a small selection of short excerpts from

manuscript 7/1988, printed 1996-98, translation provisional

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 teaserUntil now the length of the cycloid ('unrolling line') didn't appear, whereas it is the 'source of all the magic'. Because it gives us the opportunity to undertake mathematical computations and to establish a metric. Furthermore the fact, that the line is longer than a meridian of the horn torus, causes the existence of speeds that differ from the speed of light. When you look closely at Point S and a small neighborhood, you will see that a rotating horn torus does not unroll its meridians but - to avoid slippage - just this cycloid instead, that winds around the horns. So the effective speed of rolling along the axis is smaller. Fast rotating horn tori move slower - the faster the rotation the slower the locomotion along the axis. But now - for physicists - two haphazard examples of computation: we calculate the length of the cycloid between significant resonances, noting the fact that the dynamic horn torus diminishes in size, when its angular velocity of revolution increases. Related to the standard dynamic horn torus (ratio of velocities 1:1 and circumference 1) we start with the loop of the electron (ratio 1:2, size 2) and end with ratio 4:1(!). We get, with help of computer, as length of the cycloid the value 2.07944, corresponding a rotation angle of 748.6°, effective (-2x360°) 28°36', not far from Weinberg angle. Is there any connection to the four(!) bosons of electroweak interaction? Similar computation, equally random: when describing the doublets of weak isospin - for quarks (u,d), (c,s), ... - in some 5% of cases s replaces d and vice versa, and so d and s are superpositions of both, d and s. Why that? When calculating the respective length of the cycloid (direct corresponding to rotation angle!) we find: the three 'blades' of quarks u and d are twisted 44.7°, 164.7° and 284.7°, in relation to the 'zero-meridian' of the electron, the four of c and s are twisted 28.6°, 118.6°, 208.6° and 298.6°. In (298.6-284.7)/360 of cases the next figure is the four-bladed, coming from the three-bladed, and in the other direction, coming from the four-bladed, in (44.7-28.6)/360 of cases the three-bladed is next. That are 3.9 resp. 4.5 %. Maybe that leads to an attempt to answer the open question. - And maybe the cycloid will disclose some other secrets. Values of physical constants perhaps? Fine-structure constant e.g., as length of a section? - But, please, never forget: we are playing a game - just for fun! (calculated and drawn 1996 on board s/y 'funtom' in Guanaja, Honduras, with MS QBasic) close |

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

The horn torus, we discuss here, shall

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

as

so the good old Riemann sphere better should be replaced by the much more universal horn torus!

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 ;-)

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

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:

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!

mathematics?

it from bit?

... secrets!

→ invitation