Supertasks and Paradoxes (Zeno, Littlewood-Ross and Thomson’s Lamp)

Tom Rocks Maths intern Kira Miller discusses the philosophy of ‘supertasks’ and how they are related to Zeno’s Paradox, Thomson’s Lamp and the Littlewood-Ross Paradox.

Zeno’s Paradox looks at convergent infinite sequences in the context of Achilles racing against a tortoise which is given a head-start.

Thomson’s Lamp is a paradox relating to a lamp that is switched on and off at increasingly small time intervals before noon – will it be on or off as the clock strikes 12?

The Littlewood-Ross Paradox talks about filling an infinite jar with infinitely many marbles, but removing them following a defined pattern. In each case we are considering infinity minus infinity, but the results differ significantly…

Produced by Kira Miller with assistance from Dr Tom Crawford at the University of Oxford.