NATURE IS SIMPLE

and even if we specify these various respects, we need to say which ones are applicable to nature. All of them? Some, but not others? They don't all march together. The set of laws gov­erning certain phenomena might be mathematically simple while at the same time being complex because there are so many different laws.

Moreover, presumably simplicity is subject to degrees or at least to “more or less.” If so, and if nature is claimed to be simple in some particular respect—say, mathemati­cally speaking—how simple is it being claimed to be in that respect? Suppose we construct some scale of mathematical simplicity, so that a circular orbit of a planet is simpler than an elliptical one—indeed, the simplest one possible, given that the planets move around the sun. Or suppose our scale is such that that a linear path of a molecule is simpler than some zigzag one—indeed, the simplest one possible, given that molecules in a gas are in motion. Is the claim that nature is simple (together with the true assumption that the planets move in some closed orbit around the sun) supposed to en­tail, or make it likely, that planetary orbits are circular? Is the claim that nature is simple (together with the true assump­tion that molecules in a gas are in motion, not stationary) supposed to entail, or make it likely, that molecular paths are straight ones? If so, then the claim that nature is simple (in the respects specified) is false, or likely to be, since these consequences are false.

Perhaps the claim that nature is simple, when this is applied to planetary orbits or molecular paths, is to be understood as saying that whatever in fact the planetary orbits and molecular paths are, they are simple ones, even if they are not the simplest possible. Now we have made the claim even vaguer, but still clear enough to be challenged. Because of perturbations caused by forces exerted by other planets, the planetary orbits are by no means simple; the same applies to the paths of gas molecules, due to the presence of non-contact intermolecular forces. Of course, we can idealize, ignore these forces, and say what the orbits and paths would be like if these forces did not exist. Doing so, we would obtain orbits and paths that are mathemat­ically much simpler. But this idealization falls more squarely into what I have called the pragmatic view of simplicity rather than the ontological one. For certain pragmatic purposes, it may be useful to idealize and represent (parts of) nature as simple in certain respects. We can then say how close this rep­resentation is to nature. But nature itself is not idealized.

There are two more complications I will mention. First, the same fact about nature can be described in different ways, even ones that are logically or mathematically equiv­alent, one of which is much simpler than another. The shape of a petaled flower (called a polar rose) can be described by a simple equation expressed using polar coordinates, or by a much more complex equation expressed using rectangular coordinates. Is the shape itself simple or complex? It would seem that if we want to talk about the simplicity of nature, we would need to relativize this to a description or representa­tion: under one description or representation, some aspect of nature is simple, under another, it may be complex.

Second, nature may be simple at one “level” but not at another. For example, some claim that nature is simple at the most fundamental level. At this level there are “atoms” with no parts (hence, they are simple), and they are subject to simple fundamental laws that have no further explanation.

Accordingly, when we give even a slight push and poke at the vague but simple claim that nature is simple, we end up with a claim that is still vague, but now complex: in certain respects, under certain descriptions, and at some levels, but perhaps not others, nature has some measure of simplicity; in other respects, under some descriptions, and at other levels, perhaps less and in some perhaps none. Or more simply, for certain purposes, nature, or parts of it, can be represented in ways that have some measure of simplicity. Despite its vagueness, let us suppose that this resulting claim is still clear enough so that we can ask the following about it: How do we know that nature is simple—in whatever ways, or amounts, or representations, or levels, it is?

My answer is a “nonglobal” or “localist” one: the only way to know this is to do science itself and make particular judgments about particular simplicities or complexities. Given his evidence concerning the observed motions of the planets and their moons, Newton, we might suppose, was justified in believing that one force of gravity, not many, was operating on both celestial and terrestrial bodies; and that this force is an inverse-square force, not some mathemati­cally more complex one.^[70] In the case of the motions in ques­tion and the forces and laws governing this motion, Newton, we might say, was justified in believing that nature is simple. (In what follows, I will simplify the discussion by supposing that the simplicity label is assigned to the feature of nature under the representation given to it by the scientist in ques­tion or under one that is explicit or implicit in the context.) Given what was known about gaseous behavior, Maxwell was justified in believing that although the ideal gas law is a simple equation of state that works well within certain ranges, it is not an accurate one in general; a much more complex virial equation is much more accurate. In the case of the relationships between the pressure, volume, and temper­ature of gases, Maxwell was justified in believing that nature, represented more accurately, is not so simple. Nothing very interesting follows globally from individual cases such as these. In certain cases, we find that nature is, or is represent­able as, simple; in other cases, it is not.

How might a “globalist” respond?

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