WHY DO THIS CHAOS THEORY?

The Chaos Theory is a tasty contradiction, a science that predicts the behavior of "naturally unpredictable" systems. Beautifully arranged structures from a sea of ​​chaos; Is a mathematical toolkit that allows a window to the complex functioning of various natural systems such as human heartbeat and asteroids orbits.
Welcome to one of the most wonderful areas of modern mathematics.

At the heart of Chaos Theory is a fascinating thought that order and chaos do not always oppose. Chaotic systems are a sincere blend of two molds: outward, unpredictable and chaotic. But they make the inner workings open, and you discover an excellent deterministic coherent cluster that flickers like hours.

Some systems surround this priority with regular effects from turbulent and chaotic reasons.

How can an order on a small scale produce chaos on a larger scale? And how can we tell the difference between pure randomness and regular patterns covering chaos?

The answers can be found in three common features shared by the most chaotic systems.

In 1961, a meteorologist named Edward Lorenz made a deep discovery.

Lorenz was using the computers' newly discovered power to predict the weather more accurately. It, when given together with a series of numbers representing the current weather, created a mathematical model that could predict the air a few minutes in advance.

Lorenz was intent on this computer program to reproduce the predicted air over and over again to produce long-term predictions and future work with each study.

Accurate estimates on a minute-by-minute basis, days, then weeks.

One day, Lorenz decided to restart one of his predictions. To save time, he decided not to start from scratch; Instead, the computer's estimate took the majority of the first half of the work and used it as a starting point.

After a well-earned coffee break, he returned to discover something unexpected. Although the computer's new predictions began in the same way as before, the two sets of predictions soon began to differentiate. What was wrong with it?

Lorenz, while the computer was printing three-decimal steps of predictions a short while ago, saw numbers internally using six decimal places.

So Lorenz used the number of original runs of 0.506127, while starting the second run with 0.506.

The difference between a piece and a piece: The same difference that a butterfly wing can do on the surface of a wing. The initial weather conditions were almost the same. Both suggestions meant something.

Lorenz had found the chaos seeds. In systems with good behavior without chaotic effects, small differences only produce small effects. In this case, Lorenz's equations erroneously caused him to grow over time.

This indicated that small errors in measuring the available air would not be small, but increased in size each time the predictions were restored to the computer until it was completely sunk.

Lorenz showed this effect famous for his flapping flapping butterfly simulations, thus creating a hurricane as much as half the world.

A nice way to see this "butterfly effect" is to play billiards. Whether you are consistent on the first shot (with a break), the smallest difference in speed and angle you hit the white ball causes the billiard package to be wildly dissipated in different directions each time.

The smallest differences produce great effects - the stamp of a chaotic system.
They point out that the laws of physics, which determine how to play billiard games, are precise and obvious: they can not find space for randomness.

At first sight, what appears to be random behavior is completely deterministic. It just seems random; Because unrecognized changes make all the difference.

The accumulation rate of these small differences is not a time in which every chaotic system provides a guessing scale - beyond which we can more accurately predict its behavior.

In the case of the weather, the forecast horizon is now about one week (thanks to better measurement tools and models than ever).

Surprisingly, the solar system is also a chaotic system with a prediction horizon of hundreds of years. A Chaos Theory was the first chaotic system to be discovered long ago.

In 1887, the French mathematician Henri Poincare showed how gravity could perfectly predict how Newton's theory would orbit under the conditions of reciprocal attraction between two planets, but the addition of a third body of blending has rendered the equations insoluble.

Despite the long-forgotten horizon of planets dancing, the effects of chaos can not be ignored because the gravitational strife has a great influence on the orbit of the asteroids, the complex interaction between planets.

Observing the asteroids is difficult but useful because such chaotic effects can one day lead to an undesirable surprise.

On the lid side, they may also direct external surprises such as a departure from a potential collision with the comets of the tails.

