Multicomputation as a General Paradigm for Theoretical Science

https://writings.stephenwolfram.com/2021/09/even-beyond-physics-introducing-multicomputation-as-a-fourth-general-paradigm-for-theoretical-science/

by nsoonhui • 5 years ago

59 48 5 years ago

writings.stephenwolfram.com

pehta• 5 years ago

This seems hard to compute for any realistic system?

jfmc• 5 years ago

Has this gone through any peer review process?

sampo• 5 years ago

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• 5 years ago

He’s also prodigiously smart. People will read him without peer review.

danbmil99• 5 years ago

As smart as he is, as rich as he is, his ego is his downfall

amelius• 5 years ago

I still have respect for him for being able to run a business in scientific computing profitably.

Ono-Sendai• 5 years ago

'Multicomputation' is not exactly new, see nondeterministic finite automata (NFA) and nondeterministic polynomial time (NP).

sesm• 5 years ago

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?

0-_-0• 5 years ago

Physics

pwdisswordfish8• 5 years ago

The problem of coming up with new paradigms.

petermcneeley• 5 years ago

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.

jkhdigital• 5 years ago

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.

Frost1x• 5 years ago

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.

macksd• 5 years ago

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.

jjoonathan• 5 years ago

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?

Certhas2• 5 years ago

There is no science and no scientific progress in Stephen Wolframs work.

xyzzy21• 5 years ago

Not science as YOU NARROWLY understand the term.

mensetmanusman3• 5 years ago

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.

ithinkso• 5 years ago

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?

plutonorm• 5 years ago

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.

frazbin• 5 years ago

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.

gfodor• 5 years ago

It would be cool if there could be a dedicated forum to discussing the hypothesis “Stephen Wolfram has a large ego” so these threads could be about 10% of their usual size, and much higher signal.

taliesinb8• 5 years ago

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• 5 years ago

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?)

taliesinb8• 5 years ago

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• 5 years ago

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.

taliesinb8• 5 years ago

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

typon• 5 years ago

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.

daralthus• 5 years ago

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/

evanb2• 5 years ago

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....

taliesinb8• 5 years ago

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.

evanb2• 5 years ago

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.

rodrigosetti• 5 years ago

So Wolfram has initiated two of the four scientific paradigms

seg_lol2• 5 years ago

He is like the fifth force of nature.

Multicomputation as a General Paradigm for Theoretical Science

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