Computer Art and the Theory of Computation: Chapter 2: Greenberg, Modernism, Computation and Computer Art

In a short but influential piece of writing by Clement Greenberg called Modernist Painting written in 1960—and revised periodically until 1982—the art critic remarked that “The essence of Modernism lies, as I see it, in the use of characteristic methods of a discipline to criticize the discipline itself, not in order to subvert it but in order to entrench it more firmly in its area of competence.” Such sweeping generalizations are always problematical, of course. But I want to use the Greenberg quote to tell you an equally problematical story about the birth of the theory of computation and, thereby, computer art. Humor me. It’s Clement Greenberg. Come on.

The work I’ve mentioned by Gödel and Turing happened in the thirties, toward the end of modernism, which was roughly from 1900 till 1945, the end of World War II. So it’s work of late modernism.

Let’s grant Greenberg clemency concerning his conceit, for the moment, that the “essence”—itself a word left over from previous eras—of modernism, of the art and culture of that era, at least in the west, involved a drive to a kind of productive self-referentiality or consciousness of the art itself within the art itself. What work could possibly be more exemplary of that inclination than the work by Gödel and Turing that I’ve mentioned?

Turing’s paper in which he invents the modern computer and solves the Entscheidungsproblem is profoundly meta-mathematical; the Entscheidungsproblem, as already noted, is a problem of meta-mathematics. And its argument also involves interesting self-referenciality, as is pointed out in :

“Turing’s proof can be recast in many ways, but the core idea depends on the self-reference involved in a machine operating on symbols, which is itself described by symbols and so can operate on its own description.”

Self-reference is crucial also to Godel’s proof in which, among other things, the proposition “This proposition is not provable” is shown to be necessarily true but, yes, unprovable, and exemplary of a kind of proposition which Godel calls “undecidable”. Self-reference is an implicit mode of meta-mathematics because mathematics/logic is used to inquire into the nature or properties of mathematics/logic, though that doesn’t need to be any more deeply self-referential than using language to inquire into the properties of language; what else are you gonna use? Your big toe? I don’t think so.

So we can see the work of Godel and Turing as a kind of profound culmination of modernism’s “use of characteristic methods of a discipline to criticize the discipline itself”. Greenberg sees modernism as involving a meta mode of art and thought, this growing self-critical, self-aware tendency in art. Modernism culminates in the work of Godel and Turing and the consequent development of the computer, a machine that operates, as it were, at the atomic level of thought. The culmination of that self-critical, self-aware meta mode of modernism in which the work of art is aware of itself, in a sense, is the creation of a type of machine that may indeed quite literally possess the capability of becoming self-aware.

The computer age and, of course, computer art commences at the end of the modern era, signalled by the end of a world war, the invention of the theory of computation, and the atomic bomb, an understanding of the fierce chemistry of the atom, the utterly micro, at the level of the chemistry of the sun, of Apollo, of Ra, the yay very large. Looking inward and looking outward.

That knowledge of the sun’s chemistry and its harnessing in the creation of the atomic bomb does indeed reveal important things about our own nature, but the whole subject is not centrally about humans and human capacities. Whereas the theory of computation is a theory inaugurated by Turing as very explicitly being about human capacities. Recall that the Entscheidungsproblem, or the decision problem, was to demonstrate the existence or non-existence of an algorithm that would decide the truth or falsity of any mathematical/logical proposition. A large part of the difficulty of this problem was in coming to the best possible formulation of what we mean by “algorithm”. As we read at :

“Turing’s purpose was to embody the most general mechanical process as carried out by a human being. His analysis began not with any existing computing machines, but with the picture of a child’s exercise book marked off in squares. From the beginning, the Turing machine concept aimed to capture what the human mind can do when carrying out a procedure.”

From the start, the whole project of computing has been about us. And involves abstracting the process of thought into its constituent atoms, as it were. Computer art, a new form of art, goes beyond Greenberg’s meta imperative into an art that could possibly create works in which the objects do actually think. And do actually create art. The human as the meta artist; the program as the artist. A situation where, no, art is not over and the only serious artistic work left is meta art, but the liveliness and self-consciousness of the object envisioned in Greenberg’s vision of modernism is taken to the next level in the age of computers.


Here are links to the blog posts, so far, in Computer Art and the Theory of Computation:

Chapter 1: The Blooming
Chapter 2: Greenberg, Modernism, Computation and Computer Art
Chapter 3: Programmability
Chapter X: Evolution and the Universal Machine

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