never ceases to amaze us in its wonders and the unique and incredible ways it finds to do seemingly ordinary things. The quantum
relationship between higher mathematics
and honeybees is a perfect example of this.
The Dance of the Bees
It has long been known that bees, despite their extremely small brain, communicate the location of nectar sources to one another through a complex dance. This dance is well documented and all the patterns and shapes they use are known to scientists. What is not known is how they come up with this dance, or how they understand it.
There is a basic figure eight pattern that bees use to describe the location of a food source. The figure 8 sometimes looks very wide and sometimes it looks like an oval with a line bisecting it. On the line in the middle, there is a waggle on each side. This waggle is used to convey the angle from the sun to the food source. This angle is somehow measured from an imaginary vertical line through the dance and interpreted by the "recruited" bees.
The distance from the food source to the beehive is another piece of information that the bees need. This is conveyed by the basic shape of the figure 8. The wider it is, the farther away the food source is. This is all fairly straightforward until the food source is moved inward past a critical point. When this happens the dance changes drastically. The dance now varies slightly from hive to hive and is completely different from the standard dance. The bees travel in a large loop, going one way then the other. Basically it is a complete mystery to scientists why and how this happens.
Barbara Shipman is a mathematician who studies multi-dimensional manifolds at The University of Rochester. These manifolds are useful in the bizarre world of quantum mechanics. A manifold is basically just a shape, such as the surface of a saddle. In mathematics (and quantum physics) there are multi-dimensional manifolds that are really difficult to imagine. Because of this mathematicians frequently use the "shadow" of these manifolds to try and visualize them. The shadow is just like taking a 3-dimensionsal box and getting a 2-dimensional picture from it. Likewise you can take a 6-dimensional shape and make a 2 or 3 dimension picture.
Barbara was dealing with one particular shape, the flag manifold. The standard flag manifold maps to a hexagon in 2 dimensions, just like a bees honeycomb. This probably got the wheels started that let Barbara notice a startling correlation between the shadows of some shapes in the flag manifold and the dance of the bees. She had seen the dances before and they kept popping up everywhere she turned. Interested by this, Barbara developed a single variable that could be altered to replicate the bees dance from the 6-dimensional flag manifold.
When this variable is decreased beyond a certain point, the shape of the shadow alters drastically just like the dance. The correlation is far too large to be a coincidence. Scientists are now speculating and studying how the bees determine their dance, and how they interpret it.
Experimental data has shown that altering the magnetic field around the bees will alter the dance significantly. The bees must, it seems, in some way detect the quantum effects and use them to create their dance. The flag manifold is used for describing the behavior of quarks in a stable state. Shipman thinks that something in the brain of these insects is sensitive to the workings of the extremely minute, in a way that has never been anticipated.
Other scientists, such as Roger Penrose of Oxford University, have speculated as to quantum mechanics at work in nerve cells. He has a theory that small tubes in nerve cells act as quantum detectors, reading the normal quantum fluctuations of empty space. This adds a large air of mysticism and randomness to the workings of a brain.
It is small things like this that make us realize how little we still know, and how complicated even everyday things can be.