From: George Dvorsky (george@betterhumans.com)
Date: Thu Mar 02 2006 - 13:37:14 MST
[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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