Re: Devil's advocate against Max Tegmark's hypothesis

From: Alastair Malcolm <amalcolm.domain.name.hidden>
Date: Tue, 6 Jul 1999 00:02:05 +0100

[Replies to Russell Standish, Bruno Marchal also below]

----- Original Message -----
From: Jacques M Mallah <mailto:jqm1584.domain.name.hidden>
> On Sat, 3 Jul 1999, Alastair Malcolm wrote:
> > If our world can be equated to a mathematical structure which is
> > related by the physical laws that are apparent to us, then it can also
be
> > a far more complex mathematical structure which explicitly specifies the
> > universe as it has evolved during our lifetimes (for example a phase
> > space specification of all the particle positions/momenta for a universe
> > coming into existence say in 1850, and happening to obey
> > classical/quantum-mechanical laws as required to convince us that the
> > universe does follow simple laws).
>
> Yes, but that structure would not implement any computations.
> Many of us are computationalists.
>
> > Now there would seem to be far more different mathematical structures
> > where this type of scenario occurs (but with sufficient deviation from
> > 'normality' such that we would notice - the odd white rabbit scuttling
> > across a ceiling, for instance, to reuse an earlier example), than there
> > is of the relatively simple mathematical structure(s) that science
> > implies underlies our phenomenal world. So statistically we should be in
> > one of these 'contrived' universes.
>
> In the case of typical 'junk' data, yes, but there would be no
> computations.

As a counter to the challenge to Tegmark's hypothesis, I am afraid I can't
see the relevance of this or the other statement above (a contrived
computation (or appearance of computation, if you prefer) can readily be
produced from a sufficiently complex mathematical structure, and it only has
to convince us that it looks like a computation), so I'll presume you are
responding from a different, computationally-generated-universe
(cgu)standpoint. Perhaps I could just clarify why, at my rather rudimentary
level of understanding, I don't find these (cgu) kind of ideas very
attractive (with one possible exception) - apologies if I am retreading old
ground:

Any cgu idea must fall into one of two exhaustive categories:

1. There is a required process of execution of programs which leads to the
existence of universes.

For this category, then clearly any program must be executed from a universe
other than the one (or more) that is produced by it. Where does this
'higher' universe come from? Schmidhuber implies a chain of universes, but
if there is an original universe somewhere, why can't it be this (our) one,
and forget the chain? Similarly, an infinite hierarchy of TM's solves
nothing, it just sweeps the problem under the carpet of infinity. [Note to
BM: this is where the turtles come in.]

2. There is no required process of execution of programs leading to the
existence of universes.

To retain any semblance of cgu, then it would seem that either
 a) The program(s) still specify the universes, but do not need to be
formally executed . . . but this cannot be the case, since without a
computer/TM to run on, a program can be no more than a string of bits (or
however it is encoded) - another TM could well generate a totally different
universe from the same bit string; or
 b) The bit strings specifying our, and other, universes in explicit detail
are in some sense already present - no execution of a program is necessary.
If the measure is applied on all these bit strings, then not only do we hit
the flying rabbit problem again, but we are also departing from a
computational scheme, since the input program and TM process become defunct.
But if the measure is on the input side (to obtain the advantages of simple
physics via non-functional code), how can the input be responsible for the
output if no execution of a program is to be posited?

This is why Tegmark's hypothesis seems to me to have more mileage in it than
a computational scheme, if a good response can be found to the challenge I
described in my previous post.

Russell Standish wrote:

<This issue was discussed in depth in the thread "Why physical
laws?". A possible solution relates to giving greater measure to items with
smaller description. see "unlikely universes" thread (Schmidhueber)
I think this is an important problem, and I suspect the answer comes
down to the same sort of reasoning as Occam's razor. I don't think it
has been adequately resolved yet, but also don't believe it is an
effective counter argument to Tegmark's thesis.>

As I have mentioned before, my DA challenge was specifically aimed at
Tegmark's hypothesis (though I have a horrible feeling I may have just got
myself embroiled in another one), and not Schmidhuber's - I wouldn't want to
quarrell with the solutions he mentioned to the flying rabbit problem as
applied to *his* hypothesis.

As regards Ockham's Razor, it is this principle itself that suggests the
ultimate ensemble theory, which in turn *results* in the flying rabbit
paradox, so it is difficult for me to see how Ockham's Razor or an
equivalent on their own could be used to circumvent it.

Bruno Marchal wrote:

<My answer was that I don't see how Tegmark can make this challenge
effective because the collection of mathematical structures is
not definable in mathematical terms.>

Don't we only need a rough idea of the relative measure of small samples of
these mathematical structures in order to pose the challenge? Surely it is
the case that any mathematical structure entirely confined to the
specification of a relatively simple interpretation of our universe (as
implied by current physical theories) must be of far smaller measure than
that of the myriad of 'flying rabbit' type universes? (The picture that I
have in mind here, though probably not really apposite, is of the relative
number of rotation states of a cube, and a dodecahedron.)

>Could you tell us if you agree that Schmidhuber "great programmer"
>approach
>should also met the flying rabbit challenge ?

Yes, I agree that it should, and moreover on the face of it appears to do
so.

>
>And could you explain more precisely the 'turtles all the way down'
>accusation against Schmidhuber Great programmer?

Please see my reply to Jacques Mallah above (Point 1.).


Thanks for all your replies, but despite rereading the threads you have
suggested, I am still looking for a clear solution to the flying rabbit
paradox challenge to Tegmark's hypothesis!
Received on Mon Jul 05 1999 - 16:22:30 PDT