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horn torus in physics history:

why did no one realize, describe and apply the
exceptional topology,
maximum symmetry,
high complexity and
creative capabilities
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 constructively, starting from a very basic level after having achieved full abstraction from our traditional imagination of (more or less static) spaces with embedded objects and processes by strict epistemological reduction to fundamental entities, and we have to 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 we pragmatically make use of well established skills in three dimensions to illustrate the dynamic, the model is not dimensional - neither Euclidean nor non-Euclidean, neither related to any vector space nor even connected to Hilbert spaces and the respective formalism - at least not in an obviously predominant way. Horn tori, in particular the 'small' ones, induce an extremely dynamic and complex geometry and simultaneously - the 'big' ones - are capable to form a nearly static 'flat space' with Euclidean rules when approaching 'infinite size'. Conventional methods are insufficient or too laborious to describe such a hybrid of dynamic and static space properly and we maybe have to await further progress in quantum computing for an appropriate approach and adequate treatment. Then mathematics surely will experience changes, and surprises in physics cannot be ruled out. But note: here and now, on these pages, we only play a preliminary game!