Wolfram's Theory of Everything (Technical Understanding)

[Xonas Pitfall]

https://writings.stephenwolfram.com/2023/02/computational-foundations-for-the-second-law-of-thermodynamics/
https://www.actualized.org/insights/wolframs-theory-of-everything
https://www.wolframscience.com/nks/

1. Computational irreducibility
2. The Ruliad (Infinity)
3. Cellular Automaton

Has anyone looked into it with a more technical understanding? I'm leaving this topic open as I may potentially explore it in more depth, but feel free to jump in! ⚠

 

 

Edited September 21 by Xonas Pitfall

[Leo Gura]

I plan to make a video about it.

Although I won't go too much into the technical detail since it's not really necessary for our purposes.

Edited September 21 by Leo Gura

[Xonas Pitfall]

@Leo Gura Amazing! Super hyped for it.  Thank you!

Edited September 21 by Xonas Pitfall

[Ero]

From a philosophical standpoint there are very interesting and important observations, especially relating computational irreducibility, the ruliad and the hyper-ruliad. Those deserve attention and I am sure Leo will cover them in detail, which is why I will abstain from the philosophical aspect and instead give my two cents on the technical aspect of his work (after all, he claims he is doing 'Science', fundamentally rigorous in nature), given my background is in Pure Mathematics. For reference, I have read his 'New Kind of Science" and his 'Physics Project' Technical Report.

To get straight to the point, the technical aspect his work is subpar - the entirety of his arguments are heuristic and qualitative based. His 'proofs' and discoveries are mostly pictures/ diagrams and he references solely himself with sense of aggrandizement that would make you think he is the only human being who has every said anything about this topic (far from it). The actual 'physics' and math concepts he derives from his 'foundational theory' are unworkable toy examples that do not transfer at all. There are no isomorphisms, functors or representations (i.e 'bridges') that would help you put all prior existing work into his context in a way that would be expected from a 'foundational theory'.

Consider for example his 'operator' interpretation here (the bread and butter of physics)- instead of interpreting the functional space and operator algebra as is necessary in defining it, he only gives you a toy 'commutator' example that does nothing to demonstrate that his approach is even workable at the level of complexity modern science expects (i.e Hamiltonian, Langevin). For reference, the majority of Quantum Mechanics is based on non-commutative operator algebras. Furthermore, I don't see how you would even be able to define spectral decomposition of eigenvalues and eigenfunctions in his context. 

Same goes for his 'gauge invariant' interpretation - instead of defining/ representing the fundamental gauge field symmetry groups U(1)xSU(2)xSU(3), he again simply refers to a toy example without any prescriptive powers. This means that his model fundamentally fails at predicting any kind of behavior that we observe for example in particle colliders. Why on earth would then physicists use his theory? 

To put it plainly, if I were to present his work to any of my professors, I would get an 'F'. Plain and simple. You may ask, isn't this something that can be solved with some extra time and rigor? 

The problem in fact with his 'theory' is deeper - he makes a fundamental ontological fallacy. Having observed what he describes as 'complex behavior' in 1D finite state automata, he claims then it must be true the entirety of existence is based on finite, simple and discrete rules. There are two problems with this argument:

Firstly, there is no point at which he defines 'complexity' or provides us with his interpretation of it (immediate red flag for any scientist). Simply observing something as seemingly complex does not mean it inherently is. For example, if we take Kologomorov Complexity as our working definition, the entirety of his celullar automaton examples are in fact not complex because it takes very little 'space' to define them.  

The second and deeper issue is that there is nothing special about finite state automata. They are simply an instance of a larger class of systems we call 'Turing complete'. Even the representation he uses to draw the pictures is not special to cellular automata (and no, he did not invent it)- consider for example the following picture, showing three different Turing machines's tapes as they progress in time (horizontal axis). You can clearly see the parallel. Now, here is where is the problem. There are in fact many Turing-complete systems we know of, which means by definition everything he observes - rule 30, rule 110, etc. has an exact equivalent:

- The four nucleotide bases of DNA 
- Fluid systems
- Ferromagnets (Spin Glass model)
- Water pipes 
- ... and many more

