Systems Based on Numbers
The Notion of Numbers
Much of science has in the past ultimately been concerned with trying to find ways to describe natural systems in terms of numbers.
Yet so far in this book I have said almost nothing about numbers. The purpose of this chapter, however, is to investigate a range of systems that are based on numbers, and to see how their behavior compares with what we have found in other kinds of systems.
The main reason that systems based on numbers have been so popular in traditional science is that so much mathematics has been developed for dealing with them. Indeed, there are certain kinds of systems based on numbers whose behavior has been analyzed almost completely using mathematical methods such as calculus.
Inevitably, however, when such complete analysis is possible, the final behavior that is found is fairly simple.
So can systems that are based on numbers ever in fact yield complex behavior? Looking at most textbooks of science and mathematics, one might well conclude that they cannot. But what one must realize is that the systems discussed in these textbooks are usually ones that are specifically chosen to be amenable to fairly complete analysis, and whose behavior is therefore necessarily quite simple.
And indeed, as we shall see in this chapter, if one ignores the need for analysis and instead just looks at the results of computer