Some thoughts on Tegmark's paper

From: Christopher Maloney <>
Date: Thu, 03 Jun 1999 21:59:29 -0400

As a recent member of this list, I'm slowly getting up to
speed with all the reading material. I've been reading the
archives of this list, and am up to about article 150 (out
of about 650!). I'll refrain from posting on old discussions
until I've finished that, as perhaps the old issues I feel
the urge to post about have already been resolved.

Meanwhile, here are a few thoughts on Tegmark's paper. This
is about 1/2 of the review that I'm writing on it (I always
review these sorts of things for my own purposes anyway).

This was an excellent paper, which effectively explicated many of the
ideas I've been formulating over the last fourteen years. The
fundamental principle put forth is the Principle of Plenitude, that
all mathematically consistent structures exist. Basically, he makes
the statement that mathematical existence is the same as physical

He introduces the acronym SAS (self-aware substructures) for
conscious entities within a mathematical structure. This is fine by
me, but Sarah (my wife) didn't know what to say when I called her my
favorite self-aware substructure.

The initial defense of this basic principle is well presented. He
presents four possibilities, the first three of which are lumped

  1. The physical world is completely mathematical
    (a) Everything that exists mathematically exists physically
    (b) Some things that exist mathematically exist physically,
        others do not.
    (c) Nothing that exists mathematically exists physically
  2. The physical world is not completely mathematical

There is not much that can be said about choice number 2, that the
physical world is not mathematical. So this paper does not even
attempt to argue that point. I, on the other hand, am going to have
to address it head on if I'm going to direct my book towards
non-scientists. I think most non-scientists would not agree that the
world is mathematical. I think that belief reduces to materialism,
versus mysticism.

1c. can be dispensed with instantly, if you agree with Descartes that
"I think, therefore I am". I don't know if any philosophers have
seriously attempted to refute the existence of something. I wouldn't
buy it, anyway.

So that leaves the choice between 1a and 1b. He asks the poignant
question which I've read elsewhere: why would some possible
structures exist but not others? The best defense along these lines
comes in his footnote number 16, where he describes that the entire
universe could be shown to be isomorphic to a small set of data that
describes its initial conditions and its mathematical laws. This
data could probably fit on a CDROM. Now, do you really need the
CDROM in order for that universe to exist? I think he got this
argument from Physics of Immortality, by Tipler.

Section II of the paper categorizes mathematical structures, thus
putting the phrase "all logically possible universes" on a firmer
footing. This presentation was concise and fun. Interestingly, he
doesn't even need to keep the idea that the mathematical structure be
free from contradiction. Actually, and mathematical structure that
allows a contradiction immediately reduces to a trivial thing in
which all statements are provable theorems.

He made one statement, that "mathematical structures are 'emergent
concepts'", that I'm not sure I agree with. I think that I probably
don't understand what he means by this statement, but it seems to me
that mathematical structures are fundamental.

Chris Maloney
"Knowledge is good"
-- Emil Faber
Received on Thu Jun 03 1999 - 19:42:51 PDT

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