[FRIAM] neural operators seem promising

Thu Jul 17 12:39:33 EDT 2025

Yes... kind of.

I know how NOs little siblings like CNNs have done cool stuff with images,
and it makes sense to hope NOs (Neural Operators) might do similar things
in "big boy" applications like fluid mechanics, weather modelling, and
robotics control. I agree, that would be great!.

But this is still a top-down approach. We're building tools that are smart
in some ways, but they don’t really think like people. I don’t expect this
to lead to true human-like intelligence.

I wouldn’t be surprised if someone out there is quietly working on a
bottom-up way to build AI—and I think that’s where big breakthroughs could
happen.

For now, NOs and similar models will keep giving us amazing results. But
they're still just tools. Useful, potentially absolutely amazing.
Human-like? No way, Jose.

On Thu, 17 Jul 2025 at 16:50, glen <gepropella at gmail.com> wrote:

> I'm confident nobody but me cares. But just one more post, I promise.
> Perplexity is not normally my sycophant. She flat out rejected my
> extrapolation from Powell's "The Kraken" to the entirety of the Stop the
> Steal suits. And she flat out rejected my claim that the term "Scientific
> Materialism" is the best term to use for those of us who want to avoid
> teleo[logy|nomy]. But, here, she agrees with me that:
>
> "It is feasible and indeed a valuable research direction to use Neural
> Operators like those in the NNs-to-NOs repo to computationally approximate
> the full multi-scale stack from microscopic particle systems to macroscopic
> fluid equations that Deng et al. prove mathematically."
>
> Whew! So I'm not crazy, right? Of course, I'm too lazy to actually do it
> ... or maybe I'll just blame it on "brain fog" ... another term I
> absolutely loathe. >8^D
>
> On 7/17/25 6:55 AM, glen wrote:
> > Sabina's recent defense of Weinstein [⛧] seems to follow in this vein.
> And I can't help but feel similarly when I try to understand Geometric
> Algebra. What is the value of these games over and above their binding to
> the world? Or, maybe more importantly, what's their value when they fail to
> bind well to the world? My favorite writer about Gödel was Torkel Franzén,
> who spent more time debunking the runaway [ab]use of the incompleteness
> theorems than he did inferring anything from them - or maybe I was simply
> more attracted to his debunking than I was to his in-theory work. I guess
> the same is true of Barwise's tinkering around with anti-foundations or
> Shapiro's foundations without foundationalism. Now that we have things like
> Isabelle/HOL, the "theory" seems to take on a life of its own. Inference
> tools like this help me play the games I could only imagine when I was a
> kid, even if my games are childish or of no use to anyone but me. Then
> again, I don't spew grievance on
> > everyone I meet when *they* don't want to play the games I enjoy.
> >
> > Since we're still in the [F]NO thread, they do seem to fall directly in
> line with the way even the most banal of us are using AI. This result:
> >
> > Hilbert's sixth problem: derivation of fluid equations via Boltzmann's
> kinetic theory
> > https://arxiv.org/abs/2503.01800
> >
> > is out of my reach. And even with
> https://github.com/neuraloperator/NNs-to-NOs, it's not clear to me
> whether I'd be able to understand enough to mimic the analyses Anandkumar
> presented in the talk. But like with Isabelle or Lean (plus tools like
> Claude) I can just barely *taste* it. I can just barely taste what it might
> be like to be a theorist - to have the cognitive power to think such things
> through in the way Eric describes Einstein. At the end of the day, though,
> Franzén's more my speed.
> >
> >
> > [⛧] Though her less recent discussion of Thiel and the relationship
> between Thiel and Weinstein smells like smoke. Of course Carroll is exactly
> the type of person the anti-establishment would accuse of Scientism.
> :face_with_rolling_eyes:
> >
> > On 7/16/25 9:30 PM, Pieter Steenekamp wrote:
> >> It  reminds me of Gödel’s incompleteness theorems.
> >>
> >> Gödel’s incompleteness theorems show that any formal system powerful
> enough to describe arithmetic will always have true statements it can’t
> prove. This seems like a purely theoretical result, but the proof itself is
> highly constructive—Gödel uses very practical techniques like numbering
> symbols and mimicking logic inside arithmetic.
> >>
> >> In a way, it’s a perfect example of applied technique informing theory.
> A deep theoretical truth was uncovered not just by abstract thinking, but
> by rolling up sleeves and working with the system from the inside.
> Faraday/Maxwell, steam engines/thermodynamics all show how hands-on methods
> can push theory forward.
> >>
> >> On Thu, 17 Jul 2025 at 03:20, Santafe <desmith at santafe.edu <mailto:
> desmith at santafe.edu>> wrote:
> >>
> >>     I _very often_ have the thought that, were the nature of people
