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SURREAL TIME AND ULTRATASKS

Published online by Cambridge University Press:  30 August 2016

HAIDAR AL-DHALIMY*
Affiliation:
Department of Philosophy, University of Minnesota
CHARLES J. GEYER*
Affiliation:
School of Statistics, University of Minnesota
*
*DEPARTMENT OF PHILOSOPHY UNIVERSITY OF MINNESOTA 831 HELLER HALL 271 19TH AVENUE SOUTH MINNEAPOLIS, MN 55455, USA E-mail: haidar@umn.edu
SCHOOL OF STATISTICS UNIVERSITY OF MINNESOTA 313 FORD HALL 224 CHURCH STREET SE MINNEAPOLIS, MN 55455, USA URL: users.stat.umn.edu/∼geyer E-mail: geyer@umn.edu

Abstract

This paper suggests that time could have a much richer mathematical structure than that of the real numbers. Clark & Read (1984) argue that a hypertask (uncountably many tasks done in a finite length of time) cannot be performed. Assuming that time takes values in the real numbers, we give a trivial proof of this. If we instead take the surreal numbers as a model of time, then not only are hypertasks possible but so is an ultratask (a sequence which includes one task done for each ordinal number—thus a proper class of them). We argue that the surreal numbers are in some respects a better model of the temporal continuum than the real numbers as defined in mainstream mathematics, and that surreal time and hypertasks are mathematically possible.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 2016 

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