The Discovery of Numbers (Against the Gods)

Fibonacci

Most people have heard of the Fibonacci series, but it is not only a source of amusement. If you divide any of the Fibonacci numbers by the next higher number, you will find that after 3, the answer is always 0.625. After 89, the answer is always 0.618. And if you divide any number by its preceding number, you will find that after 2, the answer is always 1.6, while after 144, the answer is always 1.618.

The Greeks knew about this proportion and called it “the golden mean.”

The golden mean defines the proportions of the Parthenon, the shape of playing cards and credit cards, and the proportions of the General Assembly Building at the United Nations in New York. The horizontal member of most Christian crosses separates the vertical member by just about the same ratio: the length above the crosspiece is 61.8% of the length below it. The golden mean also appears throughout nature-in flower patterns, the leaves of an artichoke, and the leaf stubs on a palm tree. It is also the ratio of the length of the human body above the navel to its length below the navel (in normally proportioned people, that is). The length of each successive bone in our fingers, from tip to hand, also bears this ratio.

The shape of a beautiful spiral is also defined by the golden mean.

Bernoulli’s Subjectivity

Arnauld, author of a famous book on logic, PortRoyal Logic, accused people who were afraid of thunderstorms of overestimating the miniscule probability that they would be struck by lightning. But he was ignoring something important. The facts are the same for everyone. Each person knows about the unlikelihood of the event, but people who have a phobia of being struck by lightning put a heavy weight on the consequences of being hit, even if they knew the odds were small.

Similarly, people afraid of flying know that flying an airplane is safer than driving a car, but they will be terrified when on the plane. This is an unfortunate consequence of human subjectivity, but a variety of perception is a good thing.

If we all valued risk in exactly the same way, many risky opportunities would be ignored. Adventurous people place high utility on the small chance of large gains and low utility on the chance of losing. Others do the opposite, because their main goal is to protect their money.

Without adventure, the world would turn more slowly. If everyone was phobic about uncertainty, then life would be very different.

When Bernoulli extended this basic thesis, he introduced a key idea: “[The] utility resulting from any small increase in wealth will be inversely proportionate to the quantity of goods previously possessed.”

This was he first time in history that someone applied a measurement to something that cannot be counted. It was as if he created a link between intuition and measurement. This was a completely new area of study. Bernoulli laid the intellectual foundations for much that would follow, not only in economics, but in ideas about how people make decisions in every aspect of life.

Another new idea Bernoulli introduced is a force in economic growth-human capital. This idea came from his definition of wealth as “anything that can contribute to the adequate satisfaction of any sort of want …. There is then nobody who can be said to possess nothing at all in this sense unless he starves to death.”

What form does people’s wealth take? Bernoulli says that tangible assets are less valuable than productive capacity, including even the beggar’s skills. A man who can earn 10 ducats a year by begging will probably reject an offer of 50 ducats a year to stop begging, because after spending 50 ducats, he would have no way of making money. However, there must be an amount of money that would stop him from begging. If this amount was 100, then we would say that the beggar’s wealth was worth 100 ducats.

Bernoulli’s idea of utility inspired the Law of Supply and Demand, an innovation of Victorian economists. Utility also led to the development of the theory of games – the innovative approach to decision making in war, politics and business management that took place in the 20^th century.

The concept has impacted psychology and philosophy too. Psychologists define people – when their utility of wealth increases as they grow richer – as neurotic. Greed was not part of Bernoulli’s definition, or any modern definition of rationality.

The choices that people make are difficult enough even if they did have the same information. But most of the time, the facts are not the same for everyone. This asymmetry, and the idea that each person has his own interpretation of the facts, makes agreements difficult. 

As modern as Bernoulli appears, he was a man of his times. His notion of human rationality was a by-product of the intellectual environment of the Enlightenment. This was when ideas of form and order were embraced by intellectuals. During this time, Alexander Pope was filling his poems with classical allusions like “A little learning is a dangerous thing,” and that “The proper study of mankind is man.” Samuel Johnson was about to create the first English language dictionary and Diderot was going to begin work on a 28 volume Encyclopedia.

If you’re an entrepreneur and you want a quick guide to know what to think about before launching you business, check out The Myth of Entrepreneurship.