Chaos theory

Chaos theory is the study of dynamical systems that are heavily influenced by initial conditions.

Barnsley fern created using the chaos game. Natural forms (ferns, clouds, mountains, etc.) may be recreated through an Iterated function system (IFS).

CONTENT : A - F , G - L , M - R , S - Z , See also , External links

Quotes

Quotes are arranged alphabetically by author

A - F

For want of a nail the shoe was lost;
For want of a shoe the horse was lost;
For want of a horse the battle was lost;
For the failure of battle the kingdom was lost—
All for the want of a horse-shoe nail. ~ Anonymous

Mathematicians believed that prediction was just a function of keeping track of things. If you knew enough, you could predict anything… Chaos theory throws it right out the window because in fact there are great categories of phenomena that are inherently unpredictable. ~ Michael Crichton

• For want of a nail the shoe was lost;
  For want of a shoe the horse was lost;
  For want of a horse the battle was lost;
  For the failure of battle the kingdom was lost—
  All for the want of a horse-shoe nail.
  • Anonymous, For Want of a Nail, cited in: Jan Gillett (2014), Making Your Work Work: Everyday performance revolution. p. 101

• Mathematicians believed that prediction was just a function of keeping track of things. If you knew enough, you could predict anything… Chaos theory throws it right out the window because in fact there are great categories of phenomena that are inherently unpredictable.
  • Michael Crichton (1991), in Hobart A. Burch Basic Social Policy and Planning: Strategies and Practice Methods, Psychology Press, 1996, p. 63

G - L

The fluttering of a butterfly’s wing in Rio de Janeiro, amplified by atmospheric currents, could cause a tornado in Texas two weeks later. ~ Edward Lorenz

• It used to be thought that the events that changed the world were things like big bombs, maniac politicians, huge earthquakes, or vast population movements, but it has now been realized that this is a very old-fashioned view held by people totally out of touch with modern thought. The things that really change the world, according to Chaos theory, are the tiny things. A butterfly flaps its wings in the Amazonian jungle, and subsequently a storm ravages half of Europe.
  Somewhere in Adam's sleeping head, a butterfly had emerged.
  • Neil Gaiman and Terry Pratchett, Good Omens: The Nice and Accurate Prophecies of Agnes Nutter, Witch, (1990)

• Chaotic theory is mathematically based on non-linear propositions, "meaning that they expressed relationships that were not strictly proportional. Linear relationships can be captured with a straight line on a graph"
  • James Gleick, Chaos: Making a New Science, 1987

• Relativity eliminated the Newtonian illusion of absolute space and time; quantum theory eliminated the Newtonian dream of controllable measurement process; chaos eliminates the Laplacian fantasy of deterministic predictability.
  • James Gleick (1987), in "Chaos Making a New Science”, p. 6, quoted in “Basic Social Policy and Planning: Strategies and Practice Methods”, p. 63

A double rod pendulum animation showing chaotic behavior

• It is time to employ fractal geometry and its associated subjects of chaos and nonlinear dynamics to study systems engineering methodology (SEM). Systematic codification of the former is barely 15 years old, while codification of the latter began 45 years ago... Fractal geometry and chaos theory can convey a new level of understanding to systems engineering and make it more effective
  • Arthur D. Hall (1989) "The fractal architecture of the systems engineering method", in: Systems, Man and Cybernetics, Part C: Applications and Reviews, IEEE Transactions on Volume 28, Issue 4, Nov 1998 Page(s):565 - 572

• What, after all, is a better example of chaos theory than the harassment of a street vendor in Tunisia leading to a civil war in Syria?
  • Joshua Keating, in "Can Chaos theory teach us anything about Foreign Policy", at ideas.foreignpolicy.com, May 23rd 2013.

• The fluttering of a butterfly’s wing in Rio de Janeiro, amplified by atmospheric currents, could cause a tornado in Texas two weeks later.
  • Edward Lorenz (1979), as quoted in: Laura Nader (1996) Naked Science: Anthropological Inquiry Into Boundaries, p. 209

M - R

• Let us try to represent the figure formed by these two curves and their intersections in infinite number, each corresponding to a doubly asymptotic solution, these intersections form a kind of mesh, of fabric, of infinitely tight network; each of the two curves must never intersect itself, but it must fold back on itself in a very complex way in order to cross an infinite number of times all the meshes of the network. On will be struck by the complexity of this figure, which I do not even try to draw. Nothing is more likely to give us an idea of the complexity of the three-body problem and in general of all the problems of dynamics where there is no uniform integral and where the Bohlin series are divergent.
  • Henri Poincaré, Sur le problème des trois corps et les équations de la dynamique, On the three-body problem and the equations of dynamics (1889), Chap. XXXIII, Sect. 397
  • Translation from Chenciner, Alain. "A walk through the new methods of celestial mechanics." Progress and Challenges in Dynamical Systems: Proceedings of the International Conference Dynamical Systems: 100 Years after Poincaré, September 2012, Gijón, Spain. Springer Berlin Heidelberg, 2013.

S - Z

• Order is not universal. In fact, many chaologists and physicists posit that universal laws are more flexible than first realized, and less rigid—operating in spurts, jumps, and leaps, instead of like clockwork. Chaos prevails over rules and systems because it has the freedom of infinite complexity over the known, unknown, and the unknowable.
  • L.K. Samuels, In Defense of Chaos: The Chaology of Politics, Economics and Human Action, Cobden Press (2013) p. 9.

• Without chaos there would be no creation, no structure and no existence. After all, order is merely the repetition of patterns; chaos is the process that establishes those patterns. Without this creative self-organizing force, the universe would be devoid of biological life, the birth of stars and galaxies—everything we have come to know.
  • L.K. Samuels, "Chaos Gets a Bad Rap: Importance of Chaology to Liberty", Strike-The-Root, (Feb. 18, 2015)

• Chaos is lawless behavior governed entirely by law.”
  • Ian Stewart, Does God Play Dice? The New Mathematics of Chaos, New York: Penguin Books, 1989, p. 17

• Falling between order and chaos, the moment of complexity is the point at which self-organizing systems emerge to create new patterns of coherence and structures of behaviour.
  • M.C. Taylor, The Moment of Complexity: Emerging Network Culture. (2001), p. 25

• Saying “the mathematics of uncertainty” is like saying “the chastity of sex”—what is mathematized is no longer uncertain, and vice versa.
  • Nassim Nicholas Taleb , The Bed of Procrustes: Philosophical and Practical Aphorisms (2010)

• The amazing thing is that chaotic systems don't always stay chaotic, Ben said, leaning on the gate. Sometimes they spontaneously reorganize themselves into an orderly structure. They suddenly become less chaotic?" I said, wishing that would happen at HiTek. No, that's the thing. They become more and more chaotic until they reach some sort of chaotic critical mass. When that happens, they spontaneously reorganize themselves at a higher equilibrium level. It's called self-organized criticality.
  • Connie Willis, in Bellwether, Hachette UK, 23 April 2013, p. 78

See also

• Chaos
• Theory
• Probability
• The Butterfly Effect
• A Sound of Thunder