Physics. The traditional mathematical approach to science has historically had its great success in physics—and by now it has become almost universally assumed that any serious physical theory must be based on mathematical equations. Yet with this approach there are still many common physical phenomena about which physics has had remarkably little to say. But with the approach of thinking in terms of simple programs that I develop in this book it finally seems possible to make some dramatic progress. And indeed in the course of the book we will see that some extremely simple programs seem able to capture the essential mechanisms for a great many physical phenomena that have previously seemed completely mysterious.

Existing methods in theoretical physics tend to revolve around ideas of continuous numbers and calculus—or sometimes probability. Yet most of the systems in this book involve just simple discrete elements with definite rules. And in many ways it is the greater simplicity of this underlying structure that ultimately makes it possible to identify so many fundamentally new phenomena.

Ordinary models for physical systems are idealizations that capture some features and ignore others. And in the past what was most common was to capture certain simple numerical relationships—that could for example be represented by smooth curves. But with the new kinds of models based on simple programs that I explore in this book it becomes possible to capture all sorts of much more complex features that can only really be seen in explicit images of behavior.

In the future of physics the greatest triumph would undoubtedly be to find a truly fundamental theory for our whole universe. Yet despite occasional optimism, traditional approaches do not make this seem close at hand. But with the methods and intuition that I develop in this book there is I believe finally a serious possibility that such a theory can actually be found.

Biology. Vast amounts are now known about the details of biological organisms, but very little in the way of general theory has ever emerged. Classical areas of biology tend to treat evolution by natural selection as