The spirits of the Greeks and the role of the dice - first chapter in the book Against the Gods

Against the Gods, by Peter Bernstein. From English: friend song. Publisher: Attic Books and Yediot Books

Why is risk control such a (and exclusively) modern concept? Why did humanity wait thousands of years, until the Renaissance, before starting to break down the barriers that prevented it from measuring risk and controlling it?

There are no simple answers to these questions. But we can start with a hint. Since the beginning of recorded history, gambling—the very essence of risk-taking—has been a popular pastime that has sometimes reached the point of addiction. It was a game of chance that gave Pascal and Fermat the inspiration for their revolutionary breakthrough into the laws of probability, not some profound question about the nature of capitalism or some vision of the future. And yet up until that moment, and throughout history, people gambled and played games without using any of the odds measuring methods that today determine wins and losses. The act of taking the risk floated in space, without the control of risk management theory.

Gambling always worked magic on humans, because they placed them face to face with the gods of fate, without buffering. We enter this dangerous battle because we are sure that we have a formidable ally—Lady Luck: she will place herself between us and the fates (or chances) to tilt the victory to our side.

Adam Smith (Smith), the wonderful Scottish researcher of human nature, defined the motivation for gambling as follows: "The arrogant arrogance which is the lot of most people about their own abilities and their ridiculous assumptions about their good fortune." Smith was well aware that the human tendency to take risks drives economic progress, but he feared that society might suffer if this tendency got out of control. That is why he made sure to balance the moral feelings and the benefits of the free market. About one hundred and sixty years later, another great economist, the Englishman John Maynard Keynes, commented with agreement: "When the development of a country's capital becomes a by-product of casino activities, it is likely that the job was not done properly."
However, the world might be a heavenly place if people did not have vanity and confidence in their good fortune. Keynes was forced to admit that "if human nature had not felt any temptation to take risks […] perhaps so many investments would not have been made, purely as a result of cold calculation". No one takes a risk expecting to fail. When the Soviets tried to completely eliminate the existence of uncertainty through government planning and intervention, they stifled social and economic progress.

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Gambling has fascinated humans for thousands of years. People gambled everywhere, from the rejected fringes of society to the most respectable social circles.
The soldiers of Pontius Pilate, the governor of Judea on behalf of the Roman Empire, cast lots to win the cloak of Christ while he was being tortured on the cross. The Roman emperor Marcus Aurelius was always accompanied by his personal gambling man. The Earl of Sandwich invented the sandwich that bears his name so he wouldn't have to leave the betting table to eat. During the American Revolutionary War, George Washington hosted games of chance in his tent. Gambling is synonymous with the Wild West, and the song "Luck Be a Lady Tonight" is one of the most beloved songs in the musical Guys and Dolls about a compulsive gambler and his game of "floating crap" .
The earliest form of gambling known to us was a kind of dice game played with an astragalus, or joint bone. This bone, the ancient mother of the modern cube, was a square bone taken from the ankle of a sheep or deer, a solid and hard bone, without marrow, which was almost impossible to break. Astragalus have been discovered in archaeological excavations in many parts of the world. Egyptian tomb paintings depict playing with astragalus around 3500 BC, and Greek urns show young men throwing these bones into a circle. Although the Egyptians used to punish compulsive gamblers, the excavations proved that the pharaohs themselves not only gambled, but also did not hesitate to use fake dice, ones that added weight to one particular side. Craps, an American invention, originated from a variety of dice games that the Crusaders brought to Europe upon their return from the Crusades. These games were often called hazard, a name derived from the Arabic word for dice: a-zahar.
The card games developed in Asia from the ancient forms of fortune-telling, but they only became popular in Europe after the invention of printing. The cards were originally large and square, without rounded corners, and without identifying characters or symbols such as hearts, clovers, etc. The cards of the royal family - prince, queen and king - were printed with only one head instead of two heads, so the players had to recognize them even when their heads were down, since turning the card over would reveal to the opponent that it was a royal card. The square corners allowed players to cheat easily, because they could tear off small pieces from the corners to later identify the cards inside the deck. It was only in the 19th century that cards with rounded corners and double heads began to be used.
Like craps, poker is an American version of an earlier game form. This is a game that is only about 150 years old. David Hayano (Hayano) described poker as "secret conspiracies, massive lies, calculated strategies and a burning belief in deep and invisible patterns [...] a game that needs to be experienced and not enough to be observed". According to Hayano, about 40 million Americans play poker on a regular basis, and all of them are convinced that they can outwit their opponents.
It seems that the most addictive forms of gambling are the pure games of chance, which are played in the casinos that are rampant around the world today, even in countries that used to be quite conservative. A New York Times article from September 25, 1995, reported that gambling is the fastest growing industry in the United States, "a $40 billion business that attracts more customers than baseball fields or movie theaters." The Times quotes a University of Illinois professor who estimated that US state governments pay three dollars in costs to social institutions and the criminal justice system for every dollar of casino proceeds—a rate that Adam Smith might have predicted.
In Iowa, for example, which until 1985 did not even have a lottery, by 1995 there were already ten casinos, as well as a horse racing track and a dog racing track with slot machines operating 24 hours a day. The article notes that "nearly nine out of ten Iowans say they gamble." 5.4 percent of them report having a gambling problem, compared to only 1.7 percent five years ago. And this is a country where a Catholic priest was sent to prison in the 1970s for running a bingo game. Probably Zahar in its purest form is still with us.

