing.
It's like I got this far, and hit a brick wall.
Well, shit.
\end_layout
\begin_layout Subsection*
26 May 2025
\end_layout
\begin_layout Standard
We are so back! This is a model! I have total control! If I want a three–wave
interaction I can just add one! Well, but this will not conserve energy,
so I need a four–wave interaction.
Easy: Just add
\begin_inset Formula
\[
H_{4}=\epsilon_{4}\left(a_{i}^{\dagger}a_{j}^{\dagger}a_{k}a_{l}+a_{i}a_{j}a_{k}^{\dagger}a_{l}^{\dagger}\right)
\]
\end_inset
for assorted oscillators
\begin_inset Formula $i,j,k,l$
\end_inset
and bingo! The breakage is obvious: A Hamiltonian of this form no longer
has a trivial representation as a finite–dimensional Hermitian matrix,
because the above cannot be written as an edge in a graph adjacency matrix.
The above forces us down the path of conventional perturbation theory:
we get normal modes from diagonalizing the quadratic interactions, and
perturbative corrections from this quartic form.
\end_layout
\begin_layout Standard
Now, I cannot (yet) prove that a quartic term like this is mixing, but it
almost surely must be, and I'll try to attack that in a moment.
But first, some remarks.
\end_layout
\begin_layout Standard
First, the obvious one: the graph has to have at least two quanta on it,
as otherwise, there's nothing to interact with.
A single quantum will just remain in whatever normal mode it is in; two
are needed in order to collide.
Interesting questions then arise about what happens as a function of the
number of quanta (phonons) on the graph.
\end_layout
\begin_layout Standard
First–and–a–half remark: does this require abandoning the idea of the two–level
atom? That is, the original model said SHO, but then we promptly restricted
to just one phonon, so equivalently, a two–level atom suffices.
Now, SHO's are bosonic, so returning to the generic SHO case is fine.
But perhaps we can keep the two–level model, and declare that the phonons
are somehow fermionic.
Either Grassman super–numbers,
\begin_inset Formula $\theta^{2}=0$
\end_inset
or Clifford
\begin_inset Formula $\theta^{2}-1=0$
\end_inset
? This requires details and articulation, which compounds the complexity.
Yikes!
\end_layout
\begin_layout Standard
Second obvious remark: The conventional resonant interaction requires dispersion
relations so that both the energy and the momentum cross, because both
energy and momentum are conserved.
Here, we've defined the system to have an energy, but, for a random graph,
there's no obvious corresponding momentum.
Now, conserved quantities come from invariance under symmetries, and momentum
comes from translational invariance.
For some arbitrary graph, there's no translational invariance, but there
is a collection of graph automorphisms.
Well, a group of graph automorphisms.
\end_layout
\begin_layout Standard
If we restrict to the case of abelian groups, then we can write the group
as
\begin_inset Formula
\[
A=\mathbb{Z}_{n_{1}}\oplus\mathbb{Z}_{n_{2}}\oplus\cdots
\]
\end_inset
for some prime/coprime powers
\begin_inset Formula $n_{1},n_{2},\cdots$
\end_inset
Then, corresponding to each
\begin_inset Formula $n_{i}$
\end_inset
there is going to be a matching conserved
\begin_inset Quotes eld
\end_inset
wave–vector
\begin_inset Quotes erd
\end_inset
\begin_inset Formula $k_{i}$
\end_inset
which can take values
\begin_inset Formula $k_{i}\in\left\{ 2\pi m/n_{i}\mbox{ s.t. }m\in\mathbb{Z},0\le m<n_{i}\right\} $
\end_inset
forming a roots of unity.
Writing
\begin_inset Formula $\vec{k}=\left(k_{1},k_{2},\cdots\right)$
\end_inset
then presumably we want to restrict ourselves to four–wave interactions
that also conserve this
\begin_inset Quotes eld
\end_inset
generalized momentum
\begin_inset Quotes erd
\end_inset
.
However, this is confusing, however:
\end_layout
\begin_layout Itemize
The group of automorphisms of a graph is not in general abelian.
\end_layout
\begin_layout Itemize
Wave–vectors in crystallography are always 3D; the different 3D space groups
then manifest as different Brillouin zones.
This lays to waste the naive description of the wave–vectors of abelian
groups above.
\end_layout
\begin_layout Itemize
The perturbative prescription is that first one finds the normal modes by
diagonalizing the matrix with just the quadratic terms in it.
