2 comments on “The Clash (between formal mathematical methods and evolving simple programs)

  1. The answer to your last paragraph is YES.

    I’m not a mathematician or physicist but read Wolfram’s book carefully and with relish when it first came out. After finishing it I called my brother, who is what you might call a theoretical computer scientist/mathematician (and professor) to get his take. “Utter bullshit” was his speedy reply. But said he hadn’t read it – but simply knew it and Wolfram by their reputations. It seemed clear to me that his response was mostly a knee-jerk reaction to Wolfram’s ‘ego the size of a planet’ – which I understand is somewhat justified. Plus my brother worked with (I forget his name) the person who worked up the mathematical proof at the end of NKS about universality, who wound up battling Wolfram in court over the rights to said proof…none of which is mentioned in the book. It’s all “I did this” and “I did that”…(see large ego, above)

    I think I ‘got it’ because I hadn’t already been indoctrinated by math-based science…to me the Principle of Computational Equivalence is a wonderfully simple explanation of how order vs. chaos are discerned, and an amazingly transformative tool for understanding as I look at the world around me. But I’m more philosopher than scientist by a million miles. (but read math and science books for fun)

    Good post – one of the few about NKS I’ve found insightful…most are simply dismissive or downright rude.


  2. I like your use of ‘decreased marginal return’ with respect to theoretical physics. It highlights the fact that, in the study of simple programs, we have exactly the opposite problem: With very little architecture, we get much more stuff than we have time to look at! It reminds me of a professor of mine, David Cope (http://arts.ucsc.edu/faculty/cope/), who, through his music-composing software, claimed once to be the world’s most prolific composer…. Of course, he has never listened to the vast majority of his compositions!

    Certainly most mathematicians (and I assume most physicists as well) are still doing strictly pencil-and-paper math. So computation is just something they don’t have direct experience with all the time, and consequently I suppose they don’t see it as being fundamental to the world. For some bizarre reason, point particles in Minkowski space (or whatever) seem like better primitives to them than a grid of cells or a network.

    The other thing about pencil-and-paper computation is that you need to use equations that compartmentalize a large system into a few symbols, because otherwise you just can’t carry around all the information in a system. The beauty of NKS systems is that (while they presumably take place at a vastly different scale than, say, a “formal” electron), they are easy to work out step by step. As you said, this will let a high school student — probably even an elementary school student — understand the fundamental rule of the world. I expect some day a great grandchild of mine will come home from 5th grade and say that the teacher taught them the fundamental rule of physics today.

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