| … | … | @@ -7050,6 +7050,39 @@ with this third line being the abuse of notion. |
| 7050 | 7050 | Lets plow some more ravines. |
| 7051 | 7051 | \end_layout |
| 7052 | 7052 | |
| 7053 | \begin_layout Standard |
| 7054 | Footnote: |
| 7055 | I can validate that the abuse of notation above still gives the right answer, |
| 7056 | as follows. |
| 7057 | So for |
| 7058 | \begin_inset Formula $g_{\mu\nu}=\lambda^{2}\delta_{\mu\nu}$ |
| 7059 | \end_inset |
| 7060 | |
| 7061 | it follows that |
| 7062 | \begin_inset Formula $g^{\mu\nu}=\lambda^{-2}\delta^{\mu\nu}$ |
| 7063 | \end_inset |
| 7064 | |
| 7065 | because this gives |
| 7066 | \begin_inset Formula $g_{\mu\nu}g^{\nu\rho}=\delta_{\mu}^{\rho}$ |
| 7067 | \end_inset |
| 7068 | |
| 7069 | as desired, |
| 7070 | and then from |
| 7071 | \begin_inset Formula $e_{\;\mu}^{a}=\lambda\,\delta_{\mu}^{a}$ |
| 7072 | \end_inset |
| 7073 | |
| 7074 | just raise: |
| 7075 | |
| 7076 | \begin_inset Formula $e^{a\mu}=e_{\;\nu}^{a}g^{\nu\mu}=\lambda\cdot\lambda^{-2}\delta^{a\mu}=\delta^{a\mu}/\lambda$ |
| 7077 | \end_inset |
| 7078 | |
| 7079 | . |
| 7080 | So this awkward–looking expression contracting greek and roman letters is just fine and fully consistent. |
| 7081 | The awkwardness of it all, |
| 7082 | and Claude's glibness, |
| 7083 | was giving me the willies. |
| 7084 | \end_layout |
| 7085 | |
| 7053 | 7086 | \begin_layout Paragraph* |
| 7054 | 7087 | Spinors |
| 7055 | 7088 | \end_layout |
| … | … | @@ -7328,7 +7361,7 @@ Finally |
| 7328 | 7361 | \end_inset |
| 7329 | 7362 | |
| 7330 | 7363 | but this is trivially satisfied by the above results. |
| 7331 | | I think the above is correct. |
| 7364 | I think the results in this section are correct. |
| 7332 | 7365 | \end_layout |
| 7333 | 7366 | |
| 7334 | 7367 | \begin_layout Paragraph* |
| … | … | @@ -7358,7 +7391,7 @@ subject to the hedgehog boundary conditions applied at |
| 7358 | 7391 | \end_inset |
| 7359 | 7392 | |
| 7360 | 7393 | . |
| 7361 | | We comply trickery from here on out. |
| 7394 | We use trickery from here on out. |
| 7362 | 7395 | I am using Claude to find the tricks. |
| 7363 | 7396 | I'm not verifying them carefully, |
| 7364 | 7397 | they smell correct. |
| … | … | @@ -7648,7 +7681,7 @@ Pöschl-Teller potential |
| 7648 | 7681 | \begin_layout Standard |
| 7649 | 7682 | Next, |
| 7650 | 7683 | we can solve the above. |
| 7651 | | Clause guesses that its hypergeometric, |
| 7684 | Claude guesses that its hypergeometric, |
| 7652 | 7685 | and arrives at the exact solution |
| 7653 | 7686 | \begin_inset Formula |
| 7654 | 7687 | \[ |
| … | … | @@ -7670,8 +7703,9 @@ with |
| 7670 | 7703 | \end_inset |
| 7671 | 7704 | |
| 7672 | 7705 | OK, |
| 7673 | | that's trctable. |
| 7674 | | In chart coords its |
| 7706 | that's tractable. |
| 7707 | In chart coords, |
| 7708 | its |
| 7675 | 7709 | \begin_inset Formula |
| 7676 | 7710 | \[ |
| 7677 | 7711 | u=r\;{}_{2}F_{1}\left(a,b;2;-\frac{r^{2}}{1-r^{2}}\right) |
| … | … | @@ -8143,6 +8177,13 @@ I want the opposite. |
| 8143 | 8177 | call them screw–ball escapades. |
| 8144 | 8178 | \end_layout |
| 8145 | 8179 | |
| 8180 | \begin_layout Standard |
| 8181 | Well, |
| 8182 | I can tell it's not over. |
| 8183 | This didn't pan out, |
| 8184 | but burbling in the back of my mind is the idea that some other screwball twist will work.... |
| 8185 | \end_layout |
| 8186 | |
| 8146 | 8187 | \begin_layout Paragraph* |
| 8147 | 8188 | Punt |
| 8148 | 8189 | \end_layout |
| … | … | @@ -8347,12 +8388,238 @@ this will feel good |
| 8347 | 8388 | \end_layout |
| 8348 | 8389 | |
| 8349 | 8390 | \begin_layout Subsection* |
| 8350 | | 28 January 2026 |
| 8391 | 29 January 2026 |
| 8351 | 8392 | \end_layout |
| 8352 | 8393 | |
| 8353 | 8394 | \begin_layout Standard |
| 8354 | 8395 | OK, |
| 8355 | | so lets get back to the main topic.... |
| 8396 | back to the drawing board. |
| 8397 | Here I will belly–ache about AI development status, |
| 8398 | and try to see if there's some better way. |
| 8399 | There are multiple topics I've been putting off for months. |
| 8400 | Lets bullet list them. |
| 8401 | Lets not bullet list them, |
| 8402 | I can't remember them. |
