Volume 9, No. 7 (October 1999)
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Suppose you are standing on the beach, at some distance from the water. You hear cries of distress. Looking to your left, you see someone drowning. You decide to rescue this person. Taking advantage of your ability to move faster on land than in water, you run to a point at the edge of the surf close to the drowning person, and from there you swim directly toward him. Your path is the quickest one to the swimmer--but it is not a straight line. Instead, it consists of two straight-line segments, with an angle between them at the point where you enter the water.

Now consider a beam of light. Like you, it moves faster through air than through water. If it starts from point A in the air and ends at point B in the water, it will not travel in a straight line. Rather, it will take a straight path from point A to the edge of the water, turn a bit, and then follow another straight path to point B in the water. (This is called refraction.) Just as you did when rescuing the drowning person, the light beam considers its destination, then chooses the trajectory that gets it there in the least time, given its differential rate of progress in the two elements through which it must travel.

But this can't be right, can it? Our explanation for the route taken by the light beam--first formulated by Pierre de Fermat in the seventeenth century as the principle of least time--assumes that the light somehow knows where it is going in advance and that it acts purposefully in getting there. This is what's called a teleological explanation.

The idea that things in nature behave in goal-directed ways goes back to Aristotle. A final cause, in Aristotle's physics, is the end or telos toward which a thing undergoing change is aiming. To explain a change by its final cause is to explain it in terms of the result it achieves. An efficient cause, by contrast, is that which initiates the process of change. To explain a change by its efficient cause is to explain it in terms of prior conditions.

One view of scientific progress is that it consists in replacing teleological (final cause) explanations with mechanistic (efficient cause) explanations. The Darwinian revolution, for instance, can be seen in this way: Traits that seemed to have been purposefully designed, like the giraffe's long neck, were re-explained as the outcome of a blind process of chance variation and natural selection.

Actually, pretty much the opposite has happened in physics. In 1744, the French mathematician and astronomer Pierre-Louis Moreau de Maupertuis put forward a grand teleological principle called the law of least action, which was inspired by (and possibly stolen from) Leibniz. A more abstract version of Fermat's least-time principle, Maupertuis's law said, in essence, that nature always achieves its ends in the most economical way. And what was this "action" that nature supposedly economizes on? As characterized by Maupertuis, it was a mathematical amalgam of mass, velocity, and distance.

In its original form, the law of least action was too vague to be of much use to science. But it was soon sharpened by the great eighteenth- century mathematician Joseph Lagrange. In 1788, a century after Newton's Principia, Lagrange published his celebrated Mécanique analytique, which expressed the Newtonian system in terms of the law of least action. In the next century, the Irishman William Rowan Hamilton cast the same final-cause idea into a form--which became known as Hamilton's principle--from which all of Newtonian mechanics and optics could be deduced.

Since then, the law of least action has, in its various guises, continued to be extraordinarily powerful. Einstein's equations of relativity, which replaced Newton's laws, follow from an action principle not unlike the one Maupertuis set forth. "The highest and most coveted aim of physical science is to condense all natural phenomena which have been observed and are still to be observed into one simple principle," observed Max Planck, the founder of quantum theory. "Amid the more or less general laws which mark the achievements of physical science during the course of the last centuries, the principle of least action is perhaps that which...may claim to come nearest to this ideal final aim of theoretical research."

If the law of least action (or a modern version of it) really does stand at the pinnacle of science, what does this say about the world? Does it mean that there is a purposeful intelligence guiding all things with a minimal expenditure of effort, as Maupertuis, Lagrange, and Hamilton believed?

We have one set of equations that explains the world in terms of efficient causes. We have another set that explains it in terms of final causes. The second set may be simpler than the first, and more fruitful in leading to new discoveries. But the two describe the same state of affairs and yield the same predictions. Therefore, as Planck said, "on this occasion everyone has to decide for himself which point of view he thinks is the basic one." You can be a teleologist if you wish. You can be a mechanist if that better suits your fancy. Or you may be left wondering whether this is yet another metaphysical distinction that does not make a difference.

Jim Holt