Cardano wrote not just because he was a scientist who had to communicate the results of his research, or a polygraph bent on contributing to a universal encyclopedia, or a compulsive scribbler obsessed with filling page after page, but also because he was a genuine writer, who tried to capture with words something that appeared to elude them. Here is a passage about childhood memories which would merit a place in any future anthology of ‘precursors of Proust’: it is a description of visions or daydream rêveries or flights of fancy or psychedelic hallucinations to which he was subject — when he was aged between four and seven — when he stayed in bed in the morning. Cardano tries to provide the precisest possible record both of this inexplicable phenomenon and of the state of mind in which he watched this ‘diverting spectacle’.
I saw aery images which seemed to be composed of tiny rings, like those in chain mail (lorica), even though I had never seen them at that age. They rose from the right-hand comer of the bed, ascending slowly from the bottom to form a semicircle and then descending to the left-hand comer where they disappeared: castles, houses, animals, knights on horseback, blades of grass, trees, musical instruments, theatres, men dressed in different guises, particularly trumpeters playing their trumpets, though no sound or voice could be heard, and then soldiers, crowds, fields, shapes I had never seen before, woods and forests, a whole range of things which flowed past without merging into each other but instead seeming to jostle each other. Diaphanous figures, but not like empty, non-existent forms: rather they were at once both transparent and opaque, shapes which lacked only colour to make them perfect, but which yet were not only made up of air. I used to enjoy gazing at these spectacles so much that once my aunt asked me: ‘What are you looking at?’ and I refused to answer, afraid that if I spoke, the source of these displays, whatever it was, might be annoyed and stop the entertainment.
This passage comes in the autobiography in a chapter dealing with the dreams and other unusual physical features he was heir to: being born with long hair, the cold of his legs at night, his hot sweats in the morning, the recurrent dream of a cockerel which seemed permanently on the verge of uttering some dire warning, the moon he saw shining in front of him every time he looked up from the page he was writing after solving a difficult problem, his emission of sulphurous or incense-filled odours, the fact that whenever he was in a fight he was never wounded, nor wounded other people or even saw others being wounded, so that once he realised he had this gift (which however did not work on several occasions) he would fling himself fearlessly into every quarrel and riot.
His autobiography is dominated by a constant preoccupation with himself, with the uniqueness of his own person and destiny, totally conforming to the astrological belief which held that the sum of disparate particulars which make up the individual finds its origin and raison d’être in the configuration of the sky at the moment of birth.
Thin and unhealthy, Cardano was triply concerned with his own health: as a doctor, as an astrologer, and as a hypochondriac, or as we would say now, as someone with a psychosomatic condition. As a result the clinical chart he has left us is extremely detailed, ranging from lengthy life-threatening illnesses to the tiniest spots on his face.
This is the subject matter of one of the first chapters of De Propria Vita, which is a biography constructed around themes: there are chapters on his parents (‘mater fuit iracunda, memoria et ingenio pollens, parvae staturae, pinguis, pia’ (my mother was an irascible woman with a powerful memory and intellect, small in stature, fat and pious)), his birth and star sign, a physical self-portrait (which is meticulous, ruthless and complacent in a kind of inverted narcissism), his diet and physical routine, his virtues and vices, his favourite things, his consuming passion for gaming (dice, cards, chess), his manner of dress, his gait, his religion and other devout practices, houses he lived in, poverty and losses to the family patrimony, risks taken and accidents, books written, the most successful diagnoses and therapies of his medical career, and so on.
The chronological account of his life occupies just one chapter, not very much for such an incident-packed existence. But many episodes are recounted at greater length in various chapters of the book, from his adventures as a gambler both in his youth (including how he managed to escape with the help of his sword from the house of a Venetian patrician card-sharp) and when a grown man (at that time chess was played for money and he was such an invincible chessplayer that he was tempted to abandon medicine to earn a living from gaming), to his amazing journey across Europe as far as Scotland where an archbishop who suffered from asthma was waiting for him to cure him (after several unsuccessful attempts, Cardano managed to improve the archbishop’s condition by forbidding him the use of his feather pillow and mattress), to the tragedy of his son who was beheaded for killing his wife.
Cardano wrote over 200 works of medicine, mathematics, physics, philosophy, religion and music. (It was only the figurative arts that he steered clear of, almost as if the shade of Leonardo da Vinci, a spirit who resembled his own in so many other ways, was enough for that area.) He also wrote a eulogy of the Emperor Nero, and an encomium of gout, as well as a treatise on spelling and one on gambling (De Ludo Aleae). This last work is also important as the first text on probability theory: hence the attention devoted to it in an American book which, leaving aside its more technical chapters, is extremely informative and enjoyable, and is, I think, still the most recent monograph on Cardano to this day (Oystein Ore, Cardano, The Gambling Scholar, Princeton, 1953).
