[HN Gopher] Multicomputation as a General Paradigm for Theoretic...
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Multicomputation as a General Paradigm for Theoretical Science
Author : nsoonhui
Score : 50 points
Date : 2021-09-14 11:13 UTC (1 days ago)
(HTM) web link (writings.stephenwolfram.com)
(TXT) w3m dump (writings.stephenwolfram.com)
| typon wrote:
| A side comment, but I find the design in most of Wolfram's work
| very aesthetically pleasing. For example this website:
| https://www.wolframphysics.org and all the "artwork" of the
| graphs and explanations of his work in the Visual Gallery
| (https://www.wolframphysics.org/visual-gallery/) is beautiful.
| pehta wrote:
| This seems hard to compute for any realistic system?
| danbmil99 wrote:
| As smart as he is, as rich as he is, his ego is his downfall
| amelius wrote:
| I still have respect for him for being able to run a business
| in scientific computing profitably.
| Ono-Sendai wrote:
| 'Multicomputation' is not exactly new, see nondeterministic
| finite automata (NFA) and nondeterministic polynomial time (NP).
| rodrigosetti wrote:
| So Wolfram has initiated two of the four scientific paradigms
| taliesinb wrote:
| Some of the ideas in this post might pan out, some might not.
| Regardless, I do think token event graphs will turn out to be
| important. Of course, I'm biased: I coined the name TEG --
| although the underlying idea originated with Max Piskunov and his
| "local multiway systems" [0]
|
| What's promising about TEGs (and their incidence hypergraph, the
| rewrite hypergraph) is that they offer a clean methodology to
| decompose the behavior of a non-deterministic automaton into its
| causally independent parts. We're still trying to understand how
| to think about them, but the most promising approach seems to use
| the lens of (modular) representation theory, which gives us a
| rich mathematical toolkit to work with.
|
| If this methodology works, there will be possibility to represent
| many kinds of systems in disparate fields, ranging from
| distributed computation to physics to biology to machine
| learning, in the common language of TEGs and their
| representations. Of course it may turn out to be merely a
| recasting of older ideas. In particular the Krohn-Rhodes theorem
| [1], categorical Petri nets [2], and the GNS construction [3]
| seem like they might be describing the same or an analogous
| procedure.
|
| I hope to soon be describing this approach in full detail using
| quiver geometry [4].
|
| [0]:
| https://github.com/maxitg/SetReplace/blob/master/Research/Lo...
|
| [1]: https://www.wikiwand.com/en/Krohn-Rhodes_theory
|
| [2]: https://arxiv.org/abs/2101.04238
|
| [3]: https://www.youtube.com/watch?v=OmaSAG4J6nw
|
| [4]: https://quivergeometry.net
| gexaha wrote:
| Do you know, whether anyone of the approaches (yours or one of
| that you mention in the links) has had any kind of practical
| success, or maybe has been adopted by some community? I mean,
| it's nice to generalize, but did it help anyone yet? like
| practically (e. g., did epidemiologists or biologists or math.
| modellers adopted any of the approaches?)
| taliesinb wrote:
| I'm not an expert in Petri nets, but they are definitely used
| for modeling in various fields. Krohn-Rhodes theory also
| claims some successes if you read that article.
|
| As for the stuff I'm actively working on: even if it is
| successful, and uniquely suited to solve some particular
| problem, I'd imagine it would take at least a few years to be
| actively applied in the right places -- and it might end up
| being me helping to apply it!
|
| If you look back at for example graph theory, it was explored
| on the pure mathematics and computer science side for many
| decades before it spawned e.g. network science and got
| applied in sociology, economics, etc.
|
| So, yeah, don't hold your breath! If you'd prefer not to read
| any blog posts heralding XYZ as the next big thing before XYZ
| has already led to a concrete breakthrough, I think that's a
| totally fair. I myself am quite happy to work quietly on
| things until there is a satisfying and complete application,
| but Stephen isn't like that. Both stances have pros and cons.
