Thomson's Lamp
Updated 2026-08-05
INTRODUCTION
English translation pending.
CORE DEFINITION
Thomson's Lamp, posed by James Thomson, imagines a lamp toggled infinitely often within one minute: on, then off after half a minute, on after a quarter, and so on. Since the convergent series has no last term, the lamp's state at the minute's end is mathematically undefined. The thought experiment exposes the clash between the mathematical infinite and physical reality, which has a smallest scale such as Planck time.
SCAFFOLDING EFFECT
Reduce cognitive load
- Subdivision alarm: notice when a plan's steps keep being cut finer with no final step. - Completion standard: replace one more step with a defined done criterion. - Reality check: recall that physical and decision costs set a floor below which detail is pointless.
Anchor fast decisions
The lamp performs infinitely many switches in finite time; the series converges yet has no final operation, so the end state is undefined. The supertask shows that infinitely subdividing steps need not yield a terminal state, and that classical logic offers no help at the limit.
MINIMUM ACTION
In progress 0/1Practice this model in one real situation:
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Source support: Explicit
- en.wikipedia.orghttps://en.wikipedia.org/wiki/Thomson's_lampverified
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