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

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