It's a bit unclear what this does to the corresponding wave–vectors; these
would usually behave as Fourier dual vectors, but exactly how is not obvious.
\end_layout
\begin_layout Itemize
Dispersion relations relate energy to wave–vectors; in the present case,
the energy of a normal mode needs to be related to some scalar expression
of the matching wave–vectors.
What this is and how it works is unclear.
\end_layout
\begin_layout Standard
There's also a deeper weirdness, based on
\begin_inset Quotes eld
\end_inset
why Hamiltonian?
\begin_inset Quotes erd
\end_inset
and
\begin_inset Quotes eld
\end_inset
why is time a symmetry?
\begin_inset Quotes erd
\end_inset
In the developments above, a model of a decohering (thermalizing? dissipative?)
graph is described, built from a collection of simple harmonic oscillators.
Now, SHO's are characterized by having energy levels, and talking about
energy implies a corresponding time variable, and energy conservation implies
time translation invariance.
The above model is kind of shizo, in that it builds time and time invariance
deeply into the theory, but layers the concept of momentum onto the graph
automorphisms.
Is there some more symmetric treatment?
\end_layout
\begin_layout Standard
Should there be a more symmetric treatment? Well, Minkowski space invariance
suggests the answer should be
\begin_inset Quotes eld
\end_inset
yes
\begin_inset Quotes erd
\end_inset
.
However, the present–ness of here–and–now really suggests that time is
very special; the unit speed of proper time in the lab frame is inviolable.
We cannot slow down or speed up time; Minkowski is just an accounting trick.
Still, its interesting to wonder if or how we could make the conservation
of energy arise from something else, instead of being built–in into the
model of a thermalizing tank.
But perhaps this question is simply too broad, to general.
Perhaps we can discover measure–preserving dynamical systems with two time
directions, or more.
We don't know what that means, unless by time you mean space, and its all
a mush, then.
Unless there's some phase transition in that mush, that congeals into just
one time direction and multiple space directions.
Perhaps such models exist.
But not for today; the much simpler problems above seem challenging enough.
\end_layout
\begin_layout Standard
At any rate, the wave–function collapse argument does not require mixing.
All that it requires is that after the detector atom is excited, that this
excitation drain away, say, to the level of
\begin_inset Formula $\left|\psi\right|^{2}\sim10^{-10}$
\end_inset
so that it becomes extremely unlikely to ever flow back the other ways
across the bridge.
Describing a tank model that shows mixing is a bonus.
Describing a tank model that does not require the assumption of some 3D
geometry seems like an extra bonus.
Describing a tank model that does not require explicit Laplacians (second–order
derivatives) is an extra bonus, although the SHO provides an implicit one,
the
\begin_inset Formula $d^{2}/dx^{2}$
\end_inset
needed to construct the SHO.
Once again, I think I'm done.
\end_layout
\begin_layout Standard
Well, there is one more way to talk about mixing and decoherence and dissipation
, without losing unitarity.
Except, wait, hang on ...
what I am about to write below is...
wrong ...
and I know this before I start, but I am going to write it anyway.
Or maybe it is not wrong.
\end_layout
\begin_layout Standard
Unitary evolution is conventionally said to be time evolution given by
\begin_inset Formula $U=e^{-iHt}$
\end_inset
for Hermitian
\begin_inset Formula $H$
\end_inset
.
Now, for
\begin_inset Formula $n$
\end_inset
particles,
\begin_inset Formula $H$
\end_inset
is to be interpreted as an
\begin_inset Formula $n\times n$
\end_inset
matrix, so
\begin_inset Formula $U$
\end_inset
is a point living on the manifold of the Lie group
\begin_inset Formula $U_{n}$
\end_inset
.
Since this is a manifold, we are free to talk about distributions on a
manifold, and then ask about the time evolution of those distributions.
The time evolution of that distribution is presumably measure–preserving,
and thus we can apply the conventional definitions of ergodicity
\begin_inset Formula
\[
\mu\left(\bigcup_{k=1}^{\infty}T^{-k}\left(A\right)\right)=1
\]
\end_inset
and mixing
\begin_inset Formula
\[
\lim_{k\to\infty}\mu\left(T^{-k}\left(A\right)\cap B\right)=\mu\left(A\right)\mu\left(B\right)
\]
\end_inset
to argue that the distribution eventually spreads over all of
\begin_inset Formula $U_{n}$
\end_inset
.
