The dose and the odds: Cardano and Paracelsus on 24 September

Gerolamo Cardano was born in Pavia on 24 September 1501, the illegitimate son of a Milanese lawyer and geometer, Fazio Cardano, whom Leonardo da Vinci had consulted on questions of perspective, and of Chiara Micheria, who had fled Milan in the plague while carrying him and, by her son's own report, had tried beforehand to abort him. Forty years later to the day, on 24 September 1541, Philippus Aureolus Theophrastus Bombastus von Hohenheim, who had renamed himself Paracelsus, died in Salzburg at forty-seven, three days after dictating his will in a room at the Weißes Roß inn on the Kaigasse. The story that the prince-archbishop, Ernst of Bavaria, had brought him to the city is repeated everywhere; the city's own historians say they have no evidence for it, nor for where he was living, and add that he had been treating an inflammation with mercury and that mercury is probably what killed him. At his wish he was buried in the paupers' ground of the St Sebastian almshouse. In 1752 an archbishop moved the bones into a mausoleum in the church porch, where they are still visited by people who think he cured things.

They were both physicians. They both took money from prelates, Cardano from an archbishop in Scotland and a pope in Rome. They both fought with every faculty and college that would have them and several that would not. And they belong on one page for a better reason than the calendar, which is that between them they did something to the sixteenth century's picture of nature that the standard history, with its clean line from Copernicus to Galileo to Newton, has never known where to put. Each took a question that had always been answered with a quality and answered it with a quantity. Paracelsus asked what makes a substance a poison and said: the amount. Cardano asked what makes a throw of the dice a good bet and said: the ratio of favourable cases to all cases. Toxicology and probability are the two disciplines that came of it, and neither man would have recognised the word "science" as a description of what he was doing. Both would have said they were reading the book of nature, which is a different activity and, for a while, a more productive one.

Cardano: the algebra was the least of it#

The mathematics is what he is remembered for and it deserves its place. Ars Magna, printed at Nuremberg in 1545, was the first Latin treatise to give general solutions for equations of the third and fourth degree. The cubic solution he had extracted from Niccolò Tartaglia in 1539 under an oath of secrecy; when he later learned that Scipione del Ferro had found it first, before 1526, he judged the oath discharged and published, and Tartaglia's fury produced the most famous priority quarrel in the history of the subject. The quartic was the work of his student Lodovico Ferrari, credited in the text. The book also does something that had not been done: it takes seriously, and then dismisses as an "arithmetical subtlety" that is "useless", a calculation with the square root of a negative number. Cardano had walked up to the complex numbers and declined to go in. It took two centuries for anyone to admit the rooms were real.

The probability came later and was printed later still. Liber de ludo aleae, the book on games of chance, was written in the 1560s by a man who had, for long stretches of his youth, lived by dice and cards, having been kept out of the Milan College of Physicians on account of his birth until 1539. It was found among his papers and published only in 1663, nine years after the Pascal–Fermat correspondence that is usually taken as probability's birth certificate. Cardano's central move is the one every schoolchild now learns: count the equally likely outcomes, count the favourable ones, and the odds are their ratio. He also glimpsed, without proving, that the frequency of an outcome approaches its probability as the number of trials grows, which Bernoulli would establish in 1713. Those who want the eighteenth-century sequel can follow Pascal; the seventeenth-century one is Cardano, and the surprising thing is not that he was first but that he treated chance as a proper object of reasoning at all. The Stanford entry notes that he kept a distinction between outcomes a skilled player could deflect and those settled by "fatal necessity", which is the theologian and the gambler sharing a desk.

The philosophy is in two enormous books that were the best-sellers of Renaissance natural philosophy and are almost unread now. De subtilitate (1550, revised in 1554 and 1560) and De rerum varietate (1557) are encyclopaedias of everything: the elements, minerals, plants, machines, the soul, demons, dreams, the causes of marvels. Cardano throws out Aristotle's prime matter, reduces the four elements to three, earth, water and air, and makes celestial heat the active principle that moves matter and links it to the intelligible world. Nature, in his account, is animated and ordered toward a unity, and everything in it is arranged in a series of fourteen genera from the elements up through human beings to demons and God, with human matter containing, dormant, the forms of all the animals below it. He defended the immortality of the soul in 1545 on the ground that the mind is aware of itself and that "a human being is the same thing as his mind". Julius Caesar Scaliger, the most ferocious philologist of the age, replied in 1557 with the Exotericae exercitationes, nine hundred pages of objections to De subtilitate, which stayed on university syllabuses for a century and made both books famous.

What the Inquisition actually objected to#

Every popular account says Cardano was arrested in 1570 for casting the horoscope of Christ. He had done that, in print, and it did not help. But the Stanford Encyclopedia's entry, drawing on the archival reconstruction of the trial, reports that the letter from the Inquisitor of Como which set the machinery going was about a chapter of De rerum varietate on the effects of the heavenly bodies. The censors' complaint was that Cardano exaggerated celestial influence and so left no room for God's direct action in the world below the moon: he naturalised miracles, explained demons away, and was, in their reading, a determinist of the kind associated with Pietro Pomponazzi, whose De incantationibus had done the same work half a century earlier and whom Cardano had engaged directly. The horoscope was a symptom; the disease was a physics.

