Re: Infinite universe

From: Eliezer S. Yudkowsky (
Date: Sun Apr 27 2003 - 18:16:00 MDT

Ben Goertzel wrote:
>>> Now, we may invoke Occam's Razor ;) If I'm given an equivalence
>>> class C of universes, all of which are pragmatically
>>> indistinguishable to me, I'm going to assess the plausibility of a
>>> universe in C in terms of its simplicity. Simpler universes in C
>>> are more plausible. The universes with the hypothetical aliens in
>>> it are going to be rated relatively implausible, because the aliens
>>> fail the Occam's razor test -- they are extra elements, which make
>>> the hypothetical universe more complex without adding any new
>>> testable properties.
>> On the contrary, as Tegmark points out, they make the universe more
>> simple. The integer 398,745,842,209,487,873,767 contains more
>> information than the set of all integers.
> Well, that depends on your definition of "information"
> If you define "information content" as "Kolmogorov complexity" you may
> be right...
> But I think that is a flawed definition...

We were speaking of Occam's Razor, weren't we? If the information content
*relative to Occam's Razor* and the question of the "simplest hypothesis"
is to be measured in anything other than the Kolmogorov complexity, I
think Messieurs Solomonoff and Hutter would wish to know about it. I
certainly don't think the "amount of pattern present" is the right
criterion for Occam's Razor! We want the simplest explanation, not the
most boring description.

> Anyway, I think it's OK to maintain all these hypothetical universes,
> but one needs to maintain a probability distribution over them, and one
> then has a question of the "prior distribution". Is the a priori
> probability of a universe calculated using the solomonoff-levin
> measure?

If I knew *that*, Ben, I'd have solved my second hard problem and found
the One True Prior.

Eliezer S. Yudkowsky                
Research Fellow, Singularity Institute for Artificial Intelligence

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