PRAGMATIC SIMPLICITY AND MAXWELL’S “EXERCISE IN MECHANICS”
simpler equations than theories that are more complex—are easier to use for various purposes, including explanation, prediction, calculation, and communication. And, very importantly, they are easier to develop further.
They are excellent starting points from which to create more sophisticated and perhaps more complex ideas. As I noted earlier, you can hold such a view about simplicity without holding any of the other six views. Or, you can hold this view together with any or all of the other six. But since I reject the first four claims, I recommend that you accept the Pragmatic Claim, and that you understand the Aim-of-Science and Scientific Virtue Claims in such a way that they incorporate the ideas in the Pragmatic Claim.Unlike some simplicity enthusiasts, I regard the pragmatic virtue of simplicity as the most important one. Partly, I do so because I reject ontological and epistemological virtues that have been attributed to it by champions of simplicity. Partly, I do so because even though truth or empirical adequacy are virtues as well, pragmatic considerations are relevant for determining what standards of truth or empirical adequacy to require. But my main reason for defending simplicity as a pragmatic virtue is that I regard it as an important one in presenting, developing, and applying theories to solve questions about actual phenomena. I will illustrate this with a case in which simplicity plays a crucial pragmatic role.
In chapter 1, I introduced three speculations that James Clerk Maxwell developed. My reason for discussing Maxwell there was to illustrate the point that different kinds of speculations are possible, and different ways of evaluating them are appropriate. Here, I return to the 1860 paper, not because it is a speculation but because it is one in which simplicity plays an important non-epistemic, pragmatic role.
Maxwell begins the paper, as follows:
So many of the properties of matter, especially when in the gaseous form, can be deduced from the hypothesis that their minute parts are in rapid motion, the velocity increasing with the temperature, that the precise nature of this motion becomes a subject of rational curiosity.[107]
In order to see whether and how many of the known properties of gases can be explained in terms of the motions of their “minute parts” (the hypothetical molecules), Maxwell makes a series of assumptions about these parts and their motions, including that gases are composed of spherical molecules; that these molecules move in straight lines except when they strike each other and the sides of their container; that they exert forces only at impact and not at a distance; and that they make perfectly elastic collisions (the total kinetic energy before collision is the same after). He offers no evidence for these assumptions. Indeed, a year before publication, he writes to Stokes saying that he is making these assumptions “before we know whether there be any molecules.”
In chapter 1, I quoted a passage from Maxwell in which he emphasizes the important role of mechanical explanations—ones in which phenomena are explained in terms of bodies in motion subject to forces governed by laws of dynamics. In his 1860 paper, the question for Maxwell is whether a mechanical explanation of known gaseous behavior is even possible, not whether the particular mechanical assumptions he introduces in the paper are true or probable. For this purpose, it suffices to introduce simple ones—for example, that the molecules are spherical, rather than oddshaped; that they travel in straight lines, rather than in some more complex path; and that the only forces they are subject to are contact forces, rather than more complex forces that act at a distance. These assumptions are easier to express and develop mathematically than more complex ones.
(In later papers he revises these in various ways, e.g., by allowing noncontact forces that are both attractive and repulsive.) The strategy in this paper is to see how far he can get with a set of simple assumptions—ones that are “ontologically” simple (spherical molecules all of the same mass, subject to only one kind of force) and mathematically simple (e.g., in deriving his velocity distribution law, he assumes that the directional components of velocity of a molecule are independent, thus simplifying probability calculations). He is certainly not claiming that the simplicity of his assumptions makes it likely, or more likely, that they are true or close to the truth. His use of simplicity here is entirely pragmatic: by introducing simple assumptions, rather than more complex ones, he can more readily see where they lead (30 out of 32 pages of his paper are spent deriving answers to mechanical questions about these molecules). If the simple assumptions work out reasonably well in some cases but not so well in others, he can try more complex ones later.That is exactly what happened. From his simple assumptions he derived the ideal gas law relating pressure, volume, and temperature of a gas, and he explained known deviations from the law at low temperatures and high densities. But he also got some results that were not so happy, particularly specific heat ratios that were too far from observed values. In a later paper in 1865, he replaces the contact force repulsion idea with a more complex action at a distance idea and with more complex attractive and repulsive forces. And in 1875, he begins not with his simple 1860 assumptions but with a very complex virial equation relating the pressure, volume, and temperature of a gas to the total kinetic energy of the molecules in the container of gas, the force of attraction or repulsion between molecules, and the distance between molecules. This equation he takes from Rudolf Clausius, who derived it from classical mechanics for observable particles constrained to move in a limited region of space.
In short, Maxwell chose to make simple assumptions in 1860, not because he thought that simple assumptions are more likely to be true than complex ones, or because he presupposed that nature is simple, or because as a physicist he aimed to produce simple theories, or because he valued simplicity for its own sake. He chose to make simple assumptions because they are easier to develop and see where they lead in his attempt to provide a mechanical theory of gases. This, I am claiming, is the main function of simplicity—an important one, often ignored or belittled by those who believe it serves a “higher” function.
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