Re: lost in the many worlds

From: Hal Finney <hal.domain.name.hidden>
Date: Fri, 30 Jan 1998 10:12:22 -0800

Wei Dai, <weidai.domain.name.hidden>, writes:
> I now think that I was probably wrong about this, but I still don't
> understand why. Suppose our administrator takes the universal wave
> function (which assuming the Everett Postulate never collapses during
> normal evolution), collapses it into a position eigenfunction according to
> the familiar probabilistic rules, and then examines the resulting position
> eigenfunction, treating it a sort of snapshot. Now if he just picks a
> random volume of space to look at, chances are he would see some
> unstructured interstellar gas. But with probability of about 2^-L, where L
> is the length of a complete uncompressed description of my brain (WDB),
> the volume of gas he sees would by coincidence turn out to have the same
> positional structure as WDB. If I'm to believe that I'm much more likely
> to be currently instantiated as a brain made of organic chemicals rather
> than of interstellar gas, it must be that the probability of finding the
> organic brain is much higher than 2^-L, which implies that it takes much
> less than L bits of information to find a description of WDB in the
> universal wave function. However I do not know how to derive this from the
> principles of quantum mechanics.

So, the idea is that there is some probability that your brain could
form spontaneously in intergalactic space, and that probability per
brain-volume would be approximately 2^-L?

One thing I note is that you have introduced the idea of an "uncompressed"
description of the brain, which is not clearly defined. Earlier you had
just asked about the information needed to describe the brain, without
reference to whether it was compressed or not. Probably there is no upper
limit on ways of writing a description of the brain in uncompressed form,
so L as described here is ambiguous.

For this particular case, you need to look at the actual physical
nature of the intergalactic medium in order to calculate the odds of it
spontaneously forming some structure. This will no doubt be related
to the complexity of the structure, but I'm not sure it would simply
be exponential in the length of a description of the structure. Or at
least you would have to set up your description language in a certain way.

For example, intergalactic space is composed almost entirely of hydrogen
atoms. The occasional carbon or oxygen is going to be very, very rare.
So the form of the description language would have to take that into
consideration.

Then there is the extremely low density, which is going to have to
increase by something like 30 orders of magnitude over the norm in
order to form your brain. Does that just mean you have to look at 10^30
volumes the size of your brain? I don't think so. You'd have to look
at a lot more than 10 brain-volumes to find one with a density ten times
the norm. I think there may be an exponential factor just based on
the density. (Sorry to be so vague; it's been a long time since I've
studied thermodynamics.) So somehow the length L would have to become
longer to reflect the higher density of your brain, which doesn't seem
like a natural way for a description to behave.

Hal
Received on Fri Jan 30 1998 - 10:28:38 PST