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One of the frustrating things with the way Stephen Wolfram works is because he never actually defines anything it’s very hard to pin down what is actually inter

One of the frustrating things with the way Stephen Wolfram works is because he never actually defines anything it’s very hard to pin down what is actually interesting empirical science and what is data visualisation buggering around. Here, before he starts, how do we know that the bugs in the Turing machine implementation of f(n)=n+1 are in any way representative of bugs in a normal computation? He seems to be generating random state machines and then evaluating them and picking ones which are nearly but not quite correct implementations of f(n)=n+1. Is that like a normal “honest” software bug? Is it like a deliberate software sabotage like you might look for when evaluating a software supply chain risk? Is it like the sort of vulnerability you might see when fuzzing? As far as I can see, there’s no reason to think it’s like any of these. More broadly, since the “Principle of Computational Equivalence” and “computational irreducibility” are referred to as touchstones but are never actually defined or properly established how are we supposed to treat them? Interesting conjectures? Actual axioms? Something in between?

PaulHoule 3mo ago
I see it as related to the Church-Turing thesis which is also a bit fuzzy but I think comes down to the conjecture that there is no physical computer which exceeds the Turing machine in capabilities. (Quantum computers, as we know them, don't count because they can be simulated by classical computers with sufficient space and time) One thing I find tragic about Wolfram is that he found his holy grail, Rule 30, at the very beginning of his project and ever since he's found that every family of rules that he's look at that is sufficiently powerful has something like Rule 30 -- but always a bit more complex, complicated and not quite so beautiful, in fact often outright ugly... ... so he jumps into this sort of thing and samples of some of a ruliad, finds the usual things he finds in every ruliad, gets excited about it and thinks he has a "theory" and then moves on to something else and most of us are scratching our heads.
- seanhunter 3mo ago
  The Church-Turing hypothesis I agree could be crisper (ie the definition of effectively computable is a bit complicated/weasely), but it actually says something quite concrete that I can understand and potentially falsify ie that a universal turing machine, the lambda calculus and general recursion can all "effectively compute" the same things. That seems reasonable, and I can check that something I can write in lambda calculus I can compute on a Turing Machine (simulated at least). Whereas in stating the Principle of Computational Equivalence Wolfram says things like "... the evolution of weather systems can, in principle, compute the same things as a computer."[1] Well, ... wtf? What does it mean to say the evolution of a weather system can compute something? Where do we even start on understanding this? I pick up a calculator and compute the volume of a cone. It's a sunny day outside. How do I "in principle" use that to check my calculation? It literally makes no sense whatsoever on its face as a claim but it is so slippery because of that "in principle" that it doesn't give me anything to hold onto that I could even test. And that's before I even get started on the "underpants gnome" logical justification behind the claim, which seems to be: 1. Computers are complex 2. Weather is complex 3. Therefore they are "in some sense" equivalent 4. <don't worry about step 4> 5. Thus weather can "in principle" compute the same things as a computer. I'm really not trying to misrepresent him, I'm just baffled. [1] https://mathworld.wolfram.com/PrincipleofComputationalEquivalence.html https://mathworld.wolfram.com/PrincipleofComputationalEquiva...
  - mrkeen 3mo ago
    I'm of course hearing this second- or third-hand, but when I read 'evolution of weather systems' I substitute for 'cellular automata'/'Conway's game of life', vaguely recall them as being Turing-complete, then smile and nod and get back to ignoring the article.
    - PaulHoule 3mo ago
      It's handwavy but I can't help but think that because of the way symbolic dynamics works that you can't find families of approximating functions inside turbulence even though I can't see it being practical, like sensitive dependence on initial conditions will make noise overwhelm your ability to take measurements. See https://en.wikipedia.org/wiki/Chaos_computing https://en.wikipedia.org/wiki/Chaos_computing https://pubs.aip.org/aip/cha/article-abstract/35/9/093112/3361667/Homotopy-reservoir-computing-Harnessing-chaos-for?redirectedFrom=fulltext https://pubs.aip.org/aip/cha/article-abstract/35/9/093112/33...
duped 3mo ago
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marssaxman 3mo ago
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- sha16384 3mo ago
  Isn't that also the point of your comment only much lazier?
  - marssaxman 3mo ago
    Not sure how you get to "I think I am very smart" from "this guy thinks he is very smart, and his writing invariably highlights that belief to the detriment of whatever he's actually trying to communicate"... For all I know, maybe he actually is the world-class genius he believes himself to be, but it's difficult to tell underneath all the blatant self-promotion.
    - bitwize 3mo ago
      The thing is, Wolfram is that smart, having gotten his Ph.D. at 20 or something. He's just never been humbled, had a leash put on him so he could be aimed and focused on productive work (outside of maybe Mathematica). Probably because a lot of university professors in the 80s were like "wow, that kid is smart" and indulged his ego. (One major exception: Richard Feynman! https://www.cantorsparadise.com/richard-feynmans-advice-to-a-young-stephen-wolfram-1985-d572dc360c18 https://www.cantorsparadise.com/richard-feynmans-advice-to-a...) After Quake was released and the principals of Id Software broke up, John Romero pretty much spent the next few years making an ass of himself during the development of Daikatana. When asked about the delayed and beleaguered development process on Slashdot, John Carmack kind of paid him a backhanded comment saying something like "A properly disciplined Romero is a credit to any team." And that's more or less what Wolfram is: properly disciplined, he would be an asset to any cutting-edge physics research team, but as he his he'd rather go down these rabbit holes than suffer to work with people of more ordinary intellect. And it's his, and the world's, loss really.
    - dredmorbius 3mo ago
      <https://news.ycombinator.com/item?id=41406645 https://news.ycombinator.com/item?id=41406645>

