Horn Torus & Physics
A word on the - strangely enough often not even realized - lack of fundamental dynamic based theories in (quantum) physics
Classical mathematics* does not offer any well-elaborated and consistent theory of topological systems ('spaces') that
are based on (respectively 'spanned' by) continuously and dynamically changing coordinates. Most practically working physicists doesn't
bother that too much. They may be happy and content with their sophisticated software for computer simulations, animations and evaluations
as explaining models for dynamic processes, being very successful thereby - no doubt, but from a more philosophical point of view that's
not exactly the ideal solution for describing a dynamic physics. For true understanding we are in urgent need of revolutions (in thinking
and as 'turns' :-), we should reflect on the topic more fundamentally, should achieve full abstraction from our traditional imagination of
(more or less static) spaces with embedded objects and processes by strict epistemological reductions, and we should aim at a - maybe
disruptive - congruent mathematical model of physical 'reality' that comprises the pervasive and unstoppable dynamic as main
Static doesn't occur in quantum reality, and no model works sufficiently without underlying
dynamic. That's for sure!
→ view an example for a complex-valued dynamic coordinate
→ and here the
related game 'horn torus'
* With the horn torus model we leave 'classical mathematics'. Though our well established skills in three
dimensions are used to describe the dynamic, the model is not dimensional - neither Euclidean nor non-Euclidean, neither a vector space
nor even connected to Hilbert spaces or the related formalism - at least not in an obviously predominant way. Small horn tori induce an
extremely dynamic geometry with highest complexity, whilst big horn tori, when approaching infinite 'size', are capable to form a nearly
static 'flat space' with Euclidean rules.