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I always find the "finite number of atoms" argument a little misleading. Isn't it rather a question of how well we can measure things? If we could measure at infinite precision, one atom would be sufficient to encode all possible states we could dream of. I suppose quantum theory puts a lower limit on the attainable precision of measurements, but I don't know the details.

I must admit that since HTML+CSS3 requires clicks (at least in this implementation), I don't consider it to be really proven to be touring complete.

There are actually physical laws somewhere in thermodynamics that place an upper bound on the existence of information within a space. Oddly enough, the maximum information in a space is proportional to the surface area, not the volume[1]. Black holes attain this maximum, although I'm not sure if non-black-holes are capable of attaining it as well.

In a related note, Bell's Theorem (along with a few experimental results) demonstrate that no theory of (local) hidden variables can account for quantum theory[2]. This means that the limit is not just on our ability to measure the information in an atom. It literally doesn't exist for us to measure. Quantum mechanics is confusing =P.

[1] Specifically, the information measured in binary bits is bounded by the surface area divided by four. I'm not 100% sure what the unit of surface area is, but I believe it's Plank units.

[2] http://en.wikipedia.org/wiki/Bells_Theorem

We simply do not have enough information on the nature of reality to decide who is right here.

If space-time does turn out the be physically discrete at the planck length, and the limits of our measurements are actually reflecting the universe's true discontinuous nature, then this would imply that there would be a limit to how much state you could push into an atom.

Any real physicists please feel free to shoot me down in flames here. This is just my (plainly) limited understanding of the situation.

As I point out here (http://news.ycombinator.com/item?id=2302695), there is a difference between a formalized process for expressing computation being Turing complete, and implementing an actual Turing machine. The first is possible, and most general purpose programming languages are Turing complete. The second is impossible, for obvious reason.

Perhaps the confusion comes from the fact that the easiest way to prove a formalized process is Turing complete is to express a simulation of a Turing machine.

one atom would be sufficient to encode all possible states


You just need a very hot atom.

Haha :) It would still be finitely hot, though.

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