A Corbeled Gallery work

Wednesday, August 31, 2005

Deterministic Universe (step two) Chaos

I will describe Chaos Theory and how it is just a crutch to explain the untestable.

When I was about 9 years old, I stumbled upon a problem. My father had given me a BB gun for Christmas. After shooting it for a full day, I realized that some shots were harder to make because of wind, steadiness of my hand, and the exact shape of certain BBs. Because of this, I would search through my box of BBs looking for the perfect shaped BB so I could always hit a target dead on at 20 feet. I came inside after shooting for a day and played with a G.I. Joe action figure, and in my imaginary world, my G.I. Joe shot his enemy from a mile away, with a hand gun. I then realized it was impossible for this shot to be made, but I remembered that this G.I. Joe had made the same shot a hundred times before; before I realized this shot was impossible. I had to come up with an excuse as to how my G.I. Joe had made this shot, because I refused to say my made-up universe was incorrect before, as that would disrupt the value of it's continuity. My excuse for the past hundred perfect shots, was that my G.I. Joe was actually a robot, and was able to make precise calculations, based on wind, shape of the bullet, trajection of the target, and so on.

A few years later, my father had taken me shooting, and I learned about gun powder grains, which I used to alter my previous G.I. Joe's calculations, by saying he only used the most perfect bullets in existence, because he was a super special force robot. Because of all of this, he knew exactly how the bullet would act, given hundreds of stimuli which would occur before impact of his bullet.

Therefore, this G.I. Joe robot of mine was able to predict precisely where the bullet was going because he understood that every element between the firing pin and the target would have a path-altering force on where the bullet would go. Fifteen years later, I am still updating that made-up universe, to prove that this robot could have made the shot I said he did. However now I understand that there are an infinite amount of variables that would go into saying where this bullet would go. Thus, there is no conceivable way to accurately determine where there bullet would go, but you could give a very good estimate. The ultimate trajectory could be determined by investigating every influence on every measurement in every atom's width between the gun and its target.

Chaos Theory was proposed by Edward Lorenz in the early 1960's. The idea behind Chaos Theory is that minute variations can cause huge long term results. His first observation of chaos came when he tried to create a weather prediction model. We use these types of models still today. Lorenz had used a number in his model, .506123, and the computer came up with a predicted weather pattern. He ran his test again, but to save time, he plugged in the number .506. The difference, he assured himself, was not enough to make any difference, and the model should end up looking very similar to his original prediction. An hour later, he saw that the digits he left off were enough to wildly change the outcome of the computer's prediction, through many, many, insignificant changes. We thus witnessed the birth of Chaos.

I believe that Heisenberg’s Uncertainty Principle makes things appear chaotic. The Uncertainty Principle basically states that you cannot measure an object's location in space without bothering it. For instance, if you try to measure the location of an electron, you will inevitably bump it.

Assuming we were in fact able to locate an electron's position in space, it would still have an infinitesimally large number of decimal places with which you can measure it's location. For instance, say you wanted to figure out how far a computer monitor was from your face at this precise second. It may be 24 inches from your eyes. But you could then say 24.1 inches. More accurately, we could say 24.1000000000005 inches. Now, at this time, we have measured the distance better than anyone would ever need to. However, Lorenz's weather prediction saw that even the smallest detail could change the outcome drastically, given enough time. We could theoretically measure the distance of your face from the monitor with growing precision, until eventually we measure the distance between an atom on your face with an atom on the monitor. Here are the two problems that occur at this point:
1) There are still an infinite amount of decimal places you can theoretically measure, making an observer unsure of the distance.
2) Realistically, the Uncertainty Principle takes over at the atomic level, making further measurement impossible, because we alter our control by measuring further.

The more precise a measurement you are able to make, the more accurately you can predict the near future. We can now assume that if your face moved at exactly 0.0000000000001 inches per second, in the precise direction of the monitor, after exactly 1 second, your face will be 24.1000000000004 inches away from the monitor.

This is only theoretical, because the following variables are impossible to measure: the end of exactly one second, the distance our face moves, and the precise direction our face is moving.

However from a theoretical stand point, we can declare these things much like Euclid proposed a circle. Euclid defined a perfect circle as a plane figure contained by one line such that all the straight lines falling upon it from one point among those lying within the figure equal one another. Current theorem dictates that it is impossible to draw or create a perfect circle. Let us consider some basic properties of a circle: A circle is a set of points on a plane, each equally distant from a center point. If we run a vertical line through the center, we divide the circle into two semicircles, each of which is the exact mirror image of the other. We can do the same using a horizontal line. If we use both, a vertical and a horizontal line, we divide the circle into four sections, all mirror images of the rest (the mirror can be horizontal, vertical, or both). That means if we draw a tangent to the circle at each point of intersection of our horizontal or vertical line with the circumference of the circle, the tangent itself will be either horizontal or vertical. There are an infinite number of curves that have these properties (since there are, at least in theory, an infinite number of lengths l we can use). None of them will yield a perfect circle.

However, the inability to create a circle does not change the fact that we can conceive a circle. So, in the same light that Euclid defined a circle in order to build his entire geometrical universe, we can define a second as an exact second, an inch as an exact inch, and a path as an exact path, in order to determine exactly where a point on your face is, as second after it starts moving towards the monitor. By saying this, I would like to define the location of an atom as Point A. Since we have defined Point A, we know it's location to an infinite accuracy. Similarly, we can define an exact second, an exact speed, and exact path the atom on our face is taking. We can then determine exactly where the atom is after a second.

Since I can define Point A, I will now define it as, "The position of a particular atom within in the universe." This point has an exact X,Y,Z coordinate in the universe, in relation to planet Earth.

On this level of accuracy, there is no outstanding stimuli that would ruin our idea of the location of this electron. We must assume this knowledge in order to accurately predict the future. If you can measure something with infinite accuracy, you can predict the future precisely, since the more accurately a measurement, the more accurate a prediction of the future.

Ultimately, if we knew exactly where an atom is, then Chaos Theory would not exist, as it would not play a roll in the predictability of an event. In reality, an atom has a true location. Just because we cannot accurately measure an atom's location without observing it does not mean it doesn't exist at its current location. An atom will act in a certain way based on outside stimuli, as an atom cannot move in a way that goes against the laws of physics. Even after measuring an atom’s location and travel accurately, an observer would need to repeat the process for trillions of atoms, in order to predict, say, a bullet’s precise location after a second of travel. We have created Chaos Theory, to make up for this immeasurable event.

A bullet has a precise location, and it acts upon the laws of physics. Therefore if my G.I. Joe was somehow able to recognize a trillion, trillion stimuli, he could therefore hit a target of any size from a mile away with his bullet. (Additionally, I figure if he shot one bullet to observe how stimuli affected it, he would be able to even more accurately predict the path of the second bullet. I wonder if we may be able to do that with electrons? But that's a whole new topic).

At this point, there is only one hole in this argument against Chaos Theory: The probability cloud of electrons. The smallest imaginable building block of the universe ends up appearing to cause fundamental chaos, as I will describe later.

In the end, for my entertainment purposes, I decided my G.I. Joe made his calculations based on a dozen stimuli, thereby allowing him to be accurate enough to hit his target, but not accurately to hit, say, a button on his target's shirt. Then again, in my mind, I can change the laws of this character's physics, thereby discluding him from having to perform calculations at all. But I didn't know I could do that when I was 9 years old.


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