Miraculous Mathematics: André Bazin’s Film Theory

André Bazin’s film theory is filled with scientific metaphors based on his secular education between 1933 and 1938 in La Rochelle at the École Normale d’Instituteurs. There, he excelled in a wide range of subjects such as biology, physics, chemistry, and, of course, mathematics. Inasmuch as Bazin’s handling of art and religion deeply shaped his film theory, in this essay I shall limit myself to his use of algebra, arithmetic, calculus, and analytic geometry to acknowledge his debt to Henri Bergson’s philosophy, discuss his views on Henri-Georges Clouzot’s policier Les Diaboliques (1955), and explain his admiration for Vittorio De Sica’s early neorealist films such as The Bicycle Thief (1948), Miracle in Milan (1951), and Umberto D. (1952). My own discovery is that Bazin’s mathematical references from calculus and analytic geometry throw light on the radical nature of Bazin’s neorealism as a “revolutionary humanism.”¹ Its openness toward fantasy, ambiguity, and contingency is worth examining in detail. Due to Bazin’s penchant for paradoxes, my rereading of De Sica’s early neorealism will show that miracles and mathematics interrogate each other in the context of a daily life open to childlike wonder, self-questioning, and social consciousness.

From Biology to Mathematics

The scientific discipline of biology studies everything that is alive and enables new life. Biology also looks at human beings with the same detached attitude usually reserved for the study of animals or plants. By so doing, it aligns itself with the indifferent look of the camera’s nonhuman eye or lens, which can only see the world from the outside and equalizes everything it intercepts. Due to his passion for biology—the science of life—Bazin had little use for the static tendencies of ancient mathematics based on Euclidean geometry in a timeless space. Bazin upheld a Bergsonian preference for the temporality of modern mathematics through calculus, a method of computation that was originally developed by Isaac Newton and Gottfried Wilhelm Leibniz. In Creative Evolution (1907), Bergson wrote:

We believe that if biology could ever get as close to its object as mathematics does to its own, it would become, to the physics and chemistry of organized bodies, what the mathematics of the moderns have proved to be in relation to ancient geometry. The wholly superficial displacement of masses and molecules studied in physics and chemistry would become, in relation to that inner vital movement (which is transformation and not translation) what the position of the moving object is to the movement of that object in space.²

Here Bergson compares biology’s contingencies to calculus’s handling of motion because of his interest in the “creative evolution” of dynamic and organic wholes over static and interchangeable parts. Bazin extends Bergson’s analogy between biology and calculus to his conception of cinema as a spatiotemporal modeling system based on automatism and randomness. The philosopher’s turn-of-the-century work had the most influence on Bazin even though it preceded the popularization of quantum physics in the 1920s and 1930s, of which the film theorist was deeply aware. In his introduction to Bergson and Modern Thought (1987), Andrew C. Papanicolaou points out that Bergson’s

matter should be viewed as comprised of “modifications, perturbations, changes of tension or of energy, and nothing else.” In such a world . . . energies are pulsational (quantized), entries cease to be simply located (and gain wave characteristics) and indetermination becomes a fundamental feature of micro-events. (Bergson in fact urged physical scientists to look for measurable indetermination in physical nature.) It is thus, as physicist Louis de Broglie pointed out, no exaggeration to hold that in Bergson we find Heisenberg before Heisenberg, Bohr before Bohr.³

Papanicolaou’s history of science, with the French Catholic physicist Louis de Broglie between Bergson and the Danish School of Heisenberg and Bohr, fits with how Bazin included randomness and indeterminacy in his definition of modernity. Bazin’s modernity is a postwar sensibility rather than a historical period limited to the modernism of early twentieth-century avant-garde movements. His alignment with the...