# Exploring RANDOMNESS

• Gregory J. Chaitin
Book
Part of the Discrete Mathematics and Theoretical Computer Science book series (DISCMATH)

1. Front Matter
Pages i-x
2. ### Introduction

1. Front Matter
Pages 1-1
2. Gregory J. Chaitin
Pages 3-28
3. Gregory J. Chaitin
Pages 29-43
4. Gregory J. Chaitin
Pages 45-59
3. ### Program Size

1. Front Matter
Pages 61-61
2. Gregory J. Chaitin
Pages 63-72
3. Gregory J. Chaitin
Pages 73-83
4. Gregory J. Chaitin
Pages 95-108
4. ### Randomness

1. Front Matter
Pages 109-109
2. Gregory J. Chaitin
Pages 111-127
3. Gregory J. Chaitin
Pages 129-137
4. Gregory J. Chaitin
Pages 139-142
5. Gregory J. Chaitin
Pages 143-146
5. ### Future Work

1. Front Matter
Pages 147-147
2. Gregory J. Chaitin
Pages 149-159
3. Gregory J. Chaitin
Pages 161-164

### Introduction

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.

### Keywords

LISP Randomness Ringe Turing machine algorithms complexity logic sets

#### Authors and affiliations

• Gregory J. Chaitin
• 1
1. 1.IBM Research DivisionThomas J. Watson Research CenterHawthorneUSA

### Bibliographic information

• DOI https://doi.org/10.1007/978-1-4471-0307-3
• Copyright Information Springer-Verlag London Limited 2001
• Publisher Name Springer, London
• eBook Packages
• Print ISBN 978-1-4471-1085-9
• Online ISBN 978-1-4471-0307-3