Cellular Automoata and the Universe

Well, the 'controversy' of "A new kind of science" has died away almost completely; which means it's the perfect time to write a column about it.

This will be extremely scatty, even by my standards - don't expect any of the segments to link to each other well; I'm trying to put down to paper something that I can't quite visualise as a single whole.

Brief Introduction

Cellular Automata are a simple kind of system. It comprises a grid (usually two dimensional, for ease of viewing) Each entry in the grid is a 'cell' which has a number of states. In the simplest simulations, a cell may have only two states 'alive' and 'dead' - either the box is filled in, or it is empty. More complex simulations sometimes add more states - again for convenience of viewing. (It may be easily proved that any such multi-state system can be emulated by a larger binary system)

Anyway. The important thing about CA systems is that they have only LOCAL rules. A cell may know about its neighbours (or possibly about cells a small distance away) - but it doens't know about EVERY cell in the grid. There is no way for a cell to know, for example, that EVERY cell in the grid is alive - it can only know that those it can see are alive.

Then each cell obeys rules based upon the state of itself and neighbouring cells - and from that decides what state to change to itself.

This may seem pretty useless - but as one of the original systems Conway's Game of 'Life' showed - from simple rules, remarkably comples and lifelike behaviour can arise.

The theory being espoused here is that the entire universe can be approximated by some such system - and that more work should therefore be done in this field.

Determinism and Focus

Right - first thing to get out of the way. Assuming that this theory is literally correct, and the whole universe can be expressed this way - then the universe is deterministic. Free will is an illusion, newton was right after all and so on and so on.

I intend to get around that 'problem' (and a few others) with the idea of focus. We already have an uncertainty principle - this says basically that you can never examine a system too closely.

If we suggest that the 'cells' of our system are much smaller than quarks and that indeed, a quark is some analogy of a glider then you can see that even given the exact position of the quarks you cannot know how the underlying structure will evolve.

Inserting this division of scale also allows us to fudge around the problems of discreteness in space - two light wavicles (or whatever) can occupy the same point in space - but do so by their internal structures interacting.

Sadly, this is a fudge.

Discrete Time

The whole idea falls down if time is not quantised; since these systems evolve in discrete time steps. It also requires an 'arrow of time' (see book of same name) in that somehow the cells must know to run their rules forwards, not backwards.

Luckily, time has to be quantised if space is to be (otherwise you could ask 'where is this particle when it is halfway between the time it is at one cell, and the time that it is at the next) - so we merely have to justify the quantisation of space. Sadly, I can't justify this assumption - it will have to stand as an assumption.

Wavicles

Wavicle (wave particle duality) behaviour can be well explained by this system. If we postulate a photon as having no discrete existence of its own, but instead to be a pattern rippling its way through a grid then we can see how (for example) interference patterns can evolve even though the (seeming) second source of interference is blocked.

You can also conjure up nice mental images of what a particle and a field would look like, and how come they interact.

What is Life?

So - let's assume this theory is correct, and start trying to use it. We know that there are many possible sets of rules that could be used - some of which produce 'lifelike' universes, and some of which produce 'sterile' universes. Instead of asking 'how common is life on other planets?' we can ask 'how common are universes which support life?' And the answer is.. quite a lot actually.

Most sufficiently complex rules form highly active grids. Worryingly though, they seem to be arranged into families of rules. The anthromorphic principles seem to still be in the balance here.

Parting Shot at Determinism

Even if you CAN get at the precise starting conditions - there may be no way to use that knowledge. Theories of computability clearly show that in any sufficiently complex logical system some problems are 'undecidable' - that is, they never run to any completion state. Further, there is no general way to determine in advance whether or not a problem is of this type (obviously, if you run it to completion it was of the other type - but if it's still running you cannot know whether it will eventually stop or not)

This is often paraphrased as "The quickest way to determine the function of a program is to run it" And this may be the case with the universe. Which would be good.

You got here?