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Games of chance must be distinguished from games where skill is the key. The principle that operates in roulette, dice and slot machines is the same, but this principle explains only part of what is involved in games like poker, horse betting and backgammon. While in the first group of games the outcome is determined by fate, in the second group an element of choice comes into play. To bet on a game of chance you only need to know the odds of winning, but much more information is needed to predict who will win and who will lose in a game where the outcome depends on both skill and luck. There are card game and racetrack bettors who are real professionals, but no one can make craps rolling a successful profession.
Many observers see the stock market itself as nothing more than a gambling casino. Is winning in the capital market the result of skill mixed with luck, or just a successful bet? We will return to this question in chapter 12.
Streaks of losses or wins often occur in games of chance, as they do in real life. Bettors react to these events in an asymmetrical way: some turn to the law of averages to bring a quick end to a streak of losses, and some ask the same law of averages to suspend itself so that the wave of victories continues on and on. The law of averages does not turn a deaf ear to either of the two references. In the series of recent rolls of the dice there is nothing that can give information about the result of the next roll. The cards, the coins, the dice and the roulette wheels - they have no memory.
Bettors may think they are betting on a red, or a seven or a four, but in reality they are betting on the clock. The loser wants to make a short streak seem long so he still has chances. The winner wants the long streak to look like a short streak so that the odds are suspended. Away from the betting table, insurance company executives go about their business in a similar way. They set the premiums to cover the losses they will suffer in the long run, but when earthquakes, fires and hurricanes happen at the same time, the short term can be very painful. Unlike gamblers, insurance companies hold capital and keep reserves aside to use in those inevitable sequences of bad luck.
Time is the decisive factor in gambling. Risk and time are two opposite sides of the same coin, because if there was no tomorrow there would be no risk either. Time changes the essence of risk, and the time horizon shapes its nature: the future is the playing field.
Time is especially significant when the decisions are irreversible. And yet many irreversible decisions are inevitably made on the basis of partial information. A huge variety of decisions - from choosing to take the subway instead of a taxi, to building a car factory in Brazil, changing jobs or declaring war - are decisions whose irreversibility is a decisive characteristic.
If we buy a stock today, we can always sell it tomorrow. But what do we do after the cashier at the roulette table calls out "No more gambling!" Or after the poker bet has doubled? there's no way back. Should we refrain from action in the hope that the passage of time will tilt luck or probabilities in our favor?
Hamlet, the protagonist of Shakespeare's play, complained that too much hesitation in the face of uncertain outcomes is a bad thing, since

The natural color of determination
corrodes, fades, fades from thoughts,
and great plots of courage and of swing
deviating from the path and lost forever
The verb is an action.
(third act, picture 1)

But from the moment we decide to act, we give up the possibility of waiting until new information reaches us. Therefore, even inaction has value. The less certain the outcome, the greater the value of patience. Hamlet was really wrong: he who hesitates is closer to his goal.