| 8403 | They'll come back naturally as I write... |
| 8404 | \end_layout |
| 8405 | |
| 8406 | \begin_layout Standard |
| 8407 | I want to restart rewriting the learning pipeline. |
| 8408 | So I unleashed Claude and it was a total failure. |
| 8409 | Because Claude is stupid. |
| 8410 | So what I envisioned, |
| 8411 | hoped for, |
| 8412 | wanted was some autonomous file–system crawler, |
| 8413 | that would crawl and take notes, |
| 8414 | build a world–model of what it found, |
| 8415 | represented in a way that makes it easier to query than the brute–force of actually crawling the file system to find what is there. |
| 8416 | That is, |
| 8417 | the world–model is held in the AtomSpace in some |
| 8418 | \begin_inset Quotes eld |
| 8419 | \end_inset |
| 8420 | |
| 8421 | natural |
| 8422 | \begin_inset Quotes erd |
| 8423 | \end_inset |
| 8424 | |
| 8425 | representation that is easy to query in some ad hoc manner. |
| 8426 | \end_layout |
| 8427 | |
| 8428 | \begin_layout Standard |
| 8429 | There are two bootstrapping issues here. |
| 8430 | One is: |
| 8431 | what is the |
| 8432 | \begin_inset Quotes eld |
| 8433 | \end_inset |
| 8434 | |
| 8435 | natural representation |
| 8436 | \begin_inset Quotes erd |
| 8437 | \end_inset |
| 8438 | |
| 8439 | ? |
| 8440 | Of course, |
| 8441 | I can hand–design the initial one, |
| 8442 | but it would then need to be able to accrete additional information when it becomes available. |
| 8443 | So then the next question is |
| 8444 | \begin_inset Quotes eld |
| 8445 | \end_inset |
| 8446 | |
| 8447 | what is that additional information |
| 8448 | \begin_inset Quotes erd |
| 8449 | \end_inset |
| 8450 | |
| 8451 | ? |
| 8452 | and its meant to be pair–counting results, |
| 8453 | and then the marginal probabilities. |
| 8454 | So I can hand–engineer all that. |
| 8455 | I'd done it two or three times before, |
| 8456 | so this is yet another implementation. |
| 8457 | At any rate, |
| 8458 | I'm the one designi9ng where things will get stored, |
| 8459 | and when I asked Claude to do it, |
| 8460 | I got a hash, |
| 8461 | so I have to do it. |
| 8462 | \end_layout |
| 8463 | |
| 8464 | \begin_layout Standard |
| 8465 | The second bootstrapping issue is that I have to explicitly specify the file–walk algo; |
| 8466 | depth–first or breadth–first or whatever. |
| 8467 | Again, |
| 8468 | this does not happen |
| 8469 | \begin_inset Quotes eld |
| 8470 | \end_inset |
| 8471 | |
| 8472 | naturally |
| 8473 | \begin_inset Quotes erd |
| 8474 | \end_inset |
| 8475 | |
| 8476 | , |
| 8477 | but is engineered into place. |
| 8478 | \end_layout |
| 8479 | |
| 8480 | \begin_layout Standard |
| 8481 | So let me run with that idea. |
| 8482 | Can I define a set of axioms and inference rules, |
| 8483 | such that, |
| 8484 | when combined, |
| 8485 | a file–walking algo results? |
| 8486 | That is, |
| 8487 | what is the axiomatic system in which tree–walking algos are embedded? |
| 8488 | And, |
| 8489 | given this axiomatic system, |
| 8490 | what can I do to make it self–assemble, |
| 8491 | like the abelian sand–pile? |
| 8492 | i.e. |
| 8493 | to get to a critical point, |
| 8494 | where the behavior patterns at that critical point are that the avalanches are tree–walks? |
| 8495 | \end_layout |
| 8496 | |
| 8497 | \begin_layout Standard |
| 8498 | To answer that, |
| 8499 | I dig back to L–systems, |
| 8500 | and the work that Prusinkiewicz did with them: |
| 8501 | some simple grammatical rules, |
| 8502 | and you crank them, |
| 8503 | and tree structures result. |
| 8504 | Now I take them and the trees that grow are forced to conform to whatever the actual file–system tree is. |
| 8505 | \end_layout |
| 8506 | |
| 8507 | \begin_layout Standard |
| 8508 | So the new thing here for me is that with an L–system, |
| 8509 | it is incorrect to think of a single algo, |
| 8510 | walking a tree. |
| 8511 | Instead, |
| 8512 | one has creates a new agent: |
| 8513 | one for each directory and file, |
| 8514 | and that agent communicates what it finds with it's neighboring agents. |
| 8515 | Now, |
| 8516 | I can force this, |
