The limits of mathematics : a course on information theory and limits of formal reasoning
著者
書誌事項
The limits of mathematics : a course on information theory and limits of formal reasoning
（Springer series in discrete mathematics and theoretical computer science）
Springer, c1998
- : uk
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注記
Includes bibliographical references
内容説明・目次
- 巻冊次
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: uk ISBN 9781852336684
内容説明
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.
目次
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.
- 巻冊次
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ISBN 9789813083592
内容説明
This text 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. The book presents a "hands on" didatic approach using LISP and Mathematica software, and the reader should be able to derive an understanding of the close relationship between mathematics and physics.
目次
The Decline and Fall of Reductionalism.- Elegant LISP Programs.- An Invitation to Algorithmic Information Theory.- The Limits of Mathematics: examples.r, utm.r, godel2.r, omega.r, omega2.r, omega3.r, godel3.r.- Appendix: LISP interpreter in Mathematica.
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