**From:** George Dvorsky (*george@betterhumans.com*)

**Date:** Thu Mar 02 2006 - 13:37:14 MST

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[not sure if this has been posted here before]

On the intelligibility of the universe and the notions of simplicity,

complexity and irreducibility

Gregory Chaitin, IBM Research Division

http://www.cs.auckland.ac.nz/CDMTCS/chaitin/bonn.html

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.]

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