Authors: Hugh Aldersey-Williams
Vitruvius’s scheme enabled all the major features of the human form to be described in terms of simple ratios of just a few small numbers. Four digits made a palm and six palms a cubit. The height of a man was four cubits or six feet. By means of some elaborate argument, Vitruvius even managed to suggest that ‘numbers had their origin from the human body’. Today, we might sceptically observe the tricks by which Vitruvius has contrived his elegant system, picking human features to suit his ratios rather than those anybody might use – the underside of the nostrils rather than the tip of the nose, the eyebrows rather than the eyes, and so on.
Vitruvius goes on to explain that the navel is ‘naturally placed at the centre of the human body’, and that a circle drawn about that centre on a man with his arms and legs outstretched will touch both his fingers and his toes. Similarly, he writes, the arms at their full horizontal extent span four cubits, the same as the height, so that a square can also be drawn around the body. Both of these shapes – the circle and the square – were symbolically important in the design of temples because of their geometric purity, and it was important to connect them with the human figure in order to demonstrate its divine proportion.
Vitruvius left no illustration to accompany his detailed text. While several artists contributed illustrations to editions of
published in the sixteenth century, they had trouble reconciling all of Vitruvius’s required elements – the man’s dimensions, the square and the circle. Assuming that the square and the circle must be concentric, they were forced to distort the human figure to fit them both. It was only Leonardo da Vinci who was able to reconcile all of the Roman architect’s precepts in a single harmonious design.
Leonardo was probably the first artist to cut up the human body and draw what he saw. He boasted of dissecting more than ten bodies, proceeding in stages as each body gradually decayed, and repeating the whole exercise in order to gain an appreciation of the typical differences between one body and another. He described the experience in his notebooks, thrilling his readers with his account of spending ‘the night hours in the company of these corpses, quartered and flayed and horrible to behold’.
The genius of Leonardo’s solution was to take the truth of the human form as his ultimate guide and make the geometry fit around that. So he simply superimposed the standing man in the square on top of the man with limbs outspread in the circle, a delightful resolution in which the twin sets of limbs even bring a suggestion of human animation. The result is that both the square and the circle touch the ground. The figure inscribed in the circle has his navel at the centre, as Vitruvius demands, but as the centre of the square now lies lower than the centre of the circle, this coincides not with the navel but, significantly, with the genitals. Here, then, is the human figure: progenitor and progeny, creator and creation. It’s undeniably neat. But is it true? After all, why should the body be describable in terms of simple numerical ratios?
Late in his career, the twentieth-century Swiss architect Le Corbusier felt the need to reinvent Vitruvian man for the modern age. If he hadn’t chosen architecture, Le Corbusier might have been a boxer. He drew sketches of boxers and likened himself to a boxer in his professional struggles. His new ideal man, which he called Le Modulor, raises a massive fist to the sky. The first version of Le Modulor was based on a typical Frenchman of 1.75 metres, but the architect disliked the metric system, based as it is on the dimensions of the earth rather than on the human body, and later announced that his model would henceforth be a six-foot Englishman, ‘because in English detective novels, the good-looking men, such as policemen, are always six feet tall!’ To the top of that raised fist, Le Modulor is 226 centimetres high, and his navel is centrally positioned at 113 centimetres. The distances from the ground to the navel and from the navel to the top of the head are in the proportion of the golden ratio (0.618:1 = 1:1.618), as is the remaining distance from the head to the fist, and he is indeed six feet (182.8 centimetres) tall. This personal system of proportion devised in the 1940s governs the proportions of the Unité d’Habitation, Le Corbusier’s influential apartment block in Marseille. The Modulor logic yields a building that is ‘in every way as keen, sharp and terrifying as the Parthenon’, in the words of one architecture critic, even if it is a ‘semantic strength’ that is gained rather than anything magical to do with the numerical ratios employed or their intrinsic connection with the human body. Le Modulor man features as a sculptural relief in the concrete, but it seems unlikely that many of the residents know their comings and goings are overseen by an English policeman.
Le Modulor may seem a bit arbitrary, perhaps even gently mocking the notion of the ideal body, but like Vitruvian man he is sure of his height. For it is certainly true that, in order to approach any kind of human ideal, a person must not only have harmonious proportions, he or she must also be the right size.
Ancient units of measure were directly based on the dimensions of the human body. We still use quite a few of them today. One definition of the inch was the length of the (royal) thumb from tip to first joint. The foot covers a narrow spread of distances based on the lengths of human feet, among which our imperial twelve-inch foot is about average. As well as being the width of four palms, a cubit is the length from the elbow to the longest finger tip, and is usually equated to eighteen inches, but sometimes to twenty-one or more. An ell, derived from the Latin for elbow,
, was originally the same as a cubit. Later, the ell was adopted as a unit for measuring cloth at a much longer forty-five inches. It may have taken the name because measuring out involved holding the cloth in the fingers of one hand up to the opposite shoulder and then straightening the elbow until the arm is outstretched on its rightful side. At any rate, I am a little shorter than Le Corbusier’s English hero, and this distance comes to nearly forty-five inches on me.
All of these units of measurement start from a different part of the body. There is nothing that says they have to be in simple arithmetic relationship to one another. So the fact that they have been put together in just this way – twelve inches making exactly one foot, for example – is evidence that Vitruvius and his mathematizing idealism has stayed with us.
