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 of AB 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 to The Times to 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 said it 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 √5/2 rectangle, 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, the externalization 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 the Critica to 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)/2 could have had so much in it? The builder of the Great Pyramid of Ghizeh knew all about it in 4700 B.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.
A POINT OF CROCE’S
Adverting to Mr. Jay Hambidge’s rectangles of beauty I had occasion to cite Croce and his distinction between the æsthetic fact of expression and the practical fact of externalization, to which distinction, I said, Dr. Bosanquet had objected that it ignored the influence upon the artist of his medium. Dr. Bosanquet has courteously sent me a copy of a communication, “Croce’s Æsthetic,” which he has made to the British Academy, and which deals not only with this point, but with his general objections to the Crocean philosophy of art. It is not all objection, far from it; much of it is highly laudatory, and all of it is manifestly written in a spirit of candour and simple desire to arrive at the truth. But I have neither the space nor the competence to review the whole pamphlet, and I will confine myself to the particular point with which I began. While suggesting, however, some criticisms of Dr. Bosanquet’s contentions, I admit the suspicion that I may resemble one of those disputants who, as Renan once said, at the bottom of their minds are a little of the opinion of the other side. That, indeed, was why I said that many of us would be glad to hear further on the point from Croce himself. But with Dr. Bosanquet’s pamphlet before me I cannot afford to “wait and see.” I must say, with all diffidence, what I can.