THE SECRET OF GREEK ART
Mathematics may be great fun. Even simple arithmetic is not without its comic side, as when it enables you to find, with a little management, the Number of the Beast in the name of any one you dislike. Then there is “the low cunning of algebra.” It became low cunning indeed when Euler drove (so the anecdotist relates) Diderot out of Russia with a sham algebraical formula. “Monsieur,” said Euler gravely, “(a + bⁿ)/n = x, donc Dieu existe; répondez.” Diderot, no algebraist, could not answer, and left.
But geometry furnishes the best sport. Here is a learned American archæologist, Mr. Jay Hambidge, lecturing to that august body the Hellenic Society and revealing to them his discovery that the secret of classic Greek art (of the best period) is a matter of two magic rectangles. I understand that the learned gentleman himself did not make this extreme claim about the “secret” of “Art,” but it was at any rate so described in the report on which my remarks are based. Mr. Hambidge appears to have devoted years of labour and ingenuity to his researches. The result is in any case of curious interest. Buthow that result can be said to be “the secret of Greek art revealed” I wholly fail to see.
Let us look first at his rectangles. His first is2 × √5. It is said that these figures represent the ratio of a man’s height to the full span of his outstretched fingers. But what man? Of what race and age? Well, let us say an average Greek of the best period, and pass on. Mr. Hambidge has found this rectangle over and over again in the design of the Parthenon. “Closely akin” to it, says the report, is another fundamental rectangle, of which the two dimensions are in the ratio of Leonardo’s famous “golden section.” That ratio is obtained by dividing a straight line so that its greater is to its lesser part as the whole is to the greater. Let us give a mathematical meaning to the “closely akin.” Calling the lesser part 1 and the greaterx, then—
x/1 = (x+ 1)/xorx² -x- 1 = 0
which gives you
x= (√5 + 1)/2.
The square roots will not trouble you when you come to constructing your rectangles, for the diagonal of the first is√(5 + 4), or 3. If AB is your side 2, draw a perpendicular to it through B, and with A as centre describe the arc of a circle of radius 3; the point of intersection will give C, the other end of the diagonal. The second rectangle maintains AB, and simply prolongs BC by half ofAB or 1. Just as the dimensions of the first rectangle are related to those of (selected) man, and to the plan of the Parthenon, so those of the second are related, it seems, to the arrangement of seeds in the sunflower and to the plan of some of the Pyramids. Sir Theodore Cook writes toThe Timesto say that both the sunflower and the Pyramid discoveries are by no means new.
The fact is the theory of “beautiful” rectangles is not new. The classic exponent of it is Fechner, who essayed to base it on actual experiment. He placed a number of rectangular cards of various dimensions before his friends, and asked them to select the one they thought most beautiful. Apparently the “golden section” rectangle got most votes. But “most of the persons began by saying that it all depended on the application to be made of the figure, and on being told to disregard this, showed much hesitation in choosing.” (Bosanquet: “History of Æsthetic,” p. 382.) If they had been Greeks of the best period, they would have all gone with one accord for the “golden section” rectangle.
Nor have the geometers of beauty restricted their favours to the rectangle. Some have favoured the circle, some the square, others the ellipse. And what about Hogarth’s “line of beauty”? I last saw it affectionately alluded to in the advertisement of a corset manufacturer. So, evidently, Hogarth’s idea has not been wasted.
One sympathizes with Fechner’s friends who saidit all depended upon the application to be made of the figure. The “art” in a picture is generally to be looked for inside the frame. The Parthenon may have been planned on the√5/2rectangle, but you cannot evolve the Parthenon itself out of that vulgar fraction. Fechner proceeded on the assumption that art is a physical fact and that its “secret” could be wrung out of it, as in any other physical inquiry, by observation and experiment, by induction from a sufficient number of facts. But when he came to have a theory of it he found, like anybody else, that introspection was the only way.
And whatever rectangles Mr. Hambidge may discover in Greek works of art, he will not thereby have revealed the secret of Greek art. For rectangles are physical facts (when they are not mere abstractions), and art is not a physical fact, but a spiritual activity. It is in the mind of the artist, it is his vision, the expression of his intuition, and beauty is only another name for perfect expression. That, at any rate, is the famous “intuition-expression” theory of Benedetto Croce, which at present holds the field. It is a theory which, of course, presents many difficulties to the popular mind—what æsthetic theory does not?—but it covers the ground, as none other does, and comprehends all arts, painting, poetry, music, sculpture, and the rest, in one. Its main difficulty is its distinction between the æsthetic fact, the artist’s expression, and the physical fact, theexternalization of the artist’s expression, the so-called “work” of art. Dr. Bosanquet has objected that this seems to leave out of account the influence on the artist’s expression of his material, his medium, but Croce, I think, has not overlooked that objection (“Estetica,” Ch. XIII., end), though many of us would be glad if he could devote some future paper in theCriticato meeting it fairly and squarely. Anyhow, æsthetics is not a branch of physics, and the “secret” of art is not to be “revealed” by a whole Euclidful of rectangles.
But it is, of course, an interesting fact that certain Greeks, and before them certain Egyptians, took certain rectangles as the basis of their designs—rectangles which are also related to the average proportions of the human body and to certain botanical types. If Mr. Hambidge—or his predecessors, of whom Sir Theodore Cook speaks—have established this they have certainly put their fingers on an engaging convention. Who would have thought that the “golden section” that very ugly-looking(√5 + 1)/2could have had so much in it? The builder of the Great Pyramid of Ghizeh knew all about it in 4700B.C.and the Greeks of the age of Pericles, and then Leonardo da Vinci toyed with it—“que de choses dans un menuet!” It is really rather cavalier of Croce to dismiss this golden section along with Michael Angelo’s serpentine lines of beauty as the astrology of Æsthetic.