home      sitemap      contact
(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   To replace the engrams in descriptions of nature, we introduce a purely abstract model, which shall represent fundamental physical objects. Trick is, to use the well-known three-dimensional space, but only as sort of crutch, not as space where objects and processes are embedded. Our model has no dimensions, but has, instead, a very active dynamic.   As shown on front page of this website (more descriptive here), we put horn tori of many sizes into one another, nest or interlace them so that all have the same symmetry axis through their common center, every horn torus being inside the next bigger, all - more ore less - very close to another. As surface we imagine an infinitesimal thin 'membrane', actually nearly not existent. Same as we can (mathematically) imagine an infinite set of numbers on a limited line, we imagine a huge number of horn tori put together the described way. All touch one another in the same point, in the center, which we call 'Point S' - from symmetry or singularity.   Now we pull the axis from outside in one of the two possible directions and see all horn tori rolling along this axis. Simultaneously they roll along each other, and all apply exactly the same circumferential speed, just the speed with which we pull the axis. Indeed this speed is the same for all horn tori, but their angular velocities differ. The smaller the torus is, the faster turns its bulge. The rolling along the axis by performing this torsion of the bulge we call 'revolution'. So all revolution velocities are different. Very big tori approach zero angular velocity, very small ones turn extremely fast.   If one has difficulties to imagine that mechanism, take normal balls of very thin glass and with different sizes, every ball containing a smaller, laying on the 'bottom'. (You know the Russian nested Matryoshka dolls?) When you rotate the biggest around a horizontal axis, all enclosed rotate with the same circumferential speed, but with higher angular velocities the smaller the respective glass ball is, the innermost being the fastest. So far, so clear? (If not - take gear wheels :-)   Now let the horn tori additionally rotate around the symmetry axis. Allow each to choose any of both possible directions for rotation. At the beginning we don't set a particular angular velocity, perhaps leave it constant first, and we will consider later, which different mechanisms could have an effect on rotation.   The following is a really great challenge for imagination: move a very small - infinitesimal small - distance away from Point S. Hold there a pen, a marker, on the thin surfaces of all horn tori, let them run and then trace the lines, which are being drawn onto every horn torus. We get unrolling lines (cycloids, trajectories), the shape depending on the ratio of angular velocities, connected with torus size. On very small tori appear lines nearly not diverting from meridians (very fast revolution!), on 'medium' ones we see various loops with any number of 'blades' and 'coils'. At big tori rotation prevails and the cycloids converge as windings close to the torus latitudes. The array of curves and the particular (three-dimensional Lissajous) figures later will be objects of examination. We will find amazing things, that lead to obvious interpretations. (Yet again: more detailed explanations in the German version.) → example for marker trace  (Lissajous figure, unrolling line, cycloid, trajectory)  close

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

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!