Re: White Rabbit vs. Tegmark

From: Patrick Leahy <jpl.domain.name.hidden>
Date: Mon, 23 May 2005 04:00:39 +0100 (BST)

On Mon, 23 May 2005, Russell Standish wrote:

>
> I think most of us concluded that Tegmark's thesis is somewhat
> ambiguous. One "interpretation" of it that both myself and Bruno tend
> to make is that it is the set of finite axiomatic systems (finite sets
> of axioms, and recusively enumerated theorems). Thus, for example, the
> system where the continuum hypothesis is true is a distinct
> mathematical system from one where it is false.
>
> Such a collection can be shown to be a subset of the set of
> descriptions (what I call the Schmidhuber ensemble in my paper), and
> has some fairly natural measures associated with it. As such, the
> arguments I make in "Why Occam's razor paper" apply just as much to
> Tegmark's ensemble as Schmidhuber's.

Hmm, my lack of a pure maths background may be getting me into trouble
here. What about real numbers? Do you need an infinite axiomatic system to
handle them? Because it seems to me that your ensemble of digital strings
is too small (wrong cardinality?) to handle the set of functions of real
variables over the continuum. Certainly this is explicit in Schmidhuber's
1998 paper. Not that I would insist that our universe really does involve
real numbers, but I'm pretty sure that Tegmark would not be happy to
exclude them from his "all of mathematics".

>
> Conversely, if you wish to stand on the phrase "all of mathematics
> exists" then you will have trouble defining exactly what that means,
> let alone defining a measure.
>

I don't wish to, but this concept has been repeated by Tegmark in several
well publicised articles (e.g. the Scientific American one). Again, lack
of mathematical background forbids me from making definitive claims, but I
suspect that it could be proved impossible even to define a measure over
*all* self-consistent mathematical concepts. In which case Lewis was right
and Tegmark's "level 4 multiverse" is essentially content-free, from the
point of view of a physicist (as opposed to a logician).


Paddy Leahy
Received on Sun May 22 2005 - 23:08:38 PDT