The Limits of Mathematics: A course on information theory and the limits of formal reasoning (Springer Series in Discrete Mathematics and Theoretical Computer Science)

This book is the final version of a course on algorithmic information theory and the epistemology of mathematics and physics. It discusses Einstein and Goedel's views on the nature of mathematics in the light of information theory, and sustains the thesis that mathematics is quasi-empirical. There is a foreword by Cris Calude of the University of Auckland, and supplementary material is available at the author's web site. The special feature of this book is that it presents a new "hands on" didatic approach using LISP and Mathematica software. The reader will be able to derive an understanding of the close relationship between mathematics and physics. "The Limits of Mathematics is a very personal and idiosyncratic account of Greg Chaitin's entire career in developing algorithmic information theory. The combination of the edited transcripts of his three introductory lectures maintains all the energy and content of the oral presentations, while the material on AIT itself gives a full explanation of how to implement Greg's ideas on real computers for those who want to try their hand at furthering the theory." John Casti, Santa Fe Institute As a teenager, Greg created independently of Kolmogorov and Solomonoff, what we call today algorithmic information theory, a sub ject of which he is the main architect. His 1965 paper on gedanken experiments on automata, which he wrote when he was in high school, is still of interest today. He was also heavily involved in IBM, where he has worked for almost thirty years, on the development of RISC technology. Greg's results are widely quoted. My favorite portrait of Greg can be found in John Horgan's-a writer for Scientific American-1996 book The End 01 Science. Greg has gotten many honors. He was a guest of distinguished people like Prigogine, the King and Queen of Belgium, and the Crown Prince of Japan. Just to be brief, allow me to paraphrase Bette Davis in All About Eve. She said, "Fasten your seat belts, it's going to be a bumpy talk!" Ladies and Gentlemen, Greg Chaitin! [Laughter & Applause] CRISTIAN CALUDE introducing GREGORY CHAITIN at the DMTCS'96 meeting at the University of Auckland. "This book presents the final version of Chaitin's course on the limits of mathematical reasoning. This course uses algorithmic information theory to show that mathematics has serious limitations, and features a new more didactic approach to algorithmic information theory using LISP and Mathematica software. The thesis of the book is that the incompleteness phenomenon discovered by Godel is much more widespread and serious than hitherto suspected."--Jacket As well as presenting this lecture on the limits of mathematics in book format, Gregory Chaitin explains a new dialect of LISP using a long LISP run, examples.r, that contains lots of comments and reveals every feature of the language. The code for the LISP interpreter is also backed up by some mathematical code Randomness in arithmetic and the decline and fall of reductionism in pure mathematics.- Elegant LISP programs.- An invitation to algorithmic information theory.- The limits of mathematics.- Appendix: LISP interpreter in Mathematica