In the essay A. and Pangeometry El Lissitzky analyses the changing role of perspective in art and introduces axonometric projection (or parallel perspective) as a new means to represent and perceive space. It was first published in German in Europa-Almanach, (Carl Einstein and Paul Westheim, Kiepenheuer Verlag, Potsdam, 1925, p.103-113) and was reprinted in 1984.
This English translation was published in the book El Lissitzky. Life – Letters – Texts, Lissitzky-Küppers, Thames & Hudson, London, 1992 (out of print). The blog The Detached Gaze posted it a few months back.
NOTE: Abbreviations: A. = art, F. = form.
Art and pangeometry
Seeing, of course, is also an A.
In the period between 1918 and 1921, a lot of old rubbish was destroyed. In Russia we also dragged A. off its sacred throne “and spat on its altar” (Malevich 1915). At the first Dada-event in Zurich, A. was defined as “magical excrement” and man as the “measure of all tailors” (Arp).
Now after five years (five centuries in the old chronology) in Germany for example, Grosz brings only one reproach upon himself: “our only fault was that we ever took the so-called A. at all seriously.” But a few lines further on he writes: “Whether my work is therefore called A. depends on the question of whether one believes that the future belongs to the working classes.” I am convinced that it does, but neither this conviction nor the excrement and the tailors are universal criteria for A.
A. is a graduated glass. Every era pours in a certain quantity: for example, one puts 5 cm of Coty perfume, to titillate the nostrils of fashionable society: another throws 10 cm of sulphuric acid into the face of the ruling class; yet another pours in 15 cm of some kind of metallic solution which afterwards flares up as a new source of light. So A. is an invention of our spirit, a complex whole, combining the rational with the imaginary, the physical with the mathematical, √1 with √-1. The series of analogies which I am going to bring to your attention is put forward not to prove — for the works themselves are there for that — but to clarify my views. The parallels between A. and mathematics must be drawn very carefully, for every time they overlap it is fatal for A.
Plastic F. begins, like elementary arithmetic, with counting. Its space is the physical two-dimensional flat plane. Its rhythm — the elementary harmony of the natural numerical progression 1, 2, 3, 4, …
Man compares the newly-created object  — for example, the relief, the fresco — with natural objects. If, for example, in a relief, the animal in front covers a part of the animal behind, this does not mean that that part has ceased to exist, but that there is a distance, space, existing between these two bodies.
One comes to know from experience that there is a distance existing between individual objects, that the objects exist in space. This two-dimensional plane ceases to be just a flat surface. The plane begins to presume upon space and there arises the numerical progression, 1, 1½, 2, 2½ …
The space of the plane developing into view lengthens and widens, increases to a new system, which finds its expression in perspective. It is generally accepted that perspective representation is the clear, objective, obvious way to represent space. It is said that, after all, the camera also works perspectivally and at the same time one is forgetting that the Chinese once built the object-lens with concave instead of convex lenses as we have, and so would also have produced an objective and mechanical image of the world, yet quite a different one. Perspective has comprehended space according to the concept of Euclidean geometry as a constant three-dimensional state. It has fitted the world into a cube, which it has transformed in such a way that in the plane it appears as a pyramid.  The tip of this visual pyramid either lies in our eyes — therefore in front of the object — or we project it on to the horizon — behind the object. The former concept was chosen by the East, the latter by the West.
Perspective defined space and made it finite, then enclosed it; but the “universal set”  of art became richer. Planimetric space provided us with the arithmetical progression. There the objects stood in the relation: 1, 2, 3, 4, 5…In perspective space we acquired a new geometric progression; here the objects stand in a relation: 1, 2, 4, 8, 16, 32… Up to the present time the “universal set” of A. has acquired no new enrichment. In the meantime science undertook fundamental reconstructions. The geocentric Ptolemaic conception of the universe was replaced by the heliocentric system of Copernicus. The Euclidean conception of fixed space was destroyed by Lobatschewski, Gauss, and Riemann. The impressionists were the first to begin exploding the hereditary notion of perspectival space. The cubist method was more decisive. They transposed the space-confining horizon to the foreground and identified it with the area being painted. They made improvements to this fixed area through psychic features (walls covered with wallpaper and so on) and by destroying some elementary forms. They built from the perspective plane forward into space. The latest sequels are: the reliefs by Picasso and counter-reliefs by Tatlin. Continue reading