[JoachimSchipper]

Wolfram has - correctly - noted that complexity can arise from simple systems (think Conway's Game of Life, but even simpler - Wolfram is into one-dimensional equivalents). This is, he says, akin to how many biological systems work (e.g. individual cells/neurons are pretty simple, but a human is very complex).

He also - correctly - observes that the explosion in computational power afforded by modern computers make certain scientific investigations possible that were previously infeasible (e.g. the proof of the four-colour theorem relying on exhaustively testing some 1800 possible scenarios, or numerical simulation of some very complex phenomena).

He then combines these two passions of his and asserts that therefore, computation based on simple systems gives insight into the secrets of life, the universe, and everything.

[corruption]

I can understand that position. If he's correct, it would seem like a small task to search the computational landscape and find automata that predict biological behavior or physics systems better than current models. Is this his approach? I don't see many (any?) papers like this in any of the fields I'm involved in - so has it been successful?

[wwalker3]

It's harder than you might think to model real physics with a cellular automaton.

Cellular automata are simulated on regular grids of cells, which gives them anisotropic (direction-dependent) behavior. For example, moving patterns in most automata can only travel in certain preferred directions (like gliders in Conway's game of life). And patterns that can move in multiple directions usually travel with different speeds in each direction.

In the real world, we don't observe any anisotropy in space, so none of the cellular automata I've seen proposed up to this point can model real physics, even in principle.

Lattice gas automata use hexagonal grids instead of square grids to alleviate this problem somewhat, but the anisotropy never really goes away, it's just reduced.

[maxharris]

NKS covers a lot more than just 1D or 2D cellular automata. See http://www.wolframscience.com/nksonline/section-5.5 and beyond.

[wwalker3]

You're right, NKS does cover more than cellular automata, like network systems (as your reference shows). But all the examples Wolfram gives of network systems have the same anisotropy problem as a cellular automaton. He uses mostly hexagonal grids for his network systems, which are better than square grids, but still not isotropic.

Wolfram doesn't give even a simple example of how two particle-like structures might repel or attract each other in an isotropic fashion in a network system (or any other system in NKS). That doesn't prove it's impossible, but if it is possible neither Wolfram nor anyone else seems to have any idea how to even get started.

[thisrod]

Can't you get rid of the grid, and connect the cells randomly? I have an notion that Feynman did that, but I don't remember where I heard about it.

[wwalker3]

That might very well fix the anisotropy problem (I haven't seen it done yet, but it sounds reasonable). However, that leaves you with another problem -- how do you create a stable particle-like pattern that can travel over a randomly-connected grid of connections without disintegrating :) Something like a Game of Life glider will explode if it hits a differently-connected area of the grid.

But say you solve that problem too -- there are many more problems after that. How do you encode the other properties of a particle like mass, charge, spin and momentum into this pattern? How can patterns attract and repel each other at long distances like real particles do?

These problems are probably all solvable, but my point to the original poster was that it's harder than it seems at first, and it's not something that's amenable to a simple search of the state space of possible automata.

[JoachimSchipper]

That seems to be the approach he's advocating, yes. As to its success - well, you don't see many (any?) papers like this...

If you are interested in this, go read "Gödel Escher Bach". It brilliantly explores this complexity-from-simplicity theme and the consequences of various viewpoints. E.g. you can easily observe/guess whether someone likes to eat curry; however, deriving this from the atoms making up said person is utterly infeasible.