horn torus in physics history:why did no one realize, describe and apply the
high complexity and
of the unique object 'horn torus'
- for centuries ?
science ignored its existence completely or
neglected its relevance unduly, till this day
- really weird!
( But now we have 21st century :-)
Horn Torus & Physics · texts · by W. Daeumler
mathematicians, physicists and other scientists, join in and rectify the mysterious omission! - you should not relinquish such an important subject and object to the esoterics alone ...the horn torus is an excellent graphical representation of complex numbers, a compactification with considerable more properties than the Riemann sphere has, it connects zero and infinity in an amazing way, can be dynamised by two independent turns, rotation around the axis and revolution around the torus bulge, what creates an incredible complexity and forms a coherent comprehensive entity, also explaining the potential for self-interaction and fractal order of complex numbers, and finally - most important - horn tori can be interlaced into one another and so very well symbolise correlation between entities, easily interpretable as physical objects: 'space', 'time', 'particles', 'forces' ...
... and considered more generally: 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 intrinsic property.
Static doesn't occur in quantum reality, and no model works sufficiently without underlying dynamic. That's for sure! → continue
* 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.