Re: White Rabbits, Measure and Max

From: Alastair Malcolm <amalcolm.domain.name.hidden>
Date: Sat, 17 Jul 1999 15:57:56 +0100

----- Original Message -----
From: Russell Standish <R.Standish.domain.name.hidden>
> Consider universes implemented by a UTM by way of concreteness. Then
> our regular universe corresponds to finite length programs that do not
> access the data beyond the finite bit position n. Now, the contrived
> universe, presumably consists of a similar program, but with a bug in
> it causing the program to process the "don't care" bits lying beyond
> the string. Now this contrived universe will have the same measure as
> the one we observe. (What is the ratio of correct programs to buggy
> ones that work well enough to support consciousness?)
>
> However, what will we see when these "don't care" bits are processed -
> flying rabbits, fairies, non-mendacious politicians, decaying protons,
> whatever. Most of the time, we won't even recognise it as being
> something wrong, it'll just be noise. When we do - eg the flying
> rabbit incident, there will be a lot of information involved - special
> bit patterns - that we recognise as being unusual.

This is a slight variant on how I interpreted your original post, and I have
to say that I like it. When I have considered this variation before (which I
think of as the 'bolt-on' variation: flying rabbits are added to the
K-specification of our universe), I have tended to come up with the
conclusion that because different flying rabbits can be
multiply represented along the infinite bit strings, they should eventually
dominate in all possible bit string combinations, even though they are
individually extremely improbable. Consider a case where flying rabbits are
possible in one in every 10^100 bit string segments, where each equal-length
segment is of length 10^24 bits. For the first 10^124 bits of our infinite
string there will be 1 flying rabbit universe per 2^(10^124) universes. But
in the second 10^124 bits there will be a different flying rabbit universe
for each 2^(10^124) universes as well (even though there are now 2^20^124
different combinations), nearly all of which will not already have a flying
rabbit of the first type. In the limit of an infinite length string, flying
rabbits will ultimately dominate. But this is NOT the case if there is an
infinite number of 'don't care' bits and a finite number of different
possible (visible) flying rabbits (as now seems to me more likely) -
effectively the flying rabbit segments are infinitely dispersed along the
string. Even for some cases of an infinity of visible flying rabbits, I
think a good case can be made for the aleph number being lower than that of
the total bit string itself. (I personally am not worried about TM
limitations here, not being a TM enthusiast.) Moreover I have a feeling that
this basic reasoning also applies to the 'full contrived universe'
variation, which is how I interpreted your first post, and also how I
presented the flying rabbit argument in the 'devil's advocate' thread.

Perhaps I could just briefly explain part of why I consider this problem
(and its resolution) important. I do not think we are justified in
automatically assuming that mathematical existence just *is* physical
existence (as Tegmark does), but the regularities in nature imply that at
least some of physical existence can be modelled by an abbreviated
mathematical structure (a TOE). If we then consider an all possible
universes approach (for well known reasons), then we can use Tegmark's
category 1b challenge to rule out all but a few candidates. The scheme I
prefer has loose connections with Kant's thing-in-itself, but applies
maximally to all possibilities. So our universe can be represented minimally
by the values of a set of parameters (equivalent to a K-specification), but
universes exist at least corresponding to all possible values of these and
other parameters (and it is not the case that they just *are* those
mathematical structures). Call this the mtii (maximalised thing-in-itself)
approach.

Certainly we can say from this that any mathematical structure that *can*
specify a universe does in fact do so, but whether there are entities other
than those that are completely mathematically specifiable I wouldn't like to
say - though I would hazard a guess that we wouldn't tend to think of them
as universes, if they did exist. However a mathematical structure could be
represented more than once, or a difference in formulation of two
mathematical structures that are equivalent may not be reflected in the
quantity of the universes they represent. A reasonable case can be made for
mathematical structures being at the basis of any measure under the mtii
scheme, though, at least for universes containing any form of
intelligent life. So, as far as I am concerned, the only two everything
hypotheses that I know of that have a sufficiently generic and deep
philosophical ground (that is, Tegmark's and mtii (apologies to UTM
enthusiasts here)) stand or fall by their response to the flying rabbit
challenge.

Thanks again to all of you have responded on this topic, and in particular
to Russell, who may just have come up with the solution!

Alastair
Received on Sat Jul 17 1999 - 08:17:43 PDT