We are a commune of inquiring, skeptical, politically centrist, capitalist, anglophile, traditionalist New England Yankee humans, humanoids, and animals with many interests beyond and above politics. Each of us has had a high-school education (or GED), but all had ADD so didn't pay attention very well, especially the dogs. Each one of us does "try my best to be just like I am," and none of us enjoys working for others, including for Maggie, from whom we receive neither a nickel nor a dime. Freedom from nags, cranks, government, do-gooders, control-freaks and idiots is all that we ask for.
Not being a sports fan, I haven't watched Michael Jordan much, so I really enjoyed that 2-1/2 minute clip of some of his more amazing feats. I guess everyone else in the universe already knew what it was like to watch him. Wow.
The problem of the fastest path through two obstacles of different resistance (like deep snow vs. grass) was a nice example of how to use max-min solutions. It's charming that light appears to solve the problem automatically in moving first through air and then through water or glass. The footnote cites Richard Feynman's use of the "principle of least action," which was his favorite of the many ways that can be used to think about problems of this kind. Feynman wouldn't say that the light beam "solves the problem," of course, except as a kind of joke. He would say that each photon in the light simultaneously takes all of the possible paths from the source to the object, including all kinds of unlikely, slow, circuitous paths. But the path that takes the least action is the one we can discern with our eyes, because all the probabilities resonate most completely there, while the randomly slow paths, with their wildly varying speeds, tend to cancel out.
This idea that each photon takes all the possible paths at once, not just the one we expect, isn't just sophistry. You can actually manufacture a mirror in which the angle of incidence doesn't equal the angle of refraction, for instance, by inscribing the surface with tiny strips of non-reflective material -- which differentially selects for the likelihood that the photon will hit and bounce off at a certain point in its probability cycle (i.e. frequency). The trick is that the strips have to be really tiny, on the order of the electron's wavelength, so you have to use something like a crystal with molecular-sized tiny ridges of alternating reflective and non-reflective properties. It's called (I think) an X-ray diffraction grate, and, as Feynman says, it works like a charm. Light of a particular frequency comes in at one angle but reflects at another, like magic, even though it certainly appears that that was not the path of least action.