These measures, however, are all linear. The body is less helpful when it comes to areas, masses and volumes. A few units are based not on man’s dimensions but on his capabilities. An acre is the area that a man and his ox were supposed to be able to plough in a day, for example. But quantities such as the weight that a man can lift or the volume of water (or beer) he can drink are so variable that the body no longer provides a good standard. Even Vitruvian six-footers can be scrawny or stout. Nevertheless, there is a smattering of other so-called anthropic measures, even including units of time. In Hindu tradition,
is the length of a blink of an eye and
is the interval between blinking.
The importance of being the right size is made apparent in stories where it all goes wrong.
Alice in Wonderland
are two of the best-loved tales where the relative size of the central character becomes important. Alice and Gulliver undergo instructively different experiences. When Alice first drinks from the bottle labelled ‘DRINK ME’ and finds herself shrinking, and then eats the cake that makes her grow again, she extrapolates from what is happening to her to imagine the horrible consequences of being taken to the extreme of either scale – perhaps ‘going out altogether, like a candle’. Alice is in a world where measurement – and even number itself – can no longer be relied upon, as she finds when she tries to recite her multiplication tables and they too come out wrong.
Gulliver’s measure of things, on the other hand, remains rock-steady. He confidently describes the tallest trees in Lilliput as ‘seven foot high’, while in Brobdingnag one of the reapers who find him hoists him aloft ‘above sixty foot from the ground’. The reader understands from this that Gulliver retains his proper size. Calculations are a feature of
, too, most notably when the Lilliputians calculate that they must feed Gulliver 1,728 times as much food as they require for themselves, since Gulliver is twelve times their size in all three dimensions (and twelve cubed is 1,728).
Alice clearly changes size down the rabbit hole, whereas Gulliver visits different-sized lands. In both stories, though, the rule of law is strenuously asserted. ‘You’ve no right to grow
,’ the Dormouse admonishes Alice as she begins to resume her proper scale in preparation for her return above ground. ‘Rule Forty-two.
All persons more than a mile high to leave the court
,’ barks the King. The Emperor of Lilliput likewise imposes conditions on Gulliver: ‘First, the Man-Mountain shall not depart from our dominions, without our licence under our great seal.’ Size matters, and being the wrong size calls for disciplinary measures to bring the offender back into line.
Today, we have largely relinquished the notion of ideal man. The eighteenth-century painter and cartoonist William Hogarth declared that it was impossible to find geometry in human faces, and celebrated their irregularity in his satirical caricatures. In a section headed ‘Proportion not the Cause of Beauty in the Human Species’ in his famous essay of 1757,
A Philosophical Enquiry into the Origin of Our Ideas of the Sublime and Beautiful
, Edmund Burke refuted the whole concept, pointing out that ‘ideal’ proportions could be found in people judged beautiful and ugly alike. ‘You may assign any proportion you please to every part of the human body; and I undertake that a painter shall religiously observe them all, and notwithstanding produce, if he pleases, a very ugly figure.’ He reserved special criticism for Vitruvian man. Man was never based on a square; he was, if anything, more like its opposite, a cross. ‘The human figure never supplied the architect with any of his ideas.’
Thanks to a Belgian pioneer of statistics and social science, Adolphe Quetelet, we have now instead the idea of ‘average’ man and woman, a development in thinking about humanity that required the invention of statistics, with its concept of mean (average) and standard deviation (the extent of the variance either side of the average). Quetelet was the first to gather systematic data on human height and weight, introducing the concept of the average man (
) in a book of 1835. Quetelet even found a way to decouple the two measures, so that people could be usefully described as heavy or light
for their size
, introducing the index now named after him, better known to most of us as the body-mass index.
Quetelet’s new approach gave licence for a vast exercise in data collection. The field of study that emerged was christened anthropometry a few years later. In recognizing that one person was physically different from another and that measuring those variations might yield useful information, the anthropometrists implicitly acknowledged that one human was as valid as another and so in effect rejected the concept of ideal man.
Such data was too powerful to be left solely in the hands of scientists. In the Museum of the Prefecture of Police in Paris is a reconstruction of an unusual photographic studio. In addition to the huge cameras of the day, it contains an assortment of calipers and rulers and other paraphernalia for measuring subjects as well as capturing their image. This was where Alphonse Bertillon introduced the world’s first scientific identity cards. In addition to frontal and profile photographs, Bertillon’s cards gave major body dimensions – and some surprising minor ones, including sixteen characteristics describing the shape of the ear. He tried them out on members of his family. His own card, made on 14 May 1891 when he was thirty-eight, shows him with a trim beard, short wiry hair and a high forehead, his head seeming a little too large for his body. In fact, we can read from the card that his head was 19.4 centimetres tall, while his height from the waist was 78 centimetres and his chest was 95.2 centimetres around. His left foot measured 27.4 centimetres. Bertillon, curiously, came from a family that seems to have had a genetic predisposition to this sort of work: his elder brother was the director of statistics for the city of Paris; his father founded its school of anthropology; and his grandfather had developed the work of Quetelet and coined the word demographics. Bertillon’s innovations – he also introduced crime-scene photography – saw him rise from a lowly clerical position when he joined the Paris police in 1879 to lead its influential Judicial Identity Service less than a decade later. ‘Bertillonage’ was soon taken up by police services around the world. Although it could not be used to establish definite guilt, as further persons not known to the police might have similar measurements, Bertillon’s method was nevertheless good enough to rule out suspects from police enquiries if they did not match a witness’s description.