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To understand how the universe was created, Greek mythology relied on the image of a huge game of craps to explain what modern scientists today call the Big Bang. Three brothers played dice on the universe. Zeus won the sky, Poseidon the sea, while Hades, the loser, went down to the underworld as the lord of the underworld.
Probability theory seems tailor-made for the ancient Greeks, given their lust for gambling, their skills as mathematicians, their mastery of logic, and their obsession with the need to prove things. However, although they were probably the most civilized of all ancient peoples, the idea of ​​exploring this fascinating field did not occur to them. It is very surprising to discover this, since until that time the Greeks were the only recorded culture that was not under the control of a priesthood that had a monopoly on the lines of communication with the higher powers. Culture as we know it could have progressed at a much faster rate if the Greeks could anticipate and discover what their intellectual descendants, the Renaissance people, discovered about a thousand years after them.
Although the Greeks emphasized theoretical knowledge, they had very little interest in applying theory to any technology that could change their perspective and ability to manage the future. The daily life of the Greeks and their standard of living was similar to that of their ancestors for thousands of years. They hunted, fished, grew crops, had children, and used architectural techniques that were merely variations of much earlier techniques originating in the Euphrates and Tigris regions and in Egypt.
Kneeling before the spirits was the only way of risk management the Greeks took: their poets and dramatists sang repeatedly of their dependence on the spirits, and beloved children were sacrificed to appease them. And most importantly, the Greeks did not have any numbering system that could allow them to calculate instead of simply recording the results of their actions, as the Israeli scholar Shmuel Samborski explained beautifully about half a century ago, in his book Laws of Heaven and Earth.
I do not intend to argue here that the Greeks did not give their opinion at all to the nature of probability. The ancient Greek word εικος (eikos), which means similar, probable, or probable, is identical in meaning to the modern concept of probability: "expected with a certain degree of certainty". For Plato, eikos is characterized as "resemblance (or similitude) to the truth" (this, by the way, is the origin of the term "icon" in Hebrew).
Plato reveals here a subtle but very important diagnosis. The resemblance to the truth is not the same as the truth itself. For the Greeks, truth is only what can be proven with the help of logic and axioms. Their insistence on the need for proof placed truth in stark contrast to empirical experiment. For example, in the Phaedo, one of Plato's most important dialogues, Simias, Socrates' interlocutor, insists: "[…] But I know that arguments that base their proofs on certain similitudes and probabilities are pretenders, and if we are not careful about them, they deceive - in geometry, like in all other areas". In one of the famous passages in which Aristotle "scolds" philosophers who are not careful in matters of methodology, he writes (in the opening of his book Nicomachean Ethics): "The educated man will seek precision in some branch of knowledge only to the extent that the particular subject allows; And so, it is absurd for the mathematician to agree to arguments that are only plausible and nothing more, just as it is absurd to ask the writer in matters of rhetoric for the precision of a scientific proof." A thousand years later, thinking about games and playing the game itself remain completely separate activities.
Israel's Shmuel Sambursky, the historian and philosopher of science, has developed the only convincing explanation I could find for why the Greeks did not take the strategic step of developing a quantitative approach to probability. In an article from 1956, he claims that the fact that the Greeks had such a sharp distinction between truth and plausibility meant that they could not imagine any stable structure or harmony in their confused and unpredictable daily life. Although Aristotle suggested that people make decisions based on "aspiration and effort directed towards some goal", he did not offer any way of evaluating the chances of success of the actions. The Greek plays describe story after story of the helplessness of humans at the mercy of arbitrary fates. When the Greeks wanted to know what the future held in its wings, they turned to the oracles instead of consulting the wisest philosophers they had.
The Greeks believed that order can only be found in the heavens, where the planets and stars appear in their designated places with incomparable regularity. The Greeks felt enormous respect for this harmonious appearance, and their mathematicians studied it in depth. But the extent of the perfection of the heavens only emphasized the disorder of life on earth in the eyes of the Greeks. Furthermore, the ability to observe the appearance of the sky stood in sharp contrast to the capricious and foolish behavior of the gods who lived on the heights of Olympus.
The ancient sages of the Talmud came perhaps a little closer to quantifying the risk. But even here there is no hint that they developed the difficulties to the point of a systematic approach to risk analysis. Rabbi Nachum Rabinovitch, in his article "On the Theory of Probability in Rabbinic Literature", cites a passage from the Talmud (Tract of Addresses, page XNUMX, page XNUMX) which discusses the question of whether a man can divorce his wife without paying her address on the grounds that "I found an open door", that is, I discovered The bride came to the bridal bed when she was no longer a virgin. It should be noted that the discussion focuses on the period of time between the dedication and the moment when the husband claims "I found an open door", and the question asked is whether the husband is exempt from paying the ketubah or not.
"A doubt is a doubt," says the Talmud, meaning a double doubt. One element of this double doubt is that there is no certainty as to whether the event occurred after the woman had already been sanctified (and then she is forbidden to her husband), or whether it happened before the sanctification - in the language of the Talmud, "doubt under him there is no doubt under him". The second element of doubt is: "And if you find to say under it, doubt rape doubt willingly". That is, even if this is done after the woman has already been consecrated to her husband, there is no certainty whether the betrothal was done voluntarily or involuntarily. The result of the Talmudic discussion is therefore that due to the "spek spekka" (and not only "spekka"), the woman has the right to receive the full amount of her address.
If we analyze the discussion in modern terms, we can say that "sure" means a 50 percent chance, and therefore "sure enough" means only 25 percent. The sages therefore determined that there is only a one in four chance that the woman - after being consecrated to her husband - will marry someone else of her own free will even before she has devoted herself to her husband. This is certainly an impressive statistical sophistication.

