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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 - unrolling lines versus reference objects of physicists
11. Examples - a sneak peek as teaser
12. Dimensionality - not a physical term!
13. Gravitation and forces - intrinsic times and matter of rotation
Yes, I know: every somewhat creative would-be scientist eagerly endeavours to explain all unsolved problems in physics, cosmology and preferable parapsychology in addition. So, non-mainstream physicists quickly are suspected of pursuing image-cultivation in a know-it-all manner. I hope, the game I play doesn't dump me (a modest physicist and physician) into that corner. I only cheerfully enjoy the many analogies between physical phenomenons and geometrical properties of a set of dynamic horn tori, and I certainly do not intend to scratch accepted theories.
Prerequirement to see these analogies is plenty exercise with the image of nested dynamic horn tori. One should be able to suppress the common space of perception and replace it by the abstract set of tori. It's not easy, sure, but worth the effort to try. For many physical facts you can find astonishing analogies or striking equivalents in that image. Some not completely reflected or too 'self-evident' phenomenons can easily be reinterpretated with new meaning and importance or several sophisticated theories might be better understood by a second, different approach ...
We have seen that revolution of the torus bulge is not an unrolling of the meridians along the 'time-axis' but of the cycloid, resultant line when revolution is combined with rotation. Cycloids are longer than meridians, and the faster revolution or rotation (compared with the unit horn torus), the longer this line. Seen from the unrolling torus, one can not determine whether the reference axis is 'straight' or curved, whether the torus rolls along the 'time-axis' or along meridians or cycloids of other tori. That's important! The axis along which the torus rolls seems to be the 'time-axis', even when it is e.g. the average cycloid of all neighboring tori. So the torus time is different from the time, represented by the symmetry axis of all nested horn tori. We call it 'intrinsic time'. Every torus (i.e. every particle!) has its own intrinsic time, depending on its own rotation on one side and of all neighboring horn tori with their density of packing and their rates of rotation on the other side.
You may not determine the curve of the intrinsic time axis, but mathematically you can transform it into a straight line and look - from 'outside' - what happens with the other tori of the set. Big tori become bigger than infinite, what in our space of perception doesn't make any known sense, but in the new image it does. The horn tori return from infinity after having changed their direction of rotation, they quasi turn their inside out when passing infinity (resp. when reflected by infinity). It is mathematically describable, but here only an exercise for abstraction and an example for interesting effects and very special analogies. The same happens when a horn torus 'passes' size zero (changes direction of rotation/spin).
In that image, a particle (horn torus) 'mixes up' a concentration of cycloids (accumulation of horn tori of similar size) with the straight time axis and increases/decreases size during rolling on the cycloid just to that size, what physically means it converges to the respective spatial point. This can be interpreted as pull towards this accumulation of horn tori: gravitational force towards mass concentration. It is a phenomenon of big horn tori, with ratio revolution : rotation << 1. Detailed explanation will follow.
A completely different situation, but within exact the same entity, occurs at ratios in vicinity of 1 (½, 2, 3, 4, ...), 1 being the standard dynamic horn torus, the natural unit for self-metrisation. Here is the world of resonances, of Lissajous figures on horn torus surfaces. The cycloid between two resonances swings to and fro, the related horn torus size vibrates within small limits. To establish physical analogies shouldn't be too difficult. And please note: we describe macro- and microphysics by means of identic pictures. At least as an image we now possess an easy to handle instrument for unification. Let's play this instrument! - Sounds good, doesn't it? - More later ...
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. .....
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