horn torus model step by step
the horn torus is an associative aid to illustrate complex numbers.
the horn torus has two possibilities (degrees of freedom) for turns:
1. rotation as spin around the main symmetry axis (two directions)
2. revolution of longitudes, combined with an
increase of size and
kind of rolling along the main symmetry axis with constant speed c
- the axis (= horns of infinitely big tori) can be associated with time.
combine both turns with particular ratios to get different trajectories
respectively for the increasing horn torus a complex 'unrolling line'
as fundamental entity containing all possible resonances (particles)
the rate of rotation symbolises the real part of a complex number,
the unrolled distance from size zero symbolises the imaginary part
and every section of the entity is assigned to one complex number
i.e. complex numbers represent all different particles in one thread
where 'particles' don't populate any construction like vector spaces
but form their own space as aggregate of all infinitely many entities
which are represented in all spatial points
by one horn torus each