Every which way

I've having a great time reading up on the history of probability right now.  I'm coming to the end of a stint trying to get to the bottom of what the Italian Cardano actually contributed to the history of probability (separate blog post soon to come), and have found a connection with an earlier man, a Spaniard called Ramon Lull which gets to the essence of what Cardano is supposed to contributed  - combinatorics.

Both men seem to have been somewhat obsessed with sex. Now it is clearly the case that sex and gambling have always been popular activities of the rich and powerful, with no doubt the evolutionary biologist offering up the conspicuous spend implied in gambling as a form of cultural peacock feather.  But perhaps even the men who invented the subject were likewise disposed.

Cardano, one of the first men to write his own detailed autobiography, gives the following description of himself: "I was ever hot-tempered, single-minded and given to women.  From these cardinal tendencies there proceeded truculence of temper, wrangling, obstinacy, rudeness of carriage, anger, and an inordinate desire for revenge in respect of any wrong done to me." (FN David, p42).  David also tells if how Cardano's day job as a medical doctor was frustrated by the refusal of the College of Physicians of Milan to allow him to join their ranks  "..possible because of his reputation as a gambler and his licentious conduct..."( FN David, p44)  When he was a student there was apparently gossip about  his predilection for "singing boys" , which according to F.N. David became louder after his wife dies, and his university wanted to sack him due to the ".. number and character of young men who frequented his house".  His daughter eventually wrote him a letter saying she was  ashamed to be related to him.

It is somewhat ironic that his main contribution to probability was his insistence on visiting all combinations of the possible when examining simple randomisation machines.  Perhaps these complete samplings bore a similar motivation to that more famous libertine the Marquis De Sade, whose descriptions of sexual couplings was exhaustively complete.  The other ironic element of Cardano's life  was his persecution complex , which is a kind of re-telling of the more or less random facts of his life in a way which banishes randomness and replaces it with an authoritarian determinism.    He then finally loses his job by doing the very opposite to religion - he publishes a horoscope of Jesus - thereby applying the everyday use of spiritual/divinatory randomness to a religious figurehead.  In one last overturning of randomness and determinism, he is said to have forecast his own death date by divination, then proceeded to make the prediction come true by starving himself.  A weird kind of performativity. 

In "The Drunkard's Walk" (written nearly 50 years later, in 2008), we hear that the official reason for dismissal was "sodomy and incest".  We hear that his mother was promiscuous, that his daughter was promiscuous, and at 16 seduced her brother.    This son, Bernstein (p46) is described as "deaf in his right ear, ..he had two toes on his left foot, his third and fourth counting the great toe ... were joined by one membrane.  His back was slightly hunched..".  Perhaps incestuous combinations had been going on for generations, given this list of low grade genetic abnormalities.    Cardano is the first mathematician supposedly to describe so called Cardanic cycloids the geometry of circles within circles.  But these diagrams seem to me quite related to the work of early logician Raymond Lull.  He used circles within circles to enumerate many possibilities in a logical and consistent way.  His main purpose was religious, but that is hardly surprising for a 13th Century thinker.  "The beauty of women, oh Lord, has been a plague and tribulation to my eyes for because of the beauty of women I have been forgetful of thy great goodness and the beauty of thy works" Logic Machines and Diagrams (p3, Gardner).

Is it too fanciful to suggest that both men transformed a passion for exhaustive sexual coupling into the beginnings of combinatorial mathematics?  Lull's conversion happened while riding a horse - he spotted a woman he'd been  trying to fuck for some time enter a cathedral.  Still mounted, he rode into the cathedral in pursuit of her.  She arranged to meet him in a private room, whereupon she showed him her breasts - but they were riddled with cancer.  Take a good look at the foulness of this body you've been lusting after.  You would have been better advised to pursue the Christian God than my body.  Lull went on to create elaborate and exhaustive rules of combining ideas and words - partly a proto-automatic writing prop in the style of Burroughs, partly one of the second millennium's first logic machines.

In another post, I'll look at the ideas of combinations and permutations from a mathematical point of view, as they appeared in Lull and Cardano.  The kind of abstract transformation embodied in Lull and Cardano's stories reminds me of Duchamp's The bride stripped bare by her bachelors, even