Re: Is the universe computable

From: Kory Heath <kory.heath.domain.name.hidden>
Date: Wed, 28 Jan 2004 23:24:26 -0500

At 1/27/04, Hal Finney wrote:
>One way to approach an answer to the question is to ask, is there such
>a CA in which a universal computer can be constructed? That would be
>evidence for at least a major prerequisite for conscious observations.
>Do you have any examples like this?

In my opinion, computation universality is the *only* prerequisite for the
possibility of SASs, so I agree that the correct question to ask is "can a
CA with bi-directional time be computation universal?" I think that the
answer is almost certainly "yes". Let me explain why.

First, lets get a really clear picture of what we're talking about. I want
to consider a CA with only 2 spacial dimensions, because I find it easy to
picture the resulting 3D block universe. (It's too hard for me to picture
the 4D block universe that results from a 3+1D CA.) Lets imagine that the
spacial planes of this CA are stacked on top of each other, so that the
block universe looks like a tall tower, with the time dimension being the
"up" and "down" directions.

Now, the state of any particular cell of this block universe is determined
by the 3x3 square of cells directly below it, as well as the 3x3 square of
cells above it. For the rest of this discussion, lets refer to any
particular chosen cell as the "center cell", and the 18 cells below and
above it as the "neighborhood". For every possible combination of states of
those 18 cells, the rules of the CA dictate what state the center cell must
be in.

Now, lets imagine that the cells in this particular CA have three possible
states - lets call them "black" (empty), blue, and red. Lets set up the
rules of the CA in the following way. First of all, lets consider a "center
cell" whose neighborhood contains nothing but blue cells and empty cells.
Lets define our CA rule so that, in such a case, the state of the center
cell will either be blue or black, and this will be determined only by the
3x3 square of cells below it. In fact, lets go ahead and use Conway's life
rule here. So, if the lower 9 cells are all blue and the upper 9 cells are
any combination of blue and black, the center cell must be black. And so on.

Now lets imagine the exact same thing for the red cells, except this time
the state of the center cell is determined by the 9 cells *above* the
center cell. For any 18-cell neighborhood that contains *only* red cells
and black cells, the center cell will either be red or black, as determined
by the upper 9 cells.

Basically, what we have so far is a universe which contains blue "matter"
which moves "forward" in time (i.e. upwards along the tower), and red
"anti-matter" which moves backwards in time (downwards along the tower).
Each kind of matter, in isolation, will follow the old familiar rules of
Conway's life. If you were to "grow" an instance of the universe containing
only red matter or only blue matter, it would be indistinguishable from
Conway's life. And of course, we know that Conway's life is computation
universal. So this universe is capable of containing SASs.

Now, of course, we need to define what happens when matter and anti-matter
interact. In other words, for every possible combination of 18 neighbors
that contains both red and blue cells, we need to specify what the state of
the center cell should be. It should be clear that there is a Vast number
of possibilities here, each representing a unique universe. We can consider
the simplest possible rule, which is that the center cell is always empty
for any neighborhood which contains both red and blue cells. Perhaps under
that rule, matter and anti-matter will tend to obliterate each other. I can
imagine a whole range of other possible rules, some of which cause red and
blue gliders to bounce off of each other, etc. Clearly we can imagine
universes which contain large, isolated chunks of blue matter or red
matter, and those portions of the universe would be capable of containing
SASs. We can imagine stray red gliders occasionally wandering into realms
of blue space, and vice-versa, causing subtle changes, but not necessarily
destroying any of the SASs there. It seems to me that this is enough to
show that it must be possible for CAs with bi-directional time to contain
universal computation, and therefore, potentially, SASs.

After saying all of this, I'm realizing that I don't really need to
consider these bi-directional CAs to make the original points I was trying
to make. I can just as easily consider a "normal" CA like Conway's life (or
some other hypothetical CA that's more conducive to life). We can still do
the trick of running through all the possible "block universes" of a given
size, and discarding all of those that don't represent a valid evolution of
the rule in question. If our universes are big enough, some of the
remaining ones will contain patterns that look like SASs. Are these
patterns really conscious? At what point in the testing process did they
become conscious? And so on. However, it does sort of tighten the screws on
the question to recognize that there are some kinds of universes which
can't be computed in the "normal" way at all.

-- Kory
Received on Thu Jan 29 2004 - 00:29:51 PST