Turn to Your Left at the End of the Sky

The Limits of Knowledge

This just in: there are absolute, logical limits to the ability of any method (including the scientific one) for acquiring knowledge to produce a comprehensive theory of the world

Well, call off the search for a theory of everything. Physicist David Wolpert, in an article published in the prestigious Physica D (vol. 237, pp. 1257–1281, 2008), has shown that — at best — we can achieve a theory of almost everything. Wolpert’s work is very technical, but its implications are spectacular. Unlike the above mentioned limits to knowledge, which come out of empirical disciplines, Wolpert used logic to prove his point, following in the steps of the famousincompleteness theorem demonstrated by Kurt Godel in 1931. (An accessible summary of Wolpert’s discovery can be found in an article by P.-M. Binder in Nature, 16 October 2008.)

Basically, Wolpert — building on previous work by Alan Turing — formalized a description of “inference machines,” i.e. machines capable of arriving at inferences about the world (human beings are one example of such machines). Wolpert focused on what he calls strong inference, the ability of one machine to predict the totality of conclusions arrived at by another similar machine. Wolpert then logically proved the following two conclusions: a) For every machine capable of conducting strong inferences on the totality of the laws of physics there will be a second machine that cannot be strongly inferred from the first one; b) Given any pair of such machines, they cannot be strongly inferred from each other.

Of course, the article ends with the obligatory sideswipe at creationists.

Reference to original paper:

Physical limits of inference

Physica D: Nonlinear Phenomena, Volume 237, Issue 9, 1 July 2008, Pages 1257-1281
David H. Wolpert


October 23, 2008 - Posted by | Mathematics, Philosophy, Science |

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