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A Problem with Wolfram’s Theory of Relativity

Tanya writes "Eric Drexler has submitted the following critique:

Wolfram's argument that the properties of certain automata "must almost inevitably succeed in reproducing the fundamental features of relativity theory" (A New Kind of Science, p.520) appears to be misconceived. This may explain why he offers no examples of automata in which particle-like features move, as physical particles do, at a range of relative speeds.

He describes a broad class of automata (yielding "causal invariant" networks) that are insensitive to update order. In these, one can generate an invariant structure by adding nodes in any of many orders — for example, adding parallel layers at one or another angle. Differently angled slices of this sort look a bit like spacelike surfaces in moving frames of reference. Wolfram states (and makes central to his argument) that "one can interpret slices at different angles as corresponding to motion at different speeds" (p.521).

One must ask, however, motion of what? Since these networks are insensitive to update order, differing update patterns can make no difference to structures within a network, hence tell us nothing about the relative motion of any particle-like features it may contain. Angled update slices do not necessarily correspond to motion of anything within the model world.

If causal invariant networks naturally modeled motion, then one would expect Wolfram's book to include pictures showing streaks corresponding to variable-speed particles, but it does not. Offered neither a coherent argument nor a concrete example, we are left with a model of physics that lacks a model of relative motion."

8 Responses to “A Problem with Wolfram’s Theory of Relativity”

  1. The Living Fractal Says:


    Yea, that's what I call Wolfram's 'explain the universe with algorithms' idea, if you will.

    Nevertheless, the man is probably smart.

    Oh well, I just haven't seen it yet. Doesn't mean it's not there. Should I read his new book? Hmm. I have simply so many other good choices, it's a tough decision.

  2. RobVirkus Says:

    Re: Wolfram vs. Drexler

    I am surprised that Drexler chooses to critique Wolfram regarding relativity. What about nanotechnology? Wolfram mentions Drexler and seems to be quite supportive. I would defer to Wolfram on physics and Drexler on nanotechnology. Wolfram's ideas may have bearing on practical nanotechnological systems though. I have the book and am about halfway through it. Though the concepts are interesting Wolfram tends to give massive detail on the minutia of CA systems and yet almost no details on how nature may actually implement CA in real systems. He just gives a lot of hints and suggestions.

  3. Mr_Farlops Says:


    Yeah, I think I agree with the Fractal on this. Perhaps it's possible to build a universe filled with intelligent life out of cellular automata but I don't think that this universe is built out of cellular automata. The physics are too different.

    I wonder why Drexler is spending his valuable time on this. Doesn't he have more important fish to fry?

    I am also a little suspicious of the size of Wolfram's book. Powerful ideas in physics tend to be elegant. If he can't state his ideas with 20 or 30 equations and a few hundred pages of derived formulae do they really ring true? The truth, at least in physics, tends to be concise.

    Of course I haven't read his work so, my opinion really doesn't count.

  4. RobertBradbury Says:

    Re: Wolfram vs. Drexler

    As I read the comment, Eric is pointing out a fundamental problem in the architecture of Wolfram's CA model — "Since these networks are insensitive to update order, differing update patterns can make no difference to structures within a network". Though I haven't read Wolfram's work (I think it would require several months of serious study to do so), I think Eric is pointing out a causality problem in the framework that Wolfram has proposed.

    Since Wolfram seems to be basing his ideas on CA and they were developed by Toffoli and Margolus while Eric was at MIT, I would suggest that Eric is well qualified to comment on the topic.

    Nanosystems includes citations for work by both Toffoli and Fredkin whose research contributed to the foundation for robust CA research.

    Informed commentary on this topic would require people well versed in relativity theory as well as CA theory. I suspect that there are less than a few dozen people on the planet that can make such claims.

  5. Winged Cat Says:

    A way it could work

    Just because Wolfram doesn't give any examples doesn't mean there are none. If you're doing updates of particles in motion and you want the network to be insensitive to update order, then just update the particles based on their qualities as of the prior time step, regardless of what has been calculated for the current time step. For instance, if x(N,T), y(N,T), and z(N,T) give the position for spherical particle N at time T, and rad(N) gives the radius of particle N, then two particles N and M react to a collision at time T if and only if sqrt(((x(N,T-1) – x(M,T-1))^2) + ((y(N,T-1) – y(M,T-1))^2) + ((z(N,T-1) – z(M,T-1))^2)) rad(N) + rad(M)…or, in short, if and only if the distance between N and M at time T-1 is small enough that they collide. There are probably much more optimized versions of this algorithm used by professional game and simulation programmers, but this suffices for this discussion. Lack of evidence for a thing's existence, when no evidence has been sought out (an author can only print so much and address so many topics in one book), is not proof that the thing fails to exist.

  6. The Living Fractal Says:

    Re:A way it could work

    Yes, hence my caveat: "Doesn't mean it's not there."

  7. The Living Fractal Says:

    Re: Wolfram vs. Drexler

    Agreed. I'm not trying to devalue Wolfram's research in any way, but I will remain skeptical that CA can really lend us any deeper insight into the true workings of our great Universe without first being paired with an idea which has yet to be seen.

  8. RobVirkus Says:

    Re: Wolfram vs. Drexler

    I am working through Wolfram's book and I want to make the point that Wolfram does not say CA are behind everything in the universe as much as simple programs are of which CA are one example. He works through several other possibilities. He also is careful not to claim a detailed explanation as much as hints of a general direction and the great length of his tome is meant to drill in the basic idea that simple programs are a better approach to understanding the way nature works (in reality and not just as a model of nature) than closed form mathematical equations. He says we are looking for the wrong solution. To be fair I am just starting the physics chapter but based on the 400 or so pages before it, and based on Wolfram's interviews, he is not proposing a detailed final theory of physics. Detailed critiques of his examples may not disprove his central thesis just the appropriateness of his chosen examples. There has also been a lot of criticism of Wolfram on which tends to complain that all Wolfram's ideas are from others and that there is nothing new. There are a lot of one star reviews. I discount these as Wolfram bashing. Fredkin is cited as one who basically voiced Wolfram's ideas first. I read Fredkin state that he thought Wolfram's book was very important even if Wolfram cites others less than desired. What I think Wolfram is doing is putting together disparate ideas, extending them and giving them his full weight. It's important that Wolfram also seems to
    back a Drexlarian version of molecular nanotechnology. CA type rules as applied to building up of physical systems would seem to be worthy of study.

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