Against the Gods — Bernstein: COMPLETE

For the Greeks the future belonged to the gods. Lightning was the wrath of Zeus, harvests the mood of Demeter, diseases the arrows of Apollo. Whoever needed to know something about what had not yet happened traveled to Delphi, where Pythia inhaled fumes from the crevasse and answered in riddles — answers that could be interpreted in any direction, as King Croesus learned when he went to war against the Persians and a »great empire« was to fall: his own.

The oracle was antiquity's information technology for the future, and its product specification was capriciousness, not probability.

At the same time those same Greeks played dice — and had done so for millennia. Astragali, knucklebones from sheep and goats with four playable sides, are found in Egyptian graves from around 3000 BCE. Roman soldiers cast lots for Christ's robe at the cross, a detail Bernstein himself highlights. The throw of »Venus« — ones, threes, fours and sixes in a single throw — was celebrated; the throw of »the dog«, all ones, was despised.

Thousands of years of play, enormous stakes, mythology around the will of the dice — and not a single Greek or Roman wrote down how often the different outcomes actually occurred. The question was never asked.

Why not? Bernstein points to three obstacles. First, the view of science: to the Greeks, knowledge was what could be proven, as in geometry — probability, which holds only most of the time, was no knowledge at all. Aristotle had already formulated the attitude Bernstein quotes: the mark of a learned man is to be content with the degree of precision the subject permits, and not to demand exactness where only approximation is possible — an insight antiquity thus possessed, but never applied to the game of dice.

Second, the image of the gods: regularity in the chance-like would restrict the freedom of the gods. Third, the tools: without zero, and with letters as numerals, even simple multiplication became labor.

Here lies the course's core idea: everything you do as an analyst — scenarios, expected values, cohorts, margins — rests on a language invented only when people stopped asking the oracles and began counting outcomes. Bernstein summarizes his thesis on the book's first pages, here in translation: the revolutionary idea that draws the boundary between modern times and the past is the mastery of risk — the belief that the future is not merely the gods' whim and that we do not stand passive before nature.

But note the course's endpoint already now: chapter 13 is about when that belief became hubris. Margin of safety is in AKM1 a principle precisely without a number — for reasons antiquity in its own way understood better than we do.

Girolamo Cardano was born in 1501 in Pavia, the illegitimate son of a Milanese jurist and mathematician who moved in Leonardo da Vinci's circles. He became a remarkable physician — in 1552 he traveled to Edinburgh and cured Archbishop John Hamilton of an ailment of breathing that all of Scotland's medical profession had given up on — but the Collegium Medicorum in Milan rejected him twice, once for his birth, once for his sharp tongue.

He became a professor in Bologna in 1562, was imprisoned in 1570 by the Inquisition for having cast Christ's horoscope, was released and granted a papal pension. In 1576 he determined, through his own horoscope, the day of his death as the 21st of September — and died on that day, according to legend by refusing food. A man who defeated chance on paper and capitulated to it in life.

Sometime around 1564 Cardano wrote Liber de Ludo Aleae — the book on the game of dice. The manuscript was published only in 1663, a hundred years later, in his collected works, that is after Pascal and Fermat, and thus influenced no one. But it exists: half handbook, half diary from the tables. In it is the first real theory of probability: the assumption that an honest die gives every side the same chance, the idea of circuitus — the circuit, the total number of equally likely outcomes — and calculations of in how many ways two and three dice can produce each sum.

There are also entire sections on cheating: marked cards, loaded dice, drunken opponents. Cardano did the math on what he could not stop playing.

In the autobiography De Vita Propria, written toward the end of his life, he confesses the gambling addiction without embellishment: he played daily for years, both dice and cards, greedily and angrily, and he himself tells of the night he slashed at a cheating opponent with a knife. The worst years of his youth, he writes, he threw away at the gaming table when, as a physician, he scarcely had bread.

Bernstein draws the portrait with relish: the first risk theorist was no cautious actuary but a man who felt the pull of hazard in his palms. Precisely therefore he saw what no one else saw — that the table has a structure.

For AKM1, Cardano is not a curiosity but basic exercise number one: before you can talk probabilities you must count the outcome space. The scenario list in an analysis — approval or rejection, share issue or not, a launch that succeeds halfway or fully — is Cardano's circuit in modern dress. And his assumption of the honest die is the first model risk: real dice can be loaded, real reports can be manipulated.

The question Cardano put to the die — is it honest? — is the same question you put to a V19-heavy growth company's reporting: are the numbers honest, and is the outcome space complete?