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Unformatted text preview: arXiv:quant-ph/0206089v2 30 Jul 2002 Quantum Information and Computation, Vol. 1, No. 0 (2001) 000000 c circlecopyrt Rinton Press BOOK REVIEW on A New Kind of Science by Stephen Wolfram Wolfram Media, Inc., May 2002 Hardcover $ 44.95 (1192 pages) ISBN: 1579550088 Somebody says, You know, you people always say that space is continuous. How do you know when you get to a small enough dimension that there really are enough points in between, that it isnt just a lot of dots separated by little distances? Or they say, You know those quantum mechanical amplitudes you told me about, theyre so complicated and absurd, what makes you think those are right? Maybe they arent right. Such remarks are obvious and are perfectly clear to anybody who is working on this problem. It does not do any good to point this out. Richard Feynman [1, p.161] 1. Introduction A New Kind of Science , the 1280-page treatise by Mathematica creator Stephen Wol- fram, has only a few things to say about quantum computing. Yet the books goalto understand nature in computational termsis one widely shared by the quantum computing community. Thus, many in the field will likely be curious: is this 2.5-kilogram tome worth reading? Notwithstanding newspaper comparisons  to Darwins Origin of Species , what is the books actual content? This review will not attempt a chapter-by-chapter evaluation, but will focus on two areas: computational complexity and fundamental physics. As a popularization, A New Kind of Science is an impressive accomplishment. The books main theme is that simple programs can exhibit complex behavior. For example, let p i,j = 1 if cell ( i,j ) is colored black, and p i,j = 0 if white. Then the Rule 110 cellular automaton is defined by the recurrence p i +1 ,j = p i,j + p i,j +1 (1 + p i,j- 1 ) p i,j p i,j +1 for i 0, given some initial condition at i = 0. Wolfram emphasizes that such an automa- ton, even when run with a simple initial condition such as a single black cell, can generate a complicated-looking image with no apparent repetitive or nested structure. This phe- nomenon, although well known to programming enthusiasts as well as professionals, will no doubt surprise many general readers. 95 96 Book review Using cellular automata as a framework, Wolfram moves on to discuss a range of topics including the second law of thermodynamics, natural selection, plant and animal morphol- ogy, artificial intelligence, fluid dynamics, special and general relativity, quantum mechanics, efficient algorithms and NP-completeness, heuristic search methods, cryptography and pseu- dorandomness, data compression, statistical hypothesis testing, Godels Theorem, axiomatic set theory, and the Church-Turing thesis. What is noteworthy is that he explains all of these without using formal notation. To do so, he relies on about 1000 high-resolution graph- ics, which often (though not always) convey the ideas with as much precision as a formula...
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