Against the Gods

Against the Gods

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by Peter Bernstein

published 1998

Bernstein asserts that the mathematics of probability enables modern risk management, which in turn enables risk-taking in ways that advance and are critical to the foundations of modern civilization. This ability to measure risk and probabilities separates us from past civilizations far more than we realize. He traces the history of our knowledge of probability and describes how important discoveries in this branch of mathematics enabled new endeavors for the human race, mainly based on the concept of spreading risks among many people, such as insurance, annuities, and such.

The title of the book refers to the fact that ancient civilizations believed that the future was fully in the hands of deities, and that the best they could hope for was to scratch out a living in the here and now. With such faith in higher powers, concepts such as calculating the odds of future events had no relevance to their belief system and thus were wholly absent from their minds. Even the ancient Greeks, with their impressive use of logic and proof, never ventured into the realm of probabilities. Their system of numbers used Greek letters instead of dedicated numerical symbols, making mathematics difficult. And the Romans were not much better. Ever try doing long division using C, M, X, D, L ? No wonder they were philosophers and not mathematicians!

Bernstein shows how the gradual shift in power from the priesthood to the scientific/business community opened the doors for thinking about the future as something that if not controlled, could at least be measured. He notes some of the more important discoveries in mathematics, from the invention of zero by the Hindus, to the use of algebra by the Arabs and eventually double-entry bookkeeping by the Italians.

He mentions Pascal and Fermat’s early work on probability, as well as contributions by many others. One of many important contributors to economic theory was Daniel Bernoulli, who developed the concept of utility. Bernoulli, an eighteenth century Swiss mathematician, noted that in economic decisions, it was not enough the calculate the probability of an event, such as the odds of a certain number coming up on the roll of two dice. Bernoulli was the first known person to introduce the concept that in gambling and other risk assessments, human factors mattered. He postulated that “The utility resulting from any small increase in wealth will be inversely proportional to the quantity of goods previously possessed.”

This seemingly simple concept, at once obvious when we consider our own fears and motivations, had escaped the thinking class for thousands of years. Finally there was an explanation for people’s seemingly irrational fears and behaviors and their differing appetites for risk. Here we refer to the difference between probability and value. The first is a mathematical fact, the second a human judgement, unique to each individual. Simply put, if you have $100K, for most people the pain from losing that money will far exceed the pleasure from gaining an additional $100K.

Bernstein continues, more or less in chronological order of the march of mathematical progress. We learn of de Moivre’s discovery of the bell curve, or normal distribution. Then Francis Galton takes that concept and conducts hundreds of real-world experiments to find that nature is filled with normal distributions, and that these distributions have an almost universal habit of reverting to the mean (almost). The simple example here is that if we look at the offspring of a group of taller-than-average parents, the children will also be taller than average, but not as tall as their parents. And the offspring of the shorter-than-average parents will follow the same pattern: they are also shorter than average, but not as short as their parents. The most famous of these is the experiment of growing multiple generations of peas and measuring the results. Charles Darwin, who was a first cousin of Galton, found the results of this experiment to be of extreme importance.

From Galton’s work, Bernstein moves to the 20th century and devotes a fair amount of time to studies of stock and bond prices, ultimately concluding that nature’s pattern of reversion to the mean is complicated by the fact that the mean is a moving target. In other words, past results are not a guarantee of future performance. At this point in the book we have been introduced to the accumulation of ten centuries of progress in the mathematics of economics, yet are no closer to predicting the future than our ancient ancestors.

For much of the second half of the book Bernstein rambles with various examples to demonstrate that in matters of risk evaluation we can never have certainty. Despite the science of probability, we always lack complete information, and of the information we do have we cannot be certain that it is correct. And further, many of the decisions we face are so complex that even if we did have enough information, it would often be impossible to evaluate it.

After centuries of advancing the art of mathematical measurements, the neat Victorian world of mechanical mastery fell to the wholesale destruction wrought by WW1. Again the world was thrown into vast disruption followed by a world-wide depression that ultimately led to WWII. Bernstein quotes Keynes and others who break from Victorian beliefs and admit that humans are irrational and the future is unknowable. He even mentions that Einstein indicated that the long-held beliefs of Euclidean geometry are not exactly right.

Overall I found this book enjoyable, though there is not really a story here so much as a collection of brief summaries of the work of those throughout history who advanced our knowledge of probability, economics, risk assessment and the human factor. Overall takeaway is to diversify, expect the unexpected, and hope to scratch out a living while some higher powers sit behind closed doors, deciding your fate.