one mathematical code rules our world
reality is not imaginable? - so we need an analogous model!
we use the three-dimensional space for projections of abstract fundamental entities
and construct within this well-known space images of numbers, mathematical sets and manifolds,
in case of the horn torus model images of complex numbers as Riemann surfaces, modified to dynamical objects,
but - notabene - that's only a tool for imagination and better understanding, horn tori themselves are not seen in 'reality'!
complex numbers and manifolds however occur in nature and they show the same 'behaviour' as in the images we now draw of them.
the upper half of the background image with the tightly packed circles (tighter as shown) represents the imaginary part of complex numbers
(what is equivalent to the one-dimensional straight red line), then we rotate these circles once around the line and get a nested array of horn tori
and now we introduce dynamics: first we let the circles resp. horn tori roll along the line, all with same, constant circumferential speed,
what results in different angular velocity of every circle resp. horn torus, with size and angular velocity being inversely proportional,
then, as real part of the numbers, we let the horn tori rotate around the symmetry axis, allowing both directions for rotation,
and so we have two kinds of turns: 'revolutions' of the torus bulges along the line (axis) and 'rotations' around it,
and - important - all nested horn tori retain one common point on the bright red tangent.
the horn tori shall vary their linear size correspondent to the length they travel on the line,
what varies the angular velocity of revolution too, whereas the rotation speed shall remain constant first.
now we single out one horn torus, mark one point on the surface and follow the trajectory during the combined motion.
it's rather intricate and sophisticated, but easily to visualize in our familiar three-dimensional space, see the coarse animation,
which shows a section and simplifies a little, in real the trajectory continuously changes shape, interpolating between depicted lines.
we find singular significant loops and blades (Lissajous figures, 'resonances' or 'attractors'). I identify them as 'particles', as fermions,
and the lines not forming closed figures, possibly filling the whole torus surface, can be identified as mediators between them, as bosons,
what means: all kinds of elementary particles are beaded on one thread within one single size-changing horn torus, forming one 'entity'
and all existing entities, all nested horn tori, 'interact' at one single common point, where they touch their common tangent.
this point is one spatial point, and the combination of all points with different permutation of horn torus sizes, is the space.
the horn torus model illustrates reasonably comprehensible much about properties and nature of fundamental entities,
explains constancy of light speed by the principle of self-similarity, identifies Planck units, spin (isospin as well),
energy (frequency) and forces, offers possibilities to figure natural constants resulting from self-metrification,
and eventually interprets the cause of locomotion of particles, leading to an unification of all forces ...
the universe is mathematical
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horn torus (text)
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