> such that grievance and misanthropy simply didn’t do them any good, and so
> they simply never engaged in it, so many conversations would go on in such
> different ways, that we might have to adjust a bit to realize they started
> from the same query.
> >>
> >>     One such query is whether the nature of anti-theory people is
> mainly an aesthetic style of thought (seems very possible), or mainly
> motivated by a dislike of people they met earlier who (whether with warrant
> or just to serve other needs of their own) they label as “theory people”.
> I would like it if it were mostly the former; that anti-theory people were
> “born this way”; it would give me a conversation that seems interesting in
> several dimensions and that I could navigate.  Let’s suppose that such
> conversations are available somewhere, even if not everywhere.
> >>
> >>     The start of this went something along the lines of “Faraday locked
> in electromagnetism by its empirical evidences, and Maxwell put some pretty
> symbols onto it.”  (The original wasn’t exactly as I just wrote it, and I
> am over-drawing here to take the direction to its cartoon-simplified
> limit.  I am also _sure_ I can find some truly anti-theory people who
> believe this is the absolutely right take on it.  Within Chemistry, where I
> have the counterpart to this conversation fairly often, I have a good list
> of names, because it is still the prevalent aesthetic of the field.)
> >>
> >>     The sort of mind that believes that the former take on Maxwellian
> electromagnetism is indeed the only real-man’s hard-headed take, is likely
> (to the extent that it has any patience with formal logical analysis at all
> as not a priestly self-indulgent waste of time) inclined to think that
> Popper has a good description of the criteria for scientific meaningfulness
> and truthfulness.
> >>
> >>     But then we can do it recursively all the way down.  Is Newtonian
> gravity just one among an infinitude of data-compressions of Keplerian
> orbits (since, at the end, everything moving under gravity and
> approximating away other effects such as friction is on a Keplerian orbit,
> including apples, so there “isn’t” really anything else).
> >>
> >>     Let’s not answer, but simply add attested observations:
> >>
> >>     It was studying Maxwell’s field equations in school that led
> Einstein to try to construct general relativity within similar concepts.
> And presumably the very geometric flux-sphere picture that comes with
> Newtonian gravity that causes geometry to be retained as the phenomenon for
> Einstein’s gravitational field theory to be about.
> >>
> >>     One can go through such idea-chains across the sciences.  In some,
> people don’t leave pithy accounts of why they believed it occurred to them
> to do things one way rather than another; in other cases they do leave such
> trails, at least about their beliefs.  Or philosophers come along later and
> do forensics and argue that their work shows their reasons to be
> such-and-such.
> >>
> >>     A compact representation of the latter collection of
> asserted-observations is that there is some kind of work that theory is
> doing as itself, not as a proxy for something else (like description-length
> shortening for a pile of data-instances).  I remember how it seemed an
> insightful turn for me when my graduate advisor commented that the particle
> physicists had felt a sense of liberation when they could throw away the
> Particle Data Book, with the advent of first Murray’s symmetry
> classification and eventually the settling in of QCD as a theory in which
> one could stably compute things, and then the whole symmetry-grouping of
> all the elementary particles by a few terms.
> >>
> >>
> >>     Circling back to thermodynamics, Harold’s “Emergence of
> Everything”, and what is or isn’t substantial in the world of observations
> and states of mind that we take on in relation to them:
> >>
> >>     Harold was happy invoking Popper, and didn’t want to sweat a lot
> over how much Popper was trying to take over a dichotomy from first-order
> logic,  and the asymmetry between there-exists and for-all, and how much it
> doesn’t work to press that into service as a formalization for empiricist
> reasoning.  Harold was, generally, an easy-going guy, and willing for
> things to be rough, or half-wrong, supposing that if he could intuitively
> get them half-right, that would be much better than nothing, and there
> would be time to come back and fix whatever parts may have been wrong.  So
> he could like Popper as one of his half-right positions, even though it was
> the inability to deal with being half-right where Popper ultimately
> undermined himself.   btw., that’s where a very useful study of metaphor in
> science, along the lines that DaveW gave a definition of it from Quine, can
> get built up.
> >>
> >>     Probably likewise with thermo and steam engines.  For the purpose
> of making a certain point — that theory doesn’t arise in a vacuum or from
