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. (Il 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 Campanella’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 valid 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 I can 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:

I cannot hear without marvelling greatly, indeed without my intellect revolting at the concept, people attributing great nobility and perfection to the natural bodies that make up the universe just because they claim they are impassive, immutable, inalterable and so on, whereas they consider it to be a major imperfection if anything can change, grow, mutate and the like. As far as I am concerned, I consider that the Earth is most noble and admirable precisely because of the many different ways it endlessly changes, mutates and evolves. For if the Earth were not subject to any change and consisted entirely of a vast desert of sand or a mass of jasper, or if during the time of the flood the waters covering her surface had frozen and she had simply remained an immense crystal sphere, where nothing was ever born, changed or developed, I would consider the Earth a big but useless body in the universe, paralysed by inertia, and in short superfluous and unnatural: for me there would be the same difference as there is between a living and a dead creature. I feel exactly the same as regards the Moon, Jupiter and the other spheres in the cosmos…. Those who so exalt incorruptibility, unchangeability and the like, are, I think, reduced to saying such things both because of the inordinate desire they have to live for a long time and because of the terror they have of death; and they do not realise that if men were immortal, they would never have come into the world. Such people deserve to be exposed to the stare of a Gorgon’s head which would turn them into statues of jasper or diamond, so they can become even more perfect than they are.

If one puts Galileo’s passage about the alphabet of the book of Nature alongside this eulogy of the small changes and mutations of the Earth, one can see that the real opposition is between mobility and immobility, and it is against that image of the inalterability of Nature that Galileo campaigns, conjuring up the nightmare of the Gorgon. (This image and this topic were already present in Galileo’s first astronomical work, Istoria e dimostrazioni intorno alle macchie solari (The History and Proof of the Spots on the Sun).) The geometric or mathematical alphabet of the book of Nature will be the weapon which – because of its capacity to be broken down into minimal elements and to represent all forms of movement and change – will abolish the opposition between the unchanging heavens and the elements of the Earth.

The philosophical thrust of this operation is well illustrated by this exchange in the Dialogue between the Ptolemaic supporter Simplicio and the author’s spokesman Salviati, where the theme of ‘nobility’ surfaces once more:

SIMP. This way of philosophising tends to subvert the whole of natural philosophy, as well as undermining the order of the heavens, the Earth and the whole universe. But I believe that the fundamental principles of the Peripatetics are such that there is no danger that by destroying their principles one can construct new sciences.

SALV. Don’t worry about the heavens, the Earth, or their possible undermining, or even about philosophy itself, because as far as the heavens are concerned it is pointless for you to fear for something that you believe to be inalterable and impassive; and as for the Earth, we are seeking to raise her to even greater nobility and perfection by trying to regard her as similar to the heavenly bodies and in a certain sense to place her in the heavens, the place from whence your Aristotelian philosophers banished her.

[1985]