In The Unknowable I use LISP to compare my work on incompleteness with that of Gödel and Turing, and in The Limits of Mathematics I use LISP to discuss my work on incompleteness in more detail. In this book we'll use LISP to explore my theory of randomness, called algorithmic information theory (AIT).

And when I say ``explore'' I mean it! This book is full of exercises for the reader, ranging from the mathematical equivalent of trivial ``finger warm-ups'' for pianists, to substantial programming projects, to questions I can formulate precisely but don't know how to answer, to questions that I don't even know how to formulate precisely!

I really want you to follow my example and hike off into the wilderness and explore AIT on your own! You can stay on the trails that I've blazed and explore the well-known part of AIT, or you can go off on your own and become a fellow researcher, a colleague of mine! One way or another, the goal of this book is to make you into a participant, not a passive observer of AIT.

In other words, it's too easy to just listen to a recording of AIT, that's not the way to learn music. I'd like you to learn to play it on an instrument yourself, or, better still, to even become a composer!

The common theme of my three Springer-Verlag books is to study H(x), the size in bits of the smallest program for calculating x, and that you cannot really understand an algorithm unless you can see it running on a computer. And in order to program the algorithms in my theory of program size I had to invent my own dialect of LISP.

These three books differ in their emphasis and complement each other, but each hopefully stands alone and can be read independently. The Unknowable discusses the historical context of my work on program-size complexity, The Limits of Mathematics gives a detailed discussion of the metamathematical implications of these ideas, and here I present the technical core of my theory.

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