Tottenham Report: Even good ideas take time to flourish

Monday, July 15, 2024 11:00 PM
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Today, when you ask someone a question, the answer you sometimes get is “probably” or even “100%”, even if there is no element of chance in what you are asking about. 

Despite the above, we do take elements of chance in our daily lives for granted. We might not understand what it means when the weather forecaster says that there is a 65% chance of rain or a pollster says that there is an 80% chance that a certain person will win an election. If it doesn’t rain or the person does not win the election, people will say both “got it wrong”. They didn’t!  

But today, most people know that it is possible to calculate the odds of something happening. They might not know how, but they do know it is possible.  

However, this was not always the case and it has bothered me that it took so long for humans to understand that probability, the chance of a certain outcome, can be for the most part calculated. 

There are a number of ideas why this knowledge was not explored, in Western Europe at least, until the 15th century, an understanding developed in the 16th century, and fully articulated in the 17th. 

Firstly, until the Enlightenment, people thought that trying to understand the future was interfering with the gods. The gods decided the future, apparently sometimes on a whim, and it was not for man to know the domain of the gods. 

Another idea is that until the late Middle Ages, the world was thought to be deterministic. Outcomes occurred based on what went before, rather than probabilistic, in which outcomes have some “randomising” elements. So there was simply no “probability” to study.  

The third idea was that in order for science to progress, there needs to be an economic benefit from finding answers to problems. Since there was no economic benefit to be had from understanding probability, people did not bother to explore it. 

Finally, we had not developed the symbols, notations, and methods that would allow us to easily explore the mathematics behind probability. 

The first hypothesis does not really hold water. For centuries, people were looking at the entrails of various animals or cloud shapes or whatever, trying to interpret the wishes of the gods. And if it is argued that to study potential future outcomes will anger the gods and that is why no effort was made to study probability, there have always been plenty of irreligious people willing to incur the wrath of the gods. 

The second one is unlikely. Our modern understanding of determinism took hold in the late 16th and early 17th centuries, the point in time when the mathematics behind probability became understood and spread widely. It may be that comprehending determinism spurred our interest in probability. 

The third hypothesis is absurd. For gamblers, there was plenty of economic benefit to be had in playing a game for money and knowing the probability of the various outcomes. A gambler who understood probabilities could have won the world three times over, except that more likely early in their careers, they would have been accused of cheating and come to a sticky end. 

Interestingly, before people could compute the probabilities of getting various hands in a game of poker, a flush was correctly of higher ranking than a straight. Players knew that a straight would occur more frequently than a flush. 

Also, annuities had been used to finance public spending since Roman times: a bet on the expectation that the municipality, state, or other public institution would pay out if people died before a certain age. There was a significant economic benefit to be had from understanding the probability of a person dying. Many municipalities went bust, owing significant sums due to inaccurate calculations. Even Sir Isaac Newton put his name to a book that did not take the age of the annuity holder into consideration when calculating the potential returns. 

The fourth hypothesis appears most likely, even though it has a flaw. The Arabs gave us our numerals and methods to lay them out on a page, making addition, subtraction, multiplication and division easier to do. 

These systems of manipulating numbers entered Southern Europe from North Africa and it was in Southern Europe, mainly Italy, that probability was first investigated (Luca Pacioli, Gerolamo Cardarno, Galileo Galilei). Much of the development of the binomial theorem, the use of negative numbers, and methods of solving cubic and quartic equations happened in Italy at this time. 

Against the idea that we needed a system of mathematics that would easily allow us to lay out numbers on a page and compute solutions to complicated problems is an Indian tale about Nala, a prince famed for his gambling and horsemanship, from the Mahabharata, the latest version from the 5th century A.D.  

Kali is the demigod of playing dice (I kid you not) and he has his eye on a certain princess. Unfortunately for him, Nala wins her hand. Kali is so upset that he takes possession of Nala’s soul and makes him go into a frenzy of gambling, whereby he loses everything, including his kingdom, and consequently the hand of the princess. 

Nala is desolate and wanders the land aimlessly for a few years. On the advice of a snake king, he takes the job of a charioteer for a foreign king. On a trip, the king tells Nala that he can easily calculate the number of leaves and fruits on two branches of a very large tree by counting only the number on a twig. He duly counts the leaves on a twig and gives Nala the answers for the two branches. 

Nala stays up all night counting the leaves and fruits on the two branches and lo and behold, the king was correct on both counts. The king says, “I of dice possess the science and in numbers thus am skilled”. 

The king promises to teach Nala this “science” in exchange for lessons in horsemanship. The exchange of knowledge and skill takes place. Nala then uses his newly acquired knowledge to win back his riches, his kingdom, and the hand of his bride by gambling with dice. 

This story is evidence that by the 5th century A.D., the Indians understood that there was a science to gambling involving dice and that the same science was connected to using a small sample to estimate a larger whole. At that time, however, the Indians did not have the Arabic method of laying out and manipulating numbers. 

It took the Europeans another millennium to discover what the Indians knew. Before the invention of the petrol engine, the fastest ideas could spread was at the speed of a horse on land and a sailboat on the sea. There were significant trading routes from China to India and to northern Europe and plenty of time for this knowledge to spread out of India to Europe, yet it didn’t. 

I have no answer as to why something that seems so obvious now took centuries before it was investigated. In centuries to come, I dare say that people will say the same of us. Why did they not see what was in front of them?