The Emergence of Quaternions from a Discrete, Combinatorial Bit Bang

Michael Manthey

This paper will describe in detail how 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. It will be seen how a computational view supplements, and provides an interpretation for, the mathematical structures. The build-up is emergently hierarchical,compatible with both quantum mechanics and relativity, and can be extended upwards to the macro-scopic. The mathematics is that of Clifford algebras enplaced in the homology-cohomology structure pioneered by Kron. Interestingly, the structures presented here were originally developed by the author to resolve fundamental limitations of existing artificial intelligence paradigms.