Stephen Wolfram's new book

Date: Sat Oct 20 2001 - 13:12:44 MDT

Eliezer's pointer to led me to an
interview with Stephen Wolfram at
Wolfram, best known as the author of the Mathematica program for symbolic
calculation, has a book coming out in a few months which he claims could
revolutionize science.

"A New Kind of Science" proposes an alternative to the mathematical
modeling which has been the main tool for scientific analysis since the
time of Newton. Equations and formulas use simple rules and operations
like addition and multiplication, and are a good fit for some physical
phenomena, but don't work for others. Wolfram believes that there are
alternatives to equations which can provide an entirely new toolset
for the scientist. These would be based on cellular automata, arrays
of computers running extremely simple programs. As with mathematical
equations, you can have a simple model and produce complex results.
Wolfram argues in his book that CAs may be as good or better than
equations for modeling nature.

Wolfram is quite a character. His web site,,
has excerpts from the new book as well as the story of his life. A real
prodigy, Wolfram, born in 1959, got his PhD by age 20 in theoretical
physics. After doing original work in particle physics, his attention
turned in the 1980s to the problems of chaos and complexity in physical
phenomena. He got interested in CAs and was one of the founders of the
study of nonlinear dynamics and chaos theory which became such a fad in
the 1980s.

At the end of the 80s he decided to commercialize his software
package SMP which was used for computer algebra. I believe I used an
early version of SMP when I was a student at Caltech in the 1970s.
This became Mathematica, which has been a huge success and has made
Wolfram a multi-millionaire.

In the early 1990s his attention turned back to his work on CAs.
He felt that his deeper points about the importance of this study had
not been understood and that he would have to write a book to bring
everything together. It would include experimental work with different
CAs, setting up a taxonomy and classification system to show what kinds
of variety they can produce with even simple rules; theoretical work
on their properties; and even observations from nature to show specific
examples of complexity in nature which fit well into the CA model.

On his site there is an amazing page showing sea shells with complex
patterns that appear indistinguishable from the output of some of
his CAs. I don't know how many other examples he has like this but it
does seem that in at least this one case the CA model is very helpful
in understanding what is happening in those shells.

Writing the book took a lot longer than he expected. He has essentially
disappeared from the public eye for the past 10 years, and now is coming
out to promote the book. It has been a sacrifice for someone who has
been admired and famous since he was a boy. Now we will see whether he
is more than an aging wunderkind and whether the book lives up to his
rather extravagant claims.

His results would be "enough to fill hundreds - maybe thousands - of
scientific papers," according to Wolfram. The question in my mind is
whether what he says has predictive value. It's of little use to show
similarities and correspondences between disparate phenomena and his CAs.
Can you do something useful with this? Part of the reason chaos theory
has not lived up to its hype is because you can analyze and classify it,
but ultimately chaos is still unpredictable. So the theory is rather
sterile and mathematical and doesn't tend to produce experimental
predictions and validations (there are exceptions of course).

The bottom line is not whether this book is a summary of important
results; it is how many new experiments and directions of research it
suggests. That is what will determine whether Wolfram's magnum opus makes
a real contribution to science, even revolutionizing it as he suggests.
I am looking forward to the publication with interest.


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