I think it's interesting because Wolfram stumbled upon something quite profound that (from my perspective) is under appreciated by the majority of working physicists and mathematicians:
Computation arises from very simple axiomatic systems, in surprising ways, and that in turn has profound implications for quite a number of things.
But people have been playing with constructive mathematics as a foundation for a long time, but Wolfram doesn't seem to acknowledge that.
I think a lot of us who studied computer science forgot some of the magical epiphanies we had when learning about the nature of computation, so it's always fascinating when Physicists re-derive something in the field.
It's probably similar to how they view it when CS folk wade into discussion on QM and reach enlightenment.
Finally though, I give Wolfram a ton of credit not necessarily for his book, but for actually trying to derive modern physics from (his) version of constructive mathematics.
It's not often you see someone really pushing on something like this in public and willing to discuss their progress in real time.
if you get computation, you get the curry-howard-lambek correspondence for free. So you have an equivalence between logic as well as (cartesian closed) categories.
It also means some of those axioms are probably superfluous. It also means your bound by some of the same laws (? maybe the wrong term here?) that computation is (halting problem) etc.
> Wolfram stumbled upon something quite profound that (from my perspective) is under appreciated by the majority of working physicists and mathematicians:
Computation arises from very simple axiomatic systems
I disagree that his work offers profound new insights or that it has gone underappreciated.
Many mathematicians have explored the connections between computation, logic and formal systems for decades. I also take issue with the assertion that physicists have somehow "forgotten" or failed to appreciate these ideas within computer science. Many physicists are well versed in computational and information-theoretic concepts. The idea that simple rules can give rise to complex emergent behaviors is far from a new revelation.
Furthermore, Wolfram does not give due credit to this rich body of prior work. He presents his perspectives as groundbreaking discoveries, without properly acknowledging similar perspectives developed by others. This is not how science works.
The ability to give credit is something of which Steven Wolfram is in very short supply!
Never mind Wolfram's obvious debt to John Conway, John von Neumann and Alan Turing, among many.
From an interview with Steven Wolfram (FT.com, 11 April 2003. "Lunch with the FT: Stephen Wolfram" by Simon London):
Does he have any heroes, I ask, anyone in science whose work he really
admires?
The question is met with a long pause.
"I think Alan Turing would have discovered a lot of the things I have
discovered if he had lived another 20 years. He was pointed very much in
the same direction."
A hero?
"The more you learn about these people the more difficult it is to idolise
them. Turing was much more of a hacker than I am. He liked putzing around
with things in a way that is somewhat different from my interests."
How about (John) von Neumann, then?
"I'm sure I would have greatly enjoyed meeting him. He was a smart man. But
I would say he fundamentally missed deeper points in a whole series of areas
in his haste to figure things out faster than other people. It was almost
like science as a competitive sport. He skated too quickly over many areas."
Isaac Newton is summarised as "an able man who did interesting work", while
Charles Darwin "had the good feature of living basically a happy, quiet
life" although "the core of what he did is better than some of the
bandwagons he let himself climb on to".
Any living scientist he especially admires? I suggest Stephen Hawking, the
Cambridge astrophysicist, or Benoit Mandelbrot, whose work on fractals seems
adjacent to Wolfram's own interests in complexity.
Again, the reply is careful and considered.
"Hawking I view as a fascinating personal study but as a scientist...well,
I suppose he has done some decent-quality stuff. Benoit Mandelbrot I know
quite well and some of his work is quite important. In fact, I am one of
his bigger promoters. I'm just not sure he has completely internalised
quite how important it is."
fucking lol. And I mean that in the literal sense. That is hilarious. I mean sure Von Neumann maybe didn't go as deep as some others, but to dismiss Turing as just a hacker?
Thanks for sharing. It is possible Wolfram contributes something to physics by proving how far you can go with (a) constructive mathematics, but it is insane that he seems to miss the equivalences between past work, which is ironic given his entire focus of research.
My gut tells that deep learning works because of a similar underlying mathematics.
I have absolutely no mathematical proof.
But then again there is no cost to trusting my hunch…except maybe a few karma points if someone decides my opinion is worth being upset over.
I mean no matter how wrong I might be, nobody is going to die because of it.
Anyway, I think it is an important book and most of the negativity around it is because people feel threatened by Wolfram. Successful as a scientist, scholar, software developer, startup founder, and business executive.
