Re: Why our universe is open.

From: Russell Standish <>
Date: Tue, 22 Aug 2000 08:06:00 +1000 (EST)

Saibal Mitra wrote:
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> Although we now know for a very long time that the brain is a (very =
> complex) machine, we pretend as if we are somehow more than what a =
> machine ever could be. This bias will disappear as soon as there are =
> machines around that can pass the Turing test.
> This does raise interesting philosophical questions about consciousness. =
> Suppose we had a very powerful computer that allows us to simulate an =
> entire miniature universe, consisting of just one person living in a =
> prison. It is assumed that at least the brain of the person is simulated =
> in a realistic way. Using virtual reality techniques it would be =
> possible for me to visit this prisoner. The prisoner can, from time to =
> time, also visit us in the following way. At certain times the prisoner =
> is allowed into a room. In this room the computer simulates a virtual =
> reality apparatus. When the prisoner gets into the apparatus, he can =
> control a ``real=B4=B4 robot wandering in my room. This is thus virtual =
> reality ``the other way around=B4=B4. It would now be very difficult to =
> deny that the prisoner has consciousness.=20
> An interesting question can now be asked: Does the prisoner only exist =
> when the computer is simulating his universe, or does his universe exist =
> independently of our universe and simulating his universe simply means =
> that we can take look at his universe and even interact with him?=20
> If the latter is true then clearly all possible universes exist =
> independently of each other. We can then ask why we find ourselves in =
> this universe instead of the rather boring universe of the prisoner. I =
> think that this must follow from probabilistic arguments. It may be that =
> all universes are, in some sense, equally likely a priory. The =

The most logical a priori distribution is the Solomon-Levi, or
Universal Prior - see discussion in the everything list archives, or
Schmidhuber's paper.

> probability that we find ourselves in a particular universe would then =
> be given by an appropriate conditional probability. When we refer to our =
> universe we actually refer to a large class of universes, because we =
> don't have complete knowledge of our universe (we can only store a =
> finite amount of information in our brains). So, given the knowledge we =
> do have, we live in a large number of universes ``simultaneously=B4=B4, =
> and the number of ``equivalent=B4=B4 universes increases with its size. =
> We should thus ask for the probability that we live in any of the =
> equivalent universes. It is thus clear that ``our=B4=B4 universe is =
> infinitely more likely than the prisoner`s universe.=20

This is not actually the correct argument. The prisoner's universe
contains less information than ours, therefore ought to have higher
measure according to the universal prior. The trick to realise is that
most of the information in our universe is due to contingency - in our
universe we started with a very simple description of how a universe
should evolve (the Shroedinger's equation, lets say), and a simple
initial condition (a very small, very dense, very hot sphere of gas
let's say) and let the whole thing evolve. Darwinian evolution can be
considered to be a natural "Maxwell's Daemon", soaking information up
into the system that is evolving. Physics is also evolving in a
similar way, with the Anthropic Principle playing the equivalent part
to natural selection, and chance playing the part of variation.

The prisoner's universe, however, is likely to be highly arbitrary,
with many features added in by the programmer to make the environment
interesting. The features are not "compressible", in the sense of
arising from the natural dynamics of the system.

Hence the prisoner's environment is more complex (in a Kolmogorov
sense), therefore has lower measure in the space of universes.

I discuss these ideas in two of my papers "Why Occam's razor", and
"Evoltuon in the Multiverse", which you can get from my website.

> Interestingly this fits in well with observational evidence that our =
> universe is flat. From the arguments I gave above, you would expect that =
> the universe is spatially open, because such an universe has an infinite =
> volume. This infinite volume also cause me to exist in an infinite =
> number of places simultaneously in a single universe, because the =
> probability that somewhere an intelligent being emerges that has stored =
> in his brain the same information as in my brain is extremely small but =
> strictly larger than zero due to the finiteness of the amount of =
> information that can be stored in the brain. It would, of course, =
> necessarily be the case that this intelligent being is very, very =
> similar to me and that he lives on a planet which is very similar to the =
> earth.=20
> Now it would be reasonable to expect that an universe where the density =
> of ``copies=B4=B4 of me is larger is more probable. By increasing the =
> matter density of the universe I can increase the number of copies of =
> myself, but if the matter density becomes too large then the universe =
> would be spatially closed. Therefore it is reasonable to expect that we =
> live in a flat universe.=20
I was about to poohoo this idea when I realised there was a subtlety
to it. Presumably, you are talking about an ensemble of universes,
some open, some closed. Of interest is the measure of sentient beings
over this ensemble. I can see why an open universe should have greater
measure than a closed one, because a closed universe must only have a
finite number of sentient objects, compared with the countably
infinite number of such objects in an open universe. However, I don't
really follow your arguments as to why this measure should be maximised
in the flat universe case. A countably infinite number is the same as
a countable infinite number, regardless of matter density.

Also, you must be careful, as the closed universe can contain black
holes, whose interiors are complete universes in themselves. You would
need to ensure that the total volume of the closed universe,
_including_ all daughter universes was finite for the argument to
work. Similarly, you must assume that there is a particular "Mother"
universe that started the whole thing off, otherwise if there were an
infinite heirarchy of such parent universes than again the argument is


Dr. Russell Standish Director
High Performance Computing Support Unit, Phone 9385 6967
UNSW SYDNEY 2052 Fax 9385 6965
Room 2075, Red Centre
Received on Mon Aug 21 2000 - 15:00:51 PDT

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