Supertask - Wikipedia
In philosophy, a supertask is a countably infinite sequence of operations that occur sequentially within a finite interval of time.[1] Supertasks are called "hypertasks" when the number of operations becomes uncountably infinite. A hypertask that includes one task for each ordinal number is called an "ultratask".[2] The term supertask was coined by the philosopher James F. Thomson, who devised Thomson's lamp. The term hypertask derives from Clark and Read in their paper of that name.[3]
The origin of the interest in supertasks is normally attributed to Zeno of Elea. Zeno claimed that motion was impossible. He argued as follows: suppose our burgeoning "mover", Achilles say, wishes to move from A to B. To achieve this he must traverse half the distance from A to B. To get from the midpoint of AB to B, Achilles must traverse half this distance, and so on and so forth. However many times he performs one of these "traversing" tasks, there is another one left for him to do before he arrives at B. Thus it follows, according to Zeno, that motion (travelling a non-zero distance in finite time) is a supertask. Zeno further argues that supertasks are not possible (how can this sequence be completed if for each traversing there is another one to come?). It follows that motion is impossible.
Most subsequent philosophers reject Zeno's bold conclusion in favor of common sense. Instead, they turn his argument on its head (assuming it is valid) and take it as a proof by contradiction where the possibility of motion is taken for granted. They accept the possibility of motion and apply modus tollens (contrapositive) to Zeno's argument to reach the conclusion that either motion is not a supertask or not all supertasks are impossible.