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It is easy to be tempted to assume that it was only a historical mishap that led to the time gap between the invention of the astragalus and the invention of the laws of probability. The Greeks and the Talmudic sages were incredibly close to the analysis that Pascal and Fermat would reach hundreds of years later, and they only needed a little push to take the next step.
But it was not by chance that there was no such push. Before a certain society could absorb the concept of risk as part of its culture, a change had to occur, not in the perception of the present but in relation to the future.
Until the Renaissance, humans treated the future almost exclusively as a matter of luck or random changes, and most of their decisions were driven by instincts. When living conditions are so close to nature, there is not much left for man to control. As long as the needs of survival limited humans to the basic actions of having children, growing crops, hunting, fishing and taking care of shelter, they had no possibility of conceiving the conditions in which they could influence the consequences of their decisions. Saving is only meaningful to the extent that the future is more than a black hole.
Over the next few hundred years, at least until the Crusades, most people encountered only a few surprises as they dragged their burdens from one day to the next. Since they were subject to a stable social structure, they did not pay much attention to the wars that swept the land, to the occasional exchanges between bad rulers and good rulers, and even to the changes that occurred in religion. The weather was the most prominent variable. As the Egyptian culture researcher Henry Frankfort commented, "Both the past and the future - both were really not a source of concern - were all immersed in the present."
Despite the continued preservation of this approach to the future, culture has advanced by leaps and bounds over the centuries. The lack of modern approaches to risk was therefore not an obstacle to progress. However, the march of civilization forward was not in itself a sufficient condition to motivate curious people to explore the possibilities of scientific predictions.

