Monday, January 9, 2012

A New Kind of Science - Stephen Wolfram

I saw a book called A New Kind of Science online and ordered a used copy.

Meanwhile, I read it on line while waiting for the hard copy to show up. When it did the tome was huge. Yup, I like to buy books by the pound.

Any ways, The web site for the book is here. A New Kind of Science

This is not just any old book. There have been several books of science over the centuries that would be called landmark books. For example Principia Mathematica, The Origin of the Species or Godel, Escher, Bach. This book is right up there with them.

(I realize the hyperbole there and am quite serious.)

Back in Galileo and Newton's time the earthshaking idea they proposed was not just about astronomy, but was the idea that Mathematics could be used to understand and describe the natural world. Before that Mathematics was considered purely abstract, of the mind. Newton came up with calculus and linear equations to describe motion.

Because science has used solvable mathematics, proofs, and equations to discover how Things Work, that has been the class of problems solved. Some problems in biological growth, physics, and such have been impossible to solve, and so have been ignored or swept under the rug.

What Wolfram proposes in A New Kind of Science is that there are many structures and processes in the universe that can not be described by linear math. Instead there are automatons and computer programs that can easily describe and model some processes. Not only does this technique model many processes that were previously 'complex' but great complexity can often flow from very simple processes. A familiar example of this is fractals, where a simple set of rules generate a very detailed and complex drawing.

The other side of this coin is that some problems and models can never be proven no matter how long you simulate or compute them. Science hates to say 'I don't know', but Wolfram clearly states that there are some things that can not be known.

Much of the book centers around the idea of generating complexity by way of ultra simple programs, and finding out just how simple you can get and still get huge complexity.

The book touches on biological organisms, stellar systems, fluid flow, the mind, free will, evolution, religion, society, and of course, mathematics.

So, when reading the book one thing stood out as odd. One is the general use of I, My, This Science, where Wolfram's ideas and science is 'All New and Improved!' and will revolutionize science. This gives it about the same tone as crackpots on the internet with some hair-brained theory that will change the world and has never been know before (tm). The difference with this book is that Wolfram is correct! Books such as The Origin of the Species have none of that tone.

Another thing that will help with this book is to not get stuck on the huge amount of ideas and processes presented. You don't have to understand every concept and program process presented. If I read this and learned to understand every mathematical concept presented in depth it would take years to read.

In the end the core idea is of The Principle of Computational Equivalence. The idea is that it does not matter whether a program is run on a computer, in a biological system, or a flow of atoms in a fluid, it is all the same. This is much like how the equation of gravity, F = MmG/r^2 is equivalent to what actual gravity does. But the equation and computing it is not what gravity is doing in the real world. It is a model that matches what we see, so gives understanding.

The other core idea is that the only way of discovering the outcome of some simple systems is to run the system to completion. For example, it is impossible to determine whether pi ever repeats, except to keep computing digits of pi until it does. (And so far it has not after billions of digits.)

The final paragraph is a gem...

And indeed in the end the Principle of Computational Equivalence encapsulates both the ultimate power and the ultimate weakness of science. For it implies that all the wonders of the universe can in effect be captured by simple rules, yet it shows that there can be no way to know all the consequences of these rules, except in effect just to watch and see how they unfold.



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