A Combinatorial Bit Bang Leading to Quaternions

TL;DR

This paper presents a novel combinatorial approach to deriving quaternions and related structures from primitive events, offering insights into the emergence of space-time and potential applications in AI and complex systems.

Contribution

It introduces a hierarchical, combinatorial framework for deriving quaternions and fundamental physics structures from simple exclusion and co-occurrence principles.

Findings

Derivation of quaternions from primitive combinatorial events

Compatibility of the framework with quantum mechanics and relativity

Potential applications in AI, modeling, and complex systems

Abstract

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.