Computer Science. Throughout its brief history computer science has focused almost exclusively on studying specific computational systems set up to perform particular tasks. But one of the core ideas of this book is to consider the more general scientific question of what arbitrary computational systems do. And much of what I have found is vastly different from what one might expect on the basis of existing computer science. For the systems traditionally studied in computer science tend to be fairly complicated in their construction—yet yield fairly simple behavior that recognizably fulfills some particular purpose. But in this book what I show is that even systems with extremely simple construction can yield behavior of immense complexity. And by thinking about this in computational terms one develops a new intuition about the very nature of computation.

One consequence is a dramatic broadening of the domain to which computational ideas can be applied—in particular to include all sorts of fundamental questions about nature and about mathematics. Another consequence is a new perspective on existing questions in computer science—particularly ones related to what ultimate resources are needed to perform general types of computational tasks.

Philosophy. At any period in history there are issues about the universe and our role in it that seem accessible only to the general arguments of philosophy. But often progress in science eventually provides a more definite context. And I believe that the new kind of science in this book will do this for a variety of issues that have been considered fundamental even since antiquity. Among them are questions about ultimate limits to knowledge, free will, the uniqueness of the human condition and the inevitability of mathematics. Much has been said over the course of philosophical history about each of these. Yet inevitably it has been informed only by current intuition about how things are supposed to work. But my discoveries in this book lead to radically new intuition. And with this intuition it turns out that one can for the first time begin to see resolutions to many longstanding issues—typically along rather different lines from those expected on the basis of traditional general arguments in philosophy.