Response to a German Mathematician (1991)

Yes, titles have held a certain importance for me, and they have done so in fairly different ways.

To put it broadly, in the fifties, sixties, and seventies, the titles were there to give the principle, the rules of the game, of the work. They were meant, ideally, to allow the reader to

re-create the piece if he so desired. Therefore they contained the principal subjective decisions that I had made (and were rounded out by a note of the dimensions and technique). They did not call on especially evolved mathematical notions. For instance, Superposition d’une trame 0° et d’une trame 20°: in my language, trame meant a network of parallel lines, and 0˚ and 20˚ were the measures of inclination of those lines in relation to the horizontal axis.

For a dozen years or so now, my titles, while they remain descriptive, are meant rather to be derisory and humorous. For instance, Géométree signifies the marriage of a geometric system with the lines of a tree branch.

I think that, in order to avoid any misunderstanding, I should clarify more generally my position with respect to mathematics and the use of “random systems.”

My position, for forty years, has been to oppose myself to the conventional practice of painters and sculptors whose every work is composed by thousands of subjective decisions and manual imprecisions.

I therefore wanted my works to be precisely conceived and realized in a neutral manner (this attitude having been expressed already by Van Doesburg, well before the war). All of this was to reduce the number of my subjective decisions.

If I have long preferred the square to the rectangle, it is because it requires only one subjective decision in order to be defined. It is for the same reason that I have preferred the straight line to the broken line, etc.

In the sixties, I was exhausted by a certain classical and balanced constructivism. So I looked for a system whose (unpredictable) results could be chaotic, or at the very least close to a Minimalist Baroque aesthetic that I found attractive. So I imagined the possibility of having those subjective decisions I could not anticipate be made by a (simple) set of rules that would use some existing set of digits (numbers from a telephone directory or the digits of π, for instance).

The works obtained in this manner were, frankly, parodies of Baroque or Expressionist paintings. As always, each result was considerably less important than the system itself. And the system, for its part, was magnified even further because it ironically took the place of the traditional abstract painter’s empirical and instinctive genius.

So those are some clarifications that may perhaps disappoint you, but after all I am only a devotee of frivolous mathematics and absurd logic.