‘The gambling scholar’: was that Cardano’s secret? Certainly his life and works seem to be a succession of games involving risk, and the possibility of losing as much as winning. Renaissance science no longer seems to be for Cardano a harmonious unity of macrocosm and microcosm, but rather a constant interaction of ‘chance and necessity’ which is refracted in the infinite variety of things, and in the irreducible uniqueness of individuals and phenomena. The new direction of human knowledge had by now begun, aimed as it was at deconstructing the world bit by bit rather than at holding it together.
This goodly frame, the earth/ says Hamlet, with this book in his hand, ‘seems to me a sterile promontory; this most excellent canopy, the air, look you, this brave o’erhanging firmament, this majestical roof fretted with golden fire, why it appears no other thing to me than a foul and pestilent congregation of vapours…’
[1976]
The Book of Nature in Galileo
The most famous metaphor in Galileo — and one which contains within itself the kernel of the new philosophy — is that of the book of Nature written in mathematical language.
Philosophy is written in this enormous book which is continually open before our eyes (I mean the universe), but it cannot be understood unless one first understands the language and recognises the characters with which it is written. It is written in a mathematical language, and its characters are triangles, circles, and other geometric figures. Without knowledge of this medium it is impossible to understand a single word of it; without this knowledge it is like wandering hopelessly through a dark labyrinth. (II saggiatore (The Assayer), 6)
This image of the book of the world already had a long history before Galileo, from the medieval philosophers to Nicholas Cusanus and Montaigne, and it was used by contemporaries of Galileo such as Francis Bacon and Tommaso Campanella. Amongst Campanula’s poems, published the year before Galileo’s Il saggiatore, there is a sonnet that begins with these words: ‘Il mondo è il libro dove senno eterno, scrive i propri concetti’ (The world is the book in which eternal wisdom writes its own ideas).
Already in his Istoria e dimostrazioni intorno alle macchie solari (The History and Proof of the Spots on the Sun) (1613), that is to say ten years before Il saggiatore, Galileo had contrasted direct reading (of the book of the world) with indirect reading (of the books of Aristotle). This passage is extremely interesting because in it Galileo describes Arcimboldo’s paintings, offering critical judgements which remain v
alid for painting in general (and which provide evidence of his links with Florentine artists such as Ludovico Cigoli), and in particular providing reflections on combinatory systems which can be put alongside those which will be cited later on.
The only people who oppose this point of view are a few rigid defenders of philosophical minutiae. These people, as far as lean see, have been brought up and nourished from the very start of their education in this opinion, namely that philosophy is and can be nothing other than continuous study of such texts of Aristotle as can be immediately collected in great numbers from different sources and stuck together to resolve whatever problem is posed. They never want to raise their eyes from these pages as though this great book of the world was not written by nature to be read by others apart from Aristotle, and as though his eyes could see for the whole of posterity after him. Those who impose such strict laws on themselves remind me of those whimsical painters who as a game set themselves constraints such as that of deciding to depict a human face or some other figure by simply juxtaposing agricultural implements or fruits or flowers of different seasons. All of this bizarre art is fine and gives pleasure as long as it is done for amusement, and it proves that one artist is more perceptive than another, depending on whether he has been able to choose more suitably and use a particular fruit for the part of the body to be depicted. But if someone who had spent all his training in this kind of painting should then decide that in general any other form of painting is inferior and defective, certainly Cigoli and all other illustrious painters would laugh him to scorn.
The most original contribution made by Galileo to this metaphor of the book of the world is his emphasis on its special alphabet, on ‘the characters with which it is written’. To be more precise, one could actually say that the real metaphorical link is not so much between world and book as between world and alphabet. In this passage from the second day of his Dialogue Concerning the Two Chief World Systems, it is the alphabet which is the world:
I have a little book which is considerably shorter than Aristotle and Ovid, which contains all sciences, and which with just a little study can allow others to form a perfect idea of it. This book is the alphabet, and there is no doubt that the person who knows how to put together and juxtapose this or that vowel with those or other consonants, will get the most accurate responses to all doubts and he will derive lessons pertaining to all the sciences and the arts. In exactly the same way the painter can choose from different primary colours set separately on his palette and by juxtaposing a little of one colour with a little of another can depict men, plants, buildings, birds, fishes; in short, he can represent all visible objects even though there are no eyes, feathers, scales, leaves or stones on the palette. In fact it is essential that none of the things to be represented, or even any part of them, should actually be there amongst the colours, if one wants to use them to depict all manner of things, because if there were on the palette, say, feathers, these could only be used to depict birds or plumage.
