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Horn Torus - 'Geometry Of Everything'  by Wolfgang Daeumler

a small selection of short excerpts from DornTorus (German)

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?   For our common sense nothing is more self-evident than description of space as right and left, fore and aft, top and bottom, eventually combined with a point in time. So we need three resp. four coordinates: x, y, z and t. In our horn torus model it is infinitely more difficult to imagine spatial points and relation between different points. It needs effort and time - and much capability of abstraction - to learn about, exercise and handle horn tori. It won't work without. But it's really worth doing!   The most important message first: one single point, together with an infinitesimal neighborhood, contains the whole universe! Every particle of the world is represented by exactly one horn torus in the set, with one shared tangent in common Point S. The size of the horn torus represents something like 'distance' to the particle or to the 'location', where its size is zero or say minimal. To move that way, to that location, the respective horn torus has to diminish in size. Simultaneously (nearly) all other horn tori change their size, increase or decrease, according as they diverge or get closer. Only particles, that move on a 'parallel' with same 'velocity', keep their associated horn torus size constant.   The complete set of all spatial points in the universe is the set of combinations of all occurring horn torus sizes. - Wow! - Our imagined space has vanished. Only an infinite series of numbers is left. These series and permutations of them describe all the universe, but don't show any structure. Only a consciousness that picks out remarkable and significant patterns, will see laws and objects, properties and beauty, last mentioned being one of the most complex quality, that can be derived from mere numbers in these permutations. But that's another topic.   Next step of abstraction: We reduce every horn torus to the mentioned unrolling line (cycloid) on its surface 'membrane', described in the foregoing section 'Dynamic geometry'. That takes off the symmetry from the horn torus, because this line starts on one particular meridian. So the horn torus is determined by a combination of numbers: size, rotation velocity, including direction (+/-) and longitude of the meridian, the mentioned series of numbers in fact turn to matrices and the nested horn tori to a dense set of curling curves. Nevertheless, for visualisation we better remain in the picture of the complete dynamic horn tori including their virtual membrane. The term 'dynamic' comprises both kinds of turn and variation of size.   We keep this image, even when we undertake another rigorous reduction: we remove nearly all parts of unrolling lines with the exception of an infinitesimal neighborhood of Point S, because all relevant information about the further courses of all lines is included in the short snippets. We now have extended the spatial point from a set of coordinates (x,y,z,t) to a spot, that contains its relation to all other spots in universe. The spot is infinitesimal small, but much more than the accustomed point as usually defined in mathematical sense. Every spot represents nothing less than the whole universe itself, including its prospective progression! To move from one spot to an other only means to change the point of view on to the universe.   Too much for imagination? And worse things are yet to come ...   close

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

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!