Mathematical Equation On A Biological System example essay topic

Chaos In Biological Systems In today's world of high-tech methods to study just about anything that exists, we are still imperfect. Scientists continue to look for ways to understand, explain, and even predict the actions and reactions of the universe. In the last two centuries, scientists have been looking in every possible place to understand the universe; from science, to math, even religion. They have turned to mathematicians and their strange theories of determinism and predictability.

This search to understand the universe has spawned several new areas of science; there are now scientists devoted solely to the research of mere theories, such as chaos theorists. In the twentieth century, a new area of scientific study has been created. The goal of this new science is to turn the study of real life into a more easily understood, and more mathematical formula. This new science is called Ecology. Ecology is defined as "the science of relationships between organisms and their environments" (American Heritage Dictionary). Ecologists are, in large, generally biologists with a strong mathematical basis.

This is not to say that all ecologists are also mathematicians, but the math background is a major part in the ecological studies. Scientists, by nature, have always tried to make the most complex things in the universe seem as simple as possible". Scientists have always searched for simple rules, or laws, that govern the Universe. For example, Isaac Newton could explain how the stars appeared to move across the sky with his simple laws of motion and theory of gravitation.

At the beginning of the 19th century, the famous French mathematician Pierre Simon LaPlace believed firmly in a Newtonian universe that worked on clockwork principles. He proposed that if you knew the position and velocities of all the particles in the Universe, you could predict its future for all time". Hall 7 This new science is yet another attempt to do such a task. But, in this case, scientists have hit a few snags. In order to make a biological system into a simple, predictable formula, you must be able to count and measure every factor within that system.

In ecology, however, this is nearly impossible. Because ecologists focus their studies on the relationships between organisms and their environment, everything that has an effect must be considered. This ranges from each individual organism in that environment, to the weather and climate, to how much of a ripple was formed when the leaf fell off the tree and into the water. As one can imagine, this is impossible. Because it is so difficult to make this idea neat and clean, scientists try even harder to do so. Most ecologists believe that by being able to understand and predict a biological system, we can foretell how fast and large any given population of organisms will grow and expand (Clarke 1-19).

In the 1970's, scientists also developed another science, called Chaos Theory. This is theory that attempts to explain how and why the universe is deterministic yet unpredictable. This means that in most systems, scientists can foretell what should happen, but not to what extent changes will continue. Chaos Theory is a very strange and misleading science. Many people take it to believe that chaos means total disorder, whereas in the science, it has a totally different meaning. Some people believe that the entire purpose of such a science is simply to explain our own inabilities to understand.

Understand what? Anything and everything in this universe, this includes weather, astronomy, and how a raindrop will roll down a leaf. Scientists use this science to explain planetary motion, pendulums, and many other moving objects. Using this newfound science of Chaos, ecologists were able to make mathematical models to represent a biological system. For instance, using a certain mathematical formula, we " ll say next = F (x), ecologists could make a graphical representation of a population and its fluctuations (Gleick 59). This occurs because when every iterations and its solutions are plotted on a graph, it forms a fluctuating, and sometimes chaotic graph".

In the natural system of a rain forest, a co-evolutionary system depicted by a rubbery fitness landscape, the success of one species (such as a frog) may spell doom for another (a fly) that it prefers to dine on. Kauffman has claimed that the entire ecosystem may coevolve to a state poised at the edge of chaos... ". Coveney 274. However, these formulas were not perfect. The graphical pictures that were created were close to reality, but not exact.

They might follow a population for a little while, but then the graph strays from reality. Scientists continue to work at these formulas theorizing that they can create a formula that might predict a biological system extremely accurately. The problem is, there is simply too much data that must be inserted into such an equation that a perfect result is, for the most part, impossible. Not to say that it is completely impossible, but very near it. This theory should hold true to biological systems also, assuming of course that this theory had any truth behind it in the first place. In the universe, there are an infinite number of particles; it would be impossible to even count them.

If we cannot count them, how are we ever going to know their velocity and location? Even if you could measure their position, it is impossible to measure both the position and velocity of any object at the same time, as simply stated by the laws of motion. Even assuming that you could measure both the velocity and position of every particle in the universe, who is to say that you could predict the future with that information? No one, which is exactly the point, it is all just a big waste of time (Coveney 274). Scientists and chaos theorists have been spending years trying to form a mathematical equation for a biological system, a living system.

