Good Math/Bad Math

Tuesday, March 07, 2006

Cellular Automata - the key to physics? Pthppptt.

There's a book review on Salon of Decoding the Universe: How the New Science of Information Is Explaining Everything in the Cosmos, From Our Brains to Black Holes, which really gave my pseudo-math detector a nasty kick.

Now, to be clear: I haven't read the book. I'll probably take a look at it next time I'm in a bookstore. I'm not criticizing the book (yet). All I'm doing is snarking the review. But it's enough to set my teeth on edge.

The book is about the idea that the universe behaves a lot like a cellular automaton. This is a cool idea. To my knowledge, it was first suggested by Marvin Minsky sometime back in the late seventies. There's a lot to like about the idea; it has a very clean intuitive feel, and provides some intuition for explaining things like time dilation. (Short form: think of a object moving around through space as a little program moving around between points in a lattice of CAs. Each cellular computation quantum, the object/program can do one thing: move, or do some bit of computation to describe what's happening on/in the object. The quanta spent doing computation about the object are subjective time to something on/in the object. The faster it moves, the fewer quanta are getting spent on computing subjecting time - and voila, time dilation. )

Of course, this doesn't actually match the *math* of how relativity works very well. The math of relativity is a complicated structure that shows that no matter what frame of reference you choose, things work the same way: there is *no* right frame. There is no such thing as a single objective correct way of looking at things. For example, think about a simple situation where you have two particles, one of which is stationary, and one of which is moving at .9c.

There's no way to distinguish that from a situation where the particle that you said was moving at .9c, and the particle that you said was stationary was actually moving at .9c. And there's no way of distinguishing that from a situation where both particles are moving at .45c. In fact, any or all of them are perfectly valid descriptions of the situation. It is not the case that there is one view that is right - they are all equally right. (This is very hard to comprehend. I don't pretend to have a very good intuitive grasp of how it works. But the math has been worked out, and tested in great detail against physical models, and it's proved out magnificently. )

That doesn't work in the CA model. In the CA model, there is one object that is stationary, and one that is moving - and there is a huge difference between the two.

The real math of relativity and quantum mechanics has never been worked out in CA. In fact, every effort to come up with a cellular automaton that models even limited aspects of reality has failed, miserably. Steve Wolfram discusses the idea at great length in "A New Kind of Science" - but doesn't manage to come up with a really accurate model of gravity. John Case at the U of Delaware, my alma mater, has done some very cool work on modeling things using a tetrahedral 3d CA - but has not yet come particurlarly close to being able to do efficient accurate models of anything interesting.

Back to the review.

The review goes into a pile of pseudo-philosophical rubbish about how "information is as physical as matter":


"Information is physical. Information is not just an abstract concept, and it is not just facts or figures, dates or names. It is a concrete property of matter and energy which is quantifiable and measurable. It is every bit as real as the weight of a chunk of lead or the energy stored in an atomic warhead, and just like mass and energy, information is subject to a set of physical laws that dictate how it can behave."


It's the same kind of gibberish that creationists use to explain how "information can't be created". Very touchy-feely, with examples about the wonders of how the reviewer finally comprehends how her candy thermometer works.

But....

For all of her discussion, she never mentions what CA has to do with it. She's reviewing a book on a mathematical model of physics based on a simple idea - and she never bothers to talk about just what that model is!

What does she, or the author of the book mean by the physical reality of information? I know what classic CA means by it: that reality is nothing more that the data defining the states in a huge CA lattice. But that's not what the reviewer means - just read her explanation of how she understands it:


was contemplating this the other day while using a candy thermometer to figure out if the sugar syrup I was boiling had become hot enough to add to a bowl of whipped egg whites. Reading the numbers on the thermometer might seem to the casual eye like a nonphysical transmission of information, even though energy from the electric company was used to generate the light bouncing off the thermometer and into my eyes and energy from my lunch powered the neurons that fired in my brain as I read it.

But what intrigued me most about the experience was the realization that while "240 degrees" was the information I thought I was getting from the thermometer, it was really the mercury in the device that told me what I needed to know. It borrowed a little heat from the boiling syrup and expanded up the glass tube of the thermometer to give me the news. The increase in the temperature and the volume of that mercury was the true source of the information (about the heat of the syrup). My seven-minute frosting was a classic illustration of information in action!


Does the reviewer know what a CA is? Sure doesn't seem like it. Does she care? Sure doesn't seem like it. So what's she doing writing a review of what a brilliant job the author of the book does at explaining math?

9 Comments:

  • Einstein velocity addition?

    By Anonymous Anonymous, at 8:20 AM  

  • I'm with anonymous. The bad relativistic math is right where you suggest that .9c - 0 = 0 + .9c (okay so far) and then that .9c = .45c + -.45c. Nuh-uh. If that were true, two objects moving directly apart from you, each at .6c relative to you, would have a relative velocity with each other of 1.2c. That's not right. :)

    By Blogger Eh Nonymous, at 9:40 AM  

  • WHAT is that book reviewer nattering on about? "Information" is not real; the things that we derive our information from are real. A thermometer is real and the change in the metal that produces a different readout is real, but the numeric value we so anthropomorphically* assign to that reading is nothing more than the human mind seeing patterns and assigning meaning and values to those patterns.

