The Calculated Madness of Salvador Dali's Mathematical Life: An analysis
At the beginning of the twentieth century, across Europe, the innovative minds of the avant-garde movement began to delve into mathematical, scientific, and psychoanalytical inquiry to push the bounds of their art; they looked to Freud, notions of Euclidean geometry, representations of the fourth dimension, and Einstein’s nascent theory of relativity. The results of these efforts were works that would come to define their generation.
Surrealist painter Salvador Dalí (1904 — 1989) was arguably at the vanguard of these influential artists. His obsession with mathematics and science began in early adolescence, and he relied on both disciplines to produce most of his work throughout his life. Like the masters of the Renaissance, such as da Vinci, Dali believed that a great artist could not ignore the intersection of these studies with art.
The deeply intellectual relationship between mathematician and artist is unsurprising, but one may not instinctively associate it with Dalí. Looking to his own words, however, the man whose eccentric outward appearance was a defining aspect of his art, appears to have thought of his innermost being in a mathematical context: “Someone like myself, who claimed to be a real madman, living and organized with a Pythagorean precision.”
The depth of this relationship is evident in his 1948 book, 50 Secrets of Magic Craftsmanship, where Dali wrote:
“Since morphology, which is the youngest, the most modern science, which has the greatest future, has in this book just married the royal popm the most lucid aesthetic geometry of the Renaiisance, I tell you here, young painter, YES, YES, YES and YES! you must, especially during your adolescence, make use of the geometric science of gilding lines of symmetry to compose your pictures. I know that painters of more or less romantic tendency claim that these mathematical scaffoldings kill an artist’s inspiration, giving him too much to think and reflect upon. Do not hesitate at that moment to answer them promptly that on the contrary, it is in order not to have to think and reflect upon them that you make use of properties.”
Dali became acquainted with the work of Matila Ghyka (1881 — 1965), a Romanian mathematician and aristocrat whose writings concerned the divine proportion or golden ratio, in the late 1940s. Embracing classical-realism, Dali believed that Ghyka had solved the problem of geometrical composition and used a transcription of his golden section composition diagram as inspiration for many of his works. One of these is the 1949 Atomic Leda.
The artist’s interest in nuclear physics became more apparent in his art following the detonation of the atomic bomb in August 1945. It “opened up a mysterious world where a new dimension of reality and matter was possible. Intrigued by the idea that matter is made of tiny particles, he began to paint his own imagery as if it was disintegrating into multiple atoms that floated into space.” Some famous examples include his 1952 painting Galatea of the Spheres, The Disintegration of Time Persistence of Memory (1954), and a number of other works.
In Dalí’s Corpus Hypercubus or The Crucifixion (1954), “Christ's sacramental body is transfixed ambiguously within the foremost of the cubes of a Hintonian tesseract, floating in front of the Virgin above a pavement decorated with an unfolded 3D cube.” Although Dali, a Catholic without faith, had a fluctuating relationship with his religion, he ultimately “came to believe in the possibility of a fusion between modern science, the mystery of religion and the traditions of classicism and began painting his wife Gala as a Renaissance Madonna.”
As Martin Kemp writes in “Dali’s Dimensions” (1998):
“In our present context, Dali's painting does stand effectively for an age-old striving in art, theology, mathematics and cosmology for access to those dimensions that lie beyond the visual and tactile scope of the finite spaces of up-and-down, left-and-right, and in-and-out that imprison our common-sense perceptions of our physical world. The scientists’ success in colonizing the extra dimensions is defined mathematically. The artists — and Dali's corporeal Christ — reach out by visual inference.”
In the late 1960s, Dali was introduced to the catastrophe theory of mathematician and topologist René Thom (1923 — 2002) that he used to study and make predictions about processes involving sudden changes. There are two basic types of processes in nature — continuous (gradual) and discontinuous (sudden). We use calculus to study continuous processes, but because discontinuous processes happen suddenly, they are harder to investigate and predict.
According to Encyclopedia:
“As he was developing his theory, Thom collected data relating to the variables involved in sudden changes. When he then plotted these data on three-dimensional graphs, the result was a curved surface representing a catastrophe in mathematical form. Therefore, catastrophe theory allowed mathematicians to study not only numerical data from discontinuous processes but also visual data in the form of three-dimensional shapes. For this reason, catastrophe theory is considered to be a branch of geometry.
“Thom showed that even though the number of discontinuous processes in nature is essentially infinite, the graphs of these processes could be categorized into a few basic shapes. For processes involving four variables, he discovered that there are seven basic types of catastrophes. They are named for the shapes formed when their variables are graphed: fold, cusp, swallowtail, butterfly, wave, hair, and fountain.”
Although catastrophe theory eventually lost credibility, since almost all biological and sociological systems are significantly more complex than it could cover, the three-dimensional shapes and the abrupt natural phenomena that inspired them, like earthquakes, enthralled the artist. Serendipitously, both Dalí and Thom were fascinated by the Pyrenees, a fold mountain range in Perpignan created by the continental collision of the microcontinent of Iberia with the massive Eurasian plate located near the border of France and Catalonia.
Though Dali’s Perpignan Train Station (1965) depicts a railway station located in the town of the aforementioned geological feature, it predates Thom’s theory by just a couple of years. But, his Topological Abduction of Europe — Homage to René Thom (1983) featuring a long fracture, or seismic crack, inspired by the three converging tectonic plates in Perpignan, is the only work “that explicitly includes an algebraic formula” attributed to Thom’s catastrophe theory; the words queue d’aronde meaning dovetail appear on the bottom left corner of the painting.
Dali’s final painting, Swallow’s Tail and Cellos (1983), is also a direct reference to Thom’s work. Thomas F. Banchoff, a mathematician who had the coveted opportunity to meet with Dali, saw it in progress:
“Our last visit where we showed films and slides was in Pubol near Barcelona, where Dalí retired after the death of Gala. He was working on his final paintings, inspired by images from the catastrophe theory of his friend Rene Thom, and we could see next to the easel a cello with the elongated S-shape reminiscent of the integral sign and a cubic curve with an inflection point. The characteristic form of a swallow tail catastrophe represented a chalice.”
Perhaps we do not think of Dalí as both an artist and a mathematician because we so heavily associate his art with surrealism — fantastical scenes and signature melting clocks — but, there is certainly a mathematical method to the life, work, and madness of Salvador Dali.
Note* Image of The Disintegration of the Persistence of Memory (1952-1954) by Salvador Dali Worldwide rights ©Salvador Dalí. Fundació Gala-Salvador Dalí (Artists Rights Society), 2017 / In the USA ©Salvador Dalí Museum, Inc. St. Petersburg, FL 2017 | Swallow’s Tail and Cellos — Catastrophes Series (1983) by Salvador Dali, © Salvador Dalí, Fundació Gala-Salvador Dalí, Figueres, 2014.