Moving on, it is, to me at least, an interesting paradox to note that the following problem is ill-posed.
[ul]Suppose that at time t = 0 a dish is empty, and that for each non-negative integer N, at time t = 2 - (1/2)[sup]N[/sup], God takes two chips from a cache of identical chips, and simultaneously places them into the dish and removes one of the chips in the dish. How many chips are in the dish at time t = 2?[/ul]Somehow, in what order the chips are removed matters, even though they are all identical. The universe, as it were, knows in what order the chips are being placed into the dish, and, dispite their identicalness, keeps track of when each is removed. For, after all, something has to happen at the two-hour mark, and the only way for the universe to know what to do is to keep track of that information.
In other words, the problem is ill-posed because it doesn’t mention the additional presence of a sort of “tagging” operation that would be occuring, were the experiment actually performed. Even though the chips are, in all respects, indistinguishable, the universe is saying “for the duration of this experiment, you’re chip 1, you’re chip 2, …” and so on. But there are degrees of freedom to this hidden tagging operation that make different outcomes possible, depending on how the tagging operation is performed in a particular case.
Perhaps this is a clue to a solution to the paradox with the lightbulb being turned on and off at Zeno-type intervals. Is the light on or off at the 2 hour mark? This phrasing of the question seems not to determine an answer, but perhaps, in each particular case where this procedure is performed, a similar unmentioned “tagging” operation is performed in one of several possible ways, and the particular way in which it is performed does suffice to determine the outcome.