PaulHoule 3mo ago

I see it as related to the Church-Turing thesis which is also a bit fuzzy but I think comes down to the conjecture that there is no physical computer which exceeds the Turing machine in capabilities. (Quantum computers, as we know them, don't count because they can be simulated by classical computers with sufficient space and time) One thing I find tragic about Wolfram is that he found his holy grail, Rule 30, at the very beginning of his project and ever since he's found that every family of rules that he's look at that is sufficiently powerful has something like Rule 30 -- but always a bit more complex, complicated and not quite so beautiful, in fact often outright ugly... ... so he jumps into this sort of thing and samples of some of a ruliad, finds the usual things he finds in every ruliad, gets excited about it and thinks he has a "theory" and then moves on to something else and most of us are scratching our heads.

seanhunter 3mo ago
The Church-Turing hypothesis I agree could be crisper (ie the definition of effectively computable is a bit complicated/weasely), but it actually says something quite concrete that I can understand and potentially falsify ie that a universal turing machine, the lambda calculus and general recursion can all "effectively compute" the same things. That seems reasonable, and I can check that something I can write in lambda calculus I can compute on a Turing Machine (simulated at least). Whereas in stating the Principle of Computational Equivalence Wolfram says things like "... the evolution of weather systems can, in principle, compute the same things as a computer."[1] Well, ... wtf? What does it mean to say the evolution of a weather system can compute something? Where do we even start on understanding this? I pick up a calculator and compute the volume of a cone. It's a sunny day outside. How do I "in principle" use that to check my calculation? It literally makes no sense whatsoever on its face as a claim but it is so slippery because of that "in principle" that it doesn't give me anything to hold onto that I could even test. And that's before I even get started on the "underpants gnome" logical justification behind the claim, which seems to be: 1. Computers are complex 2. Weather is complex 3. Therefore they are "in some sense" equivalent 4. <don't worry about step 4> 5. Thus weather can "in principle" compute the same things as a computer. I'm really not trying to misrepresent him, I'm just baffled. [1] https://mathworld.wolfram.com/PrincipleofComputationalEquivalence.html https://mathworld.wolfram.com/PrincipleofComputationalEquiva...
- mrkeen 3mo ago
  I'm of course hearing this second- or third-hand, but when I read 'evolution of weather systems' I substitute for 'cellular automata'/'Conway's game of life', vaguely recall them as being Turing-complete, then smile and nod and get back to ignoring the article.
  - PaulHoule 3mo ago
    It's handwavy but I can't help but think that because of the way symbolic dynamics works that you can't find families of approximating functions inside turbulence even though I can't see it being practical, like sensitive dependence on initial conditions will make noise overwhelm your ability to take measurements. See https://en.wikipedia.org/wiki/Chaos_computing https://en.wikipedia.org/wiki/Chaos_computing https://pubs.aip.org/aip/cha/article-abstract/35/9/093112/3361667/Homotopy-reservoir-computing-Harnessing-chaos-for?redirectedFrom=fulltext https://pubs.aip.org/aip/cha/article-abstract/35/9/093112/33...

duped 3mo ago

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marssaxman 3mo ago

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sha16384 3mo ago
Isn't that also the point of your comment only much lazier?
- marssaxman 3mo ago
  Not sure how you get to "I think I am very smart" from "this guy thinks he is very smart, and his writing invariably highlights that belief to the detriment of whatever he's actually trying to communicate"... For all I know, maybe he actually is the world-class genius he believes himself to be, but it's difficult to tell underneath all the blatant self-promotion.
  - bitwize 3mo ago
    The thing is, Wolfram is that smart, having gotten his Ph.D. at 20 or something. He's just never been humbled, had a leash put on him so he could be aimed and focused on productive work (outside of maybe Mathematica). Probably because a lot of university professors in the 80s were like "wow, that kid is smart" and indulged his ego. (One major exception: Richard Feynman! https://www.cantorsparadise.com/richard-feynmans-advice-to-a-young-stephen-wolfram-1985-d572dc360c18 https://www.cantorsparadise.com/richard-feynmans-advice-to-a...) After Quake was released and the principals of Id Software broke up, John Romero pretty much spent the next few years making an ass of himself during the development of Daikatana. When asked about the delayed and beleaguered development process on Slashdot, John Carmack kind of paid him a backhanded comment saying something like "A properly disciplined Romero is a credit to any team." And that's more or less what Wolfram is: properly disciplined, he would be an asset to any cutting-edge physics research team, but as he his he'd rather go down these rabbit holes than suffer to work with people of more ordinary intellect. And it's his, and the world's, loss really.
  - dredmorbius 3mo ago
    <https://news.ycombinator.com/item?id=41406645 https://news.ycombinator.com/item?id=41406645>