Horn Torus & Physics

'Geometry of Everything'

by Wolfgang W. Daeumler

The geometrical horn torus model is a proposal for a different approach to physical questions by the attempts to describe fundamental physical processes graphically, namely in the form of dynamically interlaced horn tori. These are eminently suitable to illustrate complex numbers and their manifold properties, when the imaginary part is represented by numbers connected to revolutions around the torus bulge (longitudes), the real part by numbers related to rotations around the main symmetry axis (latitudes). The arising physical-geometrical analogies are amazing! Convince yourself:

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figurative visualisation of 'revolution'
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The horn torus, that we are discussing here, shall not be seen as something like a solid figure, embedded in a three-dimensional world. Our horn tori span a space of their own as  dynamically uncoiling coordinates . They bear, as entities within this space, highest symmetry, incredible complexity and creative capabilities. In the pure analogous model they symbolise manifold intrinsic properties of complex numbers, what enables them to act as quite efficient visual aids for many aspects of physical processes and laws on a fundamental level (space, time, physical objects, 'particles', interaction, ...), which often are not easily comprehensible by normal and even scientifically trained everyday's understanding, and for which physicists unfortunately not have contributed any appropriate pictorial associations to match one's receptive mental imagery. Now interlaced (nested) dynamic horn tori allow to build bridges between abstract mathematics and our inherent thinking. After intensive familiarization with the model, its analogous images and its geometrically representable dynamics, many physical terms, concepts and phenomena appear no longer mysterious and unexplained but become inevitable, logical, clear and evident*. Nevertheless the horn torus model doesn't claim to be a consistent physical or mathematical theory. Regard it as suggestion to leave fixed habits of conventional mainstream thinking - now and then, playfully, just for fun! Sometimes crackpot ideas inspire. The matter is intended to be an exciting game, to exercise imaginative power, to improve abstract thinking and to generate lots of aha moments. It has no esoteric connection! It's just based on mathematics, complex numbers and their arithmetic, associated geometry and a unique code ...   continue   or enter  step by step

This private website exists since 2006 (in German language since 2000 as DornTorus.de, some texts date back to 1988 - author used to be a theoretical physicist), it is written in meanwhile partly obsolete HTML4 and not optimized for smartphones. It contains countless explaining images and animations, that are best viewed on a bigger screen. Relevant information is spread over a great many reciprocally linked pages, occasionally - sorry for that (it's part of the game) - a little bit hidden, often embellished with algorithmic art. Along with some related websites, also part of our game, the presentation might be classified as an interdisciplinary art project with a little spice of  scientificity , at least with a deeper meaning:   DornTorus.de  horntorus.de  mathematical-universe.com  8128.info  artmetic.de  Kunstlege.de   (hundreds of pages)  © 2000...2019  W. Daeumler, Perouse
BTW: when searching online for 'horn torus' you often find sites about 'sacred geometry' and similar odd topics but hardly serious, reasonable and scientifically relevant publications which exceed e.g.  WolframMathWorld  ...  really weird !

*) many physical phenomena, conditions and relations we do not really understand at all and quite often don't even question our as reality declared perception of them: space and time, physical objects as contained structures, 'particles', their interactions, energy, mass, force, impulse, location and 'movement in space', constancy of the speed of light, its value as maximum limit, constants, quantization of values, spin, isospin, (color-)charge, non-locality, quantum entanglement, symmetries, invariances, Pauli principle, determinism, causality, complexity, arrow and reversal of time, antimatter, singularities, infinity, cosmology ...

Rigorous mathematization of space, time and all physical objects, isolated from our perception (including three-dimensional space!), seems to be the only method for reducing fundamental laws of nature to a very few principles, possibly to one unique code, that rules our universe. The horn torus model - as an intellectual game - pursues this goal. Here an excerpt (a kind of concluding summary) from the texts: