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Hello.

I am new to the game of life. So some things that I will say may be inaccurate.

This question is not specific to Conway's Game of Life. It concerns any two-state cellular automaton, two dimensional or three dimensional, using either the Moore neighborhood or the von Neumann neighborhood.


I heard that a lot of people believe that our universe may be a cellular automaton, and that there were many similarities between cellular automata and our universe.

One of them is the fact that, both in cellular automata and our universe, there is a maximum speed: the speed of light.
But I don’t find this very convincing.

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The speed of objects in cellular automata seems to be different than the speed of objects in our universe:

In cellular automata, an object can propagate at the speed of light either:
- horizontally or vertically if the von Neumann neighborhood is used
- horizontally, vertically or diagonally if the Moore neighborhood is used

But in our universe, an object can propagate at the speed of light in any of infinitely many directions.

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Distances also seem to be different in cellular automata:

Suppose we chose two random cells: the first has coordinate (x , y) the second has coordinate (x+a , y+b).

In the von Neumann neighborhood, the distance between those cells is: a+b.
In the Moore neighborhood, the distance between those cells is: max(a,b)
In our universe, the distance between those cells is: sqrt(a^2 + b^2)

And we have:
a+b >= sqrt(a^2 + b^2) >= max(a,b)
d(Neumann) >= d(universe) >= d(Moore)

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Suppose we had two objects in the center of a 7x7 grid, who will race to the edge of the grid.
Both start at the same time, and both have maximum speed (the speed of light).
But they take different paths (red and greens arrows).



In the Moore neighborhood, they would both reach the edge at the same time.
In the von Neumann neighborhood, the object which took the red path would reach the edge 2 times sooner.
In our universe, the object which took the red path would reach the edge sqrt(2) = 1.414 times sooner.

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In our universe, the set of points that are all at the same distance from a given point is a sphere.
In the Moore neighborhood, the set of points that are all at the same distance from a given point is a cube.
In the von Neumann neighborhood, the set of points that are all at the same distance from a given point is an octahedron (the dual of the cube).

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So I don’t really see where all the similarities are. I see only inconsistencies and contradictions.
It seems to me that the theory that our universe is a cellular automaton is completely impossible.

Omega Force wrote:Distances also seem to be different in cellular automata:

If a pattern in Life traversed a pseudorandom path and if distances between cells in Life were judged by the probability of the top left corner of the pattern moving from one cell to another, then this would apply.

By the way, shouldn't this be in General Discussion?

Well, it could be a continuous CA, like this. This still preserves the Euclidean nature of the universe.

To make the argument even stronger. On NxNxN grid there is K^N^3 possible states (where K is number of possible states in CA). If each state defines single direction for some directional glider, then stars that we see, would have very specific photon with very unique directional "properties". Except the fact that in this scenario we will require each photon to be built from hundreds of special "state elements", it would be very hard to explain the simplicity and the symmetry of photon behavior in every direction. Something like simple mirror would be pretty hard to construct.

All known unidirectional examples which hold also a simplistic and spontaneous properties are at the least random and usually continuous.

The assumption that our universe is discrete CA is just unnecessary complication. Adding one simple assumption of continuity solves so much with so little effort, that I don't see any reason to assume our universe is discrete CA. Of course maybe it's possible to show some VERY complex CA that has a unidirectional and same-velocity glider collection in each direction, but my question is why? why work so hard to prove so little, when you can just switch the assumption and prove so much with so little?

My main point is that someone who was so caught in CA world, though that our world is also CA based. It's just the nature of our mind to overestimate out current field of research.

On the other hand it could be shown that all current physical knowledge can be simulated in continuous CA (where the rules of the CA are simply the partial differential equations governing the physical laws).