In layman's terms, what is Chaos Theory?

Answer 1

In mathematics and physics, chaos theory describes the behavior of certain nonlinear dynamical systems that under certain conditions exhibit dynamics that are sensitive to initial conditions (popularly referred to as the butterfly effect). As a result of this sensitivity, the behavior of chaotic systems appears to be random, because of an exponential growth of errors in the initial conditions. This happens even though these systems are deterministic in the sense that their future dynamics are well defined by their initial conditions, and there are no random elements involved. This behavior is known as deterministic chaos, or simply chaos.

Examples of systems exhibiting chaotic dynamics include the atmosphere, the solar system, plate tectonics, turbulent fluids, economics, population growth, lasers and electronic circuits, and the vast variety of dissipative structures. In ecology, for example, chaos theory can explain how small random events may affect large ecosystems in an unpredictable way.

Answer 2

Good answers have already been given, but I'll add that it was Henri Poincare in the late 1800s who showed that even for something as "simple" as planetary orbits of the solar system, we cannot be sure that some planet won't someday in the future suddenly veer off its orbit. What he proved mathematically was that for many dynamical systems, it cannot be proven that they are absolutely stable. For this reason, he is often called "The father of chaos theory". The so-called "many body problem" had vexed physicists ever since Newton, who have found impossible to figure out exact equations describing gravitational systems of more than 3 bodies. Poincare showed why it was impossible. His works on "resonances" ("resonances" are kind of like pegs in a pinball machine, where balls can hit and go either way) in dynamical systems was not well or widely recieved in his time, probably because the news was depressing to physicists. But within a few decades, quantum theory was ushered in, positing an inherently probabilitistic physical reality, and so physicists moved away from Newtonian physics, and Poincare's works in "resonances" were forgotten. In the 1950s, with the advent of computers and dynamical systems simulations, his findings were rediscovered, and thus was born modern Chaos theory. Today, Chaos theory is not only a study of fundamental unpredictability in even supposedly "simple" systems, it's also a study of the strange implicit order and patterns that arise from seemingly chaotic motion, as with "strange attractors". Many of these unexpected patterns were unknown until computer modelling revealed them.

See some interesting examples of strange attractors in this Wolfram link:

Answer 3

I believe that Chaos Theory is the situation when the only logical solution to a problem is that there isn't one.

I saw a CSI: episode like this. I forget the episode title, but I do remember that it's one of the first two of season two.
A girl was killed leaving her college. A number of things were found to be possible causes of her death, but there were no leads. Eventually it was found to be that none of these were the cause of death, but all of them were part of the cause of death.

Eg. A man is shot in the chest. He stumbles into a burning building, where a support beam falls on him. What killed him?


Chaos Theory is also the title of a game. Tom Clancy's Splinter Cell: Chaos Theory.

Answer 4

A lot of posters here are just taking wild guesses as to what they THINK it means, although I think Benoit is close. That's assuming, of course, that MY guess is more or less on the mark.

Chaos Theory, simply stated, refers to how small changes in the initial conditions can have large long term effects. A popular analogy, often referred to as "the Butterfly Effect," is how the beating of a butterfly's wings can ultimately lead to the creation or avoidance of a tornado much later.

Answer 5

completely prepared is the different of chaos. Many hassle-loose phenomena (even heartbeats!) are no longer completely prepared and would stray far flung from perfection, and are consequently no longer completely predictable. If a magnetic bob is suspended as a pendulum and the pendulum is set to swing over 2 or extra magnets the path of the bob is prompted by employing the different magnets however the path would vere from one magnet to a distinctive in an unpredictable (chaotic) way.

Answer 6

The accumulation of small errors in any simulation can wreak havoc in any predictions. I read that if meteorological sensors were placed a foot apart (in 3 dimensions!) to monitor the whole atmosphere of the earth and run simulation models, we still couldn't predict the weather beyond a week or so. That isn't due to any flaws in the model, rather it is the accumulation of all the measurement errors (however small) in the data.

Answer 7

The simplest answer that I have heard is that very different outcomes can result from very small changes to the initial conditions of a situation. Thus the classic butterfly wings idea. If it flaps its wings one way then a thousand miles away we get a storm, if it flaps its wings the other way we don't.

Answer 8

The idea that you can do the same thing and get different results showing that the unexpected can happen hence chaos theory

Answer 9

It's the theory that Chaos will rule the world if they could get rid of Smart. "It's from GET SMART the old tv series

Answer 10

The study of patterns that emerge in random / chaotic systems.

See the link below for more about the difficulty of defining this mathematical term.

http://mathworld.wolfram.com/Chaos.html