On Bifurcated supertasks and related questions

TL;DR

This paper critically examines bifurcated supertasks involving infinite time division and half-curves, analyzing their implications for hypercomputation and foundational theories of infinity.

Contribution

It provides a critique of bifurcated supertasks and discusses their impact on the understanding of hypercomputation and infinitist theories.

Findings

Highlights issues with infinite time division and half-curves

Identifies conflicts in hypercomputation scenarios

Suggests reviewing foundational aspects of infinitist theories

Abstract

Bifurcated supertasks entail the actual infinite division of time (accelerated system of reference) as well as the existence of half-curves of infinite length (supertask system of reference). This paper analyzes both issues from a critique perspective. It also analyzes a conflictive case of hypercomputation performed by means of a bifurcated supertask. The results of these analyzes suggest the convenience of reviewing certain foundational aspects of infinitist theories.