The brick wall from last night was the realization that finite–dimensional
\begin_inset Formula $H$
\end_inset
is always diagonalizable, and so the paths
\begin_inset Formula $e^{-iHt}$
\end_inset
are always great circles.
\end_layout
\begin_layout Standard
Fuck me.
And now I am confusing myself.
The four–wave interaction
\begin_inset Formula $H_{4}$
\end_inset
does ...
what ...
exactly? I think it says that two particles, i.e.
two normal modes, traveling on two different great circles, can collide
with each other, with some likelihood obtained from
\begin_inset Formula $\epsilon_{4}$
\end_inset
, and then depart on two other great circles.
Thus, mixing arises because this looks like ...
a gas.
Billiards.
WTF.
How come I've never heard of anything anywhere that describes the four–wave
interaction in this way? Maybe I just slept through it, or skimmed, and
did not notice? My lack of knowledge never ceases to amaze me.
I keep thinking of these super–duper simple ideas that should have simple
answers, and whenever I get one, all I know is that I have no clue what
the answer is, and worse, the answer should have been so simple that it
should have been a part of my education, but wasn't.
Now, the profs always assigned far more than I ever actually read.
But still.
And I'm not stupid.
But still.
This should be plain and simple.
Why do I not know it?
\end_layout
\begin_layout Standard
Answer: (1) its not billiards scattering, its just plain scattering.
(2) there was never talk of manifolds (3) there was no talk of mixing,
and little of ergodicty except in hand–waving terms: appeals to the
\begin_inset Quotes eld
\end_inset
ergodic hypothesis
\begin_inset Quotes erd
\end_inset
but without detail.
(4) scattering was always in momentum space.
And that's why it wasn't in my education.
\end_layout
\begin_layout Standard
The idea is quite simple, so lets write it down.
Again, the model is of a collection of harmonic oscillators with pair–wise
interactions.
Each oscillator has an excitation
\begin_inset Formula $\left|e_{i}\right\rangle $
\end_inset
with the label
\begin_inset Formula $i$
\end_inset
denoting the i'th oscillator.
This index can be thought of as encoding the
\begin_inset Quotes eld
\end_inset
position
\begin_inset Quotes erd
\end_inset
of the oscillator (as it would be for e.g.
a crystal lattice of atoms).
But these are not normal modes aka energy eigenstates.
The normal modes are
\begin_inset Formula $v_{j}=\sum_{i}c_{ji}e_{i}$
\end_inset
where
\begin_inset Formula $e_{i}\equiv\left|e_{i}\right\rangle $
\end_inset
is just an alternate notation.
The
\begin_inset Formula $c_{ji}$
\end_inset
are complex numbers, satisfying
\begin_inset Formula $H_{2}v_{j}=E_{j}v_{j}$
\end_inset
where
\begin_inset Formula $H_{2}=H_{0}+H_{int}$
\end_inset
and
\begin_inset Formula $H_{int}$
\end_inset
is just the quadratic interactions as defined before.
\end_layout
\begin_layout Standard
The normal modes can be thought of as points on
\begin_inset Formula $\mathbf{CP}^{n}$
\end_inset
but they are kind of boring because they don't move; only the phase changes
and that's moded out.
Anything that's an energy eigenstate won't move.
If we did it right, the normal modes merely span
\begin_inset Formula $\mathbf{CP}^{n}$
\end_inset
so again, that's pretty boring.
So thinking of a manifold here is not interesting.
In particular, four paragraphs ago, thinking about
\begin_inset Formula $U_{n}$
\end_inset
also seems to be stupid nonsense, because
\begin_inset Formula $H$
\end_inset
is fixed, frozen, a constant.
So what the heck are we doing here?