They have not yet succeeded for one simple reason: it is impossible. The best they have come up with are equations and formulas that resemble how a population fluctuates to reach equilibrium. It is simply impossible due to the fact that these systems are alive, and fluctuating, according to each other. If scientists could make an exact model for every population in an environment, and know the weather and climate, they might be able to predict how many of a certain species will be there the following year. But even that is far from foolproof". For example, it is sometimes suggested that a problem might be computationally tractable, but only by a computing device with more components then there are elementary particles in the universe.

This would seem to be a contingent problem (the universe might have been bigger), but it is not naturally described as "merely practical". Finally, the situation is further complicated by recent attention to chaotic systems, systems that are deterministic but infinitely sensitive to their exact initial conditions. It is certainly possible that chaotic behavior at a lower level might thwart reduction, although it is again unclear whether this should be seen as a practical or a theoretical obstacle". (Dupre 96) This viewpoint is the perspective that taken here. There is a theory commonly discussed in courses of science and ethics that everything is simply believed to be. This means that in a biological system, no matter how simple it seems, is infinitely complex.

In a rainforest, for example, there are millions of species of plants and animals, there are even hundreds of thousands that we might not know about. Our ability to understand life and nature is limited to both what we are willing to believe, and what we are able to observe. The latter is the more crucial of the two. We have no way to know what exists where we can't look.

We cannot observe organisms that are too small to see with a very powerful microscope. This means that there could be millions of species of organisms that are as small or smaller than an atom, which we cannot possibly observe. But this would cause one to question the simply meaning of the word truth. Is something a fact, or do we believe it to be so because we have no means to determine otherwise?

Therefore we cannot come even close to predicting a system with LaPlace's theory. On the other hand, there are the biological reasons why one cannot place a mathematical equation on a biological system. First, the whole idea behind a biological system is the fact that the populations within it are alive. They are alive and thinking for themselves. Granted, animals don't actually have the ability to think, but in a way, they decide for themselves what they will and will not do. It is impossible to predict how a living being is going to act or reproduce within its population.

Every organism in an environment acts according to how it must respond to every other action in the environment. This means that whether an ant lives or dies can be determined by whether a raindrop falls to the left or right side of a tree branch at the other side of a forest. Everything in a biological system is so intertwined and codependent of each other that it is beyond our abilities to even come close to accurately predicting such a system. There is no mathematical order in a biological system, which is why scientists have failed so far. No scientist, no matter how hard he tries, can put a mathematical order on a living system. It simply isn't going to happen.

For these reasons, some believe that at this state of our scientific ability, both mentally and technologically, we cannot mathematically explain a biological system. The biology in an environment is so complexly intertwined that we do not have the capability to understand them entirely. There is hope in the future, but not yet. Populations will fluctuate according to each other's individual fluctuations, not by any mathematical factor.

Chaos theory will aid in performing such a task simply because the basis of chaos theory is to explain our own inabilities; therefore, from a chaos theorist's perspective, one can solve such a problem as predicting a biological system. In reality, the only answer given to the problem is to say that a system could do any number of things, none of which are predictable. But this statement, in a chaos theorist's view, is truly understanding that system to its full extent. Even though they are not actually predicting the system, they are determining that it is unpredictable.

So in their eyes, the job is complete, but from an ecologists view, they are far from it. An ecologist looks to understand those unpredictable fluctuations in such a system, not just show that they are there. This is a slightly easier task than making a mathematical formula to predict a system, but has more value in the long run. If one can understand why these fluctuations occur, it will be easier to make logical predictions in the future.

As scientists try to create formulas to represent populations of organisms; they are either correct or not. Whereas by understanding nature, we can make minor judgments, never right nor wrong. The best way to truly understand and predict any system, is to truly know why it acts the way it does. One must be able to find the root of any problem that system might have, and the causes of any positive reactions also. All in all, the entire theory of using chaos to explain biological systems is pretty much a waste of time...

Coveney, Peter and Roger Highfield. Frontiers of Complexity. Fawcett Columbine: New York, 1995... Hatch, John P. "Biofeedback". Encyclopedia of Human Biology. Academic Press: New York, 1997...

Dupre, John. The Disorder of Things. Harvard University Press: Cambridge, 1993... Norton, W.W. Exploring Chaos: A Guide to the New Science of Disorder.

1991. (Used in Freshmen Seminar packet, that is hall the information you provide. ). Gleick, James. Chaos: Making A New Science. 1987.

). Clarke, George L. Elements Of Ecology. Wiley & Sons, New York: 1954.