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?
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