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M. Mitchell,Is the Universe a Universal Computer, Science
2002,vol. 298, 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 digitalversion) on Stephen Wolframs website and it
constitutes a kind of authors credo on what isthe 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 Wolframs books main
thesis, what is not easy as the book counts 1200 pages. The main
Wolframs 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 Wolframs
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
doesnt 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
Wolframs work. She dedicates most of her scientific researches
to complexity and how tocope 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 Wolframs 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.
