Chaos: Where Does it Come From?

Do you feel that your life is in chaos?  You’re right.  It is inherent in your life — or any living thing (as I demonstrated in my PhD research.  See References) and may have been present immediately after the cosmos was created.

The Second International Workshop to Develop the Mutual Interaction between Specialists from Biology, Nonlinear Dynamics, Physics and Mathematics in Corsica, May 2010, stated its theme thusly: “More and more works show that biological systems have non linear dynamics, so they may have also chaotic behavior and strange attractors. In neural systems new observations show that chaos appears both on the level of one neuron and on the level of large networks. In population dynamics, chaos has been observed in experimental cultures and seems to be important in the diffusion of transmitted diseases in social networks. It becomes obvious that there is a challenging demand for studying and modeling complex dynamics of biological systems in order to describe various modes and activities. In particular, there is a need to understand the interplay between nonlinearity and stochasticity of biological processes.”

In particular, if your brain slips from its normal chaos to regular rhythm, you have an epileptic fit.  If your heart breaks from chaos to completely periodic behavior, you have a heart attack.  After we review the meaning of the word, we will look at new results about chaos and the Big Bang.

“Chaos” is a slippery thing to define.  It is much easier to list the properties in a system described as “chaotic” rather than to give a precise definition of chaos. (See this MathWorld page for clarification and citations.)  For now, a simple, if slightly imprecise, way of describing chaos is “chaotic systems are distinguished by sensitive dependence on initial conditions and by having evolution through phase space that appears to be quite random.”

James Gleick, in his National Book Award and Pulitzer Prize finalist book Making A New Science,notes that “No one [of the chaos scientists he interviewed] could quite agree on [a definition of] the word itself,” and so instead gives descriptions from a number of practitioners in the field.  For example, he quotes Philip Holmes (apparently defining “chaotic”): “The complicated aperiodic attracting orbits of certain, usually low-dimensional dynamical systems.”  Similarly, he quotes Bai-Lin Hao describing chaos (roughly) as “a kind of order without periodicity.”

S. Neil Rasband says, “The very use of the word ‘chaos’ implies some observation of a system, perhaps through measurement, and that these observations or measurements vary unpredictably.  We often say observations are chaotic when there is no discernible regularity or order.”  This week came hints that chaos was born with the cosmos.

A study announced this month, published by the journal Communications in Mathematical Physics, seems to confirm a 7-year-old theory by Northwestern University physicist Adilson E. Motter.  The authors report not only that chaos is absolute (not depending on the observer), but also the mathematical tools that can be used to detect it.  When applied to the most accepted model for the evolution of the universe, these tools demonstrate that the early universe was chaotic.

“According to the classical theory of general relativity, the early universe experienced infinitely many oscillations between contracting and expanding directions,” Motter said. But that would take me infinitely long to explain in full detail. So accept chaos into your life.  You have no choice.  You might as well enjoy it.

References:

Big Bang Was Followed by Chaos, Mathematical Analysis Shows

Katrin Gelfert, Adilson E. Motter. (Non)Invariance of Dynamical Quantities for Orbit Equivalent Flows. Communications in Mathematical Physics, 2010

Gleick, J. Chaos: Making a New Science. New York: Penguin, 1988, p.306.

Second International Workshop,  to develop the mutual interaction between specialists from biology, nonlinear dynamics, physics and mathematics.

Jonathan V. Post, "Alternating Current Chemistry, Enzyme Waves, andMetabolic Chaos", NATO Workshop on Coherent and Emergent Phenomena inBiomolecular Systems, Tucson, AZ 15-19 January 1991

Jonathan Vos Post,
"Classroom At the Edge of Chaos: Towards a Neuroscience of Pedagogy."
Unpublished 100-page Dissertation proposal of Doctorate in Education, 2009

Rasband, S. N. Chaotic Dynamics of Nonlinear Systems. New York: Wiley, 1990, p.1

Weisstein, Eric W. "Chaos." From MathWorld–A Wolfram Web Resource.

[This is #2 of a 52-week series, the #1 of which was “Laws of Physics, or Merely Local By-laws?”, 9 Sep 2010]

See Also

The Spooky World of Quantum Biology 

Jonathan Vos Post is co-webmaster, Vice President, and Chief Information Officer of Magic Dragon Multimedia.  He has taught art, astronomy, biology, chemistry, computer science, English composition and English Literature at various California colleges.  Von Post has collaborated with Isaac Asimov, Ray Bradbury, Richard Feynman, David Brin and Arthur C. Clarke, and has innumerable published articles, short stories and poems to his credit. 

 

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