I enjoyed re-reading Peter Bernstein’s book on risk - how we have progressed from believing the future was determined by the whims of the gods to our attempts to manage risk in today’s modern market economy. Bernstein doesn’t imply that we have mastered risk, but he chronicles the events and personalities that have contributed to our understanding and management of risk.

Much of the early study of risk was by gamblers, in dice games. The first serious work on the Theory of Probability, core to the concept of risk, was written by Girolamo Cardano, a sixteenth-century physician and habitual gambler. “One does not have to be a gambler or even an investor to recognize what gambling and investing reveal about risk…The dice and the roulette wheel, along with the stock market and the bond market are natural laboratories for the study of risk because they lend themselves so readily to quantification; their language is the language of numbers.”

Prior to the Renaissance, people viewed the future as little more than a matter of luck, and most of their decisions were driven by instinct. With the Renaissance came questioning, experimentation and great advancement in art, science, and mathematics.

The 1500s and 1600s were a time of geographical exploration that led to dramatic acceleration in the growth of trade and commerce. *“Trade is a mutually beneficial process, a transaction in which both parties perceive themselves as wealthier than they were before…Up to that point, people who got rich had done so largely by exploitation or by plundering another’s wealth. The newly rich were now the smart, the adventuresome, the innovators – most of them businessmen – instead of just the hereditary princes and their minions.”*

The inevitable result of trade was capitalism, the epitome of risk-taking. *“But capitalism could not have flourished without two new activities that had been unnecessary so long as the future was a matter of chance or of God’s will. The first was bookkeeping, a humble activity but one that encouraged the dissemination of the new techniques of numbering and counting. The other was forecasting, a much less humble and far more challenging activity that links risk-taking with direct payoffs.”*

The number zero is a relatively recent concept. Bernstein quotes English philosopher Alfred North Whitehead, *“The point about zero is that we do not need to use it in the operations of daily life. No one goes out to buy zero fish…its use is only forced on us by the needs of cultivated modes of thought.”* The ancient Greeks and Romans made great contributions to our civilization, but their letter based numbering system, with no zero, limited their advancements in mathematics.

Quantitative analysis as we know it, would not have been possible with the Roman, Greek, and Hebrew numeral systems in use in Europe in the year 1202. That was the year Leonardo Pisano, known today as Fibonacci, wrote, *Liber Abaci*, introducing the west to the Hindu-Arabic number system that we use today. Fibonacci learned this advanced system from an Arab mathematician in Algeria. In *Liber Abaci*, Fibonacci introduced many innovations that the new numbers made possible in commercial bookkeeping, such as figuring profit margins, money-changing, conversions of weights and measures, and calculations of interest payments.

I favored the first half of the book where Bernstein discusses gambling, Fibonacci and his fascination with numbers, and the early history of the insurance industry. In the second half of “Against The Gods” Bernstein provides the history of statistical concepts used to measure risk including the bell curve and standard deviation, the law of diminishing return and Harry Markowitz’s work on diversification.

Back to Fibonacci. He is best known for the Fibonacci series. In *Liber Abaci* he addresses the problem of how many rabbits will be born in the course of a year from an original pair of rabbits, assuming that every month each pair produces another pair and that rabbits begin to breed when they are two months old. The total number of pairs of rabbits at the end of each month would be: 1,2,3,5,8,13,21,34,55,89,144,233.

Each successive number is the sum of the two preceding numbers. Divide any of the Fibonacci numbers by the next higher number. After 3, the answer is always 0.625. After 89, the answer is always 0.618. Divide any number by its preceding number. After 2, the answer is always 1.6. After 144, the answer is always 1.618. **Amazing!**

*“The Greeks knew this proportion and called it “the golden mean.” The golden mean defines the shape of the Parthenon, the shape of playing cards and credit cards. The horizontal member of most Christian crosses separates the vertical member by just about the same ratio: the length above the crosspiece 61.8% of the length below it.”*

I plan to read more on Fibonacci’s fun with numbers.