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SURREAL TIME AND ULTRATASKS

Published online by Cambridge University Press:  30 August 2016

HAIDAR AL-DHALIMY  and
CHARLES J. GEYER
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: [email protected]
† 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: [email protected]
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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
Information
The Review of Symbolic Logic , Volume 9 , Issue 4 , December 2016 , pp. 836 - 847
Copyright
Copyright © Association for Symbolic Logic 2016 

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