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Wolfram’s Teachings. Natural Language.

I’m thinking about the mathematician/computer-scientist/physicist Stephen Wolfram today, as his company just released version 8 of the Mathematica program, a multi-faceted mathematics-helper program; it simplifies and solves algebraid equations and generates very nice graphs, among otheg things. Wolfram’s latest wrinkle is that Mathematica now (to some extent) understands natural language. So you can ask it, for instance, to draw something for you without having to use the precise Mathematica-language symbolism. Wolfram has a blog post about this, “The Free-Form Linguistics Revolution in Mathematica.”


[Some of today’s photos are partly drawn from a large Thanksgiving Day gathering we went to in the Mission yesterday, organized in part by my son Rudy.]

Over the years, Wolfram’s had a huge influence on my thinking. Indeed, my 2006 tome, The Lifebox, the Seashell and the Soul was to a large extent inspired by Wolfram’s even fatter 2002 book, A New Kind of Science

As the years go by, I’m a little surprised by how slowly our new ideas seem to be sinking in. It’s as if people never will understand that a deterministic system can be unpredictable, and that computer science has pretty well established this as empirical fact. Or that natural systems in particular, being computation universal, are inherently unpredictable. So the media is always furiously casting about for the proximate cause of the latest disaster.

Re. my impatience, Wolfram recently emailed, “It will come. But I think the bigger the concepts, the longer the time needed for humans to absorb. So we’re mostly just learning that these are in fact big concepts (even though to you and me they now seem pretty obvious)…”

For today’s post, I thought I’d summarize Wolfram’s tenets once again, drawing on a version that I recently wrote up for my forthcoming autobiography, Nested Scrolls: A Writer’s Life. The context of this passage is that I’m recalling my mixed success in proselytizing Wolfram’s teachings, as presented in his New Kind of Science book. Some audiences had been actively hostile.

First of all, Wolfram was arguing that we can think of any natural process as a computation, that is, you can see anything as a deterministic procedure that works out the consequences of some initial conditions. Fine. Instead of saying the world is made of atoms or of curved space or of natural laws, let’s see what happens if we say it’s made of computations. This notion gets some people’s goat, but if you’ve hung around computers a lot, it seems semi-reasonable.

Secondly, Wolfram made the point that, by studying cellular automata, he’d learned that there are basically three kinds of computations. The simple ones peter out or repeat themselves. The pseudorandom ones generate a seething mess. And the interesting computations lie in between. They generate patterns that seem to have some kind of structure to them, but they don’t repeat themselves or turn boring.

This second idea is simply a taxonomic observation about the kinds of things we find in the world. The in-between computations are akin to what we might earlier have called chaotic processes. I myself came to call them “gnarly computations.” So, if everything is to be a computation, then pretty much all of the interesting patterns in nature and biology are gnarly computations. Fine.

Thirdly, Wolfram argued that all gnarly computations are in some sense equally powerful, that is, given enough time and space, any given gnarly computation can in fact emulate any of the others. If everything is an equally-powerful computation, then we’re all in some sense the same.

Note that a computer doesn’t have to be made of wires and silicon chips in a box. A cloud can emulate an oak tree, a flickering flame can model a human mind, a dripping faucet can behave like the stock market. And we’re not talking about vague, metaphorical resemblances here, we’re talking about mathematically precise bit-for-bit representations. (I wrote about this idea in my recent pair of novels Postsingular and Hylozoic.)

For someone who’d become as steeped in computer science as I had, this third point also seemed reasonable, but outsiders had trouble making sense of it—and in their confusion, many of them grew angry.

Fourthly, Wolfram said that gnarly computations are unpredictable in the specific sense that there are no quick short-cut methods for finding out what these kinds of computations will do. The only way, for instance, to really find out what the weather is going to be like tomorrow is to wait twenty-four hours and see. The only way for me to find out what I’m going to put into the final paragraph-sized “scroll” of Nested Scrolls is to finish writing the book.

Wolfram’s fourth point is very nearly provable on the basis of some well-known theorems from computer science but, again, many scientists don’t like it. They still subscribe to the pipedream of finding some magical tiny theory that will allow them to make quick pencil-and-paper calculations about every aspect of the future. They haven’t taken to heart the essentially chaotic nature of the world. We can’t control; we can’t predict—but even so we can hope to ride the waves.

10 Responses to “Wolfram’s Teachings. Natural Language.”

  1. Dave Says:

    Timely post. As an aspiring mathematics teacher, and current teacher candidate, approaching my half century mark, I reflected last night on how to engage all students in math, especially the underserved, since much of today’s mathematics curricula and pedagogy is BORING, especially to me. So, the thought came to me that math is inside of everything…to some degree, however small, or large, math shaped the creation, existence, and demise of all things. I won’t make the next logical connection for fear of angering too many, but think about it…makes sense, doesn’t it? So the synchronicity of your posting, which I found via a friend’s fb post, is wonderful, indeed.

