"If death meant just leaving the stage long enough to change costume and come back as a new character...Would you slow down? Or speed up?" — Chuck Palahniuk

Tuesday, October 09, 2007

"Maniaic Monday's - The Chaos Theory!"

Even if your a casual reader of my page you should have heard me speak about the Chaos Theory...That the natural order of the universe is chaos...I try to illustrate my point by testing the theory, with this simple test...Take a handful of anything and drop it...How does it land? Does it follow the same pattern each time it's dropped or fall in the same place and direction? Even in exact tests in closed environments where the wind or any other outside force was not a factor there is no way to get a handful of anything to fall the same way twice...However there is an order to how it falls...A Chaotic order...

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)

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. 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.

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 cam to be known as chaos theory. MORE!

Just like I explained above this gives rise to a whole new theory...At the time there were two known states of order: a steady state, in which the variables never change, and periodic behavior, in which the system goes into a loop, repeating itself indefinitely. While Lorenz's equations followed a steady state where it's systems never varied, they also never came to a single point when graphed...The image would spiral but since it never repeated itself it was not periodic either, giving rise to the Chaos Theory...


The picture above is an illustration of Lorenz's equations graphed...As you can see it loops in on itself...It is the explanation of why no two snowflakes are alike, why liquids flow one way over a smooth surface versus rough surface, the swing of a pendulum, heartbeats ect...

Chaotic Systems are not random. They may appear to be. They have some simple defining features:

1. Chaotic systems are deterministic. This means they have something determining their behavior.

2. Chaotic systems are very sensitive to the initial conditions. A very slight change in the starting point can lead to enormously different outcomes. This makes the system fairly unpredictable.

3. Chaotic systems appear to be disorderly, even random. But they are not. Beneath the random behavior is a sense of order and pattern. Truly random systems are not chaotic. The orderly systems predicted by classical physics are the exceptions. In this world of order, chaos rules!
So in effect as the universe tries to right itself it adds new factors that prevent that from happening resulting in the spiraling effect of chaos graphed as an image...

A metaphor for the gas chamber is found in the Lorenzian waterwheel. This is a thought experiment. Imagine a waterwheel, with a set number of buckets, usually more than seven, spaced equally around its rim. The buckets are mounted on swivels, much like Ferris-wheel seats, so that the buckets will always open upwards. At the bottom of each bucket is a small hole. The entire waterwheel system is than mounted under a waterspout.

Begin pouring water from the waterspout. At low speeds, the water will trickle into the top bucket, and immediately trickle out through the hole in the bottom. Nothing happens. Increase the flow a bit, however, and the waterwheel will begin to revolve as the buckets fill up faster than they can empty. The heavier buckets containing more water let water out as they descend, and when the water is gone, the now-light buckets ascend on the other side, ultimately, to be refilled. The system is in a steady state; the wheel will, like a waterwheel mounted on a stream and hooked to grindstone, continue to spin at a fairly constant rate. But even this simple system, sans boxes or heated gases, exhibits chaotic motion. Increase the flow of water, and strange things will happen. The waterwheel will revolve in one direction as before, and then suddenly jerk about and revolve in the other direction. The conditions of the buckets filling and emptying will no longer be so synchronous as to facilitate just simple rotation; chaos has taken over. The explanation for the irregular movement of the gas lies at the molecular level. While the box sides may seem smooth and thus the flow of the should always be regular, at molecular levels the sides of the box are quite irregular due to the motion of atoms and molecules. After all, in any solid not at absolute zero, total entropy is positive and there must be some irregularity in the molecular structure of the sides of the box. Molecular interactions are tiny, however. How would such tiny things like slightly misplaced molecules affect the flow of the gas in such a profound way as to cause seemingly random motion? The theory behind how small deviations can lead to large deviations lies at the heart of chaos theory. The explanation is simple, and in retrospect, obvious explanation commonly known as sensitive dependence on initial conditions.

We are products of this universe, therefore subject to its laws and theories...Just a little reminder that a laws of nature cannot be changed or broken...Chaos is a law of nature...Where there is calm the underlying force is chaos...It might not be perceptible to the human eye but the Earth is in constant motion...Not only is it spinning on it's axis, it is spinning around the sun...Thus the universe is also in constant motion...As one star dies off another is born, that is the definition of perpetual motion...Change is the only constant! Anything that tries to change or modify or put into some sort of order that is understandable to the human mind will ultimately fail...Evolution is real...From the time we are born until the time we die we are in a process of evolution...We do not come fully loaded with knowledge or a full grown body...All that stuff is dictated by evolution...Evolution does not deal with how we came to be but with the changes that happened to humanity over time...When evolution stops or is impeded, no growth can happen and the society itself stagnates and eventually over time that stagnation turns into rot, left unchecked that rot can and will spread...We are at a point in human history where evolution is being impeded and the world is suffering for that...

Religion is the most destructive force against evolution, progress and true change, the fact that it is still the deciding factor in so many peoples lives even today with the wealth of knowledge that refutes everything about religion should not only lead credence to the chaos theory, but cognitive dissonance, and outright stupidity...When it really gets broken down the codes of morality we live our lives on are based on some insecure, jealous, hateful, fearful human being from some ancient time without half the understanding as our children have today...It is the repression of the natural order that causes suffering in our universe...

Chaos Rules!
The New Defenders Of Animated Fractals!

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