What is chaos theory?

Answer 1

"The name "chaos theory" comes from the fact that the systems that the theory describes are apparently disordered, but chaos theory is really about finding the underlying order in apparently random data.

When was chaos first discovered? The first true experimenter in chaos was a meteorologist, named Edward Lorenz. In 1960, he was working on the problem of weather prediction. He had a computer set up, with a set of twelve equations to model the weather. It didn't predict the weather itself. However this computer program did theoretically predict what the weather might be.

One day in 1961, he wanted to see a particular sequence again. To save time, he started in the middle of the sequence, instead of the beginning. He entered the number off his printout and left to let it run.

When he came back an hour later, the sequence had evolved differently. Instead of the same pattern as before, it diverged from the pattern, ending up wildly different from the original. (See figure 1.) Eventually he figured out what happened. The computer stored the numbers to six decimal places in its memory. To save paper, he only had it print out three decimal places. In the original sequence, the number was .506127, and he had only typed the first three digits, .506.

By all conventional ideas of the time, it should have worked. He should have gotten a sequence very close to the original sequence. A scientist considers himself lucky if he can get measurements with accuracy to three decimal places. Surely the fourth and fifth, impossible to measure using reasonable methods, can't have a huge effect on the outcome of the experiment. Lorenz proved this idea wrong.

This effect came to be known as the butterfly effect. The amount of difference in the starting points of the two curves is so small that it is comparable to a butterfly flapping its wings.

"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. So, in a month's time, a tornado that would have devastated the Indonesian coast doesn't happen. Or maybe one that wasn't going to happen, does." (Ian Stewart, Does God Play Dice? The Mathematics of Chaos, pg. 141)

This phenomenon, common to chaos theory, is also known as sensitive dependence on initial conditions. Just a small change in the initial conditions can drastically change the long-term behavior of a system. Such a small amount of difference in a measurement might be considered experimental noise, background noise, or an inaccuracy of the equipment. Such things are impossible to avoid in even the most isolated lab. With a starting number of 2, the final result can be entirely different from the same system with a starting value of 2.000001. It is simply impossible to achieve this level of accuracy - just try and measure something to the nearest millionth of an inch!

From this idea, Lorenz stated that it is impossible to predict the weather accurately. However, this discovery led Lorenz on to other aspects of what eventually came to be known as chaos theory. "

Answer 2

In a scientific context, the word chaos has a slightly different meaning than it does in its general usage as a state of confusion, lacking any order. Chaos, with reference to chaos theory, refers to an apparent lack of order in a system that nevertheless obeys particular laws or rules; this understanding of chaos is synonymous with dynamical instability, a condition discovered by the physicist Henri Poincare in the early 20th century that refers to an inherent lack of predictability in some physical systems. The two main components of chaos theory are the ideas that systems - no matter how complex they may be - rely upon an underlying order, and that very simple or small systems and events can cause very complex behaviors or events. This latter idea is known as sensitive dependence on initial conditions, a circumstance discovered by Edward Lorenz (who is generally credited as the first experimenter in the area of chaos) in the early 1960s.

Answer 3

In mathematics and physics, chaos theory describes the behavior of certain nonlinear dynamical systems that under certain conditions exhibit a phenomenon known as chaos. Among the characteristics of chaotic systems, described below, is sensitivity to initial conditions (popularly referred to as the butterfly effect). As a result of this sensitivity, the behavior of systems that exhibit chaos appears to be random, even though the system is deterministic in the sense that it is well defined and contains no random parameters. Examples of such systems include the atmosphere, the solar system, plate tectonics, turbulent fluids, economics, and population growth.

Systems that exhibit mathematical chaos are deterministic and thus orderly in some sense; this technical use of the word chaos is at odds with common parlance, which suggests complete disorder. (See the article on mythological chaos for a discussion of the origin of the word in mythology, and other uses.) A related field of physics called quantum chaos theory studies non-deterministic systems that follow the laws of quantum mechanics.

Answer 4

Mathematically chaos means an aperiodic deterministic behavior which is very sensitive to its initial conditions, i.e. infinitesimal perturbations of boundary conditions for a chaotic dynamic system originate finite variations of the orbit in the phase space; see chaos theory

Answer 5

Morbid, but honestly this battle was weak. Chaos, how does Criss Angel + Inception = Mind f*cker? I get the mindfreak part, but what does Inception have to do with f*cking? "you'se a bisexual, like shakespeare was"? smh. seriously? Yeah, the crowd's gonna go crazy after that one. and that f*ck what you heard line's been bitten so many times it can't possibly have been an accident that you put it in there. At least reference it or something. Morbid, those first 4 lines were terrible. "talking like Garfield"? So corny. I'm missing the point on these lines: "You say you’re off the Hook, I’m off the Receiver Your bars look like you lipo’d fat chicks" and "find in the dark" rhyming with "time of the month" is a serious stretch.

Answer 6

That the universe is in a constant state of chaos. Even as I am sitting here answering your question everything is changing about me. My hair is growing, cells die and new one are growing. Nothing is ever a rest.

Answer 7

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. So, in a month's time, a tornado that would have devastated the Indonesian coast doesn't happen. Or maybe one that wasn't going to happen, does.

Answer 8

any time Al Gore speaks chaos happens

Answer 9

it's related to the whole, ripple in the water affect. So don't space travel to the past and jack something up by stepping on a lady bug.

Answer 10

What an organized question. Do yo really expect a succinct
answer here to this question. Go look on the web.