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

briefly resemble stately galaxies, but their true dynamics remain infuriatingly difficult to grasp. Von Mises was not an easygoing man—he demanded of applied mathematics all the rigor of its pure cousin—and the more he worked in the unstable, fluttering world of flow, the less he liked the fixed but unexamined assumptions behind Laplace’s idea of probability; defining it as “a number between 0 and 1, about which nothing else is known.”
    The problem, von Mises thought, was that in assuming equally probable cases for our dice, coins, and urns, we had created out of nothing a parallel universe, in which things happened a certain way because they were supposed to. Instead of being messengers of the gods, the dice had become the gods. At best, the rules of probability were a tautology: the numbers 1 through 6 come up equally often in theory because we define them that way. At worst, the concept of equally probable cases prevented us from saying anything about what was before our eyes. What if the die has a few molecules missing from one corner, for instance? We have evidence, but no theorem based on equally probable cases applies to it; our probability calculus is irrelevant; we have to fall silent.
    Von Mises’ view was that the true reason for our believing that six should come up 1/6 of the time is no different from our reason for believing that the Earth takes 365.25 days to orbit the sun. That reason is our having observed it. “The probability of a six is a physical property of a given die”—a quantity derived from repeated experience, not some innate essence of creation or nature. Heads or tails, red or black, pass or no pass—these are no more phenomena in themselves than are grams, ohms, or pascals. Probability is a measure of certain aspects of consistent groups of events (“collectives,” in von Mises’ terminology) revealed when these events are repeatable indefinitely.
    The nature of the “collective” has to be very particular: one must have a practically unlimited sequence of uniform but random observations. We can conclude that we have observed a given probability for a result if the relative frequency of that result approaches a limit, not just for the basic collective, but for randomly selected and mixed subgroups of the collective. The probabilities of combinations of results (like throwing two dice or taking two balls at a time out of an urn) can also be defined by keeping careful track of the order and subgroups of observations. That means that, while rigorously banishing any preconceptions of probability from our mind, we can gradually rebuild many aspects of its calculus—as long as we insist on describing frequencies, and restrict our observations to true collectives.
    There was no doubt where science had to go to remain science: all facts were to be considered as mere probabilities, and all probabilities, frequencies of observations. As von Mises saw it, anything else was simply a kind of false consciousness.
    Given this view of pure science, it is certainly hard to see how probability could be legitimately applied to juries, deliberative assemblies, or voting systems. For von Mises, probability had only three areas of legitimacy: games of chance, certain mass social phenomena like genetics and insurance, and thermodynamics (where, as we will see in Chapter 11, it would take the leading role).
    â€œDost thou think, because thou art virtuous, there shall be no more cakes and ale?” Like all puritans, within or without the sciences, von Mises was asking his audience to give up much of what they felt made life worthwhile. People go into science because they want to discover and explain all the things around us that seem so richly freighted with meaning. But how many of the interesting phenomena of life truly are “collectives”—what fascinating event can be said to repeat exactly and indefinitely? While Laplace’s