Norman Samish writes:
> I've been looking for an idiot savant to answer this question: Perhaps
> you've heard of Thompson's Lamp. This is an ideal lamp, capable of
> infinite switching speed and using electricity that travels at infinite
> speed. At time zero it is on. After one minute it is turned off.
> After 1/2 minute it is turned back on. After 1/4 minute it is turned
> off. And so on, with each interval one-half the preceding interval.
> Question: What is the status of the lamp at two minutes, on or off? (I
> know the answer can't be calculated by conventional arithmetic. Yet the
> clock runs, so there must be an answer. Is there any way of
> calculating the answer?)
I don't think there is, but perhaps as an ad hoc answer in the context
of many-worlds, we could say that the universe splits, and in one branch
the light is left on, and in the other the light is off. Therefore, in
advance you could not deterministically anticipate seeing one particular
result, but rather that you would have a 50% chance of seeing the light
left on or off.
Of course you could get much the same effect without many-worlds by simply
positing that the light would be left on or off with 50-50 probabilties,
If you want to look through the list archives, we discussed some related
ideas in September and October, 2000,