## Exploring RANDOMNESSIn 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. |

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I haven't actually read the book, but the whole thing is found http://www.cs.auckland.ac.nz/~chaitin/ait/index.html

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a b c algorithmic information theory algorithmic probability already-scanned append bits argument assignment atom axiomatic system axioms binary data binary program bit string bound calculate Cantor car cdr cdr try Chaitin random chapter cons David Hilbert debug define definition diophantine equation element eval read-exp evaluate example extend-with-Os false formal axiomatic free-prefix free-space-pool G.J. Chaitin give given Godel graph halting probability halting problem Hilbert idea incompleteness infinite binary infinite sets irreducible mathematical Kraft inequality lambda limit LISP expression LISP interpreter log2 look loop main theorem make-assignments math minimum-size program n-bit not-yet-scanned Occam's razor oracle oracle machine output pairs physicists precisely primitive functions program-size complexity programming language proof read-bit real number relative complexity requirements set theory sets of S-expressions size-of-program smallest program Solovay there's true try no-time-limit Turing's universal Turing machine URL's words