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Sunday, Nov 8, 2009
Wolfram spent several years analyzing the results of such cellular automata setups, computer work that involved more than a million billion logical operations and the equivalent of tens of thousands of pages of output. Most of the output is relatively simple, repetitive patterns that remind one of a distinctive braid, or sometimes a snowflake, or occasionally a fractal pattern. But a few of the pictures seemed to demonstrate arbitrarily complicated patterns, long, random chains that seemed to take on a life of their own, reminiscent of the turbulence of a fluid or the curl of rising smoke.
You or I might have seen a pretty pattern and moved on, but Wolfram says using them he has seen into the clear blue depth of a new paradigm of thought. For such pictures can be seen even in cellular automata whose rules are extremely complex -- those in multiple dimensions, or based on number systems, or in a Turing machine, a very simple machine that has, logically speaking, all the power of any digital computer.
No matter how elaborate the rule, the behavior that emerges is remarkably similar to that of the simplest cellular automata, according to Wolfram. And what that means is "there are general principles that govern the behavior of a wide range of systems," Wolfram writes. "Even if we do not know all the details of what is inside some specific system in nature, we can still potentially make fundamental statements about its overall behavior."
All well and good, but Wolfram's conclusions have taken him to far greater heights of thought. The problem with traditional mathematics and physics is that it has of necessity restricted itself to simple cases that are "computationally reducible," systems such as a planet orbiting a star where mathematical analysis provides a simple equation describing the motion. But in other domains, such as predicting the weather, it has failed miserably.
Wolfram's new science -- a science largely devoid of equations -- demonstrates, he says, that there are many common systems whose behavior cannot be described except by explicit simulation on a computer. Most of the world, he asserts, is in fact computationally irreducible. The mathematical emperor does have clothes, but not much more than cotton skivvies and an undershirt with an unseemly spaghetti stain on the front.
Wolfram proceeds to attack the bulwarks of science head-on. The famous Second Law of Thermodynamics, stating that any energy associated with organized motions of microscopic particles tends to degrade inevitably into heat -- that order tends to disorder -- is "is an important and quite general principle," he writes, but his simple programs show that "it is not universally valid."
How can humans have apparent free will in a universe governed by deterministic rules? Because, Wolfram says, though our brain works by definite rules of chemistry, "our overall behavior corresponds to an irreducible computation whose outcome can never in effect be found by reasonable laws." Darwinian evolution? Wolfram believes that his methods can generate essentially any degree of complexity exhibited by life, and they have nothing to do with natural selection.
In fact, Wolfram sees no end to the possibilities of his ideas -- or his own place in scientific history. "In time," he writes in his preface, "I expect that the ideas of this book will come to pervade not only science and technology but also many areas of general thinking. And with this its methods will eventually become a standard part of education -- much as mathematics is today."
It remains to be seen how the scientific community at-large will react to Wolfram's work. (IBM computer scientist Gregory Chaikincalls Wolfram's work "a monument to experimental mathematics and the convergence of theoretical physics with computer science.") Wolfram has purposely declined to publish in the usual scientific journals, and his book is surprisingly devoid of footnoted references to the work of those who came before him (though a full third of the two-volume set consists of an appendix chock-full of general notes).
Wolfram has sought to control all aspects of the work, from establishing his own publishing house to hiring a publicist and placing an embargo on discussion of the book until its exact release date. The book has been anticipated for years, and the hype has apparently paid off: It was already ranked No. 1 on the Amazon.com bestseller list several days before its release. "Never lose a holy curiosity," said Einstein. Whether or not Wolfram's ideas launch science in a new direction -- and the great success of traditional science in explaining and shaping nearly every aspect of our world sets a very high bar indeed -- like other great scientists he has followed his instincts and blazed a new trail. One's impression is that Stephen Wolfram has never expected any less of himself.
