Against the Gods: The Remarkable Story of Risk (20 page)

The profit on an investment in goods that must be shipped over
long distances before they reach their market depends on more than just
the weather. It also depends on informed judgments about consumer
needs, pricing levels, and fashions at the time of the cargo's arrival, to say
nothing of the cost of financing the goods until they are delivered, sold,
and paid for. As a result, forecasting-long denigrated as a waste of time
at best and a sin at worst-became an absolute necessity in the course of
the seventeenth century for adventuresome entrepreneurs who were
willing to take the risk of shaping the future according to their own
design.

Commonplace as it seems today, the development of business forecasting in the late seventeenth century was a major innovation. As long
as mathematicians had excluded commercial applications from their
theoretical innovations, advances toward a science of risk management
had to wait until someone asked new questions, questions that, like
Graunt's, required lifting one's nose beyond the confines of balla and
dice. Even Halley's bold contribution to calculations of life expectancies was to him only a sociological study or a game with arithmetic
played out for the amusement of his scientific colleagues; his failure to
make any reference to Pascal's theoretical work on probability thirty
years earlier is revealing.

An enormous conceptual hurdle had to be overcome before the
shift could be made from identifying inexorably determined mathematical odds to estimating the probability of uncertain outcomes, to
turn from collecting raw data to deciding what to do with them once
they were in hand. The intellectual advances from this point forward
are in many ways more astonishing than the advances we have witnessed so far.

Some of the innovators drew their inspiration by looking up at the
stars, others by manipulating the concept of probability in ways that
Pascal and Fermat had never dreamed of. But the next figure we meet
was the most original of all: he directed his attention to the question of
wealth. We draw on his answers almost every day of our lives.

n just a few years the commanding mathematical achievements of Cardano and Pascal had been elevated into domains that neither had dreamed of. First Graunt, Petty, and Halley had applied the concept of probability to the analysis of raw data. At about the same time, the author of the Port-Royal Logic had blended measurement and subjective beliefs when he wrote, "Fear of harm ought to be proportional not merely to the gravity of the harm, but also to the probability of the event."

In 1738, the Papers of the Imperial Academy of Sciences in St. Petersburg carried an essay with this central theme: "the value of an item must not be based on its price, but rather on the utility that it yields."' The paper had originally been presented to the Academy in 1731, with the title Specimen Theoriae Novae de Mensura Sortis (Exposition of a New Theory on the Measurement of Risk); its author was fond of italics, and all three of the italicized words in the above quotation are his.*
So are all those in the quotations that follow.

It is pure conjecture on my part that the author of the 1738 article had read the Port-Royal Logic, but the intellectual linkage between the two is striking. Interest in Logic was widespread throughout western
Europe during the eighteenth century.

Both authors build their arguments on the proposition that any
decision relating to risk involves two distinct and yet inseparable elements: the objective facts and a subjective view about the desirability of
what is to be gained, or lost, by the decision. Both objective measurement and subjective degrees of belief are essential; neither is sufficient
by itself.

Each author has his preferred approach. The Port-Royal author argues that only the pathologically risk-averse make choices based on the
consequences without regard to the probability involved. The author of
the New Theory argues that only the foolhardy make choices based on
the probability of an outcome without regard to its consequences.

The author of the St. Petersburg paper was a Swiss mathematician
named Daniel Bernoulli, who was then 38 years old.' Although Daniel
Bernoulli's name is familiar only to scientists, his paper is one of the
most profound documents ever written, not just on the subject of risk
but on human behavior as well. Bernoulli's emphasis on the complex
relationships between measurement and gut touches on almost every
aspect of life.

Daniel Bernoulli was a member of a remarkable family. From the
late 1600s to the late 1700s, eight Bernoullis had been recognized as celebrated mathematicians. Those men produced what the historian Eric
Bell describes as "a swarm of descendants ... and of this posterity the
majority achieved distinction-sometimes amounting to eminence-in
the law, scholarship, literature, the learned professions, administration
and the arts. None were failures."3

The founding father of this tribe was Nicolaus Bernoulli of Basel, a
wealthy merchant whose Protestant forebears had fled from Catholicdominated Antwerp around 1585. Nicolaus lived a long life, from 1623
to 1708, and had three sons, Jacob, Nicolaus (known as Nicolaus I), and
Johann. We shall meet Jacob again shortly, as the discoverer of the Law
of Large Numbers in his book Ars Conjectandi (The Art of Conjecture).
Jacob was both a great teacher who attracted students from all over
Europe and an acclaimed genius in mathematics, engineering, and astron omy. The Victorian statistician Francis Galton describes him as having "a bilious and melancholic temperament ... sure but slow."4 His relationship with his father was so poor that he took as his motto Invito patre sidera verso-"I am among the stars in spite of my father."5

Galton did not limit his caustic observations to Jacob. Despite the evidence that the Bernoulli family provided in confirmation of Galton's theories of eugenics, he depicts them in his book, Hereditary Genius as "mostly quarrelsome and jealous."'

These traits seem to have run through the family. Jacob's younger brother and fellow-mathematician Johann, the father of Daniel, is described by James Newman, an anthologist of science, as "violent, abusive ... and, when necessary, dishonest."
When Daniel won a prize from the French Academy of Sciences for his work on planetary orbits, his father, who coveted the prize for himself, threw him out of the house. Newman reports that Johann lived to be 80 years old, "retaining his powers and meanness to the end."

And then there was the son of the middle brother, Nicolaus I, who is known as Nicolaus II. When Nicolaus II's uncle Jacob died in 1705 after a long illness, leaving The Art of Conjecture all but complete, Nicolaus II was asked to edit the work for publication even though he was only 18 at the time. He took eight years to finish the task! In his introduction he confesses to the long delay and to frequent prodding by the publishers, but he offers as an excuse of "my absence on travels" and the fact that "I was too young and inexperienced to know how to complete it."'

Perhaps he deserves the benefit of the doubt: he spent those eight years seeking out the opinions of the leading mathematicians of his time, including Isaac Newton. In addition to conducting an active correspondence for the exchange of ideas, he traveled to London and Paris to consult with outstanding scholars in person. And he made a number of contributions to mathematics on his own, including an analysis of the use of conjecture and probability theory in applications of the law.

To complicate matters further, Daniel Bernoulli had a brother five
years older than he, also named Nicolaus; by convention, this Nicolaus
is known as Nicolaus III, his grandfather being numberless, his uncle
being Nicolaus I, and his elder first cousin being Nicolaus II. It was
Nicolaus III, a distinguished scholar himself, who started Daniel off in
mathematics when Daniel was only eleven years old. As the oldest son,
Nicolaus III had been encouraged by his father to become a mathematician. When he was only eight years old, he was able to speak four languages; he became Doctor of Philosophy at Basel at the age of nineteen;
and he was appointed Professor of Mathematics at St. Petersburg in 1725
at the age of thirty. He died of some sort of fever just a year later.