Read Online Chances Are by Michael Kaplan - Free Book Online Page A

from seeking out and sustaining friendships with the people you already like most, rather than devoting too much time to the sad, the mad, or the bad alternative. Like staying away from the back ends of horses, this is a way to make the curve work for you.
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    Poisson’s distribution could be seen as a special case of the standard distribution—but as probability advanced into statistics it came upon many more curves to conquer, if the mathematics and the data were to continue their engagement. Curves spiky, curves discontinuous—scatters that could not be called curves at all, although they were still defined by functions (that is, rules for assigning a single output to any given input). Mathematics spent much of the nineteenth century seeking methods to bind such boojums and snarks, snaring them in infinite series, caging them with compound constructions of tame sine-curves, snipping them into discrete lengths of manageability—getting their measure.
    At the turn of the century, the French mathematician Henri Lebesgue brought these many techniques to their philosophical conclusion: a way to assign a value—a measure—to even the most savage of functions. Measure theory, as his creation was called, made it possible to rein in the wilder curves, gauging the probabilities they represented. It offered its power, though, at the price of intuition: a “measure” is just that. It is simply a means whereby one mathematical concept may be expressed in terms of another. It does not pretend to be a tool for understanding life.
    By 1900 it was clear that if the counterintuitive need not be false, the intuitive need not be true. The classical approach to probability could no longer conceal its inherent problems. Laplace had founded his universal theory of probability on physical procedures like tossing a coin or rolling a die, because they had one particularly useful property: each outcome could be assumed to have equal probability. We know beforehand that a die will show six 1/6 of the time, and we can use this knowledge to build models of other, less well known, aspects of life. But think about this for a minute: how, actually, do we know these cases are equally probable?
    Well, we could say we have no reason to believe they aren’t; or that we must presuppose equal application of physical laws; or that this is an axiom of probability and we do not question it; or that if we didn’t have equally probable cases . . . we’d have to start all over again , wouldn’t we? All are arguments reflecting the comfortable, rational assumptions of Enlightenment science—and all draw the same sardonic, dismissive smile from our prosecutor, Richard von Mises.
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    Lemberg, alias Lwów, alias Lviv: a city that lies at the intersection of three sets in three dimensions: Polish, Austrian, Ukrainian; Catholic, Orthodox, Jewish; applied, abstract, artistic. It remains a symbol of intellectual promise for the debatable lands between the Vistula and the Dniepr; a Baroque lighthouse in a politicogeographic tempest. Its prominent sons and daughters would be themselves enough to populate a culture: the writers Martin Buber and Stanislaw Lem; the pianists Moriz Rosenthal and Emanuel Ax; the Ulam brothers, Stanislaw (mathematician) and Adam (historian); Doppler of the eponymous effect; Redl the spy—not to mention Weegee, Paul Muni, Sacher-Masoch, and the Muslim theologian Muhammad Asad (one of the few imams to be the son of a rabbi).
    Lemberg’s Richard von Mises was a pioneer in aerodynamics, designing and piloting in 1915 Austria-Hungary’s monster bomber, the 600-horsepower Aviatik G. III. The plane was not a success, for many of the subtle local reasons that govern heavier-than-air flight. Perhaps in reaction, von Mises became increasingly interested in turbulence. Turbulence (as we will see later) lacks the pleasant predictability of the solar system; the swirls of fluid vortices may