Does Time Smoothen Space? Implications for Space-Time Representation

Abstract

The continuous nature of space and time is a fundamental tenet of many scientific endeavors. That digital representation imposes granularity is well recognized, but whether it is possible to address space completely remains unanswered. This paper argues Hales’ proof of Kepler’s conjecture on the packing of hard spheres suggests the answer to be “no”, providing examples of why this matters in GIS generally and considering implications for spatio-temporal GIS in particular. It seeks to resolve the dichotomy between continuous and granular space by showing how a continuous space may be emergent over a random graph. However, the projection of this latent space 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.

Keywords

• discreteness
• topology
• space-time representation
• epistemology
• face centered cubic packing