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 teaser

12. Dimensionality - not a physical term!

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

14. Patterns and strings - winding cycloids and tiny snippets of themLooking at one single horn torus, we see various patterns, formed by the cycloid during unrolling along an axis: coils, spirals, loops, following strictly deterministic rules. Two interacting tori combine their patterns to a different kind of dynamically changing patterns when mutually unrolling their cycloids, still in deterministic manner. The more horn tori we add to the set, the more complex become the patterns, turning into a fractal quality, dynamically swirling around, and still deterministic. With increasing number of horn tori the complexity grows as well, and it becomes difficult or impossible to detect any determinism. But the patterns persist respectively turn into a higher level of fractal complexity. The patterns not only occur in the order of elementary particles, where the ratio of angular velocities (revolution : rotation) is bigger than ½, they continue into the macroscopic world, where rotation prevails, range over all scales and leave visible marks everywhere, as molecular and crystal structures, in organic matter and organisms, in snow flakes and great many more synergetic effects. Even, only as an example (I'm not a fan of him): R. Sheldrake's term morphogenetic or morphic field could be brought to life again, now seen from a completely different angle of view and released from the stigma of inexplicability. The same with so called 'instincts' of lower animals. Maybe they have unknown special senses to detect such patterns? And considerations concerning the multiple dynamic feedbacks from the 'neighborhood' - infinitely many from the whole universe - to every single spatial point take the weight from the complexity argument in so called 'proofs of god' and strengthens position of evolutionists in a further way. We already have touched upon the fact that the whole cycloid of an unrolling horn torus can be reduced without loss of information to the part within a small neighborhood of Point S. Even an infinitesimal small piece of the line is sufficient to determine the whole curve. The patterns then equally are being reduced to an infinitesimal small bundle of snippets, characterising one particular spatial point (better: spatial 'spot'). Change of the patterns means movement to a different spot. These snippets are not the well-known strings - whereas parallels in behavior exist! - Strings are embedded in a multidimensional space and show complex apriori properties, so that they, in my opinion, don't seem to be candidates for fundamental entities, created at the beginning of the universe. They describe much, perhaps all, but they are - likewise as horn tori - a mere model of nature, as every physical theory is. I admittedly admire their mighty potency, but for
outside observers the theory sometimes impresses as play castle of brave formula heroes and
climbing wall of extravagant number crunchers. (Sorry, I wrote this 1996, in German. Today I
perhaps better should attend more and pay my respects to the meanwhile widely accepted theories,
especially the newer and auspicious loop quantum gravity, but here and now I just like to promote
the horny tori - they really have deserved this attention!)Here is the opportunity to emphasize again, that the horn tori don't exist as such, they only are a tool for imagination, to illustrate properties of numbers. They indeed only - as (dynamic!) Riemann surface resp. manifold - represent numbers, complex numbers, rotation standing for the real, revolution for the imaginary part. The values are equivalent to the longitude (real, number of rotations/spin and the particular meridian) resp. size (imaginary, effect of unrolling/revolution). These two properties already are implicated in the short snippet around Point S. The full horn torus is redundant, but very helpful for visual associations without added information ballast. The whole model only shall highlight the capability of complex numbers, to
count themselves mutually, creating manifold patterns hereby.Last sentence should be worth to think and reflect about thoroughly! - - - (fractal iteration patterns are well known examples) My personal conclusion (despite being perpetually and marveling in close contact with beauties of nature and able to revel in surprises of life): our world is self-creating, basically consists of complex numbers, is arithmetic, is mathematics ... ( hope not to be stoned for that - blasphemous - reductionism ;-) close |

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