[ExI] Macroscopic Superposition

[Lee Corbin]

Stuart L. writes

> Stathis wrote:
> 
>> > If you had an LED and you turned it on for one second,
>> > then turned it off for half a second, then turned on for
>> > 1/4th a second, then turned it off for 1/8th a second and so
>> > on . . . then at exactly 2 seconds, would the LED be on or
>> > off?
>> 
>> This is called "Thompson's lamp".
> 
> Actually I think it is a just a little bit sneakier than Thompson's
> lamp. If the lamp is incandescent, then the answer would be
> *on*, since whether current is flowing...

Oh would you quit bringing reality into it? You spoil all the fun.

I agree with Damien, the lamp would be on. Here is why :-)

It's on for 1 second, off for 1/2, on for 1/4, etc., right?
Or, to reword, it's on for 2^0 seconds, off for 2^-1 seconds,
on for 2^-2 seconds, and so forth. We want to know whether
it will be on or off for 2 to the negative omega seconds, where
omega is the first ordinal after all the natural numbers. (I am
sure it works the same for negative as positive.)

Now, is omega an even or an odd number? It turns out that
it is even! Therefore, at 2^-w seconds (w stands for omega),
it's the same as it was for 2^0 and 2^-2 seconds, namely
on. Now if it had been off for one second, on for 1/2 second,
then the answer would be reversed.

I wonder how Damien got his answer, though.

Lee

> or not, the filiment would not have time to cool down
> between very small intervals so would continue to glow.
> Lasers and consequently LEDs do not suffer from this limitation. :-)