STRONG, BEARING BEHAVIOR

Stability is desirable in many scenarios, such as flying. Commercial aircraft are aerodynamically stable so that a small turbulent push (probably related to the throttle) does not remove the plane from a straight flight path.
A major change in flight controls is required to make a big change in the air movement comfortably.

This stability, on the other hand, is part of the discomfort of war-pilot pilots who prefer their aircraft to make rapid changes with very little effort.

Modern combat aircraft achieve a great maneuverability due to aerodynamic imbalance - the smallest thrust (turbulence) is enough to change flight paths to a large extent.

As a result, you are constantly and rigorously adjusting flight surfaces to remove unwanted butterfly effects, and the pilot is equipped with built-in computers to release their exploitation. If you can illuminate the chaotic systems at the base of the scene, you can turn instability into a presence by applying a control measure on randomness.

The key to opening up the secret structure of a chaotic system is to specify the sequence of preferred behaviors - known as attractive among mathematicians.

Mathematician Ian Stewart used the following example to illustrate the attraction.

Imagine throwing a ping-pong ball away from the ocean. If it is left over the water, it will fall; if it is left under the water, it will float after surfacing.

Wherever you start, the ball will move immediately to the ocean surface very attractively. Once the chaos is turned back and forth in a real sea, the shot is glued, and if it is thrown temporarily or is thrown under the waves, it quickly returns to the surface.

Although it can not predict exactly how a chaotic system behaves, it allows us to narrow down the possibilities.

At the same time, we are able to accurately predict how the dangling system will respond.

Mathematicians use the concept of a "phase space" to geometrically describe the probable behavior of a system.

Phase space (always) is not like regular space. Each location in the phase space corresponds to a different configuration of the system.

Phase Space

The behavior of the system can be observed by placing it at a location representing the initial configuration and tracking how it moves along the phase field of that point.

A stable system in phase space will proceed towards a very simple draw (if the system is settled it will look like a single point in the phase space, or a simple loop if the system walks between different configurations).

The fractal mathematical pioneer, led by the French mathematician Benoît Mandelbröt, allows us to cope with the intricate and unresolved preference behavior of the drawer. The phase space may seem quite abstract, but it is an important application in the sense of understanding your heart beats. The millions of cells that make up your heart are constantly shrinking and relaxing as part of a complex chaotic system with complex appeal.

These millions of cells must work synchronously in the right order in the right order to produce a healthy heartbeat.

Fortunately, the complex synchronization situation is the attractiveness of the system - but not the only one. If the system is shaken in some way, it is on a totally different tractor called fibrillation for cells to constantly misjudge and relax.

The goal of a defibrillator that applies a large electrical voltage to the heart is not to "re-start" the heart cells in this way, but rather to make a kick to remove the chaotic system from the person who is experiencing fibrillation. It; It is a warning to the cells to return to a healthy heartbeat.

The main benefit of having a chaotic heart is that there are minor changes that will allow millions of people to contractively distribute the load distribution more evenly, reduce your heart wear, and otherwise pump more for decades.

The Chaos Theory only attracts attention of mathematicians. It is striking enough to bring many different field specialist physicists and biologists, computer scientists and economists together.

Chaotic systems can be found only wherever you need it, and they can share many common features regardless of where they come from.

Consider both the drip tap and the superheated liquid helium used by the Great Hadron Collider as the cooling fluid (making the LHC parts cooler in the deep region).

Both are non-chaotic systems. However, when you heat the helium slowly, small convection cells will start to build up and the dripping sounds will change when you slowly open the tap.

Eventually, the increases in temperature and water flow successively in boiling helium and rushing water.

Surprisingly, the transition from level to chaos in these systems is controlled by the Feigenbaum constant of the same number.

From dripping to dripping to LHC, from a striking heart to the dance of the planets, chaos is all around us.

The Chaos Theory reversed everybody's attention to what we understood and thought about for some time and showed us that the nature was far more complex and astonishing than we imagined.