\end_layout
\begin_layout Standard
The 4–wave scattering can be written as
\begin_inset Formula
\[
H_{4}=\epsilon_{4}\left(\left|e_{i}e_{j}\right\rangle \left\langle e_{k}e_{l}\right|+\left|e_{k}e_{l}\right\rangle \left\langle e_{i}e_{j}\right|\right)
\]
\end_inset
and applying this to the scattering of two normal modes
\begin_inset Formula $v_{a}=\sum_{m}c_{am}\left|e_{m}\right\rangle $
\end_inset
and
\begin_inset Formula $v_{b}=\sum_{p}c_{bp}\left|e_{p}\right\rangle $
\end_inset
gives
\begin_inset Formula
\begin{align*}
v_{a}\otimes v_{b} & \to\sum_{m,p\ne i,j,k,l}c_{am}c_{bp}\left|e_{m}e_{p}\right\rangle +c_{ak}c_{bl}\left|e_{i}e_{j}\right\rangle +c_{ai}c_{bj}\left|e_{k}e_{l}\right\rangle \\
=v_{a}\otimes v_{b} & -c_{ai}c_{bj}\left|e_{i}e_{j}\right\rangle -c_{ak}c_{bl}\left|e_{k}e_{l}\right\rangle \\
& +c_{ak}c_{bl}\left|e_{i}e_{j}\right\rangle +c_{ai}c_{bj}\left|e_{k}e_{l}\right\rangle \\
=v_{a}\otimes v_{b} & +\left(c_{ak}c_{bl}-c_{ai}c_{bj}\right)\left|e_{i}e_{j}\right\rangle \\
& +\left(c_{ai}c_{bj}-c_{ak}c_{bl}\right)\left|e_{k}e_{l}\right\rangle \\
=v_{a}\otimes v_{b} & +\left(c_{ak}c_{bl}-c_{ai}c_{bj}\right)\left(\left|e_{i}e_{j}\right\rangle -\left|e_{k}e_{l}\right\rangle \right)
\end{align*}
\end_inset
Note that the result of the collision is not in general another product
of normal modes.
\end_layout
\begin_layout Standard
How fast does this happen? We apply Fermi's golden rule.
Scrounging on Wikipedia, I see it is
\begin_inset Formula
\begin{align*}
\Gamma_{\left|v_{a}v_{b}\right\rangle \to\left|v_{c}v_{d}\right\rangle } & =\frac{2\pi}{\hbar}\left|\left\langle v_{c}v_{d}\right|H_{4}\left|v_{a}v_{b}\right\rangle \right|^{2}\rho\left(E\right)\\
& =\frac{2\pi}{\hbar}\epsilon_{4}\left|\left(c_{ci}^{*}c_{dj}^{*}-c_{ck}^{*}c_{dl}^{*}\right)\left(c_{ak}c_{bl}-c_{ai}c_{bj}\right)\right|^{2}\rho\left(E\right)
\end{align*}
\end_inset
which is not very edifying.
\end_layout
\begin_layout Standard
Anyway, perhaps I am wasting my time.
Clicking through, I see that perhaps I am just reinventing https://en.wikipedia.o
rg/wiki/Quantum_decoherence and doing it badly, in a bit of a ham–handed
fashion.
Maybe I should just read that article...
\end_layout
\begin_layout Subsection*
27 May 2025
\end_layout
\begin_layout Standard
I forgot to write this up yesterday: it's turtles all the way down.
The point is that if you are in the lab frame of the detector, then you
have to accept proper time as the relevant parameter for the system, which
means you work with a conjugate Hamiltonian, which implies that state transitio
ns come from Fermi's golden rule, which implies that those state transitions
appear to be mixtures in the local time–frame, for the local constant–time
slice.
The is,
\begin_inset Formula $\Gamma_{\left|v_{a}v_{b}\right\rangle \to\left|v_{c}v_{d}\right\rangle }$
\end_inset
gives you the branching ratios into the state
\begin_inset Formula $\left|v_{c}v_{d}\right\rangle $
\end_inset
and once that
\begin_inset Quotes eld
\end_inset
branch is taken
\begin_inset Quotes erd
\end_inset
, one can say that
\begin_inset Quotes eld
\end_inset
the wave–function collapsed into
\begin_inset Formula $\left|v_{c}v_{d}\right\rangle $
\end_inset
\begin_inset Quotes erd
\end_inset
.
Each of the branches are meant to be summed incoherently: one gets a mixture
of different states
\begin_inset Formula $\left|v_{c}v_{d}\right\rangle $
\end_inset
and the probability of having
\begin_inset Formula $\left|v_{c}v_{d}\right\rangle $
\end_inset
in that mixture is given by
\begin_inset Formula $\Gamma$
\end_inset
.
Stated differently, decoherence consists of a long sequence of
\begin_inset Quotes eld
\end_inset
wave–function collapses
\begin_inset Quotes erd
\end_inset
, each of which contribute a little itty–bitty piece to the canonical ensemble.
\end_layout
\begin_layout Standard
The irony here is that we started trying to describe the collapse of an
entangled state, either space–like separated, or Renninger–separated, and
we did this successfully by describing the coupling to decoherence tanks.
