Massachusetts Institute of Technology (M.I.T.) has for many years been at the forefront of mathematical breakthroughs, and now researchers at the prestigious school, such as Tristan Gilet (a visiting physicist from Belgium) and John Bush, have made remarkable achievements in one of the most difficult of all areas of "modern" mathematics: Chaos theory.
The Need for a New Experiment in Chaos
In order to create an exciting new model for something as complex (by definition) as chaos theory - a mathematical topic which explores the behavior of systems which are essentially "unpredictable," due to the sheer number of factors which affect them - the team at MIT has been looking at a rather simple experiment, one involving a tiny droplet of water floating on top of a thin film as it is vibrated by a simple $100 speaker - a rather inexpensive experiment by modern standards.
As reported in a recent Scientific American news report, the researchers were inspired to conduct their research after learning of recent experiments which studied the behavior of water droplets as they moved around on top of a fluid bath - experiments which demonstrated a chaotic behavior similar to that which exists in the Earth's atmosphere, where predictions and calculations of such minute particles become practically impossible because of a system's acute sensitivity to initial conditions and to the amplification of disturbances which quickly render a system impossible to compute, which is what makes weather reports and other predictions so unreliable at times.
In the new experiments, including one in which water droplets are actually levitated using sound waves, the researchers were able to actually control the behavior of individual water droplets as they moved about in a semi-chaotic pattern by modulating the frequencies of the sound waves being used to affect them. By doing this, they have achieved new methods of calculating the behavior of certain chaotic systems.
Results of the Water Droplet Experiment
What the MIT researchers have discovered after having attempted to mathematically explain the behaviors of their test subjects (the water droplets) was that certain seemingly chaotic behaviors are actually explainable using a surprisingly simple model, reminding mathematicians that chaos is not necessarily a rigid, definable thing. In essence, chaos is not a specific genre of mathematics as much as it is a statement of the limitations of human knowledge.
The difference between a fully predictable system and a "chaotic" system is not a consequence of nature, but a consequence of the mathematician's lack of knowledge regarding the system's initial conditions. Providing all the initial conditions are known with perfect accuracy, mathematical theory suggests that no system would be truly chaotic. Unfortunately, more often than not it is either excedingly difficult or impossible to fully know all of these conditions, which leads to factoral amplification of all variables over time, giving the appearance that a system is both truly random and utterly unpredictable.
By showing that certain chaotic systems can, in fact, be quantified using a model which is far simpler than expected, mathematicians may be provided with an exciting new insight into other, far more complex, chaotic systems such as the motion of heavenly bodies or the behavior of minute particles in the atmosphere which create weather patterns.
Chaotic systems often have a far greater impact upon the everyday lives of humans than most people realize.
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