Thread: Flashing light bulb problem

I have asked this question before but have never really had a satisfactory answer to it, so I will throw it out here and see what happens.

the problem is based on a faulty lightbulb that flashs. However it's flashing is based on the infamous infinite sequence 1 + 1/2 + 1/4 + 1/8 .....

i.e. the light is on for 1 minute and off for 1/2 a minute, goes on for 1/4 of a minute and off for 1/8th of a minute. Now it is well known that this sequence never reaches 2. Therefore at two minutes is the bulb on or off????

Now I'm well aware that this could not physically happen due to the nature of a light bulb, but I want a theoretical answer! i.e. the ideal light bulb, or an electron flipping from state spin up to spin down.

It's off, as it never reaches two. Even if it did reach two the duration would have expired at 2.000. Not anything else.

So to ask if it's on or off when it reaches two, it would have to be off. It seams pretty logical to me. As you said it never reaches 2.0, but if it did it would have to be off. The sequence would be considered in error and terminated.

Even a flipping electron or a perfect light-bulb can't change state inifinity times in a finite period.

I think that it's not meaningful to consider this situation - the trap is that you're trying to indentify a "final instance" of an infinite sequence, which is a contradiction.

If you begin with the postulate that the bulb switches inifinity times, then it's not meaningful to talk about the final state of the bulb.

If you postulate that the bulb must have a meaningful final state, then it can't have switched infinity times.

Both good points...

The sequence would be considered in error and terminated.

Don't quite know waht you mean by this. The sequence can mathematically go on for ever. i.e. the time between the flashes becomes less and less. But the two minute mark will be reached (unless time stops).

If you postulate that the bulb must have a meaningful final state, then it can't have switched infinity times.

This must be the case. I think the problems comes into the case when the time intervals between the flashes becomes very short. Perhaps when the time interval reaches Planck time, 10<SUP>-43</SUP> seconds, the light bulb will move into one of the states, meaning that it did not have to flip states an infinite amount of times.

Alternatively it could be "on" in our universe and "off" in an alternative universe (satisfying the condition of being both on and off at the same time) after flashing an infinte amount of time (according to it) but a finite amount of time (according to us)

You asked

Therefore at two minutes is the bulb on or off????

I said

The sequence would be considered in error and terminated.

Because it can't happen based on the sequence, it's an error. The logic would be broken and the sequence is over.

Don't forget also we are talking about a theoretical bulb that is able to switch and any speed needed. A real light bulb would appear to be stuck on very quickly in this sequence. Even an LED would.