HTW Berlin Fachbereich 4 Internationaler Studiengang Internationale Medieninformatik (Master) DIDACTM : The Didactics of Media Winter Term 2011/12

THOMPSON'S LAMP PARADOX:

Consider a lamp, with a switch to turn it on and off. If you hit the switch once, it turns on. Hit it again, it turns it off. Let us now imagine that we can move very fast and start playing with the lamp. First we turn it on. At the end of a minute, we turn it off. After half a minute more, we turn it on again. At the end of a quarter of a minute, we turn it off. One eighth of a minute later - you guessed it, we turn it on again. We continue, waiting exactly one-half of the time of the last interval before we use the switch again. It is easy to see that all these infinitely many time intervals add up to exactly two minutes.

QUESTION 1: At the end of two minutes, is the lamp on, or off?

QUESTION 2: Here the lamp was off when we started. Would it have made any difference if it had started out being on?