The Probabilistic View of the World — The Taming of Chance

As late as the nineteenth century, the deterministic description of the world still prevailed. Laplace (1814) held that the course of phenomena resulted from their deterministic mechanics. Science had a single ideal of explanation — find the causes, derive the trajectory, predict. This way of describing the world was regarded as the sole true one. Maxwell (1860) and Boltzmann (1872), who studied gas and its molecules, introduced the so-called macroscopic mode of describing phenomena. At the time, however, they did not call into question the nature of gas behavior — a certain mechanics of the natural world. They merely proposed a different conceptual map for describing it: a statistical description of gas, by means of a probability distribution. From that point on, we speak of two levels of description: the microscopic (trajectories, causes, mechanics), and the macroscopic (distributions, probabilities, statistics).

Meanwhile, shortly afterward — likewise in the nineteenth century — something occurred that Hacking (1990) termed the "taming of chance." Chance ceased to be regarded merely as a facet of ignorance; it acquired autonomy, as the very essence of the matter, rather than as a mode of description. The natural world was now, in itself, random, by its very nature of existence. This, in turn, opened the door to statistical tools grounded in probability calculus — already fairly well developed by that time — as fully legitimate forms of description, consistent with the very nature of things.

The process of "taming chance" likewise began within the domain of socio-economic phe-nomena. Quetelet, in the 1840s (Hacking, 1990), was the first to transfer the curve of measurement error (as used in astronomy) onto human and societal characteristics. Quetelet applied the normal distribution to describe human traits, and developed the concept of the "average man." In doing so, he inaugurated probabilistic thinking within the social sciences. The mean for a society, its distribution, ceased to be merely a possible way of viewing a population. They came to be treated as a reflection of the laws of nature governing society. This line of thought was developed further by Galton (1889), and its mathematical formalization was undertaken by Karl Pearson (1896).

In insurance, randomness as the very nature of things was already being considered in the eighteenth century by Lambert (1772), who proposed a curve describing mortality, which helped in determining an adequate insurance rate. In the modeling of rare events and natural catastrophes, probabilistic ideas were later developed in succession by the researchers — Fuller, Hazen, Foster, and Gumbel — the fruit of whose work were the two Extreme Value Theories, I and II. In economics, meanwhile, the key step was taken by Bachelier (1900), who, in 1900, applied Brownian motion — known today as the random walk process — to the description of stock prices. Bachelier, forgotten for the next fifty years, laid the foundations for the concept of the randomness of value changes as a generic feature of this process. Norbert Wiener (1923), in the 1920s, gave Brownian motion rigorous mathematical foundations (the Wiener process). Paul Samuelson (1965) initiated the rapid development of theories built on this founding axiom, and it was on this very assumption that all subsequent theories were built: Black-Scholes (1973), Merton (1974), Vasicek (1987), J.P. Morgan (VaR) (1996), and so on — theories that constitute the philosophical foundation of contemporary risk management methodologies. The implementation of catastrophe modeling within the world of economics was, in turn, undertaken by, among others, Embrechts (1997).

In this way, ideas that had originally been intended merely as an alternative form of describing the world became integrated with that world, and came to constitute its very constitu-tion. The world became random, and, if so, the natural way of describing the world became the very science that concerns itself with randomness — that is, probability theory, particularly in its mature form, following the sanctioning, in 1933, of Kolmogorov's axioms (1933).

Karl Pearson was a positivist in the philosophical sense. He maintained that science does not discover reality; science constructs economical descriptions of phenomena. Scientific theo-ries, in his view, are not claims about reality, but tools for prediction and for organizing expe-rience. A theory does not describe what the world is like. A theory either works or it does not — it is either useful or it is not. Formulas are shorthand for thought, not descriptions of deep structure. For Pearson, a distribution was a curve fitted to the data. The question "why do the data take this shape?" was, for him, an improper question — a metaphysical one, not a scientific one.

This idea was developed further by Friedman (1953). He argued that the only proper test of a hypothesis's correctness is a comparison of its predictions against experience, and that truly important and significant hypotheses have assumptions that may, in fact, be strikingly inaccurate descriptions of reality. Scientific theories are simplifications. Always. The map is not the territory. The model is not reality. Were a model as complex as reality itself, it would be useless.