An Object Without Dimensions

A small boy walks past the tower of the Garrison Church in Potsdam. Up on its gallery there are people. He takes them for little dolls and asks his mother to reach them down for him, believing, as he later put it, that she could do it by stretching out her arm.

The boy was Hermann von Helmholtz, and he did not tell the story in a memoir. He put it in section 30 of his Handbook of Physiological Optics (the complete edition appeared in 1867), in the middle of an explanation of how we judge the distance of things. "The incident stuck in my memory," he wrote, "because my mistake made the law of perspective diminution clear to me."

The argument around it is plain. A distant object casts a smaller image on the retina; if we know how big the object is, the smallness tells us how far away it is. But the relation between size and distance has to be learned "through long experience", Helmholtz says, which is why children get it badly wrong. The most reliable markers in a landscape are people and domestic animals: they are easy to pick out because they move, they vary little in size, and their size "is very well known to us". For the same reason, he adds, painters put staffage, small figures of people and cattle, into their landscapes, so that the size of what is painted can be read at all. The human figure is the yardstick of the visible world.

In 1947 Alberto Giacometti owed his New York dealer, Pierre Matisse, a list of sculptures for an exhibition. He wrote that he could not make the list without including, "though very briefly", a certain chain of events, or it would make no sense. The letter, typed, corrected by hand and full of sketches, appeared in the catalogue of the January 1948 show; the Museum of Modern Art reprinted it in facsimile, with an English translation, in 1965. That facsimile is what we read.

The chain of events is the story of a yardstick breaking. In Rome in 1920–21 the model's head "became like a cloud, vague and undefined". At the academy in Paris everyone worked too close to the model; start with the tip of the nose and you were lost, "the distance between one wing of the nose and the other is like the Sahara, without end, nothing to fix one's gaze upon, everything escapes". From 1935 to 1940 he worked from a model all day, and "a head", he wrote, "became for me an object completely unknown and without dimensions" (un objet totalement inconnu et sans dimensions).

Then he went back to working from memory. "But wanting to create from memory what I had seen, to my terror the sculptures became smaller and smaller, they had a likeness only when they were small, yet their dimensions revolted me." He would start again and, months later, end up at the same point. Sometimes the figures got so small that one last touch of the knife turned them to dust, and yet "head and figures seemed to me to have a bit of truth only when small". According to the chronology in the 1965 catalogue, when he left Switzerland in 1945 his work of those years was said to fit into six matchboxes. Drawing changed things a little that year: the figures grew, but now they looked like someone only when they were "tall and slender". In the margin of these lines he sketched tiny figures standing on bases far bigger than themselves. The letter ends: "And now I stop, besides they are closing, I must pay."

Put side by side, the two texts turn each other inside out. For Helmholtz the size of a person is the surest thing we have to go on. For Giacometti, after five years of looking at one, it is precisely the human head that has lost its dimensions. The child sees people small because he has not yet learned; the sculptor, who has learned everything, can only make them true when they are small. And memory is involved both times. Helmholtz's mistake stayed in his memory and taught him a law; for Giacometti it was working from memory that made the figures shrink.

One detail is worth holding on to. In the typed text of the 1947 letter, the word distance appears exactly once, and it is the distance between the two sides of a nose. Giacometti says nothing here about a figure seen far away, which would reduce it all to Helmholtz's perspective. What he says is "to create from memory what I had seen". Reading the figures through distance came later, and it is a fair reading: in the 1965 catalogue Peter Selz wrote that Giacometti was trying to render precisely what he sees at a given distance, about nine feet. But in the letter, memory comes before distance.

To be precise about what links these pages: we do not know whether Giacometti ever read Helmholtz, and no document we know of suggests it. This is an independent similarity, and the pairing is ours. Giacometti's relation to perception has been written about endlessly, starting with the Sartre essay that introduced the same 1948 catalogue; Helmholtz's Potsdam memory is a familiar example in the history of perceptual psychology.

What the pairing suggests is not comfortable. If Helmholtz is right, we never quite see the size of a person; we largely infer it, because we already know it. But the two pages do not describe the same experience. To the boy in Potsdam, apparent size lied, and knowledge later corrected the mistake. For the sculptor in Paris something earlier seems to give way: the very possibility of giving a measure to the head in front of him. Whether the two belong together we cannot say, and we do not try to settle it here. The first of them got a law out of his mistake. The second got years of figures a few centimetres high, like little dolls you could reach down by stretching out your arm.

When we remember someone, how big are they?