I looked into this mailing list because I thought I'd come up with a fairly cogent objection to Max Tegmark's version of the "everything" thesis, i.e. that there is no distinction between physical and mathematical reality... our multiverse is one particular solution to a set of differential equations, not privileged in any way over other solutions to the same equations, solutions to other equations, and indeed any other mathemetical construct whatsoever (e.g. outputs of UTMs).

Sure enough, you came up with my objection years ago, in the form of the "White Rabbit" paradox. Since usage is a bit vague, I'll briefly re-state it here. The problem is that worlds which are "law-like", that is which behave roughly as if there are physical laws but not exactly, seem to vastly outnumber worlds which are strictly "lawful". Hence we would expect to see numerous departures from laws of nature of a non-life-threating kind.

This is a different objection to the prediction of a complete failure of induction... it's true that stochastic universes with no laws at all (or where laws abruptly cease to function) should be vastly more common still, but they are not observed due to anthropic selection.

A very similar argument ("rubbish universes") was put forward long ago against David Lewis's modal realism, and is discussed in his "On the plurality of worlds". As I understand it, Lewis's defence was that there is no "measure" in his concept of "possible worlds", so it is not meaningful to make statements about which kinds of universe are "more likely" (given that there is an infinity of both lawful and law-like worlds). This is not a defense which Tegmark can make, since he does require a measure (to give his thesis some anthropic content).

It seems to me that discussion on this list back in 1999 more or less concluded that this was a fatal objection to Tegmark's version of the thesis, although not to some alternatives based exclusively on UTM programs (e.g. Russell Standish's Occam's Razor paper).

Is this a fair summary, or is anyone here prepared to defend Tegmark's thesis?

Paddy Leahy

Dr J. P. Leahy, University of Manchester,
Jodrell Bank Observatory, School of Physics & Astronomy,
Macclesfield, Cheshire SK11 9DL, UK
Tel - +44 1477 572636, Fax - +44 1477 571618

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