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"OH WATERS, TEEM WITH MEDICINE TO KEEP MY BODY SAFE FROM HARM, SO THAT I MAY LONG SEE THE SUN." - Rig Veda
"How could bees of little brain come up with anything as complex as a dance language? The answer could lie not in biology but in six-dimensional math and the bizarre world of quantum mechanics.(...) Von Frisch had watched bees dancing on the vertical face of the honeycomb, analyzed the choreographic syntax, and articulated a vocabulary. When a bee finds a source of food, he realized, it returns to the hive and communicates the distance and direction of the food to the other worker bees, called recruits. On the honeycomb which Von Frisch referred to as the dance floor, the bee performs a "waggle dance," which in outline looks something like a coffee bean--two rounded arcs bisected by a central line. The bee starts by making a short straight run, waggling side to side and buzzing as it goes. Then it turns left (or right) and walks in a semicircle back to the starting point. The bee then repeats the short run down the middle, makes a semicircle to the opposite side, and returns once again to the starting point.(...)
One day Shipman was busy projecting the six-dimensional residents of the flag manifold onto two dimensions. The particular technique she was using involved first making a two-dimensional outline of the six dimensions of the flag manifold. This is not as strange as it may sound. When you draw a circle, you are in effect making a two-dimensional outline of a three-dimensional sphere. As it turns out, if you make a two-dimensional outline of the six-dimensional flag manifold, you wind up with a hexagon. The bee's honeycomb, of course, is also made up of hexagons, but that is purely coincidental. However, Shipman soon discovered a more explicit connection. She found a group of objects in the flag manifold that, when projected onto a two-dimensional hexagon, formed curves that reminded her of the bee's recruitment dance. The more she explored the flag manifold, the more curves she found that precisely matched the ones in the recruitment dance. "I wasn't looking for a connection between bees and the flag manifold," she says. "I was just doing my research. The curves were nothing special in themselves, except that the dance patterns kept emerging." Delving more deeply into the flag manifold, Shipman dredged up a variable, which she called alpha, that allowed her to reproduce the entire bee dance in all its parts and variations. Alpha determines the shape of the curves in the 6-D flag manifold, which means it also controls how those curves look when they are projected onto the 2-D hexagon. Infinitely large values of alpha produce a single line that cuts the hexagon in half. Large' values of alpha produce two lines very close together. Decrease alpha and the lines splay out, joined at one end like a V. Continue to decrease alpha further and the lines form a wider and wider V until, at a certain value, they each hit a vertex of the hexagon. Then the curves change suddenly and dramatically. "When alpha reaches a critical value," explains Shipman, "the projected curves become straight line segments lying along opposing faces of the hexagon."
Convicts display the sort of camaraderie that only emerges under siege. They are polite to one another because they know the consequences of being rude. It’s as if everyone’s carrying a gun, so no one gets shot. People are respectful in prison for the same reason that soldiers step carefully through a minefield.