Chaos - James Gleick [97]
Once the experiment began, the helium rolling inside the cell inside the vacuum container inside the nitrogen bath, Libchaber would need some way to see what was happening. He embedded two microscopic temperature probes in the sapphire upper surface of the cell. Their output was recorded continuously by a pen plotter. Thus he could monitor the temperatures at two spots at the top of the fluid. It was so sensitive, so clever, another physicist said, that Libchaber succeeded in cheating nature.
This miniature masterpiece of precision took two years to explore fully, but it was, as he said, the right brush for his painting, not too grand or sophisticated. He finally saw everything. Running his experiment hour after hour, night and day, Libchaber found a more intricate pattern of behavior in the onset of turbulence than he had ever imagined. The full period-doubling cascade appeared. Libchaber confined and purified the motion of a fluid that rises when heated. The process begins with the first bifurcation, the onset of motion as soon as the bottom plate of high-purity copper heats up enough to overcome the tendency of the fluid to remain still. At a few degrees above absolute zero, a mere one-thousandth of a degree is enough. The liquid at the bottom warms and expands enough to become lighter than the cool liquid above. To let the warm liquid rise, the cool liquid must sink. Immediately, to let both motions occur, the liquid organizes itself into a pair of rolling cylinders. The rolls reach a constant speed, and the system settles into an equilibrium—a moving equilibrium, with heat energy being converted steadily into motion and dissipating through friction back to heat and passing out through the cool top plate.
So far, Libchaber was reproducing a well-known experiment in fluid mechanics, so well known that it was disdained. “It was classical physics,” he said, “which unfortunately meant it was old, which meant it was uninteresting.” It also happened to be precisely the flow that Lorenz had modeled with his system of three equations. But a real-world experiment—real liquid, a box cut by a machinist, a laboratory subject to the vibrations of Parisian traffic—already made the task of collecting data far more troublesome than simply generating numbers by a computer.
Experimenters like Libchaber used a simple pen plotter to record the temperature, as measured by a probe embedded in the top surface. In the equilibrium motion after the first bifurcation, the temperature at any one point remains steady, more or less, and the pen records a straight line. With more heating, more instability sets in. A kink develops in each roll, and the kink moves steadily back and forth. This wobble shows up as a changing temperature, up and down between two values. The pen now draws a wavy line across the paper.
From a simple temperature line, changing continuously and shaken by experimental noise, it becomes impossible to read the exact timing of new bifurcations or to deduce their nature. The line makes erratic peaks and valleys that seem almost as random as a stock market fever line. Libchaber analyzed such data by turning it into a spectrum diagram, meant to reveal the main frequencies hidden in the changing temperatures. Making a spectrum diagram of data from an experiment is like graphing the sound frequencies that make up a complex chord in a symphony. An uneven line of fuzziness always runs across the bottom of the graph—experimental noise. The main tones show up as vertical spikes: the louder the tone, the higher the spike. Similarly, if the data produce a dominant frequency—a rhythm peaking once a second, for example—then that frequency will show up as a spike on a spectrum