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Chaos Theory

By Joel Fernandez

The chaos theory, also known as the butterfly effect, is field of study in mathematics that studies the behavior of dynamical systems. It applies principles that were initially meant for fields such as physics and chemistry etc. But the concept has evolved to the point where it can be applied to several fields of study. Of all the different ways that one can implement the chaos theory, we will choose to focus on the philosophical aspects that pertain to anthropology.

In essence, chaos theory concerns deterministic systems that can, in principle, be predicted. It involves the study of both linear and non-linear events that may or may not intersect at certain points and time. By definition, a chaotic system is one that can either produce a solution or an error. A system that always produces a random error is what is known as a stochastic system. It can be defined simply as a system that is designed to fail and thus cannot be considered chaotic because chaos implies that there may be several possible outcomes.

One of the most popular aspects of chaos theory is the idea that all outcomes are a result of an initial condition, but not all initial conditions are directly correlated to an outcome. Simply put, that is like saying that a person can bounce a ball and the ball can go in any direction, but the ball can never bounce the person. The concept of the initial condition is not the only part of the chaos theory, but it is one of the few that can be explained to just about anyone.

Another aspect of the chaos theory is the concept of topological mixing or topological transitivity. This singular concept is based on the principle that a system will evolve over time and perhaps overlap with another nearby system. That is like saying that one can predict the evolution of a linear timeline when it is in its initial state and then treat the primitive state in accordance with that knowledge. Simply put, you treat an egg as if it is not shattered on the floor before it falls. You do not think of it as a shattered egg even though you are aware of what would happen if you dropped it. The act of putting the egg in the frying pan constitutes a different trajectory and thus a different perspective on the same topic, eggs.

One of the more obscure aspects of the chaos theory is the concept of periodic orbits. This principle states that every point in the space is arbitrarily close to periodic orbits. If several objects are literally moving in an orbit at a close enough distance, at some point there will be an overlap. Picture an individual person in the group as a planet within its own independent orbit. If there are several planets close by, their orbits will overlap at very specific points and time. Most of the time, collisions will happen maybe once or twice at a time. But the fact that all of the orbits overlap means that there is a mathematical probability of a simultaneous collision of all the planets at one seemingly random event. Think of it as another way of looking at the big bang.

The very act of trying to fit into a group of any size implies an overlap of behavior at very specific points and time. While planets in this part of the known universe typically orbit around a star without colliding, the same cannot be said about people. A good example of this is the concept of going to a restaurant. You might not go to any table but your own with your group. But everyone in the whole restaurant is capable of crossing paths in the corresponding bathroom. The restaurant owners cannot know if everyone in the restaurant will use the bathroom, but they are able to anticipate the use of the bathroom by making sure that it is clean.

There are indeed many interesting aspects of the chaos theory. But wait, there's more. There's also the concept of the strange attractor. It is the idea that an object an be on a very specific trajectory until it converges on a strange attractor. The topological transitivity condition states that a system can evolve over time. That evolution can manifest itself in a deviation towards a strange attractor. Therefore, the intended trajectory of an object is dictated by the strange attractor and not the initial condition. In other words, rolling a metal ball across the floor where there is magnet present will result in a deviation every single time, depending on the strength of the magnet and the proximity of the two points.

In practical terms, a person represents the metal ball, the magnet represents something of significant value to the individual. If you roll a ball past the magnet and nothing happens, that means that the ball is not made of metal. Therefore, if a person walks by an object and does not deviate from his or her course, that means that the object either held no value to the individual or it simply was not noticed. Simply put, different kinds of people will be attracted to different objects or events to varying degrees. If you understand the strange attractor (magnet), you can understand the kind of person that gravitates towards the event or object. Perhaps that is why there are different kinds of fishing lures.

It is very important to understand the difference between chaotic systems and stochastic systems. As was previously stated, a stochastic system will always produce a random error. In nature, behavior among animals and humans is determined by the probability of survival, thus all animals and people who do not adjust their behavior with survival in mind will cease to exist. As the same can be said of all living organisms, stochastic systems do not occur naturally for very long.

Therefore, the existence of an ongoing stochastic system implies deliberate design. As such, anything that can be designed can be undone by rearranging the properties that make up the stochastic system in question. Simply put, anything that took thought to build can be destroyed by another thought process that is possibly rooted in chaos theory. It should be noted that chaotic and stochastic systems are often observationally equivalent. The only question that remains is whether or not a person or group of people can tell the difference.