  2. emilio Says:

    I shared this on facebook with the comment “diminish your mind. Buy into this crazy concept that everything is a computation.” My tongue is of course in my cheek, but I do think this is the problem with folks adopting this idea. We don’t like being reduced to a computation — even smart people. People don’t like the philosophical implications of this idea. Gödel’s work seems to say the world is not knowable in the TOE sense, unless of course the theory is itself infinite. And infinite causes get us, as I believe you so ably showed in Infinity and Mind, into the realm of god(s) very quick. So the materialists get uncomfortable and the diests are strangely dismayed by an undefinable god and only the committed agnostics are happy.

    Do you think it is possible that quantum computations can escape the mechanistic reduction that Wolfram’s work represents?

  3. Dave Says:

    Right on EO. You connected the dots I steered clear of explicitly doing…now, the question is: what came first, the math or the computation?

  4. Nauka web Says:

    Is this thesis more interesting than the book Gidel Escher and Bach?
    The idea is not so new indeed, and not so developped.

    Quantum computation does not offer (from what I know) an alternative to Godel’s theorem for instance.

  5. icastico Says:

    Nice post. It always seems important when discussing Wolfram and his potential impact to take account of the serious critics. Although certain a bit acerbic in it’s tone, the review raises important points worth considering.

    http://www.cscs.umich.edu/~crshalizi/reviews/wolfram/

  6. Rudy Says:

    Icastico, I myself reviewed Wolfram’s book for the Mathematical Association of America Monthly, see this link for the review, in which I counter some of the criticisms made against the book.

    In a nutshell, my feeling is that some of the hostile reviews for A New Kind of Science had to do with a dislike of Wolfram’s vexed relations to academia, and with certain self-willed blindness to the realities of modern computer science.

    Nauka web, Godel Escher Bach was and is a wonderful book, a masterpiece. But A New Kind of Science treats a very different range of topics. Keep in mind that GEB was written at the dawn of the age of computer science, and doesn’t take into account the practical experience that we’ve gained since then.

    Dave, at some level, math and computation are somewhat similar, aren’t they. Perhaps what sets math apart is that, in general, mathematical arguments lean on using short and clever techniques rather than resorting to exhaustive searches or exceedingly long proofs.

    Regarding quantum computation, my sense is that it’s subject to the same constraints as is traditional computatoin. I go into this in The Lifebox, the Seashell, and the Soul to some extent, where I also discuss a kind of generalized Godel’s theorem which applies to the natural world:

    Principle of Natural Undecidability. For most naturally occurring complex processes and for any formal system for science, there will be sentences about the process which are undecidable by the given formal system.

  7. icastico Says:

    Thanks Rudy,
    Actually read your excellent review when I was reading NKofS. I like NKofS and think it is an important work, but I do find the debate surrounding it unusual. Some of this, I think, comes from the decision to publish outside of the peer review process. It seems this should have no bearing on substantive criticisms of the findings where they exist, nor real contributions found in the book. Similarly, people should not deflect these substantive criticisms as sour grapes, when the way it was published is mentioned, and should take extra pains to be skeptical of its claims because it was published without peer review.

  8. Rudy Says:

    Icastio, it seems like we’re somewhat in agreement. The whole reception of NKS was, as you say, kind of weird. That review you link to, for instance, is pretty much off the scale in terms of emotionality—people normally don’t review science books with such vituperation.

    I really do think some of the passion has to do with people not liking the basic message–as opposed to disliking Wolfram’s sometimes deficient academic collegiality.

    I think the real issue here is the paradigm shift. In periods of scientific revolution, people really do get as upset as the reviewer you linked to. We don’t like having to think about the world in a new way.

    Along with chaos theory, Wolfram’s writings really have permanently changed the way I perceive the world, and I see that as a rare and a good thing.

  9. John Barnes Says:

    Historically I think what makes the difference for the acceptance of a new idea is the fractionof people who must (as in job, life, something serious depends on it) before they are thirty. I pull this guess pretty much out of the air but it’s in good accord with the statistical semiotics stuff I’ve done. So people got electricity pretty quickly — from Faraday to widespread application and understanding was only maybe 40 years or so — and aviation faster still, but there were so many connections to daily life that it took no time. Special relativity and the Old Quantum are over 100 and over 80 years old, respectively, without putting much of a dent in anyone’s thinking (unless you count the substitution of the word “quantum” for “bibbity bobbity boo.”) Probability took centuries until insurance became common and widespread; Darwinism not really till genetic manipulation (and particularly analysis) became possible.

    About a generation after some large number of younger workers/citizens/consumers/whatever really have to understand Wolfram, you’ll see a change. Not much before.

  10. Yaroslav Bulatov Says:

    I think NKS would find greater audience if it came with some practical applications. I was at WRI summer school a few years ago, and the applications I’ve seen were more of recreational math kind rather than something to be used in practice


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