horn torus model step by step
the horn torus is an analogous three-dimensional image for complex numbers to explain|
their exceptional 'behaviour' and creative capability when 'interacting' with one another.
they are able to create an extremely complex and sophisticated world: ... our universe.
there is one main principle that rules the entity of the horn torus model and it consists of
a few conditions only which finally are reduced to one when we consider it dynamically
(note: the static horn torus compactification of complex numbers is a different topic):
within one isolated entity the rates of revolution and rotation primarily are constant,
they are correlated to the standard dynamic horn torus which is defined as performing
one 'full' rotation around the axis per one 'full' revolution of the longitudes and vice versa.
rotation is the simple spin of the horn torus 'around' the main symmetry axis and
revolution is the combination of a turn of the torus bulge around itself and simultaneously
the rolling (or 'unrolling') along the axis in always the same 'direction' and additionally
an increase of the horn torus size so that longitudes always equal the unrolled distance,
measured from the 'spatial point' where the entity has its origin on the axis (where the
respective horn torus size is zero) respectively a decrease when approaching this origin.
rotation around and unrolling on the axis, combined with change of the horn torus size,
results in a change of the ratio revolution : rotation, passing values from infinite to zero,
but we restrict to rational values by allowing 'full' rotations and 'full' revolutions only.
variation of the ratio obviously is caused by the change of revolution angular velocity
(constancy of the rate of revolution refers to the circumferential speed of longitudes
and not to the angular velocity which is inversely proportional to the horn torus size).
so far, the horn torus model is an intellectual game only, without concrete importance -
any physical interpretation requires far-reaching abstraction from most traditional ideas,
but having achieved the abstraction, being open-minded and familiarized with the game
one will be able to revel in new perceptions, cognitions and lots of aha experiences !!
in addition to that, the model is well approachable by already elaborated mathematics.
next step has to be the treatment of two horn tori that are nested into one another, later
the 'interaction' of more (up to infinitely many) horn torus entities, symbolising 'particles'.