Bertrand Russell once remarked that all of mathematics consists of tautologies. In this sense, we are considering as logically foundational a vast, complex panoply of equivalences, equations, symmetries and relationships asserting unproblematic definitions, references, ontologies. It may be true that from within any system of reference, any conceptual schema whatsoever only acquires and maintains aspirational […]

# Tag: geometry

## Hidden Geometry of Life in the Cosmos

Beautiful… and the fact that these spiral symmetries are ubiquitous as (a) most energy-efficient method of maintaining adaptive structural complexity is magnificent. There are abstract, logical corollaries of this. Interesting how life possesses similarities to abstract geometric patterns like this – adaptive systems that (soliton-like) autonomously self-propagate by the sustainably continuous information and energy-processing gradient […]

## Mysteries of Higher Geometry

The greatest mystery of mathematics is, to me, that all of these patterns and logical systems appear to almost (and autonomously) seek higher-dimensional self-representations. In category theory or combinatorics we can relatively simply determine and demonstrate the way a set of properties or relationships seeks something of an implicit, intrinsic and endemic higher-dimensional geometry. The […]