A Lesson with Francis Bacon Forced Me to See Outside the Software Box

As an art student, I never thought about the crossroads of art and technology until I stumbled into a lecture by Hungarian theoretical physicist Edward Teller (1908–2003) [1], “the father of the hydrogen bomb,” being hosted on Miami Dade Community College’s North Campus, 3 February 1979. He talked about his friend Albert Einstein and how, right to his death, Einstein felt guilty and sad about the outcome of the atom bomb, even though he did not participate in the making of it. Unfortunately, according to Teller, his famous equation published 1915, E = mc² [2], did. It informed scientists how a massive release of atomic energy equal to mass faster than the speed of light can impact neutrons, splitting and bombarding other neutrons into uranium, creating a radioactive chain reaction, which would result in two devastating nuclear blasts, killing 129,000 to 226,000 people in Hiroshima and Nagasaki, in 1945.

Teller told us, a group of students and software engineers, over coffee after the talk, “We have a choice: we can create or destroy, that we can control. Pandora’s box is open. We cannot put the missiles back. We can only hope it does not fall in evil hands.” After Teller’s workshop, all I wanted was to get my hands on physics and quantum theory books. I was inspired to participate in something in the larger scheme of positive energy within my reach.

Days after the lecture, I visited my favorite bookstore in Coral Gables, Florida, which sold used books, collectibles, etc. Upon entering, I noticed a comprehensive book on the artist Francis Bacon (1909–1991), titled Francis Bacon: Catalogue Raisonné and Documentation (1964) by Ronald Alley [3]. I opened the book and saw that this copy was signed by Bacon. I looked at some of the pictures of human figures in curved empty rooms and thought, Could these macabre images represent the initial physics of a thermonuclear blast rushing into flesh at 200 mph [4], as Teller discussed? I was shocked! (I also wondered, Where do you hang such disturbing art?)

I started thinking about being a painter. I was also motivated to explore computers and what software to use in order to make art with complex geometry as the subject matter.

My challenge was to learn FORTRAN 77, known as the IBM Mathematical Formula Translation System and used for many applications, including complex mathematics and geometry. It was very difficult at the beginning. I studied roughly eight hours a day for more than three weeks. With time, it started to sink in.

In 1984, mathematician and software engineer Neal Atkins, geometer and artist Enrique Castro-Cid, and I wanted to place a simple 3D drawing, called The Leonardo Room after Leonardo da Vinci’s Last Supper 1498, into a four-dimensional non-Euclidean geometry using conformal mapping w = z + 1/z transformation, the Cray X-MP supercomputer, and FORTRAN 77 [5]. What we witnessed hours later was astonishing. The Leonardo Room was transformed into an interpretation of Einstein’s general and special relativity in a non-Euclidean geometry, resulting in an atomic wave singularity blast where the white and red tile floor entangled with the receding blue wall, sending the red-and-blue singularity out to infinity to crush any matter in its path at the speed of light (Fig. 1a).

My drawing The Leonardo Room visually represents a link between the curvature of spacetime in general relativity and Bacon’s pictorial environments of curved rooms with distortions of human models that I had seen in Alley’s Catalog Raisonné.

I was very motivated in studying Bacon’s artwork. I had obtained 35mm slides of Bacon’s Pope 1953 painting and other works from the Museum of Modern Art in New York, and I would enlarge these on the wall with a slide projector. I observed the phenomenon of a complex mathematical design structure that I could relate to the Italian mathematician Eugenio Beltrami, such that curved lines might seem straight while spherical topology seemed flat [6]. His notion was groundbreaking in the new geometries, creating one of the first hyperbolic non-Euclidean models, the pseudosphere (Color Plate C[b]). The Beltrami metric also provided an inertial framework for Einstein’s conception of 4D spacetime in general relativity on effects of gravity and inertial force. Instead of pure gravity in Euclidean 3D such as we experience in the real world, in the Beltrami pseudosphere model I witnessed a geometric tractrix curve in blue and pink (Color Plate C[a]) and a geodesic in blue (Color Plate C[b]) in the iconic Bacon painting. The pseudosphere hyperbolic model fits perfectly inside Bacon’s Pope 1953 [7], possibly making it one of modern art’s first non-Euclidean geometry artifacts (Color Plate C).