> direct access to the Mind of God — Harold would be happy to overstate the
> simplicity of this position, and to evangelize for empiricism.
> >>
> >>     But of course, in the world we live in — and especially the world
> where I live, which is almost-all thermodynamics almost-all the time, and
> almost-none of it about steam engines, or even anything having to do with
> mechanics or energy — we have learned much, much more about
> nearly-everything, from thermodynamics, than there even was of
> thermodynamics, to have learned from steam engines.  At the end of the day,
> the lessons of thermodynamics, when properly understood, constitute the
> explanation for why there even are stable macro-worlds.  Of more-or-less
> anything.  In other working conversations, with other aims, Harold would of
> course have seen that too, and been happy with the statement putting it on
> record.  Even though that statement would have seemed, to a debaterly-type
> mind, to have contradicted the earlier one.
> >>
> >>
> >>     I have seen a lot of chat over the years about what is “the nature”
> of theory as something that can do work that deserves to be called
> different-in-kind, and not just different-in-cost, than listing data
> instances, thus making theory particular among data compressions (the
> latter, as a kind of generic category; obviously theories are, as one of
> their aspects, compressions of data instances; the question here is whether
> to say that is “all” they are is as good or as useful an account as we can
> give).  But at the end, I just hear the same positions reiterated, some of
> them more rhetorically elegantly (Cris Moore did a very nice job in a tiny
> soliloquy in one of the SFI public lectures), or more tritely and
> conventionally.  But I haven’t heard somebody with something really
> original to say on the question, that makes me stop and think I see things
> better, for a long time now.  I think the Philosophers of Science (I’ll
> capitalize both for DaveW) put a lot of time into this.
> >>     If I had more time I would probably try to listen to them, and I
> might find they have interesting things to say.
> >>
> >>     Eric
> >>
> >>
> >>
> >>
> >>
> >>>     On Jul 17, 2025, at 2:19, Steve Smith <sasmyth at swcp.com <mailto:
> sasmyth at swcp.com>> wrote:
> >>>
> >>>       * Anima's presentation reminded me quite nicely of the
> Numenta/Redwood work of Jeff Hawkins et al?   Cortical columns, etc.
> >>>       * Did Harold Morowitz make a strong assertion to the tune: "we
> learned more about thermodynamics from steam-engines than vice-versa"?
> EricS or StephenG might have first-hand knowledge?
> >>>       * Is this theory/practice dichotomy just another form of
> meta-scaffolding in evolution (of any system) with the cut-and-try
> providing the mutation/selection and the theory/formalism binding the
> "lessons learned" into well... "lessons learned"?
> >>>
> >>>     On 7/16/2025 2:12 AM, Pieter Steenekamp wrote:
> >>>>     Both the video of Anima Anandkumar’s Stanford seminar and her
> scientific paper on Neural Operators really got me excited—the ideas feel
> fresh and powerful.
> >>>>
> >>>>     The paper is quite technical and digs into the math behind
> Neural Operators, without talking much about robotics. In her talk, though,
> she clearly links the work to robots, and it sounds as if robotics is a big
> focus for her team.
> >>>>
> >>>>     What jumped out at me is how different her style is from
> Elon Musk’s approach with Tesla’s Optimus robot. Anandkumar begins with
> deep theory, building firm mathematical foundations first. Musk takes a
> “just build it” path—make it, test it, break it, fix it, and keep going.
> >>>>
> >>>>     This contrast reminds me of engineering school and the
> Faraday‑Maxwell story. Faraday was the hands‑on experimenter who uncovered
> the basics of electricity and magnetism through careful tests. Maxwell came
> later and wrote the elegant equations that explained what Faraday had
> already shown.
> >>>>
> >>>>     So I wonder: will the roles flip this time? Will deep theory from
> researchers like Anandkumar guide the breakthroughs first, with practice
> following? Or will practical builders like Musk sprint ahead and let theory
> catch up afterward?
> >>>>
> >>>>     Either way, watching these two paths unfold side by side is
> thrilling. It feels like we’re standing on the edge of something big.
> >>>>
> >>>>     On Wed, 16 Jul 2025 at 04:11, Jon Zingale <jonzingale at gmail.com
> <mailto:jonzingale at gmail.com>> wrote:
> >>>>
> >>>>         Even if just for the freedom of scale, learning infinite
> dimensional function spaces, etc...
> >>>>
> >>>>         https://www.youtube.com/watch?v=caZyFlSSKtI <
> https://www.youtube.com/watch?v=caZyFlSSKtI>
> >>>>         https://arxiv.org/pdf/2506.10973 <
> https://arxiv.org/pdf/2506.10973>
> >>>>
>
> --
> ¡sıɹƎ ןıɐH ⊥ ɐןןǝdoɹ ǝ uǝןƃ
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