7 ms·

Multicomputation as a General Paradigm for Theoretical Science

59 points by nsoonhui 5y ago

pehta 5y ago
This seems hard to compute for any realistic system?
jfmc 5y ago
Has this gone through any peer review process?
- sampo 5y 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 5y ago
    He’s also prodigiously smart. People will read him without peer review.
    - asdf_snar 5y ago
      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 5y ago
        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 5y ago
        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 5y ago
        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 5y ago
      >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.
danbmil99 5y ago
As smart as he is, as rich as he is, his ego is his downfall
- amelius 5y ago
  I still have respect for him for being able to run a business in scientific computing profitably.
Ono-Sendai 5y ago
'Multicomputation' is not exactly new, see nondeterministic finite automata (NFA) and nondeterministic polynomial time (NP).
m4r35n357 5y ago
Hot air alert!
sesm 5y 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 5y ago
  Physics
- pwdisswordfish8 5y ago
  The problem of coming up with new paradigms.
- petermcneeley 5y 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.
tbrt1153 5y ago
It is systemically interesting how spontaneously and reactively the concentrated, ignorant envy seems to gather here.
deleted 5y ago
[deleted]
jkhdigital 5y 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.
- Certhas 5y ago
  There is no science and no scientific progress in Stephen Wolframs work.
  - xyzzy21 5y ago
    Not science as YOU NARROWLY understand the term.
  - mensetmanusman 5y 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.
    - Barrin92 5y ago
      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 5y ago
        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-particle-physics.html?m=1 http://backreaction.blogspot.com/2017/11/how-popper-killed-p...
taliesinb 5y 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/LocalMultiwaySystem/LocalMultiwaySystem.md https://github.com/maxitg/SetReplace/blob/master/Research/Lo... [1]: https://www.wikiwand.com/en/Krohn–Rhodes_theory https://www.wikiwand.com/en/Krohn–Rhodes_theory [2]: https://arxiv.org/abs/2101.04238 https://arxiv.org/abs/2101.04238 [3]: https://www.youtube.com/watch?v=OmaSAG4J6nw https://www.youtube.com/watch?v=OmaSAG4J6nw [4]: https://quivergeometry.net https://quivergeometry.net
- gexaha 5y 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?)
  - taliesinb 5y 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 5y 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.
- taliesinb 5y 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 https://arxiv.org/abs/1405.7907
typon 5y 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 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/ https://www.wolframphysics.org/visual-gallery/) is beautiful.
daralthus 5y 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/ http://worrydream.com/LadderOfAbstraction/
evanb 5y 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=10.1.1.42.2410&rep=rep1&type=pdf http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.42....
- taliesinb 5y 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.
  - evanb 5y 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.
    - taliesinb 5y ago
      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!
rodrigosetti 5y ago
So Wolfram has initiated two of the four scientific paradigms
- seg_lol 5y ago
  He is like the fifth force of nature.

59 points by nsoonhui 5y ago

pehta 5y ago

This seems hard to compute for any realistic system?

jfmc 5y ago

Has this gone through any peer review process?

sampo 5y 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 5y ago
  He’s also prodigiously smart. People will read him without peer review.
  - asdf_snar 5y ago
    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 5y ago
      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 5y ago
        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 5y ago
        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 5y ago
    >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.

danbmil99 5y ago

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

amelius 5y ago
I still have respect for him for being able to run a business in scientific computing profitably.

Ono-Sendai 5y ago

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

m4r35n357 5y ago

Hot air alert!

sesm 5y 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 5y ago
Physics
pwdisswordfish8 5y ago
The problem of coming up with new paradigms.
petermcneeley 5y 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.

tbrt1153 5y ago

It is systemically interesting how spontaneously and reactively the concentrated, ignorant envy seems to gather here.

deleted 5y ago

[deleted]

jkhdigital 5y 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.

Certhas 5y ago
There is no science and no scientific progress in Stephen Wolframs work.
- xyzzy21 5y ago
  Not science as YOU NARROWLY understand the term.
- mensetmanusman 5y 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.
  - Barrin92 5y ago
    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 5y ago
      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-particle-physics.html?m=1 http://backreaction.blogspot.com/2017/11/how-popper-killed-p...

taliesinb 5y 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/LocalMultiwaySystem/LocalMultiwaySystem.md https://github.com/maxitg/SetReplace/blob/master/Research/Lo... [1]: https://www.wikiwand.com/en/Krohn–Rhodes_theory https://www.wikiwand.com/en/Krohn–Rhodes_theory [2]: https://arxiv.org/abs/2101.04238 https://arxiv.org/abs/2101.04238 [3]: https://www.youtube.com/watch?v=OmaSAG4J6nw https://www.youtube.com/watch?v=OmaSAG4J6nw [4]: https://quivergeometry.net https://quivergeometry.net

gexaha 5y 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?)
- taliesinb 5y 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 5y 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.

taliesinb 5y 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 https://arxiv.org/abs/1405.7907

typon 5y 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 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/ https://www.wolframphysics.org/visual-gallery/) is beautiful.

daralthus 5y 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/ http://worrydream.com/LadderOfAbstraction/

evanb 5y 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=10.1.1.42.2410&rep=rep1&type=pdf http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.42....

taliesinb 5y 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.
- evanb 5y 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.
  - taliesinb 5y ago
    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!

rodrigosetti 5y ago

So Wolfram has initiated two of the four scientific paradigms

seg_lol 5y ago
He is like the fifth force of nature.