In today’s post I’m in very good mood. It appears that I’ve solved the Gordian Knot of string theory in a very apt way. According to Wikipedia:
The cutting of the Gordian Knot is an Ancient Greek legend associated with Alexander the Great in Gordium in Phrygia, regarding a complex knot that tied an oxcart. Reputedly, whoever could untie it would be destined to rule all of Asia. In 333 BC Alexander was challenged to untie the knot. Instead of untangling it laboriously as expected, he dramatically cut through it with his sword, thus exercising another form of mental genius. It is thus used as a metaphor for a seemingly intractable problem which is solved by exercising an unexpectedly direct, novel, rule-bending, decisive, and simple approach that removes the perceived constraints.
My solution to solve the way how the knots required in string theory was not to think about knots but just let them emerge from pure mathematics. And this is exactly what happened. Before, when I forced the two turns of the helix that revolves around a spherical surface apart by introducing a linear indentation, I was able to separate the two turns, but in the case of the Higgs helix, the two loops became separe:
But when I introduced an opposite twist to the helix with a double the radius of the secondary helix, I was able to separate the strings of dots from each other.
Below I depict the four trajectories of the dots with four different colors. In this picture the distance from the opposite end of the loop is always constant, meaning that the curvature of the string is always constant.
As this shape looks like the saint Hannes cross, ⌘, but squeezed into a knot, I call this shape the Saint Hannes Knot.
And here is the shape from another angle.
As I mentioned in my last post, without knotting, the entangled loops would unravel into a circular loop. This loop would probably disproportionate into helices of light (supraphotons) in no time at all.
However, when viewed like this it is immensely logical shy the structure remains stable. Just as long as the knot is sufficiently huge, the force expressed by refraction is contained by the knot. Or more specifically the geometrical constraint of the knot is sufficient to cause to the linear motion of the dots to be bent, or refracted.
Exactly what the quantitative correlation of the geometry of the knot and refraction is, is still somewhat of a mystery to me. But I’m pretty confident that it won’t take long for me to figure out the last kinks.
Comments