Gerolamo Cardano 1501-1576: A Throw of the Dice

Every so often you read about a bunch of clever MIT students or such like who go to Vegas and by superior brainpower make a killing at the tables before the spotters notice and kick them out.  In the old days, a broken leg might have been in the cards, so to speak, but in general the experiment ends with the players getting banned from the casino and selling the story to Hollywood.

Didn’t use to be be like that.  Consider the case of Cardano.  As a twenty five year old college student taking a break in a friendly game of cards in Venice, he found that his luck turned unreasonably bad.  He also found that the a game was being played with marked cards.  A direct sort of fellow, Cardano pulled a knife, stuck it in the other guy, then fled into the night.

He seemed to have been dealt a pretty bad hand from the start. The illegitimate son of a Milanese lawyer, he mentions almost in passing that his mother tried to abort him (tentatis abortivis medicamentis frustra).  His early childhood was a cycle of abuse and neglect and dread disease (plague, they say – he got over it).  In time both parents warmed up to him. In 1514, his father,  a math geek, brought him to meet Leonardo da Vinci.  Good schooling was bankrolled, as was university (Pavia, later Padua) where he became fascinated by matters of probability, especially as they pertained to games of chance.

Necessity is the mother of invention, and he wanted to win without having to cheat (he, after all, was not the only gambler to carry a knife).  By preference, he made no bet the outcome of which he had not minutely calculated, and then only in his favor, and so he effectively invented the field of probability.   He even wrote a book on it : Liber de Ludo Aleae, loosely, How to Shoot Craps.  (Cardano’s failure to publish throws the credit to Fermat and Pascal in 1654 – the phenom of many people coming to the same problems at the same time is well known.)

His real interest, however, was medicine.  After graduation, he applied for but was denied admission to the college of physicians at Milan.  He was turned down. “Bastards need not apply” was the given reason; his erratic behavior may have had more to do with it.   Nothing daunted, he moved to his wife’s small home town and hung out a doctor’s shingle regardless.  Hard times, made worse when the dice turned against him again and he was forced to pawn not only his wife’s jewels, but also their bed.

In time things began to improve and his skill as a doctor attracted notice and patients- much to the irritation of his fellow physicians.  So did he make nice?

He did not.

Still miffed by their refusal to let him into their college, he published  De malo recentiorum medicorum usu libellus  (On the Evil Practices of Modern Medicine, Venice, 1536).  Over his lifetime, he wrote over two hundred books – this was the beginning of the age of the writer as hack.  Anyway, he must have changed a few minds – he was offered, but refused, a professorial post in medicine at the U. of Pavia.

Not trusting to hack writing or medicine alone as a way to make a living (!), he began to apply himself serious to mathematics.  He was good enough to get a second job lecturing on the subject at the University of Padua, and proved entertaining enough to fill the auditorium.

In 1545, he published his magnum opus, the Artis magnis sive de regulis algebraicis.  It was one of those staggering books that are not necessarily widely understood, but nevertheless understood to be terribly important and proof that the author is  a champion in his field.  Geek celebrity. Think Newton, or Einstein, or Stephen Hawking.  Cardano gave us negative numbers, among other things. “Cardano’s Rule for solving reduced cubic equations.”  The book made him.

This alone would have been enough to hang his reputation on, but his was a restless mind and he had an interest  in physics and the natural sciences as well: the cycle of rain from the ocean and back again, that was his.  Riffing off of Archimedes, he had some original thoughts on levers and pulleys.  Some practical advice on how to avoid demons. He made a combination lock. He invented the Cardan Grille (useful for thriller writers) and the Cardan Shaft (vital for cars).  The more you read, the more you feel that if he had only had an interest in the arts, he might be a household name today.

The college seats and books and rich patients (Archbishop of St Andrews, for instance) should have set him up for a middle and old age of personal health, wealth, and wisdom.  It didn’t happen.  Discord has to sprinkle a little poison into the pot.  His wife died in 1546.  Then there were his children.

His well loved eldest son married badly, a woman who openly mocked her husband and suggested that his son was not his son.  The husband shifted her with arsenic.  Clever lawyers (paid for by Cardano, of course) were on the point of getting him off the charge when the guilt stricken widower confessed.  Death by execution, of course, and some gratuitous torture – it was devastating for Cardano.

His daughter went on the game and died of syphilis.

His third child, Aldo, was a drunk and a thief and a gambler (who seems not to have read his father’s work).  Annoyed at not being bailed out ad infinitum (and possibly over his exasperated father having his ears cropped), Aldo is said to have conspired in bringing Cardano to the attention of the Inquisition.

No one ever expects the Italian Inquisition, least of all Cardano.  In the end he served a few months only and recanted whatever it was they wanted him to recant (the record was sealed and he sworn to silence). He was, however, stripped of his teaching position and prevented from getting it back.  One theory is that he cast a horoscope of Jesus Christ.  (Not that horoscopy itself was all that unusual, and it was one of the things Cardano studied closely.  But there were limits, and suggesting that the answer to the life of JC was in the stars was taking the science a bit to far.)

From Milan to Rome to petition the Pope to cut him a little slack.  He had the support of that Archbishop of St. Andrews (it had turned out the man was allergic to his bed).  The endorsement was enough to only to get Cardano cleared, but also the right to practice medicine again, and a small pension.  Now in his seventies,his free time he spent in writing his memoirs.  He died in bed, some say on the day his horoscope predicted.

His autobiography is not quite as outrageous as those of Benvenuto Cellini and Casanova, and reads more like scraps and jottings, but has its moments.  (Latin, not Italian, interestingly – publishing was changing just then and it becomes an interesting question whether he was looking for an international audience  a run for their money.)

Oh, and that knife fight back in Venice?  He fell into a canal and might have drowned had a passing boat not picked him up.  His rescuer turned out to be the same guy he had lately stabbed.  Given that the game was dubious to begin with, they agreed to keep the police out it and go their separate ways in peace.

Cardano’s Cosmos: The Worlds and Works of a Renaissance Astrologer by Anthony Grafton (2002)

The Rules of Algebra: (Ars Magna) by Girolamo Cardano (trans 1968)

Cardano, the Gambling Scholar by Oystein Oyre (1953)



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