Thus when Galileo speaks of the alphabet, he means a combinatory system capable of representing everything in the universe. Here too we see him introducing the comparison with painting: the combination of the letters of the alphabet is the equivalent of the mixing of colours on the palette. It is clear that this is a combinatory system of a different order from that used in the paintings of Arcimboldo in the preceding quotation: a combination of objects which are already endowed with meaning (a painting by Arcimboldo, a collage or collection of feathers, a pastiche of quotations from Aristotle) cannot represent all of reality; in order to achieve this one needs to turn to a combinatory system of minimal elements such as primary colours or the letters of the alphabet.
In another passage in the Dialogue (at the end of the first day) in which there is a eulogy of the great inventions of the human spirit, the highest place is reserved for the alphabet:
But above all other wondrous inventions, what eminence of mind was his who first devised the way of communicating his innermost thoughts to any other person however distant in time or space? the way of communing with those in the Indies, with those who have not yet been born or with those who will come into being a thousand or ten thousand years hence? and consider how simple it is: merely the different combinations of twenty small characters on a page. This must be the most wonderful of all human inventions.
If we reread the passage from Il saggiatore which I quoted at the beginning in the light of this passage, we will understand more clearly how for Galileo mathematics, and in particular geometry, performs the function of an alphabet. This point is made very clearly in a letter to Fortunio Liceti written in January 1641 (a year before his death):
But I truthfully believe that the book of philosophy is the one which is permanently open before our eyes; but because it is written in different characters from those of our alphabet it cannot be read by everyone: and the characters of this book are triangles, squares, circles, spheres, cones, pyramids and other mathematical figures which are highly suited for just such a reading.
We notice that Galileo in his list of figures does not mention ellipses despite having read Kepler. Is it because in his combinatory system he has to start from the simplest forms? or because his battle against the Ptolemaic model is still being conducted within a classical idea of proportion and perfection where the circle and the sphere are the supreme images?
The problem of the alphabet of the book of nature is connected with that of the ‘nobility’ of forms, as can be seen in this passage from the dedication of the Dialogue Concerning the Two Chief World Systems to the Grand Duke of Tuscany:
Whoever aims higher stands out more eminently; and to turn to the great book of nature, which is the proper object of philosophy, is the way to raise your eyes. Although everything we read in this book, having been created by an omnipotent Demiurge, is therefore most proportionate, those things are even more perfect and worthy in which the labour and artifice appear greater to us. Amongst those physical objects that can be perceived, the setting up of the universe, in my view, can be given the first place: since it contains all things, it surpasses everything in size, and since it governs and maintains everything else, it must outstrip all other things in nobility. Consequently if anyone was destined to stand out in intellect far above all other men, it is Ptolemy and Copernicus since they read, and observed and philosophised on the constitution of the world.
A question that Galileo asks himself several times, to poke ironic fun at the old way of thinking, is this: regular, geometric forms must be considered more ‘noble’, more ‘perfect’ than natural, empirical, irregular forms, etc. It is particularly with regard to the irregularities of the moon that this question is discussed. There is a letter by Galileo to Gallanzone Gallanzoni which is entirely devoted to this subject, but the passage from Il saggiatore conveys the idea just as well:
As for me, I have never read the chronicles and particular genealogies of the forms, so I do not know which of them is more or less noble, or more or less perfect. But I believe that they are all ancient and noble in one way, or to be more precise, that they are neither noble and perfect nor ignoble and imperfect except in the sense that for building walls square shapes, I believe, are better than spherical ones, and for rolling or driving carts, round shapes are superior to triangular ones. But to return to Sarsi, he says that I supply him with ample arguments to prove the roughness of the concave surface of the sky, because I myself claim that the Moon and the other planets (they are also bodies, albeit heavenly ones, and even more noble than the sky itself) have a surface that is mountainous, rough and irregular; and if this is true, why can one not say that such irregularity can also be found in the body of the heavens? Here Sarsi himself can take as a reply what he would answer to someone who wanted to prove to him that the sea was full of bones and scales because whales, tuna and other fish are full of those things.
As a passionate geometer one would expect Galileo to champion the cause of geometric shapes,
but as an observer of nature he rejects the idea of an abstract perfection and contrasts the image of the ‘mountainous, rough and irregular’ Moon with the purity of the heavens in Aristotelian and Ptolemaic cosmology.
Why should a sphere (or a pyramid) be more perfect than a natural shape, say that of a horse or a locust? This question recurs throughout the Dialogue Concerning the Two Chief World Systems. In this passage from the second day we find a comparison with the artist, in this case a sculptor:
That is the reason why I would like to know if it is equally difficult to represent the solid of some other shape, that is to say whether it is harder to try to shape a block of marble into a perfect sphere or perfect pyramid or into a perfect horse or perfect locust.
One of the finest and most important passages in the Dialogue comes in the first day, where we find the eulogy of the Earth as something subject to alteration, mutation and generation. Galileo evokes with terror the image of an Earth made of solid jasper or crystal, an incorruptible Earth, as though it had been petrified by Medusa: