Galileo’s Muse

Dante and Virgil contemplate the blessed spirits (Gustave Dore)

When in polite society I'm asked why I've chosen web design as a profession I always try to say something coherent about its pleasing emphasis on the necessity of blending logic and aesthetics.

That's something that could be said about any field of design: web design, print design, product design, architecture… a successful product satisfies not just because of surface appeal - its fine graphics, appealing colours, well judged proportions, and tactile textures - but also because of the sense that the same care lavished on the design's exterior was also applied to its invisible components. We feel it's just as beautiful on the inside as on the outside. Good design goes all the way down.

So, to consider my line of work, a well crafted website should appeal both to the aesthete and the engineer. The typography will be invite the eye, the colours will complement each other, the proportions will be pleasing and the graphics will intrigue. All of those design choices are considered, nothing is subjective: every decision is made in service of the project's objectives . And each element of the design is built using well considered, robust, maintainable code. Logic and aesthetics reinforce each other: the site is beautiful because it is logical, and its logic is beautiful.

I suppose I could be considered one of the many web designers who entered this strange new profession from an 'arts' background. I specialised in subjects like English, art, history, politics and philosophy through school and university, and my early jobs were in fields like journalism and public relations. But I've never regarded my becoming a web designer as a radical shift to a 'technical' discipline. It's always seemed to me that developing real skill in the humanities requires just as much mastery of technique as is needed for scientific professions. Poets impose disciplined frameworks upon verse. Authors work within robust narrative structures. Composers have to master complex laws of harmony. Painters employ rules of colour theory and perspective.

This continuum between the arts and the sciences was undoubtedly acknowledged more openly in the past. The 'classical' curriculum dominant in Europe till the past couple of centuries grouped arithemetic, geometry, music, poetry and painting as related subjects, not as severely demarcated worlds unto themselves. During a few days off last week I had took the opportunity to read a book that makes radical, but compelling, claims for just how seamless the relationship between the 'arts' and the 'sciences' once was.

Renaissance mathematics and the arts

Galileo's Muse: Renaissance Mathematics and the Arts by Mark Peterson, a Professor of Mathematics and Physics at Mount Holyoke College, studies in fine detail the extent to which the scientific revolution of the 16th and 17th centuries was rooted in the art rather than the science of the Renaissance. The book might be considered an intellectual biography of Galileo Galilei, who along with Isaac Newton pioneered modern science, making critical breakthroughs in the study of the laws of freely falling bodies and the trajectory of projectiles, inventing the modern telescope, and of course establishing the essential correctness of the Copernican model of a heliocentric solar system, deposing the age-old orthodoxy of the Earth-centred Ptolemaic model.

Detail of a Galilean drawing of the moon

The book's opening chapters chart the young Galileo's immersion in the arts. Like all Tuscans he revered Dante, and also Ariosto and Tasso. At one point he wanted to be a painter, and developed a deep understanding of the rules of perspective discovered by artists and architects. And like his father he was a fine musician, playing the lute to a high standard.

Peterson argues that Galileo's subsequent discoveries owed much more to the mathematical and scientific insights developed by poets, painters, musicians and architects in pursuit of their respective arts than to the rather moribund scientific orthodoxy of his day. The science of the 16th century was more concerned with preserving arithmetical and geometrical systems developed by the ancient Greeks than in seeking to use them to unlock the workings of the physical world. The notion of what we today understand as mathematical physics didn't yet exist. Euclidean geometry, for example, was admired for its abstract beauty, but was employed for guiding metaphysical speculation about the music of the spheres rather than for furthering understanding of the physical laws governing the material world.

The dimensions of Hell

The book is particularly effusive about the genius of Dante, arguing that the 14th century Florentine should be considered one of the finest mathematicians of his day, as well as one of the greatest poets of any age. There's a fascinating - though complicated! - chapter describing how Dante, in the Paradiso, the last book of his epic Divine Comedy, effectively invented new mathematical principles by himself in order to give precise expression to his vision of heaven. His geometry of the heavenly spheres involved complex intersection of circles and planes that can only be grasped mathematically, not visually.

Peterson goes on to describe how one of Galileo's most important discoveries was inspired by consideration of the dimensions of Hell set out in the Inferno, the first book in the Comedy. In 1588 the 24-year-old Galileo made his name by delivering a celebrated lecture series at the Florentine Academy titled On the Shape, Location and Size of Dante's Inferno, in which he explored scholarly efforts to prove the plausibility of the poet's description of the massive cylinders descending to the centre of the Earth that constituted the infernal architecture. After the lectures Galileo realised that Dante's measurements weren't theoretically viable after all - a real Inferno as described would have collapsed under its own weight - but the sophistication of the poem's speculations served as the impetus for Galileo's subsequent development of new principles of structural engineering that have undergirded modern architecture. This witty little animation created for The Boston Globe's review of Peterson's book illustrates the episode well:

Perspective and proportion

Other chapters consider the influence on Galileo of theories of perspective developed by artists and architects, including Piero della Francesca, Leon Battista Alberti, and Filippo Brunelleschi. Peterson notes that Galileo's intimate knowledge of perspective was important to his astronomical discoveries, enabling him, for example, to interpret the landscape of the moon. He noted correctly that shadows on its surface indicated the presence of valleys, craters and mountains, an observation that seems obvious to us now but which in Galileo's time was novel: there were all kinds of theories as to what the moon markings represented.

Peterson goes on to suggest how Galileo's knowledge of musical theory might have influenced his theories and applications of proportion and measurement. Galileo and his father undertook extensive investigation of the tuning of instruments, experimenting with string length and weights to obtain musical intervals such as octaves, fourths and fifths. These exercises in calibration helped Galileo invent the telescope and to take the accurate measurements that confirmed that correctness of the Copernican model of the solar system.

A holistic vision

This has already turned into quite a long blog post and I've just touched the surface of the book: it offers so many striking insights into the Renaissance mind, into a holistic worldview that saw maths and the arts as seamlessly interwoven. It's was a world where artists didn't hesitate to take on tough logical problems to further their art, and scientists steeped themselves in poetry, music and draughtsmanship in search of the imaginative insight that would allow them to look at problems from fresh angles and open the way to discovery.

I'm aware that it's much harder for us, in the 21st century, to see relationships between disciplines. Each field of study is just so complex. And we don't share the Renaissance confidence that everything is of a piece, that art and science both strive towards the revelation of some higher Truth. We now consign questions like that to the realm of theology. But our appreciation of good design, I think, is related to the same desire for unity that drove great thinkers like Galileo.

If you're interested in finding out more about the book I recommend this interview with the author: Galileo's Muse: An interview with Mark Peterson.

(By the way, did I mention that the book itself is very handsome, nicely illustrated and set, appropriately, in the Centaur typeface, a fine 20th century take on some of the best Renaissance fonts.)