By his argument, is then the entire world the genetic code of some organism? A large magnet? A large glass of water? The sewage system of some alien's house? There is nothing that gives basis for making the claims he does. And as much as he wants you to believe that he is the only one doing this kind of work, there are entire disciplines dedicated to studying integrable systems. Mathematicians and physicists know all too well about the problem of uncomputatbility, lack of definedness, etc., and instead of discarding the entire field of mathematics as he proposes we do, they build tools specifically to find one's way around it. My research into Heavy-Tailed Matrices is an example. You can also consider scattering resonances, chiral models, etc. and much more. The fields of mathematics and statistics are in fact much ahead of him than he wants you to think. 

TLDR: Philosophically interesting, technically subpar

 

[Leo Gura]

@Ero Interesting analysis. Thanks.

[CARDOZZO]

2 hours ago, Ero said:

From a philosophical standpoint there are very interesting and important observations, especially relating computational irreducibility, the ruliad and the hyper-ruliad. Those deserve attention and I am sure Leo will cover them in detail, which is why I will abstain from the philosophical aspect and instead give my two cents on the technical aspect of his work (after all, he claims he is doing 'Science', fundamentally rigorous in nature), given my background is in Pure Mathematics. For reference, I have read his 'New Kind of Science" and his 'Physics Project' Technical Report.

To get straight to the point, the technical aspect his work is subpar - the entirety of his arguments are heuristic and qualitative based. His 'proofs' and discoveries are mostly pictures/ diagrams and he references solely himself with sense of aggrandizement that would make you think he is the only human being who has every said anything about this topic (far from it). The actual 'physics' and math concepts he derives from his 'foundational theory' are unworkable toy examples that do not transfer at all. There are no isomorphisms, functors or representations (i.e 'bridges') that would help you put all prior existing work into his context in a way that would be expected from a 'foundational theory'.

Consider for example his 'operator' interpretation here (the bread and butter of physics)- instead of interpreting the functional space and operator algebra as is necessary in defining it, he only gives you a toy 'commutator' example that does nothing to demonstrate that his approach is even workable at the level of complexity modern science expects (i.e Hamiltonian, Langevin). For reference, the majority of Quantum Mechanics is based on non-commutative operator algebras. Furthermore, I don't see how you would even be able to define spectral decomposition of eigenvalues and eigenfunctions in his context. 

Same goes for his 'gauge invariant' interpretation - instead of defining/ representing the fundamental gauge field symmetry groups U(1)xSU(2)xSU(3), he again simply refers to a toy example without any prescriptive powers. This means that his model fundamentally fails at predicting any kind of behavior that we observe for example in particle colliders. Why on earth would then physicists use his theory? 

To put it plainly, if I were to present his work to any of my professors, I would get an 'F'. Plain and simple. You may ask, isn't this something that can be solved with some extra time and rigor? 

The problem in fact with his 'theory' is deeper - he makes a fundamental ontological fallacy. Having observed what he describes as 'complex behavior' in 1D finite state automata, he claims then it must be true the entirety of existence is based on finite, simple and discrete rules. There are two problems with this argument:

Firstly, there is no point at which he defines 'complexity' or provides us with his interpretation of it (immediate red flag for any scientist). Simply observing something as seemingly complex does not mean it inherently is. For example, if we take Kologomorov Complexity as our working definition, the entirety of his celullar automaton examples are in fact not complex because it takes very little 'space' to define them.  

The second and deeper issue is that there is nothing special about finite state automata. They are simply an instance of a larger class of systems we call 'Turing complete'. Even the representation he uses to draw the pictures is not special to cellular automata (and no, he did not invent it)- consider for example the following picture, showing three different Turing machines's tapes as they progress in time (horizontal axis). You can clearly see the parallel. Now, here is where is the problem. There are in fact many Turing-complete systems we know of, which means by definition everything he observes - rule 30, rule 110, etc. has an exact equivalent:

- The four nucleotide bases of DNA 
- Fluid systems
- Ferromagnets (Spin Glass model)
- Water pipes 
- ... and many more

By his argument, is then the entire world the genetic code of some organism? A large magnet? A large glass of water? The sewage system of some alien's house? There is nothing that gives basis for making the claims he does. And as much as he wants you to believe that he is the only one doing this kind of work, there are entire disciplines dedicated to studying integrable systems. Mathematicians and physicists know all too well about the problem of uncomputatbility, lack of definedness, etc., and instead of discarding the entire field of mathematics as he proposes we do, they build tools specifically to find one's way around it. My research into Heavy-Tailed Matrices is an example. You can also consider scattering resonances, chiral models, etc. and much more. The fields of mathematics and statistics are in fact much ahead of him than he wants you to think. 