He was arrested on 6 October 1570 and held for forty-three days. In February 1571 he made the abiura de vehementi, the abjuration required of someone "vehemently suspect of heresy", lost the right to teach in the universities and to publish, and moved to Rome, where the papacy gave him a pension and the Roman College of Physicians admitted him at once, which tells one something about how seriously the sentence was meant. He died there on 21 September 1576, three days short of seventy-five. The story that he starved himself to die on the day his own horoscope had predicted is a story; it appears in later writers and not in any document from his lifetime. Pomponazzi's own case, a week ago in this series, is the natural companion piece.

What he wrote in Rome is the reason philosophers still open him. De vita propria, composed in 1575 and 1576 and printed by Gabriel Naudé in Paris in 1643, is an autobiography organised not by date but by topic: his body, his ailments, his diet, his manner of walking, his gambling, his dreams, his enemies, his errors, the things he has invented and the things he has got wrong. It records without ornament that his elder son, a physician, poisoned an unfaithful wife and was beheaded in Milan on 13 April 1560, and that the father never recovered. Montaigne, whose Essais began to appear in 1580, is usually given credit for inventing the modern first person; Cardano was there first, with less grace and more clinical detail. The Stanford entry's summary of his method, "suggestive and rich in original intuitions, but cluttered and inconsistent", would do as a description of the man. Anthony Grafton's Cardano's Cosmos (1999) is the book that took him seriously as an astrologer rather than apologising for it, on the argument that for Cardano the horoscope, the medical case and the moral essay were one enterprise: reading a life as a text written in the stars and the body together. Montaigne's own turn appears in the entry for 13 September.

Paracelsus: burn the book, weigh the dose#

Paracelsus was born near Einsiedeln in Switzerland in 1493 or 1494, the son of a physician, and by his own account learned his trade in mines, army camps and bath-houses across Europe rather than in lecture halls, though he seems to have taken a doctorate at Ferrara. In 1527 he was called to Basel to treat the printer Johann Froben, succeeded, and was appointed town physician with the right to lecture at the university. He lectured in German instead of Latin, which was an outrage in itself, and at the St John's Eve bonfire on 23 June 1527, in the market square, he put a copy of Avicenna's Canon of Medicine into the fire. Whether Galen's works went in with it depends on which account one reads. The point of the gesture is not in doubt: the thousand-year edifice of humoral medicine, four fluids in balance and disease as their imbalance, was to be replaced by observation and by chemistry. By February 1528, after a lawsuit over a fee with a canon of the cathedral, he had left the city in a hurry, and he did not hold a post again.

His alternative had three parts. Disease is not an internal imbalance but an external agent, a seed that settles in a specific organ; the remedy is specific too, and is to be found by working on minerals and metals, so that the purpose of alchemy is medicine rather than gold. Matter is made of three principles rather than four elements: sulphur, which burns; mercury, which flows and evaporates; salt, which remains. And the human being is a microcosm, a small world corresponding point for point to the great one, so that a physician who knows the heavens and the mines knows the body. Von der Bergsucht (written about 1533, printed 1567) is the first systematic description of the diseases of miners, and thus of occupational medicine. And in the third of his Seven Defences, written in 1538 against the charge that his new prescriptions were poisonous, he wrote the sentence that toxicology has adopted as its motto: "All things are poison, and nothing is without poison; the dose alone makes a thing not a poison." Sixteen words, in the German, that move the question from what a substance is to how much of it there is.

Why the textbooks cannot place them#

The difficulty is that neither man can be cleaned up. Paracelsus believed in astral influence, in the doctrine of signatures, by which a plant shaped like a liver treats the liver, and in elemental spirits, and he wrote about all of it in the same breath as the dose. Cardano cast horoscopes for a living, interpreted dreams as providential messages and put demons into his physics. The nineteenth century's solution was to keep the toxicology and the probability and discard the rest as the superstition of the age. Walter Pagel's Paracelsus (1958) made that solution untenable by showing that the two halves were not separable: the chemistry came out of the alchemy, the specificity of disease out of the theory of seeds, the dose out of a picture of a cosmos in which everything acted on everything and the physician's art lay in measure. Foucault made the same point from the other side in Les Mots et les choses (1966), taking Paracelsus and his followers as the type of a sixteenth-century episteme in which knowledge was the reading of resemblances and signatures, and arguing that the classical age did not so much refute that episteme as stop being able to see it. Readers who want Foucault's larger claim about how a way of knowing produces the objects it knows will find it here, and the longer history of how a concept gets made is here.

That leaves the two of them where they were on the day, which is in the middle. Cardano, as Grafton's book documents, was read across Europe as a serious natural philosopher for a century and then largely forgotten except by historians of algebra. Paracelsus was, in Thony Christie's phrase, a major force "in the promotion of iatrochemistry and the turn away from book learning towards empirical investigation", and also, in the same treatises, a man who gave the elemental spirits and the stars a say in what happened to a patient's liver. Both are evidence that the scientific revolution did not come out of a cleaned-up rationalism. It came out of rooms like theirs, and it kept, without acknowledgment, the two questions they had learned to ask with a number: how much, and how likely.

A note on Lech#

The Philosophicum Lech runs until Sunday in the Vorarlberg under the title "Betreutes Denken", supervised thinking, and tomorrow evening at nine, at the Lechwelten, its Tractatus essay prize of 25,000 euros goes to Maria-Sibylla Lotter of Bochum for Opfer: Über Verwundbarkeit als Selbstbild, published by Hanser this year. The jury's citation praises the book for sharpening "our eye for the dangers of a picture of humanity that knows only victims and perpetrators and leaves no room for ambivalence and self-empowerment". The rest of the season is in the October conference diary, and the most recent entry of this series in the archive is here.