| naasking wrote:
| Aren't these multiway systems essentially what we see with
| ambiguous grammars that yield parse forests rather than parse
| trees? The "forest" here is a forked parallel computation started
| upon encountering any ambiguous rewrite.
|
| One application of these might be to resolve the meaning of
| probabilities under the many-worlds interpretation of quantum
| mechanics. When an interaction takes place, a number of worlds
| are created for each possible outcome, but it was never clear how
| to formally derive the probability of finding yourself in any
| given world (the Born rule).
|
| Under the section titled "Observers, Reference Frames and
| Emergent Laws" in this article, you can see some branches merging
| again in that first graph, so perhaps the probabilities of the
| Born rule are due to parallel computations that merge in this
| way, ie. the probability you'd find yourself in the BBBB world
| rather than the AA world at step 3 of the computation is 2/3 vs.
| 1/3, respectively. If rules generate recurring patterns as shown
| there, these might show up as stable probabilities in aggregate.
| taliesinb wrote:
| > Aren't these multiway systems essentially what we see with
| ambiguous grammars...
|
| Yes.
|
| > One application of these might be to resolve the meaning of
| probabilities under the many-worlds interpretation...
|
| There's some ways to go before we Hilbert spaces, operator
| algebras, and the like, but yes, the idea would be that some
| path counting procedure would be used to derive the Born rule.
| It would be great to bridge with Carroll's self-locating
| uncertainty paper [0]
|
| > Under the section titled "Observers, Reference Frames and
| Emergent Laws" in this article, you can see some branches
| merging again in that first graph, so perhaps the probabilities
| of the Born rule are due to parallel computations that merge in
| this way...
|
| Right!
|
| [0]: https://arxiv.org/abs/1405.7907
| daralthus wrote:
| Seems like an application of the ladder of abstraction. [0] That
| is, abstracting over every possible value of a variable in a
| system.
|
| In this case we abstract over time in a system of computation. To
| be more precise the system is a non-deterministic automata, so we
| abstract over time and all the possible branches too.
|
| Mapping out all state of a non-deterministic automata, you
| eventually find overlaps of different branches. To Wolfram this
| is a big revelation since instead of the system getting more
| complicated you found some simplification, aka. generality.
|
| [0] http://worrydream.com/LadderOfAbstraction/
| tbrt1153 wrote:
| It is systemically interesting how spontaneously and reactively
| the concentrated, ignorant envy seems to gather here.
| m4r35n357 wrote:
| Hot air alert!
| [deleted]
| jkhdigital wrote:
| Stephen Wolfram seems to be the quintessential intellectual
| DIYer. He writes 20,000 words on a highly abstract and technical
| subject, and every single hyperlink in the article goes to either
| one of his own websites, or to Wikipedia.
|
| I respect his ability to integrate a huge body of scientific
| knowledge in a single brain and then articulate it in books like
| _A New Kind of Science_ , but I have to wonder whether his
| approach is designed to maximize scientific progress, or to
| maximize his personal reputation. His eagerness to claim credit
| for ideas that could hardly be credited to a single person is a
| bit of a warning sign.
| Certhas wrote:
| There is no science and no scientific progress in Stephen
| Wolframs work.
| xyzzy21 wrote:
| Not science as YOU NARROWLY understand the term.
| mensetmanusman wrote:
| Define science. He is certainly doing experiments and is very
| public about it. Better than what is going on in academia
| with the reproducibility crisis and the fear of publishing
| ideas that don't pan out.
| Certhas wrote:
| No it's not better than what is going on in academia. It's
| like the extreme version of all the problems of academia
| rolled into one: Hyperbolic storytelling, massive vague
| claims, not citing anyone but yourself, and nothing backed
| up by evidence matching the claims.
|
| I spent way too much time looking at the Physics Project
| when it came out, there is just nothing of substance there.
| And no, he is not doing experiments that back up his
| claims, he's just running some random simulations and
| waving his hands at the pictures that come out.
|
| One key aspect of the scientific method is to acknowledge
| that it's very easy to fool yourself into thinking you have
| understood something "up to ironing out some details".
