Lagrangian Mechanics is Intelligent Design?

Via Kevin Beck I just learned that Sal Cordova, famous (in some circles) for rank dishonesty and general lack of mathematical aptitude, has been claiming that Lagrangian mechanics was inspired by Intelligent Design. For those who are not au courant with physics, Lagrangian mechanics is an alternative take on the classical physics — think billiard balls, pendulums, planets orbiting the Sun — studied by Newton. The enterprise is named for Joseph-Louis Lagrange, who along with Euler and others laid the groundwork. It’s equivalent to Newton’s F = ma approach, but more convenient for some problems, and because it talks about the same physics in a different way, it provides a different and useful starting point for developing new theories. (For example, Barton Zwiebach’s First Course in String Theory generalizes the Lagrangian description of zero-dimensional objects, particles, to invent a theory of one-dimensional objects, strings. This is much easier to do in a Lagrangian rather than a Newtonian formalism.) Phenomena in relativity and quantum field theory are also often studied via a Lagrangian approach.

Many people are familiar with basic characteristics of light. We know, for instance, that light travels in straight lines; when light bounces off a mirror, the angle of incidence equals the angle of reflection; light can be spread out or focused together using lenses; and so forth. When we study optics, we can derive all these disparate facts from a very simple, central premise: when traveling from point A to point B, a light ray takes that path for which the travel time is a minimum. (A more precise statement is that the physical path taken by the light ray is such that a small perturbation to the path does not significantly change the travel time; this is connected to the calculus idea that the slope of a curve at a minimum or maximum is zero. For our purposes, we won’t have to worry about these details.) If there’s nothing in the way to change the light’s propagation speed, or if the material through which the light travels is uniform, then the path of minimum time is a straight line. Requiring that the light go from A down to a mirror and bounce back up to B means — I leave the geometry as an easy exercise to the interested reader — that the angles of incidence and reflection will be equal.

Lagrangian mechanics takes a similar approach, taking the idea of a “minimum principle” and applying it not to light, but to the motion of matter — balls, planets, frightened cats and so forth. Instead of calculating the travel time, as we did with light, we consider the energy of the moving objects; more precisely, our calculations involve the difference between kinetic and potential energies. The “Lagrangian” for classical problems — remember, we can generalize the ideas later — is the difference between the kinetic energy and the potential, and we find the path through space an object will take by adding up, or integrating, the Lagrangian along all possible paths. The physical path, the one the object really follows, is the one whose total Lagrangian, or “action,” is a minimum.

Now, what in blazes does any of this have to do with Intelligent Design?

This is, indeed, what Cordova claims, with what I presume is the textual equivalent of a straight face:

Much of the discussion of ID has been in biology. But the notion of ID and teleology has permeated the history of physics from the beginning to the present day.

To an extent, Cordova’s assertions resemble those of his compatriot, Michael Egnor, who insists that all order in Nature is really “design,” thus making all science an expression of “the design inference.” (When in doubt, redefine all terms to ensure victory!) Cordova quotes several paragraphs from Barrow and Tipler’s Anthropic Cosmological Principle to support his claim; unfortunately, I don’t have the book at hand, so I can’t immediately check to see if this constitutes yet another Cordovan quote mine. The number of ellipses in Cordova’s quotations is truly staggering, and somebody should look up the originals — but never mind that now, we can see the ludicrous nature of Cordova’s assertions without such measures.

As is common in creationist circles, Cordova makes much of the religious leanings of the various scientists who worked out the notions of these “least action principles.” But what does that have to do with anything today? They knew less than we know now, and whether science supports a particular conclusion depends upon the scientific knowledge we have now. Furthermore, a wide variety of motives have pushed people into doing science and making valuable discoveries: up until the time of Newton, chemistry and even medicine were deeply immersed in alchemy, yet nobody claims that modern physics is searching for the philosopher’s stone.

