This paper describes in detail how (discrete) quaternions - ie. the abstract
structure of 3-D space - emerge from, first, the Void, and thence from
primitive combinatorial structures, using only the exclusion and co-occurrence
of otherwise unspecified events. We show how this computational view
supplements and provides an interpretation for the mathematical structures, and
derive quark structure. The build-up is emergently hierarchical, compatible
with both quantum mechanics and relativity, and can be extended upwards to the
macroscopic. The mathematics is that of Clifford algebras emplaced in the
homology-cohomology structure pioneered by Kron. Interestingly, the ideas
presented here were originally developed by the author to resolve fundamental
limitations of existing AI paradigms. As such, the approach can be used for
learning, planning, vision, NLP, pattern recognition; and as well, for
modelling, simulation, and implementation of complex systems, eg. biological.Comment: 23 pages, 4 figure
