Consider the curious habits of the Sphex wasp. She lays her eggs underground, then flies off to get a cricket, which she paralyzes and places in the burrow for the hatchlings to eat when they emerge. In doing so, she follows a strict routine: after dragging her prey to the burrow, she goes inside to check on the eggs, then comes back out and finishes the task of dragging the cricket inside. Now, if some devious human moves the cricket away from the entrance to the burrow while she is inside checking on the eggs, she comes out, drags the cricket to the entrance again, and once again goes inside the burrow to check on the eggs.
If again the cricket is removed a few inches while the wasp is inside, once again she will move the cricket up to the threshold and re-enter the burrow for a final check. The wasp never thinks of pulling the cricket straight in. On one occasion this procedure was repeated forty times, always with the same result.
(Wooldridge, quoted in Dennett, Elbow Room, p. 11.)
The first thing to note about the strange behavior of Sphex is that this is not a case of an agent doing the exact same thing under the exact same microscopic conditions. It doesn't matter if the experimenter moves the cricket three inches or four, the "same behavior" is repeated. And by "same behavior", we don't mean the microscopically exact same behavior, rather we mean the same general class of behavior. This is, I think, a much more interesting question than the question of whether we would do the exact same thing under the exact same conditions. Is there some general class of conditions under which I, as a human, would necessarily produce the same general response? If so, this is a more serious threat to free will than the possibility that I would do the exact same thing under the exact same conditions.
What is so striking about Sphex is the mindless predictability of her behavior. She apparently never stops to think, "Hey, didn't I just do this? Do I really need to do it again?" She is apparently pre-programmed to execute a series of steps. If those steps are interrupted, the series must be re-started at the point of interruption.
Are humans at all sphexish? Are there circumstances under which we will mindlessly repeat a certain behavior? We seem to be exempt from such behavior because of our ability to reflect on our own actions. Yet, if we behave according to (reasonably) deterministic laws of nature, there ought to be some (perhaps very small, yet not microscopically exact) set of conditions under which we would produce nearly the same behavior.
We can imagine someone, a burglar, say, who somehow gets hold of a complete physical description of someone - down the quantum state of her very molecules. The burglar uses this information to predict when the victim will be out of her house, and then goes in and robs her.
This seems a reasonable concern, if the universe runs according to strict physical laws. But the laws of physics have been invoked to conjure up the spectre of sphexishness, and now the laws of physics rush in to the rescue. In a sufficiently complex, deterministic system, something called "chaos" comes into play. In a chaotic system, the set of conditions needed to produce with certainty a particular outcome is exponentially small. If we stipulate that humans are sufficiently complex, then the set of conditions needed to guarantee a particular human behavior will be smaller than the quantum limit allows, even for very short times. In other words, it will be impossible, without violating the laws of quantum mechanics, to predict the future behavior of a human from physical principles for more than some very short time.
If we move to a quantum mechanical description of our human (supposing such a thing to be possible, which is doubtful), one thing improves: quantum systems are never chaotic, as long as the Hamiltonian (the function that describes how the system changes with time) is completely known. So at first glance we seem to be better off with a quantum description, in terms of being able to predict outcomes. However, there are several problems with the quantum approach.
First problem: the Hamiltonian is never completely known as long as the system interacts with its environment. So, we could apply quantum mechanics to a person who was completely isolated from everything (including air, water, food, etc.) - an unattractive prospect - or we could try to include the entire environment in our quantum description, greatly magnifying the difficulty of the task.
Second problem: Even with an exact quantum description (of, say, the person plus her environment) we will only get probabilistic results. That is, we can say she will have eggs for breakfast with 38% probability, jam and toast with 12% probability, etc. This is no more useful - and no more a violation of free will - than taking a survey of her eating habits.
Finally, I should point out that the problem I glossed over, of obtaining an exact quantum description of someone (to say nothing of her environment) is not just difficult, it is physically impossible. This is because of the no-cloning theorem I mentioned last time: it's impossible to take an unknown quantum system and make an exact copy of it.
So it seems that, from the point of view of predictability, free will has nothing to fear from the fundamental laws of physics. That is not to say that there couldn't be some higher-level laws that provide more predictability. After all, the same quantum considerations apply to Sphex, who remains quite predictable. (Not to mention a rock - also, presumably, a quantum system - whose behavior is extremely predictable.) So there is no way at this point to rule out the possibility of a nefarious burglar who exploits some as-yet-undiscovered psychological principles to generate useful predictions. But from what we have seen, there is no reason to think that the existence of such laws follows necessarily from the physical description of humans.
Next time: Electrons R Us.