Deep Thoughts

[Ghoulish Delight]

Originally Posted by SzczerbiakManiac

Catch up in time to win an x meter race or catch up ever? If the latter, yes.

But how, asks Zeno? For every distance X Achilles covers, the tortise moves ahead by X/10 meters.

Consider this similar conundrum:

Consider a lamp, with a switch. Hit the switch once, it turns it on. Hit it again, it turns it off. Let us imagine there is a being with supernatural powers who likes to play with this lamp as follows. First, he turns it on. At the end of one minute, he turns it off. At the end of half a minute, he turns it on again. At the end of a quarter of a minute, he turns it off. In one eighth of a minute, he turns it on again. And so on, hitting the switch each time after waiting exactly one-half the time he waited before hitting it the last time. A simple series evaluation shows that if you add up all of the intervals on into infinity, this will actually continue for precisely two seconds.

So, at the end of 2 seconds, is the lamp on or off?