It made me realize why structures in biology might arise in very short time spans "fully formed" as opposed to the the relatively slow process of natural selection (which is an important part of the evolutionary process, but strikes me as insufficient given the short time scales at play).
It makes sense if simple rules can create complex structures. Then it would just be a matter of "exploring" this universe of complex structures which would likely produce this wild assortment of distinct organisms, gradually shaped and refined over time.
I don't think it's the full picture, but it adds an interesting perspective I never considered before.
If the universe of complex structures is limited to those that can be produced from simple rules, and the rules are uniform throughout space, then extraterrestrials (if they exist) are likely more similar to terrestrial life than different.
Which means that there are likely aliens with leopard print and zebra stripes.
I don't think that's necessarily true. The laws of physics may be uniform everywhere but we are a product of our environment on Earth during a very slim time window.
It's rather high-IQ technobabble, which is somewhat less common.
It's not gibberish. For the most part, it's correct. It's just not very interesting. He's convinced that certain coincidences are meaningful, and they're just not.
Yes, this. I read it back when it came back and while it drew many parallels between computed systems with very few rules and real world phenomena, it never really did more than show examples and say, "Look, look how similar this is, this could be a thing, right?"
It was interesting and one of the best explorations of automata that I've seen, but I don't think anyone could draw any conclusions from it.
When a new technology is discovered, it takes a while for it to be woven into the fabric of everyday life. There are many new connections to the existing ways of doing things that get discovered in due course. Stephen has a head start on the rest of us, but I believe there are plenty of practical uses to the areas of math nearby to physics that he's mapping out for us all.
Cellular automata bridged math and CS for me and it's beautifully chaotic. It's the same backwards with deep learning. Chaos to structure in classifying numbers or "doing" math.
The illustrations are gorgeous and thought provoking. The text wildly overstates its own importance and boils down to "simple chaotic systems are cool (and everywhere (and occasionally isomorphic))".
Verdict: good to flip through when you're in an expansive mood.
Have you seen the stuff he "works on" lately? What a pretentious use of pseudo-scientific jargon that means absolutely nothing. If someone piles on layers upon layers of concepts over many years, but nobody else uses those concepts, this is not science, not even a "new kind" of science.
I think the fundamental idea of "start thinking in graph structures for spacetime instead of rubber sheets" is good and going to eventually pay off. But right now it doesn't offer anything testable and thus is useless for anything but thinking about while high.
It’s intriguing as a thought experiment that gives insight into how the complex physical structure of the world can emerge due to interactions of pieces according to (some known but many as yet unknown) locally embedded rules.
It seems intuitively correct as an analogy. And maybe obvious and not so new as the name claimed, as others have pointed out.
Beyond that I’m glad for him that he has Wolfram language to play with, because that seems much more practical, more about doing stuff, not just ruminating.
We do need people out there willing to take risks in research. Many of his claims may not be correct, however some findings may be made or may stimulate productive directions.
The problem with this work is with the messenger. His massive ego does not allow for doubt nor does he allocate credit to the science that has preceded him. His off-putting manner and unwillingness to collaborate in the usual way science is done means that even if there is significant merit, few will develop it out further.
"As the saying goes, there is much here that is new and true, but what is true is not new, and what is new is not true; and some of it is even old and false, or at least utterly unsupported."
Its an exploration on the fact that not everything has a math equation that can be applied to it.
Most of the book deals with unique aspects of this, but its definitely not new. Anyone who has done CFD in depth already knows this. Computing turbulence is a game of approximation, because if you want results at a certain point, you basically have to start simulating very small areas of air in parallel and their interactions with one another in terms of particle momentum, temperature, density, e.t.c. (which is pretty much how reality works).
The "science" aspect is his claim that researchers should focus on studying this phenomenon as explanation for everything in the universe, missing the fact that a) this already happens and b) in many cases, actual math is much quicker.
The more interesting thing in recent years is this concept is very key to AGI (in the sense of all knowing all powerful AI) being pretty much highly impossible.
32 comments
[ 8.4 ms ] story [ 1196 ms ] threadComputation arises from very simple axiomatic systems, in surprising ways, and that in turn has profound implications for quite a number of things.
But people have been playing with constructive mathematics as a foundation for a long time, but Wolfram doesn't seem to acknowledge that.
I think a lot of us who studied computer science forgot some of the magical epiphanies we had when learning about the nature of computation, so it's always fascinating when Physicists re-derive something in the field.
