M. Mitchell,

*Science *vol 298, 4 October 2002, pp 65 – 68

Abstract

The text is a critical review of a book written by Stephen Wolfram, A New Kind of Science, published in 2002 by Wolfram Media. The book itself is available for free (in a digital version) on Stephen Wolfram’s website and it constitutes a kind of author’s *credo *on what is the nature of the world and in consequence how science should be practiced. In the first part of her article Melanie Mitchell briefly makes the reader familiar with Wolfram’s books main thesis, what is not easy as the book counts 1200 pages. The main Wolfram’s idea can be however described quite simply: The structure of the physical world bases upon the theory of cellular automata, originally proposed by two mathematicians, Stanislaw Ulam and John von Neumann. Any other mathematical structures, discovered by the scientists are accidental and very rare in nature. The main feature of some cellular automata, is that they are able to product very complex structures, hard to decipher and to discover any regularity, on the basis of the very simple instructions (programs) originally encoded in the automaton. Wolfram claims that science should be practiced so that, we would rather look for those “simple programs” in nature, then effortlessly try to describe the observed regularity in terms of standard mathematical equations. The key phrase is “computational equivalence” which is the new law of nature according to Wolfram and this new principle can illuminate many aspects of natural phenomena as well as fundamental philosophical questions.

Melanie Mitchell is not totally critical towards Wolfram’s proposals. She thinks that in general he is on the right track. It seems like simple computer models can sometimes better explain the complex structures then traditional approach. It doesn’t however constitute any “new kind of science”. Wolfram simply continues to develop the very significant work of the pioneers of computer age and computability, Neumann, Turing, Wiener. The works of those scientists are often disregarded in Wolframs book.

Many of his claims are rather speculations or suspicions which are not supported by any evidences. Especially, although we can observe in nature the structures which seems to be a product of simple programs, we cannot say, as Wolfram would like to do, that such structures are common as well as common is the ability to support the universal computation. On the contrary the analytical approaches to illuminating complexity in nature has been much more successful so far then cellular automata.

Commentary

Melanie Mitchell is doubtless specially competent to write a critical review of the Stephen Wolfram’s work. She dedicates most of her scientific researches to complexity and how to cope with it. As the specialist in complex systems she is aware that in order to illuminate them and to decipher the rules that govern the behavior of complex systems in nature we probably have to look for entirely different methods then the traditional mathematical linear equations. The direction of Wolfram’s researches seems to be right. But it is not Wolfram who put mathematicians, physics, biologists and even economists on that track. Even if the direction is correct we have to be critical towards ourselves in our courageous ideas. Especially as the cellular automata are surely not the only way to cope with complexity, and not even the most effective. It is far too early to bury the old methods. They still work in many areas much better then cellular automata.

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