horn torus - geometry of space, time, physical objects


For centuries science ignored the existence of the geometric figure horn torus completely or neglected its relevance unduly. Nearly nobody realized, described and applied the exceptional topology, maximum symmetry, high complexity and creative capabilities of this unique object. Now, in recent years, it increasingly appears in publications, mostly in context of particle and quantum physics and in connection to cosmological questions. The subject is developing and promises to stay exciting for a good while.
The static horn torus already shows pretty interesting properties, e.g. as replacement of the Riemann sphere, but it becomes most thrilling when we add dynamic to the figure, when we let it turn, around the main symmetry axis and around the torus bulge, when we let it change its size during the turns, when we combine all these motions and when we finally interlace two, more or even infinitely many such dynamic horn tori into one another, as roughly indicated in the image above. Their 'unrolling' trajectories symbolise all occurences in one spatial point.
A detailed description, combined with many animations, is provided on the link below. There the horn torus model is presented as a kind of intellectual game, first to exercise imaginative power, to improve abstract thinking and to generate lots of aha moments, then as proposal for a different approach to physical questions, and finally as part of an interdisciplinary art project: