HOUSE_OVERSIGHT_013653.jpg

predict how the fluid will flow upon it. If we start with a simple bowl, a parabolic basin, then the attractor itself is a point at the bowl’s very bottom. Changing the value of some influential parameter may induce the sudden formation of a small hill, growing at the center of the basin’s bottom. Now fluid flow in the attractor bowl runs down to a path around the hill at its bottom. The autonomous motion of the fluid flows takes place now in a circular orbit. The basin of the new attractor is the original bowl minus the point at the top of the central hill. The fluid flow around the hill at the bottom of the basin is circular and is called a limit cycle. Note that the direction of the rotation of the limit cycle can circle in one direction or the other. In some computational simulations, motion alternates between directions. This suggests the aspect of the born again amphetamine religions, splitting. There is an unstable and intermixed probability of right versus left turning directions and their alternation. This vulnerability to directional splitting and often unpredictable alterations in action themes can represent what seem to be paradoxical combinations of both good and evil in the same strongly faithful, for example, the apparent bidirectional morality of generous and loving, pederast priests.

These mathematically flavored images of the sudden emergence of a limit cycle in complex systems was made biologically concrete to me by research conducted by one of my first graduate students, David Segal. He is now a professor of psychiatry at the University of California in San Diego. His program of work involved the administration of very gradually increasing doses of amphetamine to rats while their behavior was being monitored and recorded by a continuously running video camera. He documented the behavior of rats in a walled rectangular space within which, without drugs, they first wandered about randomly and then settled down to rest in an individually selected, favorite home corner. Segal called all of these phenomena, patterns of exploratory behavior. At doses of amphetamine below 2.5 milligrams (mg) per kilogram weight (kg), the exploration of the entire bounded space proceeded faster than was the case with their salt-water treated controls, their paths being more uniformly distributed throughout the box. They spent less time resting in their home corner. At almost precisely 2.5 mg/kg, the rat’s behavior changed dramatically into an entirely new pattern of continuous circling. As

153

HOUSE_OVERSIGHT_013653