    The silly reviewer should have gotten over the revelation afterglow before writing; maybe then the review would actually reflect the contents of the book!

    andrea

    * Fahrenheit system is even more anthropomorphic than Celsius, originally based upon human body temperature, with "100" as human body temperature, except the guy had a fever, so the average normal human body temperature reads as 98.6°F (well, that's the story as I know it; kindly correct me if I'm wrong).

    By Anonymous andrea, at 10:15 AM  

  • Yeah, I think that rather than v=0.45 you want v=0.627, so that 2v/(1+v^2) will be 0.9. Yes? Something like that. It doesn't affect your point, except to emphasize that the reviewer you're reviewing is not even wrong...being (definitely, provably) wrong is a good thing because it's a starting point. (Hence the name of my own occasional blog, mistakesByTJM).

    Another trivial issue: the idea that the universe is a CA seemed obvious to me as a sophomore physics student in October 1970, when I read Conway's Life article in Scientific American. Well, maybe I didn't read it until a bit later, since I was in Buenos Aires at the time, but I know that in the following spring I was allowed to defend a CA model (in which I tried to derive the least action principle) as my oral exam in classical mechanics, and I know that I wasn't claiming to have invented the idea. "late 1970s" is too late for an origin here.

    (Andrea, there are four versions of the Fahrenheit invention story at wikipedia. Each of them reflects a Fundamental Truth. :-) )

    By Blogger Tom Myers, at 12:31 PM  

  • Argh. Yes, I'm an idiot, and I'm guilty of exacly what I'm supposed to be criticizing :-(.

    In my super-quick Einstein rant about relativity, I didn't do the relativistic adjustments to make the speeds work.

    I'm (seriously) deeply ashamed.

    -MarkCC

    By Blogger MarkCC, at 1:03 PM  

  • andrea:

    I think that the book reviewer just totally misunderstood the point of the book. (I don't know that the book gets it right, but my suspicion is that the reviewer blew it.)

    If you're talking about a model of the universe as CA, then information is as physical and real as anything in the universe - because everything in the universe is precisely a bunch of information represented in a CA lattice. I suspect that that's what the author of the book was saying. The reviewer just totally blew it - skipped the CA level of things entirely (even though that is the supposed point of the book), and tried to apply the concept to macro-level reality.

    There is a sense where information is physically real even at a macro level - see the old Hawkings debate about whether information can ever leave a black hole. But again - that doesn't seem to be what the reviewer is talking about either.

    By Blogger MarkCC, at 1:08 PM  

  • Mark,
    FWIW, I think you're wrong to be ashamed of being wrong. :-) I really mean it when I (as another CS Phuddy-duddy) try to distinguish between "wrong" (e.g., what you wrote) and "not even wrong" (what you were criticizing) The phrase is due to Pauli, but I think of it as a computer geek's phrase: a simple clear statement like the one you gave is one that can then be used as a starting point for debugging; it's part of the process of good math, it just happens to be unfinished. The fuzz that you were criticizing is bad, not because it's false, but because it's not even false. It cannot be debugged.

    Sure, there are times when pseudo-math appears to say something false -- I'm thinking of a creation science book I read long ago which explained why evolution violates the second law, and they made some definite statements which were true and others which were false. But mostly their argument was about "complexity" in a sense that had nothing to do with any thermo textbook; it wasn't even wrong. And they will never (I'm making a prediction here, but I don't think I'm sticking my neck out very far) actually fix the errors because the not-even-wrong part is their center.

    If I had to feel bad about the programming errors I make every day, much less the bigger errors with which I started out my own blog, I really couldn't live with myself at all.
    But the t-shirt I'm wearing right now says "If at first you don't succeed / call it version 1.0". Works for me.

    So go on making mistakes...and fixing them. (Unless it gets to be not-fun, of course. Whatever.)

    By Blogger Tom Myers, at 3:33 PM  

  • How about Stephen Wolfram's book A New Kind of Science - he develops this theme very thoroughly through its 1200 some pages.
    Not only does he show that many natural systems may be precisely modeled as CA, but that Science as we know it has avoided systems which behave in chaotic ways, and which may be well modeled by simple rules in a computational context.

    By Anonymous Ted, at 10:34 PM  

  • ted:

    I haven't read Wolfram's book yet. I've been meaning to pick up a copy, but every time I look it up in a bookstore, I end up leaving it on the shelf. It's a very big book, on a subject which I really enjoy, but which is unrelated to my work... I just know that when I get a copy, I'm going to want to hack up some experiments to try them out, and I just don't have the time for than right now. So I've been stalling.

    But I'll make up for it: I'm going to go buy a copy right now. Having a math blog is a good excuse for spending some time with a fun book like that.

    By Blogger MarkCC, at 9:00 AM  

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