Statistical Metalinguistics and Zipf/Pareto/Mandelbrot <http://www.csl.sri.com/users/neumann/#12a>I frequently see cryptic references to the magic of Zipf or Pareto or Mandelbrot, with reference to linguistic and other structures, and sometimes in the context of 80-20 rules relating to almost anything. (See Note.)
There is no surprise at all in the Zipf/Pareto/Mandelbrot theories once you understand that each formula can be derived mathematically. In 1959, my old Russo-Belgian friend Vitold Belevitch [2 Mar 1921--*26 Dec 1999] (see On the Statistical Laws of Linguistic Distribution, *Ann. Soc. Sci. Bruxelles 73,* III, 1959, 310-326) considered a wide class of more or less well-behaved statistical distributions (normal or whatever), and performed a functional rearrangement that represents the frequency as a function of rank-ordered decreasing frequency, and then did a Taylor expansion of the resulting formula. Belevitch's lovely result is that "Zipf's Law" follows directly as the first-order truncation of the Taylor series. Furthermore, "Mandelbrot's Law" (which seem even more curious and mysterious to most people) follow immediately as the second-order truncation. and this delightful tidbit later (possibly apropos the recent thread about language and how we think)Multiply-Mixed Metaphor Mania * Pandora's cat is out of the barn, and the genie won't go back in the closet. [This polymorphic statement can be variously applied to cryptography, export controls, viruses, spam, terrorism, outsourcing, and many other issues.] * It's like shooting a straw herring in midstream. [Straw men have a difficult time catching red herrings!] An alternative version that I have used is ``It's like flogging a straw herring in the foot.'' * In an article by John Schwartz in *The New York Times*, 30 Mar 2001, on Internet technologies in business, reflecting on the acceleration being a double-edged sword, I was quoted as saying, ``Many of the swords have more than two edges -- sort of a Swiss Army Knife with the blades in upside down, so that you keep cutting yourself on some of the implements whenever you try to take one out.'' but really the whole thing <http://www.csl.sri.com/users/neumann> is just a delight to read. Thank you Peter. -- Charles
