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Eliezer's pointer to http://www.scitechdaily.com/ led me to an

interview with Stephen Wolfram at

http://www.newscientist.com/opinion/opinterview.jsp?id=ns230516.

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, www.stephenwolfram.com,

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.

Hal

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