But if we look at each tank, we see that it in turn is a very deep cascade
of branching measurements.
How should that be described? What is the formalism there? What are the
equations that give a foundation to the intuition?
\end_layout
\begin_layout Standard
Well, for starters, it helps to articulate the tensor algebra more precisely.
A single–particle state is described by
\begin_inset Formula $\left|v\right\rangle \in V$
\end_inset
where
\begin_inset Formula $V\cong\mathbb{C}^{n}$
\end_inset
for the
\begin_inset Formula $n$
\end_inset
–oscillator system.
The Hamiltonian up to quadratic terms is
\begin_inset Formula $H_{2}=H_{0}+H_{int}$
\end_inset
and we have a choice of notation: either
\begin_inset Formula $H_{2}:V\to V$
\end_inset
or
\begin_inset Formula $H_{2}\in V^{\dagger}\otimes V$
\end_inset
given the standard bilinear inner product
\begin_inset Formula $\left\langle a|b\right\rangle =\delta_{ab}$
\end_inset
.
The two–particle interaction
\begin_inset Formula $H_{4}$
\end_inset
is thus
\begin_inset Formula $H_{4}:V\otimes V\to V\otimes V$
\end_inset
or equivalently
\begin_inset Formula $H_{4}\in V^{\dagger}\otimes V^{\dagger}\otimes V\otimes V$
\end_inset
.
Normally one does not have to say these parts out loud, since the extension
of operators from tensor spaces to the full tensor algebra follows from
the universal property of the tensor product (i.e.
it follows from category theory.) I'm taking the effort to say this out
loud to focus attention on the needed pieces–parts to assemble everything.
\end_layout
\begin_layout Standard
Part of the deal is that when
\begin_inset Formula $V\cong\mathbb{C}^{n}$
\end_inset
has a basis
\begin_inset Formula $\left\{ e_{k}\right\} $
\end_inset
then
\begin_inset Formula $V\otimes V$
\end_inset
can be given the basis
\begin_inset Formula $\left\{ e_{jk}=e_{j}\otimes e_{k}=\left|e_{j}e_{k}\right\rangle \right\} $
\end_inset
We are free to choose the basis as desired, so its handy to use the normal
modes
\begin_inset Formula $\left\{ v_{k}\right\} $
\end_inset
as the basis, with the normal modes understood as diagonalizing the quadratic
Hamiltonian:
\begin_inset Formula $H_{2}v_{k}=E_{k}^{\left(2\right)}v_{k}$
\end_inset
.
The quartic interaction means that the basis
\begin_inset Formula $\left\{ v_{jk}=v_{j}\otimes v_{k}\right\} $
\end_inset
is not orthogonal w.r.t
\begin_inset Formula $H=H_{2}\otimes H_{2}+H_{4}$
\end_inset
.
Note the funky way that I wrote this: instead of writing
\begin_inset Formula $H=H_{2}+H_{4}$
\end_inset
as would be conventional on QM textbooks, I'm using the tensor product
to explicitly draw attention to
\begin_inset Formula $H_{2}$
\end_inset
being a single–particle operator.
In the end, its exactly the same thing, because, again, the universal property
of tensor products extends automatically, and this extension can be implicitly
assumed.
I'm just trying to be unambiguous and clear, here.
The point is that
\begin_inset Formula $H$
\end_inset
is hermitian:
\begin_inset Formula $H^{\dagger}=H_{2}^{\dagger}\otimes H_{2}^{\dagger}+H_{4}^{\dagger}=H_{2}\otimes H_{2}+H_{4}=H$
\end_inset
and so it is possible to orthogonalize this in terms of states
\begin_inset Formula $\left\{ w_{k}:w_{k}\in V\otimes V\right\} $
\end_inset
solving
\begin_inset Formula $Hw_{k}=E_{k}w_{k}$
\end_inset
.
