The Lorenz Experiment: Chaos In All It's Glory
In Chaos: Making A New Science, James Gleick outlines the evolution of the chaos theory. By reviewing specific experiments, from numerous fields, the reader is given a comprehensive introduction to the fundamentals of chaos. These experiments are introduced with a brief overview of the scientist who conducted the experiment, and relates their discoveries to prior breakthroughs. The novel starts out with the beginning of the chaos theory with Edward Lorenz and his Lorenz Attractor, and then continues with other chaotic developments such as: Smale’s horseshoe, fractals and bifurcations. Gleick also details the progression of disorder in chemistry, biology, ecology, astronomy, meteorology and geometry.
One of the most fundamental experiments in Chaos is Lorenz’s waterwheel. To prove that chaotic systems were rooted on a specific pattern, Lorenz constructed a wheel consisting of eight buckets, each with a small hole. Water was fed into the system at the top, through a constant drip. Lorenz figured that if the source of water remained unvaried, a steady rotation and pattern would develop. This pattern would either consist of a steady rotation in one direction, or a repeated oscillation. He predicted that if the water flow was too slow, the bucket would never fill fast enough, to lower and rotate the wheel. If the flow was too fast, the wheel would rotate too quickly. This would not allow enough time for the empty buckets to fill, and result in the heavier buckets gathering enough speed to rotate further. This imbalance of buckets would cause the wheel to reverse direction, and if the water was pumped at the correct rate, the wheel would rotate at a constant speed. Lorenz observed through many tests, that if the rate of water was increased, and fixed, the wheel would reverse itself but never fit into a repeating pattern.
This observation strayed from the knowledge of simple Newtonian physics, and led Lorenz to develop three equations, with three variables, that outlined his experiment. The results of these equations were used as co-ordinates to plot a three-dimensional graph. These numbers created a sequential, infinitely complex line, which is now known as the “Lorenz Attractor” (p.29). This concept outlined the basic theory of chaos. Since the line never overlaps itself, the system never has an exact moment recur. The Lorenz Attractor is also known as The Butterfly Effect, due to the double loop image that is produced.
This infinitely complex line proved that chaos was present in a predictable system. Since the line never returns to it origin, a cycle is never completed. Without a period for the cycle to repeat in, predictions can never be made. This proved that while a system may contain some order, it is not enough to base any assumptions. The Lorenz waterwheel was an experiment that proved the fundamental properties of instability.
One of the most fundamental experiments in Chaos is Lorenz’s waterwheel. To prove that chaotic systems were rooted on a specific pattern, Lorenz constructed a wheel consisting of eight buckets, each with a small hole. Water was fed into the system at the top, through a constant drip. Lorenz figured that if the source of water remained unvaried, a steady rotation and pattern would develop. This pattern would either consist of a steady rotation in one direction, or a repeated oscillation. He predicted that if the water flow was too slow, the bucket would never fill fast enough, to lower and rotate the wheel. If the flow was too fast, the wheel would rotate too quickly. This would not allow enough time for the empty buckets to fill, and result in the heavier buckets gathering enough speed to rotate further. This imbalance of buckets would cause the wheel to reverse direction, and if the water was pumped at the correct rate, the wheel would rotate at a constant speed. Lorenz observed through many tests, that if the rate of water was increased, and fixed, the wheel would reverse itself but never fit into a repeating pattern.
This observation strayed from the knowledge of simple Newtonian physics, and led Lorenz to develop three equations, with three variables, that outlined his experiment. The results of these equations were used as co-ordinates to plot a three-dimensional graph. These numbers created a sequential, infinitely complex line, which is now known as the “Lorenz Attractor” (p.29). This concept outlined the basic theory of chaos. Since the line never overlaps itself, the system never has an exact moment recur. The Lorenz Attractor is also known as The Butterfly Effect, due to the double loop image that is produced.
This infinitely complex line proved that chaos was present in a predictable system. Since the line never returns to it origin, a cycle is never completed. Without a period for the cycle to repeat in, predictions can never be made. This proved that while a system may contain some order, it is not enough to base any assumptions. The Lorenz waterwheel was an experiment that proved the fundamental properties of instability.
posted by Phantom at 6:47 PM
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