GREGORY CHAITIN : "On the intelligibility of the universe and the notions of simplicity, complexity and irreducibility"

"On the intelligibility of the universe and the notions of simplicity, complexity and irreducibility"


Gregory Chaitin is at the IBM Watson Research Center in New York.
His theory of algorithmic information develops an idea in Leibniz's Discours de métaphysique, VI, and focuses on randomness and on the limits of formal axiomatic reasoning.
It was while working on this theory that Chaitin discovered the remarkable Ω number.
His two most recent books are Conversations with a Mathematician, published by Springer-Verlag, and From Philosophy to Program Size, published by the Institute of Cybernetics at Tallinn Technical University. Chaitin has an honorary doctorate from the University of Maine, and is an honorary professor at the University of Buenos Aires and a visiting professor at the University of Auckland.
Gregory Chaitin has shown that God plays dice not only in quantum mechanics, but even in the foundations of mathematics, where Chaitin discovered mathematical facts that are true for no reason, that are true by accident. This book collects his most wide-ranging and non-technical lectures and interviews, and it will be of interest to anyone concerned with the philosophy of mathematics, with the similarities and differences between physics and mathematics, or with the creative process and mathematics as an art.



"Abstract: We discuss views about whether the universe can be rationally comprehended, starting with Plato, then Leibniz, and then the views of some distinguished scientists of the previous century. Based on this, we defend the thesis that comprehension is compression, i.e., explaining many facts using few theoretical assumptions, and that a theory may be viewed as a computer program for calculating observations. This provides motivation for defining the complexity of something to be the size of the simplest theory for it, in other words, the size of the smallest program for calculating it. This is the central idea of algorithmic information theory (AIT), a field of theoretical computer science. Using the mathematical concept of program-size complexity, we exhibit irreducible mathematical facts, mathematical facts that cannot be demonstrated using any mathematical theory simpler than they are. It follows that the world of mathematical ideas has infinite complexity and is therefore not fully comprehensible, at least not in a static fashion. Whether the physical world has finite or infinite complexity remains to be seen. Current science believes that the world contains randomness, and is therefore also infinitely complex, but a deterministic universe that simulates randomness via pseudo-randomness is also a possibility, at least according to recent highly speculative work of S. Wolfram. [Written for a meeting of the German Philosophical Society, Bonn, September 2002.]"


http://www.cs.umaine.edu/~chaitin/bonn.html


``Chaitin has put a scratch on the rock of eternity.''
— Jacob T. Schwartz, Courant Institute, New York University, USA

``[Chaitin is] one of the great ideas men of mathematics and computer science.''
— Marcus Chown, author of The Magic Furnace, in NEW SCIENTIST

``Finding the right formalization is a large component of the art of doing great mathematics.''
— John Casti, author of Mathematical Mountaintops, on Gödel, Turing and Chaitin in NATURE

``What mathematicians over the centuries — from the ancients, through Pascal, Fermat, Bernoulli, and de Moivre, to Kolmogorov and Chaitin — have discovered, is that it [randomness] is a profoundly rich concept.''
— Jerrold W. Grossman in the MATHEMATICAL INTELLIGENCER