Gino Severini, Luca Pacioli’s De divina proportione, Pinocchio and the mathematics of art

Here’s the rest of the story of the Cubists and Luca Pacioli’s De divina proportion (‘Of the divine proportion’, 1509), his mystical treatise on maths, art and God illustrated by Leonardo da Vinci.

As I said here on 12 March, De divina proportione inspired the first Cubist exhibition in Paris in 1912, which the artist Jacques Villon named ‘Section d’Or’ (golden section or ratio) after the title of Pacioli’s book. The Cubists used the golden ratio in the mathematical organisation of their compositions, but Italian Futurist¬†Gino Severini¬†believed they were using it only superficially and decided to probe more deeply into the maths and logic of the ancient rules of painting.

In his autobiography, The Life of a Painter, Severini explains his need for more than mere discussion of mathematics:

‘Many artists like to discuss geometry and mathematics … In the case of a valid artist, such intentions helped him to compose, to rationalise his paintings; these same theories were helpful to many a distinguished work. But I found this insufficient. I thought that geometry and mathematics should be used more precisely, that artists should apply, and would benefit from, strictly observed laws of geometry and mathematics. These rules had meanings (I was beginning to realise) beyond their constructive value. I am referring not only to that universal, cosmic sense that the Greeks gave to mathematics and to numbers, but to something strictly innate to artistic creativity.’

Lanciers italien au galop, 1915

Following the Greeks, Severini articulates his sense of the connection of all art to the cosmos, of the artist to the ‘collective soul’ and of their relation to mathematics. ‘Poetry and art belong to a profound stratum of being, common to all forms of expression, and therein is the pure source that animates everything, holds everything together, that is, the artist to the universe, the work to the cosmos, the individual to the collective soul; the measure of all this is in numbers. This accounts for its metaphysical value, beyond human values, divined, moreover, by Rimbaud.’

In Paris after the First World War Severini decided to ‘bring to line and to form that scientific spirit that the Neo-Impressionists had brought to colour’. And so he began researching ancient essays on art, from Vitruvius to Leon Battista Alberti.

‘In all of them I found the confirmation of what we painters had often discussed, but without ever pinning down the ideas, because, basically, none of our ideas was precise enough; I found that there were geometric and numeric laws fundamental to architecture that served as its backbone … So I glimpsed the path leading to the infinite, towards absolute purity, superhuman poetry and perfect harmony, in numbers. Nonetheless, for the time being I was obliged to simply enrich my knowledge of technique and construction.’

Disillusioned with his attempts to understand the mathematics of Albrecht Durer’s work on perspective, Severini found a professor of mathematics who lectured on geometry and the fine arts at the National Conservatory of Arts and Crafts in Paris. The mathematician, Raoul Bricard, agreed to teach Severini the secrets of descriptive geometry. Severini writes: ‘What saint made this mathematician’s heart and soul compassionate and interested in me, such an ignorant artist, I will never know. Perhaps he was moved by my fervent desire to learn.’

Thanks to his geometry lessons with Bricard, Severini began to understand the exact meaning of the term ‘Section d’or’: ‘Now that I knew what a “ratio” and a “proportion” were, I knew what the Golden Mean meant.’¬†Through his studies Severini became ‘quite accomplished at using conjugated orthogonal projections’, ie at the Renaissance art of perspective painting, a la Piero della Francesca.

Piero della Francesca

One day Severini showed up at his lesson with a drawing for Bricard made with the geometry he’d learnt from him. It was a large drawing of a vertical and horizontal projection of the human head and torso, three quarters turned and ‘full of life’. Severini recalls its impact:

‘My professor was completely amazed and enthusiastic and said quite frankly: “I taught you these things just to appease you, but thought that it was a matter of an artist’s peculiarity, not that you would put them to use.” The most amazing part was that I was surprised by this too. It was a bit like a doll manufacturer who, all of a sudden, sees one of his creations jump up, walk, and talk; Geppetto, the carpenter, who feels his wig being pulled by Pinocchio, while he is still in the act of carving him. In fact, the expression of life that springs out of certain forms is extraordinary. These are the ones conceived exclusively in our souls, and from pure geometry they pass to an even more distant imitation of reality. They provoke intense, vivacious emotions. I then began to understand how certain great masters of the past, the Greeks for example, were able to construct according to numbers or geometric shapes, and thereby to express life.’

Arlequin, Portrait de Nino Franchina, 1938

Leonardo da Vinci, another painter who applied mathematics to his work, tells a similar story of the life force of one of his paintings: ‘It previously happened to me that I made a picture representing a holy subject, which was bought by someone who loved it and wished to remove the attributes of its divinity in order that he might kiss it without guilt. But finally his conscience overcame his sighs and lust, and he was forced to banish it from his house.’

Leonardo da Vinci, from ‘The Virgin of the Rocks’

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