While finalizing my dissertation in 1985, I met Francis Bacon in London. He invited me to visit his 7 Reece Mews studio, asking me to bring all the materials of my thesis, “Painting Next to Zero.” I showed him drawings I created with the mathematical models in the non-Euclidean geometry using human figures in caged rooms entangled in 4D transformational grids. I told him about mathematical art representation (MAR), a term I coined, used in conformal mapping where space maps z = (x,y) into another space w = (u,v), and each coordinate z = space (real) mapped into the w = space (imaginary) [8]. It was w = z + 1/z conformal mapping transformation that reflected Bacon’s aesthetic deformations.

Bacon understood and praised the flow of the mathematical grid geometry within the composition—most important to me was how he saw these new 4D computer representations as affirmations of his distorted rooms and twisted, spasm-afflicted bodies and faces. He looked through the materials for about 35 minutes at a nerve-wrackingly slow pace, then the mathematical diagrams along with my paintings for another 25 minutes, while whispering and mumbling to himself. He lashed out rudely, dismissing the math as fine for schoolwork, then quickly became silent. “What academics do is they put you in a box just like that,” he finally said.

Bacon proceeded by painting on my 8-×-11-inch spiral notebook. He appeared to be agitated. I was scared he was going to rip up all my thesis diagrams—he had a reputation for slashing canvases with a knife when fed up with them. “This is how I do it,” he said. “I am in the real, the real is what I paint, not academic shit.” He started with black markings composing a sitting figure in a cage room, as he explained. I told him I really loved the portraits he made in the 1960s, how he twisted and stretched the topology of the eyes and sockets and interconnected at times the jaw with a shoulder and parts of the room, a technique and style he used in most triptychs of that time. Mumbling to himself again, he moved to another spiral sheet, the first image in the lesson triptych. He swirled black paint around, interlacing thick gestural markings of infinite space crammed into finite space similar to the supercomputer model plotting out coordinates onto a non-Euclidean 4D space.

Bacon completed the triptych by painting it in sky-blue and yellow-orange washes, hues that had become his palette of colors in triptychs and paintings of the 1970s and 1980s. He gave me the artifacts on paper and said, “Here’s your lesson.” I was speechless! What took the supercomputer hours to plot—a Leonardo-Bacon room with a female nude, and about 30,000 coordinates in conformal mapping—Bacon manifested as a triptych in less than 20 minutes. Moreover, I saw Einstein’s special relativity, how the speed of light can bend energy and mass in spacetime, in the way Bacon bowed the yellow floor in the triptych like a reed. Francis made it clear that the 3D Cartesian plane room in panel 2 in the triptych represented “gravity” curved in general relativity in a 4D non-Euclidean geometry, formulating pictorially in the art piece the one-toone unity of the real and imaginary complex plane that Einstein was dreaming of in a simple projection, like a child’s stick drawing for a theory of everything.

Looking back many years later, my mentor Edward Teller inspired me to use the same knowledge of electromagnetism to create, not destroy. The knowledge of the H-bomb can destroy the planet, and maybe the consciousness of art can save the planet. It was Francis Bacon who freed me from the linear obsession of the limited software mentality of the 1980s, allowing me to release myself from the box and just create using my surroundings as elements and putting them into my work (Fig. 2). “If the geometric grid works, use it,” Bacon said.

geodesics

the shortest line between two points that lies in a given surface.

non-Euclidean geometry

used to state the theory of relativity, where space is curved. The measurement of the distances, areas, angles of different parts of the earth is done with the help of non-Euclidean geometry.

pseudosphere

a surface of constant Gaussian negative curvature.

tractrix

a curve in which the part of the tangent between the point of tangency and a given straight line is constant and which is an involute of a catenary.