Thomson's Lamp is a puzzle that is a variation on Zeno's paradoxes. It was devised by philosopher James F. Thomson, who also coined the term supertask.

Consider a lamp with a toggle switch. Hit the switch once, the lamp turns on. Hit it again, the lamp turns off. Imagine a being able to perform the following task. First, he turns it on. At the end of one minute, he turns it off. At the end of another half a minute, he turns it on again. At the end of another quarter of a minute, he turns it off. At the next 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. Mathematicians have developed a way to determine the sum of all these increasingly smaller times: exactly two minutes.

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

Another Question: Would it have made any difference if the lamp had started out being on, instead of off?

References

• Thomson, J., 1954-55, ‘Tasks and Super-Tasks’, Analysis, XV, pp. 1-13.