| Every crackpot is convinced of this. And that's why science
| operates on the foundation of convincing others of the
| understanding we have reached. Not any random others, but
| other people that have invested the time to master what is
| already known, and are making a good faith effort to
| understand. I am not talking about peer review, I am
| talking about the long conversation that unfolds over many
| many publication, conference talks, heated seminar
| discussions, etc.
|
| Nothing Wolfram has done/contributed to in the last 30
| years that has convinced anyone of note. Deep thinkers in
| all branches of science that he touches upon have
| unanimously found his output to be a vanity project of no
| scientific value. That is not to say that there are no
| interesting and valuable ideas in the texts he produces,
| it's simply that these ideas are already known, not his,
| and he does not acknowledge or tackle the problems that
| they have. In turn he has not made a good faith effort to
| engage with the work of others that is pertinent to his
| claims (usually because this would show that his claims are
| vastly exagerated and known to be problematic).
|
| He good at one thing: Selling himself as a genius outsider
| to people not willing or qualified to come to their own
| conclusions on his work.
|
| (I rather enjoyed this review of ANKS which goes into some
| detail for a number of the points I make here:
| http://www.bactra.org/reviews/wolfram/ I personally looked
| quite deeply into the "papers" produced at the time of his
| "Physics Project", by Gorard. Some of these are things I
| have studied very deeply in the past and feel qualified to
| judge. There simply is _nothing_ there.)
| Barrin92 wrote:
| there is no empirical aspect at all to Wolfram's work, so
| it cannot be said that he is conducting experiments in any
| meaningful sense.
|
| Wolfram's 'new science' of physics _improves in no way at
| all over existing models_ when it comes to making
| predictions about the physical world.
| mensetmanusman wrote:
| This is true at the """"cutting edge"""" of physics where
| most hypothesis that are taken "seriously" are not
| falsifiable.
|
| http://backreaction.blogspot.com/2017/11/how-popper-
| killed-p...
| plutonorm wrote:
| He has a massive ego for sure. But this idea of building up
| from the most general to the more specific appeals very much to
| me.
| ithinkso wrote:
| His posts are very hit or miss and the one linked in this
| thread is unfortunately a huge miss. He describes
| nondeterministic automata (and pretends he doesn't) and gives
| them way too much significance. Even the 'computational
| paradigm' he's saying it replaces is only a paradigm in
| Wolfram's mind
|
| The 'applications' section at the end is just ramblings at best
| and borderline crankpotty at worst. Which is weird since he is
| undeniably smart and educated, maybe an overflow?
| Frost1x wrote:
| >He writes 20,000 words on a highly abstract and technical
| subject, and every single hyperlink in the article goes to
| either one of his own websites, or to Wikipedia.
|
| Exerpt: _" But then--basically starting in the early 1980s--
| there was a burst of progress based on a new idea (of which,
| yes, I seem to have ultimately been the primary initiator): the
| idea of using simple programs, rather than mathematical
| equations, as the basis for models of things in nature and
| elsewhere."_
|
| He also draws out everything more than it needs to be in this
| long winded narrative and explicit self-congradulatory form
| that makes me usually wait until someone else reputable with a
| computer or computational science background reads it and
| summarizes to see if it's worth suffering through the time to
| read it myself. Not only is it questionable (Conway and many
| others come to mind, would have to check dates to see origins
| but honestly who cares), it's just off-putting.
| jjoonathan wrote:
| In your example quote, he only managed to shoehorn in his
| cellular automata work. The reader is left hanging -- for an
| entire sentence! -- as to whether or not he was a child
| prodigy. Is that growth? Or is his game slipping?
| macksd wrote:
| It sounds to me like he's claiming credit for ideas behind
| weather modeling used as much as 20 years earlier, and
| fractal curves that were being clearly talked about in the
| previous decade.
