Supertasks: A further strand of thought concerns what Black (1950–51) dubbed ‘infinity machines’. Black and his followers wished to show that although Zeno’s paradoxes offered no problem to mathematics, they showed that after all mathematics was not applicable to space, time and motion. Most starkly, our resolution to the Dichotomy and Achilles assumed that the complete run could be broken down into an infinite series of half runs, which could be summed. But is it really possible to complete any infinite series of actions: to complete what is known as a ‘supertask’? If not, and assuming that Atalanta and Achilles can complete their tasks, their complete runs cannot be correctly described as an infinite series of half-runs, although modern mathematics would so describe them. What infinity machines are supposed to establish is that an infinite series of tasks cannot be completed—so any completable task cannot be broken down into an infinity of smaller tasks, whatever mathematics suggests.