Systems Thinking

The Butterfly Effect: Top 10 Quotes

“[…] the least initial deviation from the truth is multiplied later a thousand-fold. Admit, for instance, the existence of a minimum magnitude, and you will find that the minimum which you have introduced, small as it is, causes the greatest truths of mathematics to totter. The reason is that a principle is great rather in power than in extent; hence that which was small at the start turns out a giant at the end.” (St. Thomas Aquinas, “De Ente et Essentia”, cca. 1252)

“In every moment of her duration Nature is one connected whole; in every moment each individual part must be what it is, because all the others are what they are; and you could not remove a single grain of sand from its place, without thereby, although perhaps imperceptibly to you, altering something throughout all parts of the immeasurable whole.” (Johann G Fichte, “The Vocation of Man”, 1800)

“A tenth of a degree more or less at any given point, and the cyclone will burst here and not there.” (Henri Poincaré, “Sur le probleme des trios corps et les equations de la dynamique”, Acta Mathematica Vol. 113, 1890)

“Throwing a small stone may have some influence on the movement of the sun.” (Grigore C Moisil, “Determinism si inlantuire”, 1940)

“If a single flap of a butterfly’s wing can be instrumental in generating a tornado, so all the previous and subsequent flaps of its wings, as can the flaps of the wings of the millions of other butterflies, not to mention the activities of innumerable more powerful creatures, including our own species.” (Edward N Lorenz, [talk] 1972)

“The flapping of a single butterfly’s wing today produces a tiny change in the state of the atmosphere. Over a period of time, what the atmosphere actually does diverges from what it would have done.” (Ian Stewart, “Does God Play Dice?”, 1989)

“Symmetry breaking in psychology is governed by the nonlinear causality of complex systems (the ‘butterfly effect’), which roughly means that a small cause can have a big effect. Tiny details of initial individual perspectives, but also cognitive prejudices, may ‘enslave’ the other modes and lead to one dominant view.” (Klaus Mainzer, “Thinking in Complexity”, 1994)

“Unlike classical mathematics, net math exhibits nonintuitive traits. In general, small variations in input in an interacting swarm can produce huge variations in output. Effects are disproportional to causes — the butterfly effect.” (Kevin Kelly, “Out of Control: The New Biology of Machines, Social Systems and the Economic World”, 1995)

“Chaos theory reconciles our intuitive sense of free will with the deterministic laws of nature. However, it has an even deeper philosophical ramification. Not only do we have freedom to control our actions, but also the sensitivity to initial conditions implies that even our smallest act can drastically alter the course of history, for better or for worse. Like the butterfly flapping its wings, the results of our behavior are amplified with each day that passes, eventually producing a completely different world than would have existed in our absence!” (Julien C Sprott, “Strange Attractors: Creating Patterns in Chaos”, 2000)

“One of the remarkable features of these complex systems created by replicator dynamics is that infinitesimal differences in starting positions create vastly different patterns. This sensitive dependence on initial conditions is often called the butterfly-effect aspect of complex systems — small changes in the replicator dynamics or in the starting point can lead to enormous differences in outcome, and they change one’s view of how robust the current reality is. If it is complex, one small change could have led to a reality that is quite different.” (David Colander & Roland Kupers, ”Complexity and the Art of Public Policy: Solving society’s problems from the bottom up”, 2014)

More quotes on the “Butterfly Effect” at the-web-of-knowledge.blogspot.com.

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