A tango of two squares

In 1974, Vera Molnár went to the Centre de Calcul Universitaire at Orsay and used the university's computers to make two squares dance. Twenty-two years later the result was published as an artist's book — 202 pages, orange linen boards, a format so wide it barely fits on a shelf. It is called Tango 74, and a copy is in the collection.

What makes the book worth writing about is not only the plates. It is the short text Molnár wrote to accompany them, dated Le Home-sur-Mer, été 1995, which spends its first paragraph refusing to tell you that the subject is geometry at all.

Deux êtres sont face à face. Se regardent-ils ?

Two beings stand face to face. Are they looking at one another?

They approach, stop, draw back, come forward again. Their movements are calm and smooth, and she notes — this is the tell — that on pourrait les transcrire par des lignes droites: you could transcribe them as straight lines. Then they leap, embrace, pass through one another. The pure straight lines, she writes, font place aux courbes convulsives — give way to convulsive curves. It pitches back and forth entre intellectuel et érotique, ascèse et déchaînement, entre Apollon et Dionysos: between the intellectual and the erotic, asceticism and abandon, Apollo and Dionysus.

Only in the second paragraph does she say it plainly: les deux êtres sont, en réalité, deux carrés. The two beings are, in fact, two squares.

The description that follows is a specification. Eight vertices, each moving in its own way, mostly left and right and only slightly up and down. The squares leave behind their vieilles peaux de carrés, their old square skins, and muent — the word for an animal shedding, a bird moulting — into quadrilaterals. Then the vertices stop being joined by straight lines and are joined instead by segments de paraboles, d'hyperboles ou de folles sinusoïdes: parabolas, hyperbolas, wild sinusoids. The stretching happens across the width, en x, beaucoup moins en y — and that asymmetry, she says, is what produces comme un tango de deux carrés.

That is a remarkable piece of writing about one's own algorithm. It is a parameter list and a description of two bodies on a dance floor, and they are the same list. She wanted it to work, borrowing Anne Tronche's terms, "à la manière d'un rébus, d'un commentaire, ou d'une traduction" — in the manner of a rebus, a commentary, or a translation — entre géométrie et rêve, between geometry and dream.

Then comes the postscript, which is the best thing in the book:

P.S. Cet ouvrage, peu sérieux, échappant à ma plume, a été réalisé sur les ordinateurs préhistoriques du Centre de Calcul Universitaire à Orsay, en 1974.

This work, not a very serious one, which escaped from my pen, was made on the prehistoric computers of the Centre de Calcul Universitaire at Orsay, in 1974.

She had been at Orsay for six years by then, and had got in sideways. Her machine imaginaire — the algorithms she executed by hand through the 1960s, having no other way — became a real machine in 1968, when her friend the algorithmic composer Pierre Barbaud opened a door to the university's computing centre. She worked there unofficially, clandestinely as she put it, mostly evenings and weekends, renting time on the machine by the minute alongside the scientists. She has described the department head's reaction to her request as a look suggesting he was weighing up whether to call for a nurse to sedate her. He let her in anyway.

She goes on to thank the institute's director of the day for letting her run Tango at all — a piece, as she puts it, aux antipodes des pratiques de cet institut à vocation scientifique pure et dure: at the very antipodes of the practices of an institution devoted to pure and hard science.

Two things in one sentence. "Prehistoric computers" — written in 1995 about machines from 1974, by someone who had been programming since 1968 and knew exactly how fast the ground was moving under her. And the thanks to a director who let an artist onto a serious scientific installation to make squares tango. Nearly every early computer artwork has a version of that person somewhere behind it: someone with authority over a machine who decided that this counted as a legitimate use of it. They are almost never named. Molnár, twenty-one years later, still wanted to say thank you.

The book is catalogued here: Tango 74, 1996 — with photographs of the cover, the tracing-paper title leaf, and the plates.