Writing
\begin_inset Formula
\[
\left|w_{k}\right\rangle =\sum_{ij}a_{kij}\left|v_{i}v_{j}\right\rangle
\]
\end_inset
then
\begin_inset Formula
\begin{align*}
H\left|w_{k}\right\rangle & =\left|w_{k}\right\rangle \left\langle w_{k}\right|H\left|w_{k}\right\rangle \\
& =\left|w_{k}\right\rangle \sum_{ijlm}\left\langle w_{k}\right|\left.v_{i}v_{j}\right\rangle \left\langle v_{i}v_{j}\right|H\left|v_{l}v_{m}\right\rangle \left\langle v_{l}v_{m}\right|\left.w_{k}\right\rangle \\
& =\left|w_{k}\right\rangle \sum_{ijlm}a_{kij}^{*}a_{klm}\left\langle v_{i}v_{j}\right|H\left|v_{l}v_{m}\right\rangle \\
& =\left|w_{k}\right\rangle \sum_{ijlm}a_{kij}^{*}a_{klm}\left\langle v_{i}v_{j}\right|H_{2}\otimes H_{2}+H_{4}\left|v_{l}v_{m}\right\rangle \\
& =\left|w_{k}\right\rangle \left[\sum_{ij}a_{kij}^{*}a_{kij}E_{i}^{\left(2\right)}E_{j}^{\left(2\right)}+\sum_{ijlm}a_{kij}^{*}a_{klm}\left\langle v_{i}v_{j}\right|H_{4}\left|v_{l}v_{m}\right\rangle \right]\\
& =E_{k}\left|w_{k}\right\rangle
\end{align*}
\end_inset
and so
\begin_inset Formula
\[
E_{k}=\sum_{ij}a_{kij}^{*}\left[a_{kij}E_{i}^{\left(2\right)}E_{j}^{\left(2\right)}+\sum_{lm}a_{klm}\left\langle v_{i}v_{j}\right|H_{4}\left|v_{l}v_{m}\right\rangle \right]
\]
\end_inset
is the eigenvalue of the two–particle mode that was previously taken to
be
\begin_inset Quotes eld
\end_inset
interacting
\begin_inset Quotes erd
\end_inset
.
In this way, we can orthogonalize all of the two–particle states.
These are pure states.
They are orthogonal, by construction, whenever the eigenvalues differ,
and can be made orthogonal by finding a
\begin_inset Quotes eld
\end_inset
complete set of commuting operators
\begin_inset Quotes erd
\end_inset
.
Right now, we only have this as a theorem, with no constructive suggestions
for how to go about finding this complete set.
Doesn't seem like this should be hard, I think this is solvable.
\end_layout
\begin_layout Standard
At any rate, since these are pure states, and there are no higher–order
terms in the Hamiltonian, these are non–interacting.
Fermi's golden rule no longer applies, no longer matters, because there
are no more superpositions, no more interactions, no more scattering, and
thus, no more
\begin_inset Quotes eld
\end_inset
wave–function collapse
\begin_inset Quotes erd
\end_inset
.
Now, if one attached some device to a single oscillator, to measure whether
or not that oscillator is in the excited state at some particular moment
in time in the lab frame, then a wave–function collapse does occur, and
we repeat the analysis with a third decoherence tank, connected by a
\begin_inset Quotes eld
\end_inset
narrow bridge
\begin_inset Quotes erd
\end_inset
to the oscillator we are measuring.
Similarly, if there was a device for measuring the normal modes of the
quadratic Hamiltonian, then again, we're attaching a third tank, just in
a different way.
Crank the algebra, but nothing changes in the overall theory.
\end_layout
\begin_layout Standard
Note that, for
\begin_inset Formula $\dim V=n$
\end_inset
we have
\begin_inset Formula $\dim V\otimes V=n\left(n+1\right)/2$
\end_inset
so for
\begin_inset Formula $n\sim6\times10^{23}$
\end_inset
this gets to be explosively large.
We can reasonably talk about
\begin_inset Formula $n\sim10^{6}$
\end_inset
for a single pixel in some CCD camera, and still, things get explosively
large, explosively fast.
\end_layout
\begin_layout Standard
Still, can we say anything intelligent bout the three–excitation state?
This consists of states
\begin_inset Formula $\left|\psi^{\left(3\right)}\right\rangle \in V\otimes V\otimes V=T^{3}V$
\end_inset
.
My gut sense says that this is where we have to start talking about bialgebras,
and eventually shuffle algebras, because the four–wave
\begin_inset Formula $H$
\end_inset
acts only on
\begin_inset Formula $T^{2}V$
\end_inset
but which
\begin_inset Formula $T^{2}V$
\end_inset
? God help us, I think there is no braiding, but this word
\begin_inset Quotes eld
\end_inset
braiding
\begin_inset Quotes erd
\end_inset
is lurking on the edges, waiting to pounce on the unwary.
