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(explanatory video)

Horn Torus - 'Geometry Of Everything'  by Wolfgang Daeumler

a small selection of short excerpts from DornTorus (German)
manuscript 7/1988, printed 1996-98, translation provisional

1.  The Elimination Of Emptiness - a short creation story

2.  How did Emptiness count numbers? - quintessence of idleness

3.  Mental leaps - time is redundant

4.  Has time a direction? - what means time reversal?

5.  Real or imaginary world? - imagination and decision made easy

6.  Engrams - impediment to comprehension

7.  Dynamic geometry - renunciation of dimensionality

8.  Spatial point - without dimensions - what in the world is that?

9.  Analogies - dynamic geometry versus physical entities

 10. Identifications  - one trace of an unrolling line on horn torus surface versus various well-known reference objects of physicists -   First we recap the identifications we already have made: the most important, significant and obvious is the axis of symmetry, which we had identified as axis of time, but straightaway had deprived this meaning of its importance, because of the equivalence to horns of very big tori. The total of all big horn tori represents time already. A distinct variable or dimension time is not necessary, is redundant. When using it yet, time will be an auxiliary variable, only for simplification of things, to match our engrams.   The circumferential speed of the tori, when rolling along the axis, shall be the same for all. Constancy is not required, because self-similarity of the whole system equals it instantly, so that within the system it seems to stay constant. Moreover there is nothing outside, no reference, what could define a particular value for the speed. In our world we only know one omnipresent speed, and so it's logical to let the tori perform their revolution (turn of latitudes) with speed of light c.   Now we switch to the imagined unrolling line, that we let emerge on the surface of a dynamic horn torus through its simultaneous rotation (turn of longitudes). Without the extensive explanations in the original (German) text and without mathematical elaboration we try to associate properties of the line with physical objects. Rotation itself can be associated with quantities like energy, frequency, spin of particles etc.   The whole line (the complete cycloid), reaching from infinitesimal small to very big horn tori is one entity, divided in many parts. On big sizes, when the ratio of angular velocities revolution to rotation is small, the line winds very often around the torus including the horns, with small angle to the latitudes - at least off the thin thread near Point S, mostly filling the whole surface after many rotations. At certain ratios, with rational values and especially as integers, the line concentrates to significant patterns, Lissajous figures. The line never shows a discontinuity, but in form of these concentrations different kinds of 'attractors' or 'resonances'. These one can associate with particles, fermions, and the sections of the line between the fermions as their mediators, bosons. See coarse animation.   In this picture elementary particles are local manifestations of one single entity, reaching from inside a nucleon, quark or even smaller to farthest distances of the universe. The outermost boson, with mentioned ratio smaller than 1/2, where there are no significant Lissajous figures, is the photon and at 1/2, as the first striking resonance, we find the electron.   Ratio 1 is a sort of mysterious 'mirror', where the big outer world of 'free' photons and electrons with little manifestation of structure changes into the inverse world with enormous accumulation of resonances, the first being ratio 2, representing a pair of nucleons. Between electron and first half of the two nucleon-loops, which we identify as proton, we find a 'caged' photon as mediator. Further down, at ratio 3, the line next is 'constructing quarks', being not less interesting at ratio 4 then ... and our game has started to be fun.   close

11. Examples - a sneak peek as teaser

12. Dimensionality - not a physical term!

13. Gravitation and forces - intrinsic times and matter of rotation

14. Patterns and strings - of winding lines and tiny snippets

15. Metric - when dynamic processes induce discrete values

16. Grand unification - in plain common speech

17. .....

all texts in one file as   docx   or as   pdf
Note:
The horn torus, we discuss here, shall not be seen as something like a three-dimensional solid figure!
Horn tori are not embedded in our three-dimensional world, but span a dynamic space of their own.
In the pure analogous model they only symbolise manifold intrinsic properties of complex numbers:
as dynamised entities they bear highest symmetry, creative capabilities and incredible complexity,
so the good old Riemann sphere better should be replaced by the much more universal horn torus!

Remark:
The horn torus model is not 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
and ability to think in abstract terms (helpful for understanding physics ;-)

Motif:
mathematical rules exist 'all the time' since there is more than nothing
in other words: mathematical rules are involved in creating the universe
or: emerging of a mathematical rule is equivalent to well-known Big Bang

nature is mathematical, one mathematical code rules our world

that code and mathematics in itself definitely are not inventions of humans -
we only have developed a complex language to describe simple preexisting laws!
we still are far away from seeing the simplicity in natural laws, but we know:

all really fundamental physical laws are pure mathematics

and it's impossible to comprehend laws of nature without playing the math game
mystic, spiritual and all esoteric reflections do not lead to true knowledge -
like it or lump it - so clear away the space-occupying rubbish in the brains!