The Turing machine doing the simulating does not experience pain, but the human being being simulated does.
Similarly, the waterfall argument found in the linked paper seems as though it could as-easily be used to argue that none of the humans in the solar system have intelligence unless there's an external observer to impose meaning on the neural patterns.
A lone mathematical equation is meaningless without a mind able to read it and understand what its squiggles can represent, but functioning neural patterns which respond to available stimuli causally(/through reliable cause-and-effect) are the same whether emboided in cell weights or in tape states. (So, unless one wishes to ignore one's own subjective consciousness and declare oneself a zombie...)
For the actual-versus-potential question, I am doubtful regarding the answer, but for the moment I imagine a group of people in a closed system (say, an experiment room), suddenly (non-lethally) frozen in ice by a scientist overseeing the experiment. If the scientist were to later unfreeze the room, then perhaps certain things would definitely happen if the system remained closed. However, if it were never unfrozen, then they would never happen. Also, if they were frozen yet the scientist decided to interfere in the experiment and make the system no longer a closed system, then different things would happen. As with the timestream in normal life, 'pain' (etc.) is only said to take place at the moment that it is actually carried out. (And if one had all states laid out simultaneously, like a 4D person looking at all events in one glance from past to present, then 'pain' would only be relevant for the one point/section that one could point to in which it was being carried out, rather than in the entire thing.)
Now though, the question of the pain undergone by the models in the predicting scientist's mind (perhaps using his/her/its own pain-feeling systems for maximum simulation accuracy) by contrast... hmm.
I recently read Scott Aaronson's "Why Philosophers Should Care About Computational Complexity" (http://arxiv.org/abs/1108.1791), which has a wealth of interesting thought-food. Having chewed on it for a while, I've been thinking through some of the implications and commitments of a computationalist worldview, which I don't think is terribly controversial around here (there's a brief discussion in the paper about the Waterfall Argument, and its worth reading if you're unfamiliar with either it or the Chinese room thought experiment).
That said, suppose we ascribe to a computationalist worldview. Further suppose that we have a simulation of a human running on some machine. Even further suppose that this simulation is torturing the human through some grisly means.
By our supposed worldview, our torture simulation is reducible to some finite state machine, say a one tape turing machine. This one tape turing machine representation, then, must have some initial state.
My first question: Is more 'harm' done in actually carrying out the computation of the torture simulation on our one tape turing machine than simply writing out the initial state of the torture simulation on the turing machine's tape?
The computation, and thus the simulation itself, are uniquely specified by that initial encoding. My gut feeling here is that no, no more harm is done in actually carrying out the computation, because the 'torture' that occurs is a structural property of the encoding. This might lead to perhaps ill-formed questions like "But when does the 'torture' actually 'occur'?" for some definition of those words. But, like I said, I don't think that question makes sense, and is more indicative of the difficulty in thinking about something like our subjective experience as something reducible to deterministic processes than it is a criticism of my answer.
If one thinks more harm is done in carrying out the simulation, then is twice as much harm done by carrying out the simulation twice? Does the representation of the simulation matter? If I go out to the beach and arrange sea shells in a way that mimics the computation of the torture, has the torture 'occurred'?
My second question: If the 'harm' occurring in the simulation is uniquely specified by the initial state of the Turing machine, how are we to assign moral weight (or positive/negative utility, if you prefer) to actually carrying out this computation, or even the existence of the initial state?
As computationalists, we agree that the human being represented by the one tape turing machine is feeling just as real pain as we are. But (correct me if I'm wrong), it seems like we're committed to the idea that the 'harm' occurring in the torture simulation is a property of the initial state, and this initial state exists independent of us actually enumerating that state. That is, there is some space of all possible simulations of a human as represented by encodings on a one tape turing machine.
Is the act of specifying one of those states 'wrong'? Does the act of recognizing such a possible space of encodings realize all of them, and thus cause an uncountable number of tortures and pleasures?
I don't think so. That just seems silly. But this also seems to rob a simulated human of any moral worth. Which is kinda contradictory--we recognize that the pain a simulated human feels is real, yet we don't assign any utility to it. Again, I don't think my answers are *right*, they were just my initial reactions. Regardless of how we answer either of my questions, we seem committed to strange positions.
Initially, the whole exercise was looking for a way to dodge the threats of some superintelligent malevolent AI simulating the torture of copies of me. I don't think I've actually successfully dodged that threat, but it was interesting to think about.