Chaos Theory: from randomness to order

By Steve Dotson, special contributor

Chaos Theory is an honors course with an interdisciplinary appeal. Three professors from different fields at Columbia College converge to instruct students in both chaos as understood through tradition, and chaos theory, as it applies to the newest findings in mathematics.

Dr. Ann Bledsoe, associate professor of mathematics, is teaching the section of the Chaos Theory course that deals with the mathematics of chaos and the structures of complexity. Dr. Anthony Alioto, Schiffman Chair in Ethics, Religious Studies and Philosophy, teaches a history of chaos through myth and ways of exploring consciousness using chaos theory. Dr. Robert Boon, instructor of Humanities, teaches the literary part of the course, but also covers language development.

     

The idea for the course began as casual conversation between the three professors. Bledsoe, Alioto and Boon realized that they all had different ways of approaching chaos theory and began designing the basic structure of the course out of curiosity.  

Students who enroll in Chaos Theory must have honors eligibility. By the end of the course, they are expected to be able to demonstrate a conceptual knowledge of chaos theory, use mathematics to understand chaos, explore imaginative approaches to the theories through literature and investigate consciousness from a number of perspectives. Both sides of the brain come together for an hour of unpredictability.    

In chaos theory, scientists have determined that randomness creates variety while eventually resulting in an ordered system. This is evident in areas such as economics, weather and biology. In other words, the world as we know it is constantly changing and creating variety by doing so.

“Chaos and order are two sides of the same coin,” said Alioto. “Chaos is interrelated with order. It keeps stagnation from setting into any one system.”

Bledsoe said, “Mathematicians and scientists in the west, at least, would say that there is no chaos, that everything is order and everything is pattern. We just haven’t found it yet.  Random generators, if left to run long enough, will start to have order.”

Mythology and early science have presented ideas of chaos to explore.  Alioto said, "In many mythologies the creation of the universe is symbolized by the gods of order conquering chaos. While the universe, including the gods, may originate from chaos, order seems to emerge also. Order banishes chaos but never really destroys it.”

Historically, science and mathematics assumed that all outcomes could be determined. In other words, early science held the belief that every natural event could be predicted. The idea was that everything follows the same rules, in the same way, all the time. “Chaos, randomness and chance do not really exist but are due to human ignorance of causes. Chaos theory seems to contradict this assertion,” Alioto said.   

Each professor approaches the subject in a different way. “Bob is going to talk about the development of language. Think about that. Everybody starts with the same basics and it comes out differently,” said Bledsoe. Humans start off in life with the same language base, but as evidenced through various dialects and languages that exist, variations set into any one system.   

     

One can see the variation in language development. But how is chaos expressed as an idea through literature?  “Not pure chaos theory as an English teacher,” said Boon, who wrote a counseling course in 1989 using the theory. His focus is mainly on both language as a human trait, as well as language through literature. 

     

Boon mentioned the novel “Pfitz” by Andew Crumey. Crumey tells the story of a perfect city and the consequences that occur when someone attempts to over-organize a complex system. Since the 1970s chaos theory has been making its way into our culture through the media and books like "Pfitz". The popular 2004 movie “The Butterfly Effect,” with Ashton Kutcher, revolves around the idea that time traveling can interfere with reality by creating infinite future possibilities through small changes in the past.

The course appeals to the mathematical, philosophical and literary minded. This semester only five students are enrolled in Chaos Theory; however, Bledsoe says several students have expressed an interest in taking the course.  

     

One might not precisely know what they are getting themselves into when they enroll. Ironically, unpredictability is one of the lessons that can be taken away from chaos theory. 

Fractals are mathematical models expressed visually 

that illustrate how chaos creates variety in a bigger system.
Photo from coolmath.com 

 

The origins of chaos theory

Chaos theory comes from mathematics as early as 1888. James Yorke, distinguished university professor of Mathematics and Physics at the University of Maryland, was the first to use “chaos” as a term in 1975. Since then he has continued looking at complex systems using mathematics. A meteorologist named Edward Lorenz discovered randomness while trying to predict the weather. He is known as one of the primary pioneers of chaos theory.