Re: My So-Called Universe

From: Wei Dai (weidai@weidai.com)
Date: Thu Aug 21 2003 - 15:16:38 MDT


On Thu, Aug 21, 2003 at 04:57:01PM +1000, Damien Broderick wrote:
> http://aca.mq.edu.au/PaulDavies/Multiverse_StanfordUniv_March2003.pdf

Quoting from that paper:
> It would be instructive to quantify and compare the degree of credulity we
> might attach to various competing multiverse and theological models, using
> a formalization of Occamís razor in the form of algorithmic information
> theory.
> [...]
> I will make an even stronger claim. I believe that naÔve deism and the
> general multiverse concept will turn out to be of equivalent complexity
> because they are contained within each other.

Unfortunately Paul Davies does not know his algorithmic information
theory. It's not true that two objects have equivalent complexity if they
are contained within each other. Here's a simple counterexample.

Consider the shortest program that prints out an infinite repitition of
the first googolplex bits of pi. This program is pretty small, so the
resulting infinite binary string X has a low algorithmic complexity. Now
pick a random incompressible number with a google digits, and call it y.
Consider the infinte binary string Z, which is X with the first y bits
removed. X and Z both contain each other, but the algorithmic complexity
of Z is much larger, because the program that prints out Z will have to
contain an encoding of y.



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