| 8517 | project this back down to a single traditional comp–sci algo that is depth–first or breadth–first, |
| 8518 | but that is a projection (in the sense of a fibre bundle projection) If instead, |
| 8519 | I am L–system inspired, |
| 8520 | the fibre of my fibre–bundle is the L–system. |
| 8521 | Now, |
| 8522 | the agent at each directory and file is very nearly almost totally trivial: |
| 8523 | the only thing it can do is to communicate with neighbors. |
| 8524 | And maybe not even that: |
| 8525 | it can just statically denotes connections (and I statically represent these in the AtomSpace). |
| 8526 | The one non–trivial agentic behavior is that when an agent determines |
| 8527 | \begin_inset Quotes eld |
| 8528 | \end_inset |
| 8529 | |
| 8530 | oh hey I am a directory |
| 8531 | \begin_inset Quotes erd |
| 8532 | \end_inset |
| 8533 | |
| 8534 | then the grammatical production rules say |
| 8535 | \begin_inset Quotes eld |
| 8536 | \end_inset |
| 8537 | |
| 8538 | grow a new agent, |
| 8539 | one for each inode in the directory |
| 8540 | \begin_inset Quotes erd |
| 8541 | \end_inset |
| 8542 | |
| 8543 | . |
| 8544 | \end_layout |
| 8545 | |
| 8546 | \begin_layout Standard |
| 8547 | At this meta–level, |
| 8548 | at this L–system level, |
| 8549 | each new agent gets enqueued onto some run–time queue, |
| 8550 | so that the CPU goes over that queue, |
| 8551 | and alots some CPU time to each agent. |
| 8552 | Since agents that have already explored all of their inodes don't really need any more CPU time, |
| 8553 | they become |
| 8554 | \begin_inset Quotes eld |
| 8555 | \end_inset |
| 8556 | |
| 8557 | dead |
| 8558 | \begin_inset Quotes erd |
| 8559 | \end_inset |
| 8560 | |
| 8561 | (or dormant) and can be dequeued, |
| 8562 | I guess. |
| 8563 | This search algo is naturally |
| 8564 | \begin_inset Quotes eld |
| 8565 | \end_inset |
| 8566 | |
| 8567 | parallelizable |
| 8568 | \begin_inset Quotes erd |
| 8569 | \end_inset |
| 8570 | |
| 8571 | , |
| 8572 | because L–systems are naturally parallel. |
| 8573 | And, |
| 8574 | as I write this, |
| 8575 | I realize that I could also do this for the query engine. |
| 8576 | \end_layout |
| 8577 | |
| 8578 | \begin_layout Standard |
| 8579 | Let me explore the query–engine idea for a moment. |
| 8580 | Every for–loop is parallelizable in this way: |
| 8581 | it enqueues a job to explore every item in the loop. |
| 8582 | Sounds sexy, |
| 8583 | the reality is data locality: |
| 8584 | the items being walked in the loop have to be fetched from RAM, |
| 8585 | or, |
| 8586 | if its running on a GPU, |
| 8587 | it has to be copied across some bus to that GPU. |
| 8588 | Copying is automatic, |
| 8589 | for CPU's: |
| 8590 | data is automatically copied from RAM to 3rd, |
| 8591 | second then 1st level cache, |
| 8592 | then registers, |
| 8593 | and I don't have to think about that data movement problem, |
| 8594 | because the good folks at Intel/AMD have already solved it for me. |
| 8595 | For GPU's, |
| 8596 | it is much more hands–on, |
| 8597 | because the GPU sits on the far side of the PCIe bus, |
| 8598 | and I have to think about how to convert the body of my for–loop into a vector that I can efficiently pass over to the GPU side. |
| 8599 | So this is hard and tricky. |
| 8600 | Thinking about L–systems and agents is inspirational, |
| 8601 | but hits a wall when I say |
| 8602 | \begin_inset Quotes eld |
| 8603 | \end_inset |
| 8604 | |
| 8605 | oh gee, |
| 8606 | I want each agent to run on a GPU, |
| 8607 | but my agents are so trivial that they do almost nothing |
| 8608 | \begin_inset Quotes erd |
| 8609 | \end_inset |
| 8610 | |
| 8611 | , |
| 8612 | and that almost the only thing that they do is to vectorize and enqueue the next set of agents to be enqueued on the runtime queue. |
| 8613 | So this is ... |
| 8614 | abstractly interesting but profoundly mis–matched to what hardware can actually do. |
| 8615 | \end_layout |
| 8616 | |
| 8617 | \begin_layout Standard |
| 8618 | Hmm. |
| 8619 | Anyway. |
| 8620 | it is beautiful outside, |
| 8621 | so I am going for a bike ride now. |
| 8622 | Later. |
| 8356 | 8623 | \end_layout |
| 8357 | 8624 | |
| 8358 | 8625 | \begin_layout Section* |