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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

Date: Wed, 28 Jan 2004 23:24:26 -0500

At 1/27/04, Hal Finney wrote:

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

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