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Does Time Smoothen Space? Implications for Space-Time Representation
Version 1
: Received: 18 October 2022 / Approved: 21 October 2022 / Online: 21 October 2022 (11:38:12 CEST)
A peer-reviewed article of this Preprint also exists.
Sang, N. Does Time Smoothen Space? Implications for Space-Time Representation. ISPRS Int. J. Geo-Inf. 2023, 12, 119. Sang, N. Does Time Smoothen Space? Implications for Space-Time Representation. ISPRS Int. J. Geo-Inf. 2023, 12, 119.
Abstract
The continuous nature of space and time is a fundamental tenet of many scientific endeavours. That digital representation imposes granularity is well recognized but whether it is possible to address space completely remains unanswered. Part 1 argues that Hales’ proof of Keppler’s conjecture on the packing of hard spheres suggests the answer to be ‘no’, providing examples of why this matters in GIS generally and spatio-temporal GIS in particular. Part 2 seeks to resolve the dichotomy between continuous and granular space, showing how a continuous space may be emergent over a random graph. However, its projection into 3D/4D imposes granularity. Perhaps surprisingly, representing space and time as locally conjugate may be key to addressing a ‘smooth’ spatial continuum. This insight leads to the suggestion of Face Centered Cubic Packing as a space-time topology but also raises further questions for spatio-temporal representation.
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Keywords
Discreteness; Topology; Space-Time Representation; Epistemology; Face Centered Cubic Packing
Subject
Environmental and Earth Sciences, Other
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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