A New Kind of Science
Wolfram, Stephen. A New Kind of Science. Champaign, IL: Wolfram Media, Inc.,
2002. This is another blockbuster book by Wolfram, the creator of Mathematica.
The title is ambitious to say the least. The systematic study of cellular automata -- the
main research tool used by Wolfram for his book -- may well become a new scientific
discipline. But Wolfram's vision is much broader. He feels he has identified some
global principles, and he is deeply exploring the boundaries and interactions between the
mental (mathematical) and physical worlds. This makes him a major pioneer in
observer physics.
A key theme of Wolfram's work is what he calls the principle of "computational
equivalence" -- the ability of mathematics to mimic the physical world. If I understand
him correctly, he means by this idea that as a system grows in complexity, there is a
threshold beyond which all systems behave the same. (Does this mean that God -- and
the aliens -- are no smarter than we are? Is this anthropomorphic jingoism? Or does it
just mean that everyone is equally good at making a mess?) Perhaps Wolfram is talking
here about the limit where complexity becomes pure randomness. Wolfram's idea of
"Computational Irreducibility" refers, it seems, to the notion that at some point any model
of a system essentially reproduces the system in another medium with the same
complexity. Related to this is the mathematical notion of "universality" -- that a certain
program can be set up to emulate a whole class of programs. A similar idea is the
notion that you can emulate algebra with geometry and vice versa.
Wolfram's starting point in the creation of his "New Kind of Science" was his discovery
that very simple programs can produce great complexity and even randomness. This is
not really a new discovery. Mathematicians have known this since the discovery that a
simple ratio such as pi is an irrational quantity that generates a decimal with an infinite
string of random digits. Linguists are familiar with ways to generate randomness (or at
least great complexity) from simple grammars, and more recently the fractal and chaos
people have made a great deal of progress generating infinite complexity with simple
mathematical structures such as the Mandelbrot set. (In Observer Physics we discuss the
example of the growth equation with the Verhulst factor included so as to make the
system nonlinear.) What may be special about Wolfram's approach is the importance and
generality he attaches to this principle. Its flowering as a principle definitely is a
product of the computer age. But, although Wolfram may not be the first to notice that
a new kind of science is emerging, he is definitely one of the significant pioneers in this
new science.