It's probably similar to how they view it when CS folk wade into discussion on QM and reach enlightenment.
Finally though, I give Wolfram a ton of credit not necessarily for his book, but for actually trying to derive modern physics from (his) version of constructive mathematics.
It's not often you see someone really pushing on something like this in public and willing to discuss their progress in real time.
It also means some of those axioms are probably superfluous. It also means your bound by some of the same laws (? maybe the wrong term here?) that computation is (halting problem) etc.
I disagree that his work offers profound new insights or that it has gone underappreciated.
Many mathematicians have explored the connections between computation, logic and formal systems for decades. I also take issue with the assertion that physicists have somehow "forgotten" or failed to appreciate these ideas within computer science. Many physicists are well versed in computational and information-theoretic concepts. The idea that simple rules can give rise to complex emergent behaviors is far from a new revelation.
Furthermore, Wolfram does not give due credit to this rich body of prior work. He presents his perspectives as groundbreaking discoveries, without properly acknowledging similar perspectives developed by others. This is not how science works.
The ability to give credit is something of which Steven Wolfram is in very short supply!
Never mind Wolfram's obvious debt to John Conway, John von Neumann and Alan Turing, among many.
From an interview with Steven Wolfram (FT.com, 11 April 2003. "Lunch with the FT: Stephen Wolfram" by Simon London):
Thanks for sharing. It is possible Wolfram contributes something to physics by proving how far you can go with (a) constructive mathematics, but it is insane that he seems to miss the equivalences between past work, which is ironic given his entire focus of research.
I have absolutely no mathematical proof.
But then again there is no cost to trusting my hunch…except maybe a few karma points if someone decides my opinion is worth being upset over.
I mean no matter how wrong I might be, nobody is going to die because of it.
Anyway, I think it is an important book and most of the negativity around it is because people feel threatened by Wolfram. Successful as a scientist, scholar, software developer, startup founder, and business executive.
YMMV.
It made me realize why structures in biology might arise in very short time spans "fully formed" as opposed to the the relatively slow process of natural selection (which is an important part of the evolutionary process, but strikes me as insufficient given the short time scales at play).
It makes sense if simple rules can create complex structures. Then it would just be a matter of "exploring" this universe of complex structures which would likely produce this wild assortment of distinct organisms, gradually shaped and refined over time.
I don't think it's the full picture, but it adds an interesting perspective I never considered before.
If the universe of complex structures is limited to those that can be produced from simple rules, and the rules are uniform throughout space, then extraterrestrials (if they exist) are likely more similar to terrestrial life than different.
Which means that there are likely aliens with leopard print and zebra stripes.
It's not gibberish. For the most part, it's correct. It's just not very interesting. He's convinced that certain coincidences are meaningful, and they're just not.
After two decades, zero predictions of any phenomena in nature. Please correct me if I’m mistaken.
Performing a calculation that produces patterns that sort of resemble some natural forms is not a prediction of anything.
It was interesting and one of the best explorations of automata that I've seen, but I don't think anyone could draw any conclusions from it.
It's the unexpected that's exciting.
Verdict: good to flip through when you're in an expansive mood.
It seems intuitively correct as an analogy. And maybe obvious and not so new as the name claimed, as others have pointed out.
Beyond that I’m glad for him that he has Wolfram language to play with, because that seems much more practical, more about doing stuff, not just ruminating.
The problem with this work is with the messenger. His massive ego does not allow for doubt nor does he allocate credit to the science that has preceded him. His off-putting manner and unwillingness to collaborate in the usual way science is done means that even if there is significant merit, few will develop it out further.
"As the saying goes, there is much here that is new and true, but what is true is not new, and what is new is not true; and some of it is even old and false, or at least utterly unsupported."
Most of the book deals with unique aspects of this, but its definitely not new. Anyone who has done CFD in depth already knows this. Computing turbulence is a game of approximation, because if you want results at a certain point, you basically have to start simulating very small areas of air in parallel and their interactions with one another in terms of particle momentum, temperature, density, e.t.c. (which is pretty much how reality works).
The "science" aspect is his claim that researchers should focus on studying this phenomenon as explanation for everything in the universe, missing the fact that a) this already happens and b) in many cases, actual math is much quicker.
The more interesting thing in recent years is this concept is very key to AGI (in the sense of all knowing all powerful AI) being pretty much highly impossible.