For a while, in the 1980s and early 1990s, chaos was touted as the next big revolution in science, on par with quantum mechanics. Storytellers embraced its principles and worked them into their novels, films and plays. Almost everyone remembers how "Jurassic Park" treated chaos, with self-proclaimed chaotician Ian Malcolm letting drips of water run along Ellie Sattler's hand to prove that the liquid never takes the exact same path. In the Michael Crichton novel, which came out in 1990, chaos takes on even greater thematic importance. Crichton organizes the book into iterations, just like the iterations used to generate bifurcation diagrams and fractals. And Malcolm provides much deeper insights into the science of chaos than his onscreen persona:
The same year Spielberg hit pay dirt with a dinosaur theme park run amok, Tom Stoppard published his play "Arcadia," which uses chaos theory as a vehicle to explore broader themes, such as the mystery of sex and the conflict of emotion with intellect. At one point, the character Valentine Coverly offers an explanation of chaos that any mathematician would appreciate: "If you knew the algorithm and fed it back say ten thousand times, each time there'd be a dot somewhere on the screen. You'd never know where to expect the next dot. But gradually you'd start to see this shape ..."
Then, despite all of this attention, chaos theory seemed to recede into the shadows. Some questioned whether the subject deserved all of the hype it received in the 1990s. But in reality, chaos is less of a new science than a progression in thinking, a shift in world views, from Newtonian determinism to nonlinear unpredictability. As such, the principles slowly uncovered by the likes of Poincaré, Lorenz, Smale, Young and others touch all of science, forming a lens through which problems in any discipline can be studied. One Harvard scientist puts it this way: "[Chaos] is a collection of tools, and it's a way of understanding phenomena that occur over a wide range of fields" [source: Ornes].
Medicine may be the next frontier to benefit from the insights of chaos. For example, physiologists have discovered that cardiac rhythm is extremely sensitive to initial conditions and that when heart rate becomes highly regular, the muscle tissue is less capable of adapting to demands, predisposing a person to arrhythmias and myocardial infarction. Researchers also suspect chaotic behavior in brain function and are trying to find links between a patient's cognitive power and his or her electroencephalogram (EEG), the record of brain activity produced by electroencephalography. Is it possible that your ability to perceive and analyze information is related to the fractal dimension of your EEG?
Perhaps one day, thanks to chaos, we'll know the answer. But don't count on getting any closer to having a reliable 10-day forecast. As much as we hate to admit it, some things are simply beyond the grasp of our Newtonian science.
Author's Note: How Chaos Theory Works
Back in college, I took a course on population biology, thinking it would be like other ecology courses -- a little soft and mild-mannered. It ended up being one of the hardest classes I took as a biology major, filled with differential equations and complex concepts. I don't remember dynamical instability being discussed, but I suspect now, after writing this article, that we ventured regularly into the land of chaos. Had I not been so focused on making it through the course without wrecking my GPA, I might have seen some of those concepts for what they were -- manifestations of a fundamental, and sometimes frightening, shift in how we view the world.
- Bradley, Larry. "Chaos and Fractals." Space Telescope Science Institute. Johns Hopkins University. 2010. (Jan. 14, 2013) http://www.stsci.edu/~lbradley/seminar/index.html
- "Chaos : A pictorial introduction." La Trobe University. Jan. 12, 2000. (Jan. 14, 2013) http://johnbanks.maths.latrobe.edu.au/chaos/index.html
- Dance, Scott. "50 years ago, Ocean City was washing away." The Baltimore Sun. March 5, 2012 (Jan. 14, 2013) http://www.baltimoresun.com/news/weather/bs-md-ash-wednesday-storm-20120305,0,3279194.story?page=1&track=rss
- Dizikes, Peter. "The meaning of the butterfly." Boston.com. June 8, 2008. (Jan. 14, 2013) http://www.boston.com/bostonglobe/ideas/articles/2008/06/08/the_meaning_of_the_butterfly/?page=full
- Elert, Glenn. "The Chaos Hypertextbook: Mathematics in the Age of the Computer." (Jan. 14, 2013) http://hypertextbook.com/chaos/
- Fractal Foundation. "What is Chaos Theory?" (Jan. 14, 2013) http://fractalfoundation.org/resources/what-is-chaos-theory/
- Gleick, James. "Chaos: Making a New Science." Open Road. 2011.
- Laplace, Pierre-Simon. "A Philosophical Essay on Probabilities." Translated by Frederick Wilson Truscott and Frederick Lincoln Emory. John Wiley & Sons. 1902. (Feb. 4, 2014) https://archive.org/stream/philosophicaless00lapliala#page/4/mode/2up
- Li, Tien-Yien and James A. Yorke. "Period Three Implies Chaos." The American Mathematical Monthly. Vol. 82, No. 10 (Dec. 1975). (Feb. 4, 2014) http://www.its.caltech.edu/~matilde/LiYorke.pdf
- Oestreicher, Christian. "A history of chaos theory." Dialogues in Clinical Neuroscience. 2007.
- Ornes, Stephen. "Whatever Happened to ... Chaos Theory?" Discover Magazine. April 4, 2007. (Jan. 14, 2013) http://discovermagazine.com/2007/apr/whatever-happened-to-chaos-theory#.UPS90HBGJ5Q
- Read, Wolf. "The Big Blow of Columbus Day 1962." University of Washington. Feb. 9, 2005. (Jan. 14, 2013) http://www.climate.washington.edu/stormking/October1962.html
- The StarChild Team. "Urbain Le Verrier." NASA/GSFC. (Feb. 4, 2014) http://starchild.gsfc.nasa.gov/docs/StarChild/whos_who_level2/leverrier.html
- Taylor, Richard P. "Order in Pollock's Chaos." Scientific American. December 2002.
- Trump, Matthew A. "What is Chaos?" Ilya Prigogine Center for Studies in Statistical Mechanics and Complex Systems, University of Texas. Aug. 14, 1998. (Jan. 14, 2013) http://order.ph.utexas.edu/chaos/
- Wang, W. "Bifurcation." Encyclopedia of Ecology, Volume One. Elsevier. 2008.