The key ideas

Against the Gods: The Remarkable Story of Risk

Peter L. Bernstein, 1996

For thousands of years, people asked oracles and soothsayers about the future. Peter Bernstein tells how gamblers, merchants, mathematicians and psychologists learned to measure the unknown: from Indian numerals and Pascal's puzzle to insurance and prospect theory. You will see how thinking about risk works, and where the calculation breaks down.

Who it is for

For anyone who makes decisions without knowing how they will turn out: about money, work, a move or an investment. And for anyone curious where probability, insurance and the investment portfolio came from.

The word "risk" derives from the early Italian risicare, which means "to dare." In this sense, risk is a choice rather than a fate.

The future no longer belongs to the gods

Picture a merchant three thousand years ago, sending a ship across the sea. He can offer a sacrifice, consult an oracle, watch the flight of birds. The one thing he cannot do is work out the chances that the ship will come back, and what that uncertainty is worth. In his world the future is either the will of the gods or a repeat of the past.

Peter Bernstein, an American financier and historian of economic thought, wrote a book in 1996 about how people crossed that line. His central point is this: one revolutionary idea separates modern times from the past, the idea that risk can be managed. The future is more than a whim of the gods, and people are not helpless before nature.

The story Bernstein tells is a story of people. You will meet gamblers and merchants, a mathematician monk and a London haberdasher, insurers in a coffee house, economists and psychologists. Each one added a tool: easy arithmetic, probability, statistics, insurance, the portfolio. And at the end the book shows where the calculation breaks down: inside us.

In these pages you will see the origins of the ideas used today to price loans, insurance and pensions. And you may start making your own risky decisions differently.

The Greeks had logic, but never counted the odds

The ancient Greeks loved to play dice. For dice they often used astragali, small bones from the heel of a sheep or goat that land on one of four sides. The Greeks created geometry, logic and philosophy. And yet, Bernstein notes, not one of them tried to count how often each side came up.

Why? The author offers several answers. For the Greeks the outcome of a throw, like the future in general, was decided by the gods, so there was nothing to calculate. Besides, they looked for truth in proof, not in frequency. What was merely likely seemed to them second-class knowledge next to what was proven.

There was a very practical obstacle too: the numbers themselves. Try adding and multiplying large numbers written in letters of the Greek alphabet or in Roman numerals. Without a convenient notation it is hard to calculate, and without calculation you cannot measure the unknown.

This leads to the idea the whole book rests on. To manage risk, people needed more than formulas. They needed a change of outlook. They had to believe that the future depends, at least in part, on what they do. Until that belief existed, no mathematics would have helped: why measure something that has already been decided for you?

Read in Livria

About the author

Peter L. Bernstein (1919–2009) was an American economist, investment adviser and historian of financial thought, and the founding editor of the Journal of Portfolio Management.

All books by this author: Peter L. Bernstein

Terms from the book

  • Kahneman
  • Galton
  • Darwin
  • Bernoulli
  • St. Petersburg paradox
  • Utility
  • Pascal
  • Fermat
  • law of large numbers
  • Algorithm
  • Regression to the mean
  • Diversification
  • Tversky
  • Loss aversion
  • Astragalus: A small heel bone from a sheep or goat. In ancient times it was thrown like a die: it lands on one of four sides.
  • al-Khowarizmi: Muhammad ibn Musa al-Khowarizmi (c. 780 – c. 850), a mathematician and astronomer who worked in Baghdad. His writings introduced the Arab world, and later Europe, to the Indian way of counting.
  • Fibonacci: Leonardo of Pisa, known as Fibonacci (c. 1170 – c. 1250), an Italian mathematician who introduced Europe to Hindu-Arabic numerals.
  • Liber Abaci: The Book of Calculation, Fibonacci's 1202 work on arithmetic with Hindu-Arabic numerals and its use in trade.
  • Hindu-Arabic numerals: The ten digits from 0 to 9 and the positional way of writing numbers that we use today. Invented in India, they reached Europe through Arab mathematicians.
  • Cardano: Girolamo Cardano (1501–1576), an Italian physician, mathematician and astrologer. One of the first to calculate the odds in games of chance systematically.
  • Paccioli: Luca Paccioli (c. 1445–1517), an Italian Franciscan friar and mathematician. In 1494 he published a large textbook of mathematics that also described double-entry bookkeeping.
  • de Méré: Antoine Gombaud, Chevalier de Méré (1607–1684), a French writer, man of society and keen gambler. He put questions about dice games to Pascal.
  • Pascal's Triangle: A triangle of numbers in which each number is the sum of the two above it. It makes quick work of counting combinations and probabilities.
  • Port-Royal: A convent near Paris, the center of Jansenism in the 17th century. Its theologians Antoine Arnauld and Pierre Nicole wrote the textbook known as the Port-Royal Logic (1662).
  • Graunt: John Graunt (1620–1674), a London haberdasher. In 1662 he published observations on the lists of the dead, which are usually taken as the start of statistics.
  • Bills of Mortality: Weekly lists of deaths in London with the causes of death. They began in the 16th century as a way to keep watch on the plague.
  • Sampling: Judging the whole by a part of the cases. For example, estimating the population of a whole city from the records of a few parishes.
  • Lloyd: Edward Lloyd (c. 1648–1713), the owner of a London coffee house where sailors and merchants gathered. The Lloyd's insurance market grew out of it.
  • Underwriter: Someone who takes on a risk for a fee, such as an insurer. Literally, the one who writes their name underneath.
  • Markowitz: Harry Markowitz (1927–2023), an American economist who created portfolio theory. Winner of the 1990 Nobel Prize in Economics.
  • Framing effect: A finding of Kahneman and Tversky: a person's choice changes depending on how the very same options are described.
  • Prospect theory: Kahneman and Tversky's 1979 model of how people actually choose between risky options.
  • Arrow: Kenneth Arrow (1921–2017), an American economist, winner of the 1972 Nobel Prize in Economics.

All terms

Similar books