Came across this connection between the bee dance and quantum mechanics. Anybody game to read it? If you look up "flag manifold" it will not make you feel good. For this article I think flag manifold=mathematically defined space.
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."
The smooth divergence of the splayed lines and their abrupt transition to discontinuous segments are critical--they link Shipman's curves to those parts of the recruitment dance that bees emphasize with their waggling and buzzing. "Biologists know that only certain parts of the dance convey information," she says. "In the waggle dance, it's the diverging waggling runs and not the return loops. In the circle dance it's short straight segments on the sides of the loops." Shipman's mathematics captures both of these characteristics, and the parameter alpha is the key. "If different species have different sensitivities to alpha, then they will change from the waggle dances to round dances when the food source is at different distances."
If Shipman is correct, her mathematical description of the recruitment dance would push bee studies to a new level.
[size="1"][ December 23, 2005, 09:03 AM: Message edited by: dickm ][/size]