[c1ccccc1]

If a box of gas (or a bar of iron, or a meteor shower) is capable to doing arbitrary computations, then go ahead and use a box of gas to factor some big numbers. The gas has 10^23 atoms that are all colliding with other atoms extremely often, so the amount of computing power available should be vastly greater than our current capabilities and it should be possible to factor correspondingly larger numbers.

Of course, any real-life attempts to use a box of gas to do such computations will fail. What's missing is the enormously complicated mapping between the starting and ending states of the gas, and the inputs and outputs of the factoring problem. This mapping is not just a matter of mapping bits in a local way into positions of gas atoms, but requires incredibly non-local dependencies between components. Interpreting the position of just a single atom in the gas requires knowing what pretty much all the other atoms in the gas are doing as well. If you had to actually compute that mapping, it would be about as difficult as both both simulating the gas's dynamics, and factoring the number.

At this point, a reasonable person would probably start to suspect that the actual factoring calculation is being shoved into the interpretation of the inputs/outputs of the system, and that the box of gas itself is not doing any calculations at all. Indeed, suppose that rather than letting the gas sit for a time t equalling perhaps a few seconds in order to do its computation, we instead let t=0. In this case, that atoms don't move at all during the "computation", but by clever mapping of inputs and outputs, we can still interpret this as "factorizing the number". Clearly the actual computation is happening in the "mappings" not in the gas.

[puffoflogic]

So I take it you agree with TFA, or at least the relevant part? "The cleverness is in the interpretation" is essentially the same argument as "the computer and its information are in the eye of the beholder".