| frazbin wrote:
| I was so excited by the headline... and then I was so bummed by
| the domain name that I now doubt myself for being excited by
| the headline. I clicked.. there's still no danger of confusing
| this guy with a scientist or an academic. If somebody is real
| smart, but also real self serving, it kinda cancels out their
| smartness. He's not the worst, but still.. it's like if a
| paperclip maximizing super AI was trying to convince you to let
| it out of its box. He's not gonna teach you anything.
| evanb wrote:
| All of this business about multiway computation and even "rulial
| space" seems to have been anticipated by Toffoli to some extent
| in "Action, or the Fungibility of Computation" [0].
|
| The brilliant point of this paper is to point out that in the
| same way entropy describes our ignorance of the microscopic state
| of a system, the action (the time integral of the Lagrangian
| [itself equal to kinetic energy - potential energy]) seems to
| quantify our ignorance of the microscopic law that governs a
| system.
|
| It's not made explicit, but as a lattice gauge theorist it's an
| easy analogy to make: the gauge configurations that contribute
| correspond to different Dirac operators (ie. PDEs) for matter---
| gauge symmetry is in some sense a "rulial space" but... you
| know... discovered 100 years ago.
|
| [0]
| http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.42....
| taliesinb wrote:
| Thanks for the link! I'd be curious if you know about other
| information-theoretic approaches to understanding phenomena
| even in say classical mechanics (let's put aside statistical
| mechanics where the connections are already well understood).
| I'm dimly aware that there are fields like "symbolic dynamics"
| but not sure of the best entry point into that literature, or
| where to find the most powerful perspectives it offers without
| getting stuck in the weeds.
| evanb wrote:
| Not sure I have anything concrete to say, except that the
| "try all rules" rulial space seems to be an interesting way
| to make Tegmark's mathematical universe hypothesis [or at
| least the more limited computable version] into a concrete
| thing. But I have to admit that when I read Toffili's paper I
| found it amazing, exciting, and otherwise hard to see how to
| advance. I reread it every few years and get something new
| each time.
| taliesinb wrote:
| Wow, it looks extremely interesting!
|
| You know, it's bizarre, I recently pursued a similar
| approach, attempting to derive quadratic kinetic energy of
| an automaton controlled by a computer program (it used a
| circular tape to decide whether to move left or right). I
| set up a coarse-groaning, identifying energy with
| information, well, negentropy of the state of the tape, and
| arrived at similar results: higher energy = fewer
| microstates, in other words, there are fewer programs that
| move at the speed of light than at some slower speed. Which
| makes sense! There is only one tape that tells the
| automaton to move right at every step. Toffoli says exactly
| this: "A low-energy state is 'cheap' because it is
| 'common', there are so many ways to achieve it".
| Conservation of energy is exactly microscopic
| reversibility! What could be cleaner?
|
| That whole approach is on the shelf for now, because I
| first want to develop a discrete version of contact, and
| thence symplectic geometry, since that will provide the
| mathematical formalism to express a kind of "discrete
| classical physics", rather than just a single toy model.
|
| Anyway, I'm beyond grateful for this reference!
| jfmc wrote:
| Has this gone through any peer review process?
| sampo wrote:
| > Has this gone through any peer review process?
|
| No. Stephen Wolfram is wealthy. He doesn't need to operate or
| publish within the academic system.
| jmeister wrote:
| He's also prodigiously smart. People will read him without
| peer review.
| asdf_snar wrote:
| I believe that he is very bright. Do you think it is
| possible that he has also gotten so wrapped up in his own
| thoughts that he can no longer distinguish "good" theory
| from "bad" theory? It happens to a lot of mathematicians.
| Michael Atiyah a while back claimed to prove the Riemann
| hypothesis. Even Hamilton got so wrapped up in quaternions
| that he spent the rest of his days obsessing over them
| (they are useful, especially in graphics, but did not
| revolutionize physics the way he thought they would).
|
| I glance at his writings over the past few years and most
| often think that unless he uses his theory to solve a
| problem others care about, his line of research will be
| abandoned after he passes.