I find it interesting how smoothly Cordova elides mention of Pierre-Simon Laplace, the mathematician heavily influenced by Lagrange whose Traité de Mécanique Céleste (1799) was a crowning work of classical mechanics. When asked by Napoleon why the Traité de Mécanique Céleste described the formation and behavior of the solar system without making mention of God, Laplace replied, “Sire, I had no need of that hypothesis.” (It’s said that when Lagrange heard of this exchange, he quipped, “Ah, but that is a fine hypothesis. It explains so many things.” Indeed, it explains everything which happens and everything which does not, equally well!)

Cordova makes much of the idea that principles of least action are “teleological.” He asserts that this is the case with no more support than a sentence in Tipler and Barrow, a sentence which doesn’t itself explain what least-action principles are, just what “Max Plank” [sic] thought about them. (Again, I wouldn’t rely upon any quotation from any source when it’s passed through creationist hands.) Teleology implies goals and purpose, of which one finds precious little in the motions of planets, whether those motions be described by Newtonian or Lagrangian means. What, moreover, does it mean when the Lagrangian description can be recast, with complete exactitude, in a Newtonian or a Hamiltonian formalism? Is teleology present in one description of nature and not in another?

Perhaps one could caricature the Lagrangian view of classical mechanics as saying, “A particle wants to minimize its action; its goal is to find the path for which the integral of the Lagrangian is a minimum.” But this is just the same as saying, in the Newtonian framework, “A particle wants to make F equal to ma. Its purpose is to accelerate in proportion to the net applied force and inversely with its mass!”

UPDATE: Immediately after posting these remarks, I noticed that Torbjörn Larsson, OM located the original source of one quotation Cordova used. Cordova attributed the statement to the physicist Edwin Taylor, but Taylor’s own website indicates that it comes from Thomas A. Moore’s entry on least-action principles in the Macmillan Encyclopedia of Physics (1996)!

ADDITIONAL ENTERTAINMENT: Why not watch Richard Feynman expound on “minimum principles”? Remember, this is the man who said of religious belief, “The stage is too big for the drama.”


UPDATE (27 June 2007): Oh, the pain. Cordova has now let loose a new volley of nonsense, called “Cosmological ID in 1744,” in which he cites a 1744 essay by Pierre Louis Moreau de Maupertuis, “Derivation of the laws of motion and equilibrium from a metaphysical principle.” First, let me repeat that date: 1744. Everything I said before about knowing more now than people knew centuries ago still applies.

M. de Maupertuis has a few issues of his own:

The argument based on the suitability of the different animal parts for their needs seems more solid. Feet seem to be made for walking, wings for flying, eyes for seeing, mouths for eating and other parts for reproducing their kin. All these things seem to feature intelligent design in their construction. This argument carried as much weight with the ancients as it did with Newton.

Paging Dr. Pangloss, paging Dr. Pangloss. . . . To his credit, M. de Maupertuis recognizes limitations to human knowledge:

Truly our perspective is limited to where we are; we cannot see far enough to appreciate the order and interconnectedness of things. If we could, we would undoubtedly find the marks of God’s wisdom as well as His intelligence in its execution. But, given our limitations, let us not confuse the two attributes. For although an infinite intelligence necessarily brings with it wisdom, a finite intelligence may yet lack wisdom; and there is as much evidence showing that the universe is a soulless machine, as showing it to be the work of an Intelligent Designer.

Unfortunately, he fails to devote time to the possibility that the order and interconnectedness we discover tomorrow will not accord with the notions of God we had yesterday. Come to think of it, Michael Egnor has had problems with this same concept, too.

Interestingly, the term “Intelligent Designer” in the original French is une telle intelligence (“such an intelligence”). I count three instances of une intelligence & un dessein (“an intelligence and a design”), but nothing which translates directly as an “intelligent designer.” Whether this is a big cheat or a little one I leave to the Gentle Reader to decide.

It’s also interesting to see all the ways in which physics has advanced beyond M. de Maupertuis’s understanding. For example, he doesn’t think that the conservation of momentum is “a universal principle, a general law of motion.” In contrast, today we know this law is deep and fundamental; in fact, the very principle of least action advanced by M. de Maupertuis was the beginning of our understanding of how fundamental that law really is!