TLDR: Philosophically interesting, technically subpar

 

What if his work is a pointer to a new scientific paradigm?

[Ero]

@CARDOZZO Pointers and actual maps are different things. I can point you in the right direction and you can sill fall off a cliff and kill yourself. I do agree with the need for a new paradigm, which is why I started a journal here explicitly with this goal:

Thing is, far more accomplished and cogent arguments have been made for the new of a scientific paradigm. I mention some of them in the first post above, but they include Nobel Laureates like Ilya Prigogine, Fields Medalists like Alexander Grothendieck, and the most accomplished neuroscientist of all time - Karl Friston. The first two have worked on 'a new paradigm' since before Wolfram was born. Saying this from the standpoint of someone who reads hundreds of pages of scientific literature a week, Wolfram's writings are some of most tedious and excruciating to read and not because they are conceptually hard, but rather the opposite - it's just fluff. 

Edited September 22 by Ero

[gettoefl]

he was on Kurt's TOE podcast last month with Donald Hoffman and gave a pretty poor showing

he obviously believes consciousness is emergent while DH's view is that it is fundamental

[Ero]

52 minutes ago, gettoefl said:

he was on Kurt's TOE podcast last month with Donald Hoffman and gave a pretty poor showing

he obviously believes consciousness is emergent while DH's view is that it is fundamental

Agreed. Hoffman is a far more accomplished scientist in any aspect you can think. Yet Wolfram's hubris in the conversation is truly unbearable. His biggest strength of a hyper-intellect is also his worst flaw since it makes him think he is superior despite not having done the actual work. Growing up a prodigy has its pitfalls. 

[gettoefl]

3 minutes ago, Ero said:

Agreed. Hoffman is a far more accomplished scientist in any aspect you can think. Yet Wolfram's hubris in the conversation is truly unbearable. His biggest strength of a hyper-intellect is also his worst flaw since it makes him think he is superior despite not having done the actual work. Growing up a prodigy has its pitfalls. 

yes precisely, thanks for your eloquence and insights ... Wolfram doesn't like to play second best

[Leo Gura]

Wolfram and Hoffman are just doing very different kinds of work. I see no point in pitting them against each other.

Wolfram is a genius. But don't go asking him to explain consciousness. And for that matter, don't ask Hoffman to explain consciousness because he has no idea what it is.

Edited September 22 by Leo Gura

[CARDOZZO]

I'm not a math/physics genius. 

What I am concerning about is that maybe (just maybe), Wolfram is so ahead of its time that even top physicists don't understand how brilliant he is.

One thought experiment:

What if Wolfram's work will be the fundamental theory to create a new paradigm/science using AI? (Ruliology)

What happens when AGI merges with the Ruliad?

 

[Ero]

33 minutes ago, Leo Gura said:

Wolfram and Hoffman are just doing very different kinds of work. I see no point in pitting them against each other.

Yet that is exactly what Wolfram does himself in that interview. There is nothing about his demeanour or arguments that suggests otherwise.

34 minutes ago, Leo Gura said:

Wolfram is a genius.

Wolfram is a Layman’s genius. He clearly has prodigious level intelligence, yet as my argument above shows, nothing of his technical work is really “genius”. He hasn’t invented any of the concepts, hasn’t made any substantive contributions or predictions for that matter. When someone doesn’t have a technical background, it is hard to discern between the two, hence the term “Layman’s genius”.

[CARDOZZO]

Jonathan Gorard is brilliant. I like his takes on Wolfram's Project.

Edited September 22 by CARDOZZO

[CARDOZZO]

 

[Ero]

12 minutes ago, CARDOZZO said:

Jonathan Gorard is brilliant. I like his takes on Wolfram's Project.

