Supertasks
Updated 2026-09-10
INTRODUCTION
English translation pending.
CORE DEFINITION
A supertask is a hypothetical task consisting of infinitely many steps that is completed in a finite amount of time. Discussed since pre-Socratic times, it remains a major tool for philosophers, logicians, and physicists studying infinity, limits, and physical possibility. The classic puzzles ask what state a system is in at the end of the process, and whether the scenario is logically coherent, physically realizable, or intelligible at all.
SCAFFOLDING EFFECT
Reduce cognitive load
- Limit testing: check whether the final state depends continuously on the whole infinite process. - Convergence construction: use a convergent series to judge whether infinitely many steps can fit into finite time. - Possibility sorting: separate what is logically conceivable from what is physically realizable.
Anchor fast decisions
The key to completing infinitely many steps in finite time is that the durations of the steps form a convergent infinite series with a finite sum. The difficulty is that if the final state does not depend continuously on the process, no limit exists and the end state is undefined; in certain relativistic spacetimes an observer can exploit infinite proper time to finish infinitely many computations.
MINIMUM ACTION
In progress 0/2Practice this model in one real situation:
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Source support: Explicit
- plato.stanford.eduhttps://plato.stanford.edu/entries/spacetime-supertasks/verified
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