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As Christianity progressed and spread across the Western world, the will of a single God arose and became the point of orientation on the way to the future. This god replaced the multiple gods that humans worshiped from ancient times. This resulted in a considerable change in perception: the future of life on Earth remained a mystery, but from now on it was dictated by a higher power whose intentions and demands were clear to anyone who took the time to study them.
And when thinking about the future became a matter of moral behavior and faith, the future was no longer as foggy as it was before. However, it does not yet seem open to any mathematical prediction. The early Christians limited their prophecies to what would happen in the afterlife, even if at the same time they implored God with all their might to tilt the events of this world in their favor.
And yet, of course, the desire for a better life on earth continued. By 1000 AD, Christian seafarers were already sailing far and wide, meeting new peoples and encountering new ideas. Then came the Crusades - a real cultural earthquake. The people of the West clashed with the Arab empire that arose on the initiative of Muhammad and spread its influence as far as far away India. The Christians, with their faith in the future, met the Arabs who achieved a much greater intellectual sophistication than that of the Christian invaders who came to dislodge them from the holy places.
The Arabs, following their invasion of India, learned the Indian method of counting, which allowed them to integrate the intellectual achievements of the Far East into the knowledge they had gained themselves and into their scientific research and experiments. The results were weighty, first for the Arabs and then also for the West.
In the hands of the Arabs, the Indian numbers revolutionized mathematics and astronomical measurements, navigation and trading systems. New methods of calculation gradually replaced the abacus, which was for hundreds of years the only tool for making calculations around the world, from the Mayan realms in the Western Hemisphere through Europe to India and the Far East. By the way, the word abacus originates from the Greek word abax, which means sand tray: inside the trays, rows of pebbles were arranged on the sand. As for the word calculate, its origin is calculus, the Latin word for pebble.
For the next 500 years, while the new numbering system gradually replaced the simple abacus, the suit dictated the mobile accessories for making calculations. The written calculation served as fertile ground for abstract thinking, and this opened the way to new fields in mathematics that were never known before. Sea voyages could now be longer, time measurement became more precise, architecture could be more ambitious and production methods more complex. The modern world would be very different if we continued to measure and count with the Roman numerals I, V, X, L, C, D, and M, or with the Greek or Hebrew letters that represented numbers.
But the Arab numbers were not enough to push the Europeans to investigate the radical idea of ​​replacing randomness with systematic probability and the conclusion accompanying this idea - that the future can be predicted and perhaps even controlled to one degree or another. This step had to wait until people realized that they are not completely helpless in the hands of fate, and that their fate on earth is not determined solely by God.
The Renaissance and the Protestant Reformation in Christianity prepared the ground for gaining control over the concept of risk. As mysticism progressed and retreated from science and logic, from 1300 AD onwards, Greek and Roman architecture began to replace Gothic structures, church windows were opened to allow light in, and sculptures began to show men and women standing firmly on the ground instead of depicting figures in stylized poses, without muscles and without weight . The ideas that led the changes in art also contributed to the Protestant Reformation and weakened the absolute control of the Catholic Church.
The meaning of the Reformation was more than just a change in the relationship between man and God. By abolishing the institution of confession, the Reformation warned people that from now on they would have to walk on their own feet and take responsibility for what resulted from their decisions.
But if men and women are no longer at the mercy of unknown gods and random luck, they can no longer remain passive in the face of an unknown future. They had no choice but to start making decisions in a wide variety of circumstances and over much longer periods of time than in the past. The ideas of contentment with little and frugality that characterized the Protestant ethos testified to the growing importance of the future compared to the present. And with this spread of choices and decisions, people began to recognize more and more the fact that the future holds not only dangers but also opportunities, that everything in it is open and full of promise. The 16th and 17th centuries were a period of geographical discovery, confrontation with new continents and new human societies, as well as experimentation in art, literary forms, science, architecture and mathematics. The new sense of an impending opportunity led to a dramatic acceleration in the growth of commerce of its kind, and this in turn served as a powerful incentive for change and further discoveries. Columbus did not go on a pleasure cruise in the Caribbean; He was looking for a new trade route to India. The hope of getting rich is a powerful motive, and few are those who get rich without making a bet.
This firm statement contains more than it seems at first glance. Trade is a process that benefits both parties - an economic process at the end of which both parties consider themselves richer than they were before. What a radical idea! After all, until that time, people who got rich did so mainly by exploiting or looting the wealth of others. Even if the Europeans continued their robberies overseas, the accumulation of wealth at home became accessible to the many and not just the few. The new rich were now the clever, the adventurous, the innovative—most of them businessmen—instead of the princes who inherited their principalities and proteges.
Trading is also a risky business. And when the growth of commerce turned the principles of gambling into wealth creation, the inevitable result was capitalism, the pinnacle of risk-taking. But capitalism would not have been able to thrive without two activities that were redundant as long as the future was seen as a matter of luck or God's will. The first operation is book management - a modest operation but one that sparked the need to develop new numbering and counting techniques. The second is forecasting - an action much less modest and much more difficult to perform, an action that links risk-taking with the direct profits resulting from it.
No one would plan to sail goods across the ocean, or store goods for sale, or borrow money, without first trying to find out what the future holds. To plan in advance so that the ordered materials arrive on time, to ensure that the items for sale are produced on time, and to prepare the sales sites at the right moment - all this must be done before the customers show up and place their money on the counter. A successful business manager is above all a forecaster; The purchase, production, marketing, pricing and organization come only later.

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The people you will meet in the following chapters recognized that the discoveries of Pascal and Fermat were the beginning of a new wisdom, and not just a solution to a complicated intellectual puzzle related to a game of chance. They were bold enough to confront the many aspects of risk in the face of issues of increasing complexity and great practical importance, and to recognize that these are issues involved in the most essential philosophical issues of human existence.
But philosophy needs to give up its place on the stage for a moment, because the story needs to be told from its beginning. The modern methods of dealing with the unknown begin with measurement, with chances and with probabilities. The numbers come first. But where did they come from, the numbers?