AI and cognitive psychology rant (getting more and more OT - tell me if I should shut up)

[Stephen Horne]

On Tue, 28 Oct 2003 15:49:04 +0100, anton at vredegoor.doge.nl (Anton
Vredegoor) wrote:

>mis6 at pitt.edu (Michele Simionato) wrote:
>
>>A good rule of the thumb is "never believe anything you read and you don't
>>understand". Sometimes, you should not believe even what you think you
>>understand ...
>
>In Scientific American (I think it was the may 2003 issue) I read
>something about parallel universes. One idea goes like this (adapted
>to make it fit my brain).
>
>Suppose you're sitting in a chair in the middle of a virtual 2X2X2
>cube. Next imagine a cube filled with protons (or some even smaller
>particles) as tightly as possible. The difference between this cube
>and the cube you are sitting in is that in your cube some of the
>protons are absent. The cubes could possibly be represented by Python
>long integers [1], where the full cube would be a long with all bits
>set to one and different cubes would have some zero bits at
>corresponding positions.
>
>There can not be more different cubes than 2**(number of protons per
>cube) so in an infinite universe (or even in a big enough universe) at
>some distance from you a cube identical to the one you are occupying
>would exist, or else one would need a very good reason why the cube
>you are occupying is unique.

That has little to do with the many worlds interpretation of waveform
collapse. These 'universes' do not interact with each other in the way
that superpositions of particles do.

Actually, if you imagine that cube full of protons again, according to
quantum theory many of those protons may be in superposed states. That
is, a single proton may be in several states, including being in
several positions. 

How many states may a single proton have within that cube? Well, it
isn't just the number of combinations of possible superpositions of
states of protons. For example, the state where two superpositions
happen to be identical (indistinguishable state - think of polynomials
with repeating roots) but other superpositions have measurably
different states would have measurably different consequences to that
where there is only one occurence of each uniquely recognisable
superposed state for that proton. In fact, you can have an infinitite
number of states for that cube of space with only one proton in that
space by simply counting all possible sets of superposed states for
the proton.

Which means that the number of possible states of matter is not finite
even if we ignore the states where some superposed states of a
particular proton are inside the cube while others are outside it.

I hope you also realise that your cube, defined in space only, is not
sufficient to define a parallel universe. Each proton has momentum as
well as position, and a proton may well have an infinite number of
possible kinetic energy levels. The cube thus becomes a hypercube with
time as one dimension, and each proton is represented by a curve - not
just a single point position. How many curves can exist in that
hypercube, even for a single proton?

Even ignoring momentum, what about quantum uncertainty - just because
the current state of that cube is identical (and ignoring any
influence from surrounding cubes of space) the future states of
different instances of the supposedly parallel universe may play out
differently. We may well discover in future a more general model which
recovers perfect determinism, but given current evidence we cannot
assume that.

Finally, how can you assume that there is only a finite number of
possible positions of a proton within that space? A quick look at
relativity tells us that space is not like graph paper. Spacetime
itself may have different shapes, dependent on matter outside as well
as inside that cube.


There are, of course, important theories which measure the amount of
information in any region of spacetime - and the amount of information
turns out surprisingly small - but I am not convinced that the measure
is of all information in that region as opposed to, for instance, all
information that is accessible to an outside observer. Certainly there
is something rather odd going on which cannot be explained by proton
counting.


-- 
Steve Horne

steve at ninereeds dot fsnet dot co dot uk