It's an interesting book (so i understand), and and interesting review. However, i think both Wolfram and Egan have completely misunderstood chaos theory and, indeed, science in general; none of Wolfram's interesting conclusions which Egan finds so exciting are really novel.
I'm going to take some out-of-order quotes to back this analysis up.
Chaos and complexity
Wolfram's notion of intrinsic complexity suggests that even very simple, isolated systems, with no unknown influences, can generate equally complex behaviour.
Complexity need not arise from an overwhelming morass of details and connections, too vast to fathom. Sometimes it grows on the spot from simple rules.
So, Complexity [...] grows on the spot from simple rules, does it? Well, that's chaos theory in a nutshell. The classic examples of chaos are the logistic equation and the Lorenz attractor, which are bloody simple equations without any sign of a morass of details and connections, too vast to fathom.
When that's the case, though predictions might remain beyond our grasp, we can still achieve understanding.
Excuse me while i throw up.
[...] we need to abandon the prejudice that says complex rules are needed for complex behaviour.
The whole point of the chaos and complexity work is to show that simple rules can generate complex behaviour. Indeed, that is the single central idea of chaos. Duh.
Science
Traditional science, Wolfram claims, focuses on systems with behaviour so simple that it can be summed up with a mathematical formula, a short-cut which lets us compute in a single stroke what the system will be doing at any future time. To find out what a computer program does, though, there is often no faster method than actually running the program. One consequence of universality in nature, then, will be computational irreducibility: the absence of any short-cuts to predicting the way the system will behave. Wolfram believes that it will take a new kind of science, based on an understanding of the behaviour of simple programs, to explain how much of nature works.
It's certainly true that traditional physics has tackled simple systems which are amenable to total analytical solution, but that's not the same as saying that it's treated the entire universe likes that. No physicist claims that, say, the three-body problem can be summed up with a mathematical formula [...] which lets us compute in a single stroke what the system will be doing at any future time; everybody knows that things like the n-body problem, fluid flow and the weather (oh, and biology) are really, really hard, intractable problems. I don't see any fundamental difference between Wolfram's computational irreducibility and the existing understanding that some things are really, really complicated, despite having simple basic mechanics; i suppose you could call it 'vertical' and 'horizontal' complexity, where one is complexity of the equations and the other is complexity of the configuration (i know that doesn't really explain it; let's face it, i'm not the science writer round here).
With examples like these, Wolfram shows that we can often get a good sense of how things work by capturing a few essential features. Trying to make use of everything we know about a system can mire us in irrelevant details [...]
Surely capturing a few essential features is precisely what mathematical modelling has always been about? The old 'assume a spherical cow' business.
Anyway, yeah. Learn some real science, you bit-twiddling gimps!
Well, having not read Wolfram or ANKOS, I shouldn't comment on those.
However, to the point: "Wolfram believes that it will take a new kind of science, based on an understanding of the behaviour of simple programs, to explain how much of nature works."
While probably a useful exercise, I think that runs the risk that one learns more about the *tool* of one's investigation than one does the object/system/phenomena that one is investigating.
Unless, of course, I've completely misinterpreted the meaning of the word 'program.' :-)
I empathise with your concern about learning a lot about tools (or at least models) rather than reality, but i think Wolfram's belief is that the lessons learned from the models can be applied to reality. That's happened before in science (in fact, models are one of science's most powerful tools), but it is vital to remember that they are merely models.
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Physicists suck
Date: 2002-12-02 04:00 pm (UTC)I'm going to take some out-of-order quotes to back this analysis up.
Chaos and complexity
So, , does it? Well, that's chaos theory in a nutshell. The classic examples of chaos are the logistic equation and the Lorenz attractor, which are bloody simple equations without any sign of a .
Excuse me while i throw up.
The whole point of the chaos and complexity work is to show that simple rules can generate complex behaviour. Indeed, that is the single central idea of chaos. Duh.
Science
It's certainly true that traditional physics has tackled simple systems which are amenable to total analytical solution, but that's not the same as saying that it's treated the entire universe likes that. No physicist claims that, say, the three-body problem ; everybody knows that things like the n-body problem, fluid flow and the weather (oh, and biology) are really, really hard, intractable problems. I don't see any fundamental difference between Wolfram's and the existing understanding that some things are really, really complicated, despite having simple basic mechanics; i suppose you could call it 'vertical' and 'horizontal' complexity, where one is complexity of the equations and the other is complexity of the configuration (i know that doesn't really explain it; let's face it, i'm not the science writer round here).
Surely is precisely what mathematical modelling has always been about? The old 'assume a spherical cow' business.
Anyway, yeah. Learn some real science, you bit-twiddling gimps!
ps why doesn't blockquote work?
Re: Physicists suck
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Well, having not read Wolfram or ANKOS, I shouldn't comment on those.
However, to the point: "Wolfram believes that it will take a new kind of science, based on an understanding of the behaviour of simple programs, to explain how much of nature works."
While probably a useful exercise, I think that runs the risk that one learns more about the *tool* of one's investigation than one does the object/system/phenomena that one is investigating.
Unless, of course, I've completely misinterpreted the meaning of the word 'program.' :-)
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Re: Physicists suck
Date: 2002-12-03 02:29 pm (UTC)I empathise with your concern about learning a lot about tools (or at least models) rather than reality, but i think Wolfram's belief is that the lessons learned from the models can be applied to reality. That's happened before in science (in fact, models are one of science's most powerful tools), but it is vital to remember that they are merely models.
-- Tom