| taliesinb wrote:
| Shame, Atiyah was senile at that point. A sad note to end
| on after a brilliant career. But whatever you may think
| about him, Wolfram is not senile.
| lanstin wrote:
| The book is under-whelming, however. There might be
| something worth investigating, although the basic mapping
| between finite automata and QFT is not made explicit, nor
| even how it could be. One type of maths is pretty firmly
| embedded in continuous maths on manifolds and the other
| is inherently discrete. And one has probability density
| and is only deterministic in the calculation of the
| probability densities, while the other is apparently
| completely deterministic. And how can non-local
| entanglement occur with the automata model? That said,
| there are some interesting hints in modern physics that
| information is related to some very fundamental
| processes, e.g. the entropy of black holes being related
| to information held by the black hole, etc. But he (in my
| opinion, a mathematically advanced amateur, and no master
| of QFT) has too much excitement for his own idea and too
| much hand-waving over the details.
|
| I did buy and read most of it, as I also have bought many
| of Penrose's popular books, so perhaps I'm just a
| disgruntled purchaser.
| taliesinb wrote:
| I largely agree about the book: I think there might be
| something there, but the case is far from being made. One
| small correction: the rewriting systems he proposes are
| not deterministic.
|
| As for how non-local entanglement can occur, I'll just
| offer my current speculation, having spent about a year
| working on this kind of approach. You'll have to give up
| SR in its traditional sense. There will be a preferred
| reference frame, which is the rule application order that
| the automata uses in any particular history. The
| challenge becomes to explain why it is not observable and
| you have approximate Lorentz covariance. I think this
| will be less hard than one imagines -- even in Feynman's
| lectures you see explanations of SR that involve an
| aether (or a global frame if you prefer) and clocks
| defined by light bouncing between mirrors moving in this
| aether. Of course all physical _laws_ have to be
| covariant, and explaining how this happens requires you
| to know how the physical laws are "microphysically". But
| the graph itself in graph-automata models is a good
| candidate for an ether, with particles being e.g.
| topological defects. Somehow covariance must reflect how
| a dynamical account of defect behavior changes as one
| foliates rule application order, mysterious but not
| inconceivable.
|
| Now, entanglement: one imagines entanglement is
| implemented by long-range connections, which in graph-
| type models could take many forms. This is a kind of
| discrete version of the "ER = EPR" proposal. But they
| will have to be such a limited form of connection that
| they do not permit signaling, and I think they way they
| can do this is via some sort of knot-theoretic braiding.
| Only be comparing measurement outcomes classically will
| it be possible to deduce the way the braiding was
| effected by measurement and confirm you had e.g. a GHZ
| state.
|
| Now, QM is more than just entanglement, but in the words
| of Jaynes: "QM is a peculiar mixture describing in part
| realities of Nature, in part incomplete human information
| about Nature - all scrambled up by Heisenberg and Bohr
| into an omelette that nobody has seen how to unscramble."
| When scrambled, all the ingredients look inextricably
| connected. I think the unscrambling will seem beyond hope
| until one has the exact recipe to recreate the omelette.
| p_j_w wrote:
| >He's also prodigiously smart.
|
| That doesn't mean what he's saying has any value. I'm not
| saying what he's written here doesn't, but the prodigiously
| smart are just as capable of being intellectually lazy as
| anyone else. Anyone making grandiose claims like "our
| Physics Project [... is] showing us something even bigger
| and deeper: a whole fundamentally new paradigm for making
| models and in general for doing theoretical science"
| doesn't get to rest on their laurels if they want to be
| taken seriously.
| sesm wrote:
| Did he get any significant results with his new paradigm? What
| unsolved problem he was trying to solve in the first place when
| he developed this paradigm?
| petermcneeley wrote:
| The significant result would be a multiway-graph that
| represents say the evolution of electron in a vacuum. He has
| not got this result yet. I think he started down this path to
| try to further physics by going beyond traditional analytical
| mathematics.
| 0-_-0 wrote:
| Physics
| pwdisswordfish8 wrote:
| The problem of coming up with new paradigms.
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