Siegfried, Tom. "7 Quetelet’s Statistics and Maxwell’s Molecules--Statistics and society, statistics and physics." A Beautiful Math: John Nash, Game Theory, and the Modern Quest for a Code of Nature. Washington, DC: The National Academies Press, 2006.
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A Beautiful Math: John Nash, Game Theory, and the Modern Quest for a Code of Nature
exhibit patterns of behavior that equations could capture. Psychohistory might not be quite as accurate as the laws governing gases, but that’s only because there are many more molecules than people. As one of Asimov’s characters explained, “The laws of history are as absolute as the laws of physics, and if the probabilities of error are greater, it is only because history does not deal with as many humans as physics does atoms, so that individual variations count for more.”2
Still, psychohistory was fiction, and using math to describe something as complex as society still strikes many people as an overly ambitious goal for real life. On the other hand, in the mid-19th century math seemed similarly useless for physicists pondering the complexities of molecular motion in gases. Gross properties of gases could be observed but not understood without a way to quantify the apparent anarchy of molecular interactions. How could anyone grasp the inner workings of a mass of molecules too numerous to count and too small to be seen? Yet the Scottish physicist James Clerk Maxwell found a way, by using statistics— mathematical descriptions of the average behavior of large groups of molecules.
Calculating such averages provided amazing predictive power. Although you couldn’t say exactly what any one molecule was up to, you could predict precisely what a sufficiently large group of molecules would do in certain circumstances. Measuring the temperature of a gas, for instance, tells you something about the average speed of its molecules, and you can calculate the effect of altering the temperature on the gas’s pressure. Similar methods were developed to deal with matter in all sorts of situations. Knowing the average amount of energy possessed by molecules of various substances, for instance, allows you to predict whether a chemical reaction will proceed or not—and if so, how far. You can use the statistical approach to describe a substance’s magnetic or electric properties, or whether it will snap or stretch when under tension. In Asimov’s psychohistory, features of society corresponded to variables like the temperature and pressure of a gas or the ebb and flow of chemical reactions or the fracture of a beam in a building.