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The Infinite and Its Demise in Art and Science
Arthur Chandler

San Francisco State University

In Western culture, and in no other before the twentieth century, the belief in infinite space was the basic assumption behind every visual and scientific image of the structure of reality. In painting, perspective gave coherence to every work by placing all acts, sacred and profane, within a rigidly mathematical system of converging lines that met on the horizon at infinity. 

 Hans Vredeman de Vries,  The Book of Perspective  (1604-1605)   

Hans Vredeman de Vries, The Book of Perspective (1604-1605)


In physics, the Newtonian calculus was applied to immovable, infinite space in order to discover the basic laws that govern reality. Physicists employecd calculus measure “instantaneous rates of change” by transforming time into a point-value in the motionless grid of the Cartesian coordinate plane.

Both artists and scientists searched for a world of motionless perfection, a world where space triumphs over time. Motion thereby was entirely subordinated to space. Time was frozen into a moment of instantaneous eternity: the single, significant, universal act that epitomized the very essence of the event translated into a pictorial or numerical image. In painting, time was transmuted into space by stopping the Significant Instant within a grid of perspective space: an arm pointed heavenward to indicate the world of ideas, an arm extended forward to emphasize the importance of ethical principles brought to bear in human interaction. 

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The concept of absolute space appealed so deeply to the Western spirit that a number of thinkers equated the infinite with God. Isaac Newton and his contemporary Samuel Clarke wrote of infinite space as the sensorium of God – that is, the place where the universe was perceived simultaneously and everywhere by the Divine Presence. Henry More, the Cambridge Platonist , also ascribed the same attributes to infinite space as to God; and since there could not be two infinities, in his view, God and infinite space are One and the Same.

The deification of the infinite continued down to the nineteenth century. Kant had called infinite space the “receptacle of the Divine Presence,” and called on the “a priori validity” of Euclidean geometry to justify the innate knowledge of God in space. But there were new visions of space germinating in the minds of thinkers and painters alike that would end the reign of infinity. And by the second quarter of the twentieth century, the absolute supremacy – and therefore the divinity – of infinite space was ended.

At the end of the nineteenth and the beginning of the twentieth centuries, both painting and physics underwent revolutions so cataclysmic that the fundamental structures of both enterprises were completely altered. In physics, infinite space gave way to the vision of the universe as a finite and unbounded (like the surface of a sphere) field of space-time. This field is not a godlike matrix of all activity like its predecessor, absolute space. Instead, the field is conceived of as an energy condition of space in time, and is utterly dependent – as absolute space was not – upon the distribution of matter within it. Furthermore, the new universal field is not “straight” (Euclidean) like Newtonian space or the space of perspective painting. It is a “manifold” of constant positive curvatures (Euclidean space would have zero curvature), in which there are no straight lines, and in which there is no overall simultaneity of events (as there was with Newtonian space). And in the place of the divinity of Absolute Space, there is the new absolute of the Velocity of Light.

The Cubists were the first to explore the plastic equivalent of the space-time of physics. A scene was viewed from several different viewpoints, reduced to its most basic geometric components, then rendered as a simultaneous whole on canvas. Some artists, like the Futurists, experimented with a kind of chronometric succession of events, in which multiple outlines of a subject were superimposed, one after another, to give the impression of movement:

 Giacomo Balla, "Dynamism of a Dog on a Leash" (1912)

Giacomo Balla, "Dynamism of a Dog on a Leash" (1912)

 Umberto Boccioni, "Unique Forms of Continuity in Space" (1913)

Umberto Boccioni, "Unique Forms of Continuity in Space" (1913)

But it soon became apparent that painting, in spite of its bold venture into space-time, was in fact still addicted to volume and the old formula of art as “the imitation of nature.” During the second decade of the twentieth century, though, Piet Mondrian took the decisive step toward evolving a new kind of painting that would derive its principles not from the observed appearances of reality, but from the intrinsic properties of painting itself. Just as the physicists had been forced to abandon absolute space for the field determined by the space-time properties of matter-in-space-and-time, so Mondrian treated the canvas not as a stage for imitation, but as a field in which the mutual interdependence of plastic elements – the primary colors plus black and white, the rectangular opposition of the horizontal and vertical position, and the balanced relationships of equilibrium among them – controls the final image of reality that lies behind appearance and makes up the essence of the true composition.

