Idle Chatter

I don't feel like working on Samuelson today, having had a very difficult week of doing similar things. I'll need to do it tomorrow though, or I'll never get back to it.

What is the name of the derivative of the arctan function? That is, the pdf of the Cauchy distribution. In a problem of static superconductors, the magnetic field is distributed (in one direction) as a Cauchy distribution. This is cool and all, but is there a name for that bell-curve-esque shape? You might wonder why this would be the case. Electro and Magnetostatics can be thought of as non-varying fields, true, but they can also be thought of as asking what are the stable distributions for randomly walking electrons in a given geometry. In any other configuration the electrons would move and they'd drag field around with them. In the discrete electrostatic case, the unique solution is given by Kirchhoff's circuit laws, in the continuous case by Laplace or Poisson Equations. These equations can get very interesting, I've examined a fairly fundamental case that has given rise to cauchy distributions and chaos! The study of harmonic functions truly is a noble cause.

My least favorite philosopher of science is Paul Feyerabend, who I think was not only wrong on every level, but deeply and unsalvageably wrong. Popper is drenched in technical errors and shortcomings, but might be saved on some level (in fact, I think he has been and that level is called learning theory). Lakatos is good, but not interested in the questions I happen to be. But then there's Feyerabend!  For instance, I can't understand how he could even have opinions on the materiality of the mind, why should he reject the evidence of psychic phenomena, not to mention angels and other spirits. There are standards when he wants (in Against Method, he defends voodoo), but not when he doesn't. Feyerabend on renormalization is a hoot. Even if he understood it, he doesn't seem to ever have expected that it would be used throughout material science (or, at least, in its condensed matter underpinnings) - that most practical of beasts - and doesn't even seem to have understood what was difficult about it in the first place. Perhaps I should write something on that, I like multi-scale methods better than perturbation ones and they are not as widely reprinted. Feyerabend wrote an accidentally hilarious letter asking why physicists don't seem to be engaging with philosophers (or course, that he was personally insufferable explained why they didn't interact with him...), never seeming to realize that physicists just got over the puzzles that bothered philosophers like him. His personal judgements were completely off-base: we all remember how stuffy and overly professional Feynman was right? His lack of charity towards physicists was typical of him. He would likely claim that he was not being critical, but I regard his self-claims as nearly as worthless as those of Popper (apparently nobody ever understood Popper, apparent criticisms were all shallow misreadings, of course). Perhaps Feyerabend is better at criticism ("All these philosophies make these mistakes") than at positive construction. If so, is there any reason for a non-philosopher to take Feyerabend seriously?

A brief  thought: Everyone knows the "broken window fallacy", just because people are put to work to replace windows doesn't mean that society is richer. But stealing a window doesn't break it. People are put to work, and we still have a window! What is the welfare basis for property? Why do animals have property?