Thomson's lamp
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.
| Time | Lamp state |
|---|---|
| 0:00:00 | off |
| 1:00:00 | on |
| 1:30:00 | off |
| 1:45:00 | on |
| 1:52:30 | off |
| ... | ... |
| 2:00:00 | ? |
Consider a lamp with a toggle switch. Flicking the switch once turns the lamp on. Another flick will turn the lamp off. Now suppose a being able to perform the following task: starting a timer, he turns the lamp on. At the end of one minute, he turns it off. At the end of another half 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 he continues thus, flicking the switch each time after waiting exactly one-half the time he waited before flicking it previously. The sum of all these progressively smaller times is exactly two minutes.
Questions
- Is the lamp on or off after exactly two minutes?
- Is the lamp switch on or off after exactly two minutes?
- Would it make any difference if the lamp had started out being on, instead of off?
Contrast with Zeno's Paradoxes
Two notable features of contrast between Thomson's Lamp and Zeno's Paradoxes is that in the case of the lamp the focus is on two discrete positions and there is a pause between them. Several proposed solutions to Zeno's Paradoxes fail if there is a pause before each movement in the series.
Reference
- Thomson, J., 1954-55, ‘Tasks and Super-Tasks’, Analysis, XV, pp. 1-13.
