Patrick Irvin Chaos and the Logistic Map February 2001

Full Report (MS Word document)

An Investigation into Chaos

Normal operation of the heart and brain seem to depend on seemingly abnormal rhythms. Cardiac arrest and seizures can be detected when the rhythm of the heart and brain waves begin to line up in clock-like synchronization. It appears that these things need occasional irregularities in their rhythm to keep themselves in cadence. Seizures can sometimes be triggered by flashing or flickering lights, or even geometric shapes or patterns. This fairly rare condition is known as photosensitive epilepsy. (NSE) I would conjecture that the regularity of strobe lights and beats in music can cause the brain activity in photosensitive people to line up because their brain can't override tin music can cause the brain activity in photosensitive people to line up because their brain can't override the incoming signals, which triggers a seizure in them. The non-linearity of the beats can be explained with help from chaos theory, which deals with non-linearity. The most orderly synchronous activity can be represented by strictly periodic signals of low complexity. Less synchronous activity, reflecting a less orderly state, can be represented by signals of increased complexity with multiple frequencies, quasiperiodic signals, and increasing chaotic behavior of the signal. (EC, 3) It appears that seizures take place when chaos in the brain breaks down to linearity.

Chaos theory can also help to explain the causes of schizophrenia, by examining the mechanics of a schizophrenic's eye movement as he watches a slowly swinging pendulum. Following a slowly swinging pendulum with one's eyes is an ostensibly simple task which most people have no trouble with it, but a person with schizophrenia cannot do it, their eyes jump about in disruptively small increments, over shooting or undershooting the target and creating a constant haze of extraneous movements. Whereas the tradition analysis has been from a physiological point of view, chaos theory introduces the idea of small errors begetting large errors (disruptive eye movements). It also introduces the possibility that there are universal elements of motion (Chaos, 276) rather than just a boatload of body parts working together to prod boatload of body parts working together to produce a result.(Chaos, 276)

Works Cited

NSE: Edward Draper, PhD, Photosensitivity, http://www.erg.ion.ucl.ac.uk/NSEhome/photo.html, viewed: 2/18/01.

Chaos: James Gleick, Chaos, Viking: New York, 1989.

ES: Gregory K. Bergey and Piotr J. Franaszczuk, Epileptic Seizures are Characterized by Changing Signal Complexity, (preprint?), http://erl.neuro.jhmi.edu/pfranasz/CN00/cn00.pdf, viewed: 2/19/01.