The physical process is simply that the atoms in the bar of iron start in one Turing machine state, obey the laws of physics, and end up in another Turing machine state.
I don't see how this addresses the key point -- those aren't random distinct states; there's an explicit description of how one state transitions to the next. That's part of the definition of the Turing machine!
If you could describe a mapping from the state of your iron bar to a Turing machine's state, such that the bar correctly transitions from one machine state to the next, then yes, it is a computer! Although as others have noticed, you'd need a ludicrously large and complex mapping; the infinitesimal tail would be wagging the infinite dog. At that point you could certainly argue that the computation is really happening in the mapping itself.
> there's an explicit description of how one state transitions to the next. That's part of the definition of the Turing machine!
A Turing machine does indeed describe which states the machine transitions between (by its definition). So, it might say that if it reads a "1" and is in state "A", transition to state "B".
However, crucially, a Turing machine does not specify the physical mechanism by which this state transition occurs. You just have to enumerate the rules for state transitions. The definition of a Turing machine says nothing about whether or not these states are voltages, the locations of rocks, or the magnetic moments of iron atoms. Nor does it say whether the transition is being implemented by a CPU or a human being manipulating rocks.
So the only rigorous way you can make a connection to a physical computer is to just identify a mapping from physical states to Turing machine states, and observe whether or not it performs all the state transitions correctly. If it reads a "1" and is in state "A", did it go to state "B"? If it did, it is behaving as a Turing machine. If it did not, it is not behaving as a Turing machine.
> At that point you could certainly argue that the computation is really happening in the mapping itself.
The mapping is fixed, so I don't see how it can do any computation. Others have objected to the fact that the mapping in the iron bar is obviously extremely complicated, but this strikes me as ultimately being an objection that this doesn't "feel" like computing.
But as a counterexample, you can do computations under homomorphic encryption. Suppose you have encrypted a computer program that sorts a list using homomorphic encryption. You hand it to me to run on my CPU. When I observe the voltages of the CPU, they will appear completely random to me. Only if I have the key can I provide the correct (complicated) mapping from physical states to Turing machine states and interpret what is going on on the CPU. But if we reject "complicated" mappings as not being "real" computations, then you're forced to say that computation under homomorphic encryption isn't "really" computation --- even though you've handed me a program to sort a list, it ran on my machine, and it handed you back a sorted list.
I think you’re skipping over one or two crucial steps there; let me try to put my finger on it.
The key feature of a universal Turing machine is that it can perform any computation, if fed the right program.
In your thought experiment where you’re mapping the internal state of an iron bar, to claim it’s a valid mapping to a Turing machine, it must be possible to feed in any program, after the mapping has been defined. Otherwise it’s not a universal machine.
You are mapping a well-defined structure into essentially a block of random numbers -- a one-time pad. You can only perform “any” computation that way if you map the full execution trace of the machine onto the random block. But that way, the computation occurs before the mapping is defined. That’s what I meant by “the computation is really happening in the mapping itself”.
The homomorphic encryption scheme is different, because while it looks random, it’s generated by a well-defined and reversible process. So I can use a mapping of bounded complexity to inject any program, and in principle to step through its execution.
> it must be possible to feed in any program, after the mapping has been defined.
This is absolutely correct and gets to the heart of it. We define a mapping and we can imagine even setting some of the spins of the atoms in the bar to input a particular "program." Then we sit back and watch the spins randomly flip and see if they correspond to what a universal Turing machine would do.
The reason that a hot iron bar in practice is not a computer is that there is no way we can easily find the correct mapping before we observe the bar. The process of finding this mapping will take more work than the computation itself. (I think this is what you mean in saying "the computation is really happening in the mapping itself.") So for our purposes it's useless for performing any computations. Nevertheless, some mapping from the bar's states to a Turing machine executing the program we've given it exists.
This is why this is different for the case of consciousness. Because consciousness exists independent of whether or not we're aware of it, it doesn't matter whether or not we can find this mapping beforehand. It just matters that such a mapping exists.
It would be different if I made the claim that the iron bar is sorting a list. I might say, "there exists a mapping of the states of the iron bar to a Turing machine running quicksort. Therefore the iron bar is sorting a list." The appropriate response would be "So what? If I consider all random permutations of the list, obviously one of them will be sorted --- but how does that help me find it? It takes me the same amount of work to find this mapping as it does to sort the list."
But if we are to say that consciousness is fundamentally a computational phenomenon, it doesn't matter if you find the mapping or not --- it exists independent of you.
I don't see how this addresses the key point -- those aren't random distinct states; there's an explicit description of how one state transitions to the next. That's part of the definition of the Turing machine!
If you could describe a mapping from the state of your iron bar to a Turing machine's state, such that the bar correctly transitions from one machine state to the next, then yes, it is a computer! Although as others have noticed, you'd need a ludicrously large and complex mapping; the infinitesimal tail would be wagging the infinite dog. At that point you could certainly argue that the computation is really happening in the mapping itself.