Andrew Smith
There are two distinct, discrete spirals. Equal-length, straight lines compose both. One has equal distance between its windings. Plato’s math teacher, Theodorus of Cyrene, created that one 2400 years ago. In 2005, I created the other, the Protogon spiral, whose windings grow farther apart.
The “Time Hook” is a metaphysical concoction contrasting the two spirals. My supposition is, in a quantum world where only straight lines exist, there are only two spirals. I imagine they ornament either side of the beak of a creature which rules time. It feasts by piercing the veil of space in a quantum manner, parting pixels where no curves are available. Space flow reflects one spiral while the wayward side exudes an eddy of the opposing spiral.
The version illustrated above, “Beak 2”, expresses its outside circumference (OC) increased at a rate of twice its thickness. Therefore, “Beak 1/2” would be a beak with its thickness twice its (OC).
The plane on which each spiral rests is concave. It approaches but never reaches, 90 degrees to its starting direction.
When the spirals start away from each other on the same plane, there is a short limit in growth before a beak begins to self-destruct. Because of this, it takes only four steps for my Protogon spiral, while seven steps for the Theodorus spiral, to swing past 180 degrees and overlap the other. I consider this phenomenon the “Fenix Factor”. It suggests why galaxies have so few windings and yet there are so many of them.