Thanks for the share. I am not familiar with his work, so I will look into it.

[Ero]

37 minutes ago, CARDOZZO said:

What if Wolfram's work will be the fundamental theory to create a new paradigm/science using AI? (Ruliology)

Look, I am not saying what he does is entirely useless. The main argument I made in my first post in this thread which I will repeat again, is that there isn't anything special about the structure he examines.

Every graph he draws, I can encode in a matrix. Matrices are so powerful for two reasons - there is something called Cayley's theorem, which states that any abstract group (the underlying structure in math) can be embedded in a permutation group (i.e how many ways you can re-order n numbers) and every permutation has a matrix representation. This essentially means that all of math can be 'found' inside the space of matrices.

What I described to you above is a 'bridge', i.e a functorial/ representational relationship that allows me to switch perspectives. These bridges are used to establish the equivalence I mentioned with other Turing-systems. What my argument is, is that he has simply decided to focus on one Turing-complete system (cellular automata initially, now dynamic graphs) and base his entire theory on it. Again, there is nothing special about that structure, it is simply an instance of a larger formalism which he refuses to acknowledge. Sure, we can work only in his 'ruliad universe'. But why do that when we get better results in a different formalization that may be more suited for the task at hand - for example fluids and stochastic systems. 

If you are actually interested in what could serve as the foundation of AI (and I mean rigorous theories), then read the work of people who have actually built  AI models - Peter Velickovic at DeepMind (Category Theory Paper), Philip Rigollet at MIT (Mathematical Perspective on Transformers). See the difference? There are rigorous statements about relevant models and predictions for those, something you don't find at all in Wolfram's work. Show me where he has made a clear and concise statement that is falsifiable. All he does is say "suggests", "indicates", expecting the reader to trust him because of his 'brilliance'. That is not who science and mathematics work. No matter how smart you are - even if you are Terence Tao or Noam Elkies (who has actually taught me), you still carry the burden of proof. Period. 

Edited September 22 by Ero

[Ero]

I wrote more in detail in my journal why this approach of seeking a 'fundamental theory' instead of building bridges is fundamentally problematic: 

 

[CARDOZZO]

26 minutes ago, Ero said:

Thanks for the share. I am not familiar with his work, so I will look into it.

He works with Wolfram on the project.

[CARDOZZO]

16 minutes ago, Ero said:

Look, I am not saying what he does is entirely useless. The main argument I made in my first post in this thread which I will repeat again, is that there isn't anything special about the structure he examines.

Every graph he draws, I can encode in a matrix. Matrices are so powerful for two reasons - there is something called Cayley's theorem, which states that any abstract group (the underlying structure in math) can be embedded in a permutation group (i.e how many ways you can re-order n numbers) and every permutation has a matrix representation. This essentially means that all of math can be 'found' inside the space of matrices.

What I described to you above is a 'bridge', i.e a functorial/ representational relationship that allows me to switch perspectives. These bridges are used to establish the equivalence I mentioned with other Turing-systems. What my argument is, is that he has simply decided to focus on one Turing-complete system (cellular automata initially, now dynamic graphs) and base his entire theory on it. Again, there is nothing special about that structure, it is simply an instance of a larger formalism which he refuses to acknowledge. Sure, we can work only in his 'ruliad universe'. But why do that when we get better results in a different formalization that may be more suited for the task at hand - for example fluids and stochastic systems. Why on earth 

If you are actually interested in what could serve as the foundation of AI (and I mean rigorous theories), then read the work of people who have actually built and AI models - Peter Velickovic at DeepMind (Category Theory Paper), Philip Rigollet at MIT (Mathematical Perspective on Transformers). See the difference? There are rigorous statements about relevant models and predictions for those, something you don't find at all in Wolfram's work. Show me where he has made a clear and concise statement that is falsifiable. All he does is say "suggests", "indicates", expecting the reader to trust him because of his 'brilliance'. That is not who science and mathematics work. No matter how smart you are - even if you are Terence Tao or Noam Elkies (who has actually taught me), you still carry the burden of proof. Period. 

Thanks for your clarification.