In this article, we reflect on hexagonal information geometry. The multiscale topology of pattern formation is discussed. Coupled oscillator dynamics and triplet synergism are described in 5-dimensional information binding.

Scale-space waves

I used to sit by the sea on long winter nights. Here, in a small town on the Montenegrin coast, southern winds roughen the sea in the evening hours, washing the beach shore. If one stays longer at night, the northern wind usually picks up from the mountains, which quiets the sea and makes wavy patterns along the sandy beach.

It takes both directions to look at a time dimension in a quantum theory. In this beachside story, both the southern wind in the evening and the northern wind later in the night make a cascade of wavy patterns. In the language of mathematics, stochastic resonance synergies write the memory of the nightlong story along the beach shore. The sea and wind in action were visible the next morning.

A multiscale topology of information geometry

Saturn's North Pole appears to be a complex cloud structure, as seen with the current satellite technology. A massive hexagon with the pole vortex at its center is spinning counterclockwise. Conjoined by the surrounding cloud structure, spinning clockwise.

Although dynamical, Tesla's 3-phase induction motor is topologically a hexagon, too. The stator's triangle rotates in synchrony with the inducted rotor. The rotor's triangle, weighing a load, follows behind the stators. The coupled oscillator dynamics of Saturn's hexagon and Tesla's motor are opposite in the interpretation of quantum information electromagnetism. Clockwise and counterclockwise information flows resonate in the Saturn's, while both rotate in the same direction in the Tesla's motor. The hexagon in Saturn's atmosphere appears in a static formation of its information geometry.

Triplet synergism and 5-dimensional information binding

"3-6-9" mathematical structure has been introduced in the theory of stochastic resonance synergies. The invariance property of this mathematical structure has been described. The atomic composition of stochastic resonance synergies and their group periodic arrangements have been discussed.

The asymptotic freedom of motion in the triplet synergistic dynamics translates to the so-called “fine structure constant." In addition, the invariance of prime numbers structure distribution confirms Riemann’s hypothesis. Showing a new way of looking at the significance of quantum number descriptors in this mathematical interpretation.

Bela Julesz refers to the information geometry of visual textures in his texton theory. Triplet synergisms in human perception and movements have been studied across the modalities in our work. Color-constancy, intensity-independent auditory distance perception, and the synergistic control of equilibrium positions in reaching movements have been analyzed. Topological maps of 5-dimensional information binding have been shown to scale multidimensional information dynamically.

Concluding remarks

The mystery of the origin of Saturn's hexagon ring continues. Open for future exploration with improved resolutions, revealing its full complexity. Stability of the hexagonal form in Saturn's turbulent cloud structure implies, in our view, evolving dynamics of memory formation. From complex geometries of molecular shapes to double-helix arrangements of information carriers in life forms, Quadrupole information carriers have been described in our reports, and holographic memory expressions have been proposed. For the beauty of it, snowflakes in clouds originate in hexagonal form, too. It is the difference in their paths, the way they evolve toward the Earth that makes them have a unique shape.


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