What is Chaos Theory?

S. Mithra

Chaos theory refers to the behavior of certain systems of motion, such as ocean currents or population growth, to be especially sensitive to tiny changes in starting conditions that result in drastically different outcomes. Unlike what it implies colloquially, chaos theory doesn't mean the world is metaphorically chaotic, nor does it refer to entropy, by which systems naturally tend toward disorder. Chaos theory relies on the uncertainty inherent in measurements, the precision of predictions, and the non-linear behavior of seemingly linear systems.

The "butterfly effect" concept holds that a seemingly insignificant action -- such as a butterfly flapping its wings -- can have a dramatic effect on a system -- such as weather.
The "butterfly effect" concept holds that a seemingly insignificant action -- such as a butterfly flapping its wings -- can have a dramatic effect on a system -- such as weather.

Before quantum mechanics, chaos theory was the first "weird" idea of physics. In 1900, Henri Poincaré thought about the relationship between values at different time points of a system whose general behavior could be accurately predicted, such as a planet in orbit. He realized that a measurement, like position, speed, or time, can never be exactly pinpointed because every instrument that could possibly be developed would have a limit on its sensitivity. That is, no measurement is infinitely precise.

Poincaré knew that motion is deterministically described by a series of equations that can accurately predict things like where a ball will end up if it is rolled down a ramp. He theorized, however, that a tiny difference in initial conditions, based on almost insignificant variations in a measurement like mass, could result in two completely different macroscopic outcomes far, far in the future. This theory was called dynamical instability, and later scientists confirmed the veracity of his ideas.

Chaos theory, therefore, studies how organized, stable systems cannot always yield meaningful predictions for a much later time, even though short-term behavior more closely follows expectations. In fact, any predictions it does yield might be so wildly divergent that they are no better than guesses. It is counterintuitive that a more precise value would not yield a more precise output.

The snowball effect of a minute change in influential circumstances is referred to as the butterfly effect. This metaphor suggests that a butterfly flapping its wings, an almost imperceptible influence, could contribute to the development of a hurricane on the other side of the globe. Edward Lorenz did the first computer simulations in the 1960s that demonstrated dynamical instability with actual equations and data.

Initial conditions cannot be inferred from later conditions, nor vice versa, in several important systems, such as atmospheric pressure and ocean currents that contribute to weather and climate. This is not merely a real-life scenario, resulting from something like too few thermometers in the ocean. Chaos theory is a verifiable, mathematically consistent theory that shows that sometimes increasingly precise measurements plugged into equations do not yield increasingly precise predictions, but rather such extreme diverging values that they are practically useless.

Some physicists are working on connections between this seeming randomness and large-scale structure. They are investigating patterns in global climate, mass distribution of galaxies in superclusters, and population variation on a geologic time scale. They hypothesize that on a macroscopic level, certain kinds of organization and consistency have only been made possible through the disorder and inconsistency of chaos theory.

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Discussion Comments


This theory could work itself out in the study of genetics in terms of how a person is made to function. If the initial conditions of how the baby is made to be determine how that baby will grow up and who he will become, than the theory holds true. We must also take into account, however, all the environmental factors. The happy medium exists between solid determinism and the idea of mere "tabula rasa" or blank slate thinking in terms of what makes up childhood psychology.


Black Swan theory is similar to Chaos theory, but refers more to unquantifiable fringe events or personalities who have a significant impact on events. Like a rare black swan, these elements are not normal, but stick out and cause strange things to happen. Examples of black swans in history are people like Hitler, Mao Tse-Tung, and even Albert Einstein. These men were certainly not normal, but came to have a very significant impact. This kind of theory can tend to render theories concerning trends and humanity to be obsolete and/or show them to be limited.



I think that these two concepts have a lot in common, but one is scientific in nature (dynamic instability), while the other, the butterfly effect, is more of a general philosophical/mathematic explanation for trends in various areas of studies. So, in a sense, dynamic instability is part of the way in which the butterfly effect works itself out in the realm of science.


Are Dynamical Instability and the Butterfly Effect the same thing? It sounds like it to me but then why would they use one to demonstrate the other if they are the same?

So what is the difference that I am not getting?

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