M. de Maupertuis calls the principle of least action a “principle so wise and so worthy of the supreme Being,” but one could say the same thing about Newton’s F = ma or even Aristotle’s notion that heavenly motions are always circular. What matters is whether the principles one postulates actually work. Do they accurately predict the results of experiments? Least action, yes; Aristotle, no. From the mere fact that the supreme Being is wise, one can deduce absolutely anything, and thereby deduces nothing at all. Going in the opposite direction, as M. de Maupertuis tried to do, from the elegance and simplicity of a physical law he understood only imperfectly to the wisdom of a supreme Being, also gets you nowhere, because if you pursue that program with any integrity at all, the Being you deduce is neither the God of Abraham nor even concerned with your daily affairs.

Who can honestly pray to the Euler-Lagrange Equations or the law of gravity?

4 thoughts on “Lagrangian Mechanics is Intelligent Design?”

  1. At the risk of repeating you:

    It seems like there are two appeals he’s making. One is that he seems to think you can’t be an atheist and be interested in optimization principles. That’s demonstrably not true: there are folks like Feynman and Laplace, and Richard Dawkins made his name by explaining traits and behaviors of living things with a maximization principle.

    It’s also 180 degrees wrong philosophically. Scientists want useful, simple descriptions of the world. Optimization can be a relatively easy thing to think about: we spend our days trying to maximize this or that (lines of code per cup of coffee, or whatever), so it’s evocative to imagine a light ray trying to get through the lens as quickly as possible. And some of these optimization rules happen to be easier to remember or write out: I can’t remember Snell’s law but I can remember the principle of least time. A technique of math and thought either describes the natural world well or it doesn’t; if it does, a scientist wants it.

    The other appeal Cordova’s making by implication is that the very existence of minimization principles itself somehow challenges atheism.

    The first thing to realize here is that lots of simple rules produce optimization. Little bits of mercury are attracted to each other but not to the air. You wind up with surface tension, as they call it, and your mercury takes on more or less the shape that minimizes surface area for a given volume, namely a sphere. Evolution occurs given very simple rules of the game—the existence of critters with inherited traits and varying reproduction rates—and bam, it gives you the principle of maximum gene fitness as a handy approximation in biology and behavior. Optimization rules don’t deserve a unique aura of mystery. (If they did, that still wouldn’t imply optimizing for a moral purpose or any of that, but that’s another story.)

    Now, what Cordova didn’t get into is the simplicity of physical laws, which is all kinds of interesting but isn’t an argument for belief in a god. If anything, the amenability of the world to naturalistic study and description should encourage us to keep going down that road, and discourage us from introducing bearded law-givers, giving up on scientifically describing life, and so forth. If physics were bizarre and arbitrary like the U.S. tax code, that might be an argument for a Congress in the Sky. :p

    Also, I didn’t know that light didn’t actually follow a principle of least time. Much less that the path it takes might be at a saddle point and not even a local max or min!

  2. The physical path, the one the object really follows, is the one whose total [difference between an object’s potential and kinetic energies], or “action,” is a minimum.

    Unless I’m missing something, that sounds a lot like a consequence of the Law of Conservation of Energy. “Teleological” my arse: more like a result of sitting down, applying the laws of physics and doing the maths.

  3. Conservation of energy applies to the sum of kinetic and potential energies, strictly speaking: it says that the sum doesn’t change over time. By mandating that the laws of physics have time-translation symmetry — that a self-contained experiment will do the same thing if you start it today and if you start it tomorrow — then energy conservation can be derived from the Lagrangian equations. This is a consequence of “Noether’s Theorem,” and Feynman talks a little about it (at a lay level) in the second video clip.

    One can actually use the Lagrangian and Hamiltonian tools in a situation where energy is not conserved (say, where friction is bleeding some of it off), but people generally seem to consider that a more advanced topic.

    Your statement about “sitting down and doing the maths” is, nevertheless, spot-on.

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