Re: Variations in measure

From: <hal.domain.name.hidden>
Date: Wed, 19 Dec 2001 09:39:09 -0800

Wei writes:
> If you think about it more, I think you'll realize that the greater number
> of observer-moments observing flying rabbits or similar happenings can't
> make up for the much smaller measure of each such observer-moment.
> Unfortunately right now I can't find a way to easily articulate the
> reasoning behind that conclusion.

Here is an example. Suppose we had a universe which was a CA system
like Conway's Life game, but more complex. It still has a fairly
simple program to represent its functions and so will have generally
high measure.

Now suppose we modify that program to be, "follow the normal rules except
at position X, always set the cell to 0". This represents a "flying
rabbit" universe, one which has relatively simple laws of physics but
where there is an exception.

If the universe is very large, then to specify X will take a large number
of bits. Hence the flying rabbit universe program is much larger than
the simple universe program, and its measure is much less. This is the
explanation I accepted for why we are not in a flying rabbit universe.
(I am assuming the universal distribution as a measure, where the measure
of an n-bit minimal program is 2^(-n).)

However if you consider all possible universes of this type, that is,
all possible values of X, then there are 2^n of these if X is n bits
long, exactly countering the loss in measure due to the size of X.
The collection of this kind of flying rabbit universes has only modestly
less measure than the simple universe. The only decrease is due to the
size of the "except at position" and "set to 0" clauses, which might be
only a few bits long.

And this is only one possible kind of exceptional universe. If we
consider the various other special-case exceptions to the normal rule
then the collective measure of all of these will come even closer to
the simple case.

This suggests that the simplicity explanation against flying-rabbit
universes is not strong, because the total collection of flying-rabbit
universes is close in measure to the simple universe to which they
rerpesent exceptions. That's the problem as I see it.

Hal
Received on Wed Dec 19 2001 - 09:41:33 PST