Tuesday, November 4, 2008

A theory of "almost" everything is the best we can do?

P.-M. Binder of the Department of Physics and Astronomy, University of Hawaii at Hilo
thinks that David Wolpert, writing in Physica D (Wolpert, D. H. Physica D 237, 1257–1281 (2008) has demonstrated "that the entire physical Universe cannot be fully understood by any single inference system that exists within it" :

In proving his theorems,Wolpert defines U as the space of all world-lines (sequences of events) in the Universe that are consistent with the laws of physics. He then defines strong inference as the ability of one machine to predict the total conclusion function of another machine for all possible set-ups. Finally, he uses ‘Cantor diagonalization’ (Box 1) to prove, among others, the following two statements:

(1) Let C1 be any strong inference machine for U. There is another machine, C2, that cannot be strongly inferred by C1.

(2) No two strong inference machines can be strongly inferred from each other.

The first of these statements posits that there is a portion of ‘knowledge space’ (that inferable by C2) that is not available to any C1 machine. The second is a statement about the non-equivalence of inference machines; it implies that, at most, only one machine at one instant in time can infer all others. The two statements together imply that, at best, there can be only a ‘theory of almost everything’.

Memo to LaPlace's demon: Get a job, Mr. Know-it-all.

Citation: Nature 455, 884-885 (16 October 2008) doi:10.1038/455884a; Published online 15 October 2008
A provocative contribution to the logic of science extends the theorems of Kurt Gödel and Alan Turing, and bears on thinking about prediction, the standard model of particles, and quantum gravity. (paywall)