Discrete Mathematics and Theoretical Computer Science

In The Unknowable I use LISP to compare my work on incompleteness with that of G6del 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 oftrivial "fin­ ger 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 offinto the wilder­ ness 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 AlT. In other words, it''s too easy to just listen to a recording of AIT, that''s not the way to learn music.