 Mondrian, "Composition " (1921)

Mondrian, "Composition " (1921)

Mondrian developed his ideal of an absolute law of plastic form by destroying the old canons of the Significant Instant frozen in optical space, which he felt were alien to the essence of pictorial space. But Jackson Pollock  comes even closer to the Einstein-Minkowski formulation of a dynamic field of space-time with his “action” paintings, in which pictorial forms emerge as a result of the inherent properties of paint in motion. And though his technique was often denounced as a kind of resurrected Dada charlatanism, there is no question but that his works better incorporate the dynamics of time into the building up of the pictorial image than did the early Cubist compositions, with their labored superimposition of static forms.

 Jackson Pollock, "Lavender Mist" (1950)

Jackson Pollock, "Lavender Mist" (1950)

In spite of the radical efforts of Mondrian and Pollock to show forth a logic of painting independent of visible reality, neither painter – nor any other – succeeded in replacing the universality of perspective with his own system. The physicists were successful in replacing the old absolute space with the new vision of curved space-time. But painters only proliferated one subjective system after another, and no one invented or discovered a universally persuasive vision of the structure of reality.

Why did physics succeed where painting failed? Because the world picture of physics is essentially abstract, and can be grounded in any coherent system that is amenable to mathematical treatment and produces integrated results. Painting, though, seems by its very nature incapable of incorporating the actualities of fluid time into its domain. All attempts to “temporize” painting – Cubism, Rayonism, Futurism, Action Painting – have resulted in motionless images that do not capture the continuous succession of events. The four-dimensionality of space-time cannot be rendered, except schematically and by implication, in a still, two-dimensional medium. What was required for the visual arts to match the new paradigm of space-time was a visual medium that could portray time on an equal basis with space, and which could command enough unity of technique among its practitioners so that its audience could learn a new way of seeing. And the new medium with the most inherent promise of fulfilling this mission was film.


In most respects, film seems to a be a hybrid of drama and painting. Scenes are usually rendered spatially along Renaissance lines, with normal lenses for “true” perspective. But it is not the scenes themselves but their movement from one sequence to another – the cuts, dissolves, and fades – that are both cause and effect of genuine changes in our habits of perception. After only a century, all cultures in the world have learned to shift, in a fraction of a second, from one scene to another, one time to another, one emotional set to another, no matter how near or far apart they might be from one another. One of the most striking examples of this kind of quantum jump in perception occurs in the famous jump-cut in Stanley Kubrick’s 2001: A Space Odyssey , when the man-ape flings his bone club into the air, where its slow motion spinning suddenly transforms into the majestic flight of a spacecraft through the void. The leap of hundreds of thousands of years and thousands of miles, from earth to outer space, from an exultation of blood-lust to a cosmic “machine-ballet” – all combine to furnish a stunning example of a visual technique unavailable to painters and dramatists. These instantaneous quantum-jump movements, those less dramatic than Kubrick’s, occur on an average of every few seconds in a television detective thriller. And yet our culture is so thoroughly acclimated to these blitzing changes that a film without frequent cuts, fades, and dissolves seems intolerably boring.

 Stanley Kubrick,  2001: A Space Odyssey  (1968)

Stanley Kubrick, 2001: A Space Odyssey (1968)

Before the twentieth century, space and time were seen and treated as separate parts of reality; and there were arts that dealt with one or the other part exclusively or predominately. But as the twentieth century progressed, space-time was seen more and more as the defining unity of reality; and the arts, along with all other branches of human endeavor, had to incorporate and express this unity. So music, the traditional art of time-shaping, has been exploring the spatial characteristics of time (including the phenomenon of the mobile listener). Sculpture, formerly an art of absolute immobility, has been exploring the mutations of time, in which the movements of the molded body alter its shape and give it temporal direction.

But painting seems, at this point, to be locked into a purely spatial system of representation. No one has yet proposed a system that can incorporate the dynamic of the space-time field into painting and command universal assent from audience and painters alike. If the situation is endemic, painting, like mosaic, will recede as a major art of the culture. Films, its successor, found the paradigm it needed, and has succeeded in effecting a qualitative change in the habits of thought and vision of the whole world.


— published in magazine, fall 1984