A Computational Mathematics View of Space, Time and Complexity

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dc.contributor.author Bailey, DH en
dc.contributor.author Borwein, JM en
dc.date.accessioned 2017-02-07T03:37:17Z en
dc.date.available 2017-02-07T03:37:17Z en
dc.date.issued 2016 en
dc.identifier.citation CDMTCS Research Reports CDMTCS-498 (2016) en
dc.identifier.issn 1178-3540 en
dc.identifier.uri http://hdl.handle.net/2292/31755 en
dc.description.abstract Modern computational mathematics requires a philosophical perspective largely at odds with that of traditional mathematics, since current computational mathematics (as distinct from computer science) is by its very nature is discrete, not continuous, and tied to the real world in ways that the more theoretical branches of mathematics (and computer science) often are not. Indeed, computational mathematics provides a means to escape the trap feared by John von Neumann when he wrote, [T]here is a grave danger that the subject [of mathematics] will develop along the line of least resistance, that the stream so far from its source [in empirical reality] will separate into a multitude of insignificant branches, and that the discipline will become a disorganized mass of details and complexities. But even a computational approach to mathematics has limits, not the least of which are the uncertainties of errors in hardware, software and algorithms that inevitably are part-and-parcel with computation, although there are ways to limit these uncertainties. In our chapter, bulwarked by concrete examples, we will try to situate past, present and future mathematical views of space, time, infinity and certainty within a computational context in which, for example, error due to quantum effects begins to compete with traditional sources of logical and numerical inaccuracy. We shall also argue that traditional taxonomies of complexity and completeness are not only outmoded but actually destructive of progress. en
dc.publisher Department of Computer Science, The University of Auckland, New Zealand en
dc.relation.ispartofseries CDMTCS Research Report Series en
dc.rights Items in ResearchSpace are protected by copyright, with all rights reserved, unless otherwise indicated. Previously published items are made available in accordance with the copyright policy of the publisher. en
dc.rights.uri https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm en
dc.source.uri https://www.cs.auckland.ac.nz/research/groups/CDMTCS/researchreports/index.php en
dc.title A Computational Mathematics View of Space, Time and Complexity en
dc.type Technical Report en
dc.subject.marsden Fields of Research en
dc.rights.holder The author(s) en
dc.rights.accessrights http://purl.org/eprint/accessRights/OpenAccess en

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