How do I do this safely, without getting mugged? What I think I'm trying
to do here is a pure tensor–algebra variant of the BBGKY hierarchy, without
any mention of positions or momenta.
Informally, I guess you could say I've replaced
\begin_inset Formula $\left(q,p\right)$
\end_inset
pairs by the SHO.
\end_layout
\begin_layout Standard
...
and as I write this, I get totally distracted.
I glance at https://en.wikipedia.org/wiki/Ergodic_hypothesis and at the figure
labelled
\begin_inset Quotes eld
\end_inset
Maxwell's tunnel
\begin_inset Quotes erd
\end_inset
, and I promptly realize the question is about the illumination problem.
https://en.wikipedia.org/wiki/Illumination_problem And this is what I write:
\end_layout
\begin_layout Standard
\emph on
[[File:Ergodic hypothesis w reflecting rays.jpg|thumb|The question of ergodicity
in a perfectly collisionless [[ideal gas]] with [[specular reflection]]s.]]
The article currently has the figure at right.
It can be construed as being answered in the negative, and/or being a misleadin
g figure.
The problem is the caption: "a perfectly collisionless ideal gas with specular
reflections." which is the setting for the study of "[[Illumination problem|unil
luminable room]]s".
The thing called "Maxwell's tunnel" is illuminable.
I'm not aware of any youtube video showing this, but there's a cottage
industry of those.
I assume the illumination guys can even provide a theorem that, as drawn,
its illuminable; they seem to be able to do this kind of stuff, but I dunno.
The WP article also gives examples of unilluminable rooms, so if you limit
yourself to "perfectly collisionless" motion, then the ergodic hypothesis
fails.
Collisions are required, for the ergodic hypothesis to apply.
There are several ways of hand–waving this: for waves, one must have a
[[resonant interaction]] to have ergodicity and mixing, and for quantum
systems, one has to have a QM version thereof, involving either fermion-photon
scattering, or four–particle scattering (four, because the QM version of
the [[three-wave equation]] cannot conserve both energy and momentum (and
particle–number, for a single field).
Unless you're a gluon, in which case it can.
But gluons are non–obvious, and anyway we don't have non–microscopic systems
that behave like gluons, so three–particle scattering would have to be
a very arcane example.
\end_layout
\begin_layout Standard
\emph on
What am I saying here? The figure is ...
well, its just wrong.
It's trying to illustrate the ergodic hypothesis using some unusual geometry,
which made sense in Maxwell's time, 150 years ago, but is now outmoded!?
[[Special:Contributions/67.198.37.16|67.198.37.16]] ([[User talk:67.198.37.16|talk]])
00:05, 28 May 2025 (UTC)
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Sooo ...
the lightbulb that goes off in my mind is of course the QCD lightbulb.When
I was young, and didn't yet understand stuff, I imagined that the Dirac
equation could be thought of as the product of two
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derivative
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operators, one acting on space–time, and one acting on the internal spin
states.
i.e.
that the gamma matrices are a kind of derivative (Lie derivative?) acting
on the su(2) algebra and I spent a lot of time trying to make this analogy
work, but always got stuck because I had not yet invented the diary format
I use here, of talking to myself much more informally than I would care
to admit to outsiders.
But anyway, I think that, appropriately construed, the analogy of a gamma
matrix as a kind–of derivative is broadly correct, and the Dirac eqn couples
unbounded degrees of freedom (spacetime) to internal degrees of freedom
(Bloch sphere, or the tangent thereon.) And so I'm suddenly
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holy fuck, is the su(3) just a three–wave coupling (three–wave equation,
https://en.wikipedia.org/wiki/Three-wave_equation but for internal degrees
of freedom?
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Well, of course it is.
Just ...
not scalar.
It's non–abelian.
And so can I use this insight to say something that has not been said before?
Fuck me.
Life is too short, I have too many daydreams, too many tasks, not enough
time.
Dammit.
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28 May 2025
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For the life of me, I cannot figure out how to get mixing in a quantum system.
All that happened above is I found that two–particle states are non–interacting.
That is, the quartic
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has two–particle as eigenvectors, and these are non–interacting.
Period.
End of story.
I need to somehow create turtles all the way down.
That is, I need a system that measures entangled states *all the time*,
in order to get mixing.
How can I force such measurements to occur all the time? I can imagine
several ways, but they are dissatisfactory.
I'll have to come back to this later.
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The End
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This is the end of Part Ten–D of the diary.
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