Rational Figuring

Book Reviews

Against the Gods:  The Remarkable Story of Risk
by Peter L. Bernstein
John Wiley & Sons, 1996, 1998, 383 pages, $24.95

I was originally introduced to economics by the writings of John Kenneth Galbraith.  I have come to disagree with Galbraith on many things, but his practical demonstration that the ideas of economics can be expressed, as they ought to be, in fine English had great value as a starting point.

There are some things on which I still concur with him.  Long before it became policy consensus, Galbraith agreed with Milton Friedman and Karl Marx that capitalism, if you were lucky enough to get it, was definitely the best option for developing countries.  (There always was a great difference between the intelligent Left and the lumpen-Left:  one is reminded of the late Joan Robinson's comment that the one thing worse than being a Third World country that a multinational wanted to exploit was being a Third World country that no-one wanted to exploit).  On the cover of the softcover edition of this brilliant, and brilliantly lucid, work by Wall Street investment adviser Peter Bernstein, Professor Galbraith is quoted as saying

With his wonderful knowledge of the history and current manifestations of risk, Peter Bernstein brings us Against the Gods.  Nothing like it will come out of the financial world this year or ever.  I speak carefully:  no one should miss it.

Absolutely.

It is difficult to know where to start in praising this work.  It brings intellectual history alive in a way only very few scholars -- one thinks of the late Sir Isaiah Berlin -- have managed.  Bernstein has the talent of the truly great expositors -- of making everything he writes clear to any interested lay reader.

The virtue which stuck in my mind the most, however, was the way that Bernstein brings alive how much of our current commonplaces about simple arithmetic and -- even more -- risk and probability are profoundly new -- and extremely powerful -- ways of looking at the world.  The great Renaissance genius Leonardo had a level of arithmetical understanding that today would allow him to "barely squeak by in a third-grade arithmetic class" (page 43).  The idea that one could put numbers on chance was foreign to the ancient or medieval mind:  they were close, but, prior to the adoption of the Hindu-Arabic numbering system with its vital concept of zero and easy basis for calculation (try doing long division in Latin numerals some time) and to the acceptance of the idea of a changeable -- and different -- future they never took those crucial extra steps.

Steps which started with gambling.  Bernstein's story has its forgotten pioneers -- people who made path-breaking discoveries whose work was ignored, or entirely unpublished, during their lifetime.  A sixteenth-century physician and gambler, Girolamo Cardano (1500-71) was one such.  His Liber de Ludo Aleae (Book on Games of Chance) -- the first serious study of games of chance -- was written in 1525, re-written in 1545 but not published until 1663.  He was, however, a popular lecturer, so his ideas may well have been disseminated anyway -- Galileo's 1623 essay Sopra le Scoperte dei Dadi (On Playing Dice) covered much of the same ground.  After millennia of slow movement, things took off in a rush.  The key ideas of probability theory -- the study of outcomes for a world where more can happen than will happen -- were developed in the seventeenth century -- particularly by Pascal (he of the famous Wager) and Fermat (of the Last Theorem) in 1654.  As Bernstein writes "after 1654, mumbo jumbo would no longer be the forecasting method of choice" (page 72).  By the late 1660s, Dutch cities were able to put the annuities they sold as financing arrangements on a reasonably actuarially sound basis.

The late seventeenth and the eighteenth century saw the development of sampling and other elements of statistical theory, starting with John Graunt's 1662 book Natural and Political Observations Made upon the Bills of Mortality, a path-breaking analysis of births and deaths in London from 1604 to 1661.  Charles II insisted that Graunt -- a merchant of buttons, needles and such like -- be admitted to the Royal Society, whose august members were not keen on admitting a mere tradesman.  The King replied that "if they found any more such tradesmen, they should be sure to admit them all, without any more ado".  Admission followed.  Graunt reasoned about raw data in ways which are the normal stuff of analysis now, but which no-one had done before -- including inferring from what had been observed to what had not:  what is now known as "statistical inference".  Graunt's work was taken further by Edmund Halley (he of the Comet) who used more complete data from Breslaw to work out improved life expectancy tables.  Halley thus superseded the work of Ulpian -- whose AD 225 tables had been the standard work for 1400 years!

It took a while for the full implications to catch on:  the English government started selling annuities in 1700 which repaid their purchase price over 14 years.  It was not until 1789 that they began to take into account the age of the buyer.  Then we come to the gathering of underwriters in the coffee shop that Edward Lloyd opened in 1687 and Bernstein takes us into the history of the commercial application of risk management.

There is far more in this wonderful book (the foregoing only takes us to page 89).  His descriptions of the interaction between the development of theory -- particularly concepts of rationality and rational decision-making, including game theory -- and commercial practice, in particular, are greatly enlightening.  The story is, in many ways, inspiring, as it is about humanity's search to understand the world around us and to seek ways of rationally dealing with that most obscure of all things -- the future, the key extra elements which made the Renaissance the "take off" point being "freedom of thought, the passion for experimentation and the desire to control the future" (page 54).

I recommend the book heartily.