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
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
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