p>The Atlantic Monthly, Volume 05, No. 30, April, 1860 / A Magazine of Literature, Art, and Politics
THE LAWS OF BEAUTY
The fatal mistake of many inquirers concerning the line of beauty has been, that they have sought in that which is outward for that which is within. Beauty, perceived only by the mind, and, so far as we have any direct proof, perceived by man alone of all the animals, must be an expression of intelligence, the work of mind. It cannot spring from anything purely accidental; it does not arise from material, but from spiritual forces. That the outline of a figure, and its surface, are capable of expressing the emotions of the mind is manifest from the art of the sculptor, which represents in cold, colorless marble the varied expressions of living faces,—or from the art of the engraver, who, by simple outlines, can soothe you with a swelling lowland landscape, or brace you with the cool air of the mountains.
Now the highest beauty is doubtless that which expresses the noblest emotion. A face that shines, like that of Moses, from communion with the Highest, is more truly beautiful than the most faultless features without moral expression. But there is a beauty which does not reveal emotion, but only thought,—a beauty which consists simply in the form, and which is admired for its form alone.
Let us, for the present, confine our attention to this most limited species of beauty,—the beauty of configuration only.
This beauty of mere outline has, by some celebrated writers, been resolved into some certain curved line, or line of beauty; by others into numerical proportion of dimensions; and again by others into early pleasing associations with curvilinear forms. But, if we look at the subject in an intellectual light, we shall find a better explanation. Forms are the embodiment of thought or law. For the common eye they must be embodied in material shape; while to the geometer and the artist, they may be so distinctly shadowed forth in conception as to need no material figure to render their beauty appreciable. Now this embodiment, or this conception, in all cases, demands some law in the mind, by which it is conceived or made; and we must look at the nature of this law, in order to approach more nearly to understanding the nature of beauty.
We are thus led, through our search for beauty, into the temple of Geometry, the most ancient and venerable of sciences. From her oracles alone can we learn the generation of beauty, so far as it consists in form alone.
Maupertuis' law of the least action is not simply a mechanical, but it is a universal axiom. The Divine Being does all things with the least possible expenditure of force; and all hearts and all minds honor men in proportion as they approach to this divine economy. As gracefulness in motion consists in moving with the least waste of muscular power, so elegance in intellectual and literary exertions arises from the ease with which their achievements are accomplished. We seek in all things simplicity and unity. In Nature we have faith that there is such unity, even in the midst of the wildest diversity. We honor intellectual conceptions in proportion to the greatness of their consequences and to the simplicity of their assumptions. Laws of form are beautiful in proportion to their simplicity and to the variety which they can comprise in unity. The beauty of forms themselves is in proportion to the simplicity of their law and to the variety of their outline.
This last sentence we regard as the fundamental canon concerning beauty,—governing, with a slight change of terms, beauty in all its departments.
Beginning with the fundamental division of figures into curvilinear and rectilinear, this dictum decides, that, in general, a curved outline is more beautiful than a right-lined figure. For a straight-lined figure necessarily requires at least half as many laws as it has sides, while a curvilinear outline requires, in general, but a single law. In a true curve, every point in the whole line (or surface) is subject to one and the same law of position. Thus, in the circle, every point of the circumference is subject to one and the same law,—that it must be at a certain distance from the centre. Half a dozen other laws, equally simple, might be named, which in like manner govern every point in the circumference of a circle: for instance, the curve bends at every point by a certain fixed but infinitesimal amount, just enough to make the adjacent points to be equally near the centre. Or, to take another example, every point of the elastic curve, that is, of the curve in which a spring of uniform stiffness can be bent by a force applied at the ends of the spring, is subject to this very simple law, that the curve bends in exact proportion to its distance from a certain straight line. Now a straight line, or a plane, is by this definition a curve, since every point in it is subject to one and the same law of position. A plane may, indeed, be considered a part of any curved surface you please, if you only take that surface on a sufficiently large scale. Thus, the surface of water conforms to the surface of a sphere eight thousand miles in diameter; but, as the arc of such a circle would arch up from a chord ten feet long by only the ten-millionth part of an inch, the surface of water in a cistern may be considered a plane. But no figure or outline can be composed of a single plane or a single straight line; nor can the position of more than two straight lines, not parallel, be defined by a single simple law of position of the points in them. We may, therefore, regard it as the first deduction from our fundamental canon, that figures with curving outline are in general more beautiful than those composed of straight lines. The laws of their formation are simpler, and the eye, sweeping round the outline, feels the ease and gracefulness of the motion, recognizes the simplicity of the law by which it is guided, and is pleased with the result.
Our second deduction relates principally to rectilinear figures; it is, that symmetry is in general, and particularly in rectilinear figures, more beautiful than irregularity. It requires, in general, simpler laws to produce symmetry than to produce what is unsymmetrical; since the corresponding parts in a symmetrical figure are instinctively recognized as flowing from one and the same law. This preference for symmetry is, however, frequently subordinated to higher demands of the fundamental canon. If the outline be rectilineal, simplicity of law produces symmetry, and variety of result can be attained only at the expense of simplicity in the law. But in curved outlines it frequently happens, that, with equally simple laws, we can obtain much greater variety by dispensing with symmetry; and then, by the canon, we thus obtain the higher beauty.
The question may be asked, In what way does this canon decide the question, of proportions? Which of the two rectangles is, according to this dictum, more beautiful, that in which the sides are in simple ratio, or that in which the angles made with the sides by a diagonal are in such ratio?—that, for instance, in which the shorter side is three-fifths of the longer, or that in which the shorter side is five hundred and seventy-seven thousandths of the longer? Our own view was formerly in favor of a simple ratio between the sides; but experiments have convinced us that persons of good taste, and who have never been prejudiced by reading Hay's ingenious speculations, do nevertheless agree in preferring rectangles and ellipses which fulfil his law of simple ratio between the angles made by the diagonal. We acknowledge that we have not brought this result under the canon, but look upon it as indicating the necessity of another canon to somewhat this effect,—that in the laws of form direction is a more important element than distance.
We have said that a curved line is one in which every point is subject to one and the same law of position. Now it may be easily proved, that, in a series of points in a plane, each of which fulfils one and the same condition of position, any three, if taken sufficiently near each other, lie in one straight line. A fourth point near the third lies, then, in a straight line with the second and third,—a fifth with the third and fourth, and so on. The whole series of points must, in short, form a line. But it may also be easily proved that any four of these points, taken sufficiently near each other, lie in the arc of a circle. How strange the paradox to which we are thus led! Every law of a curve, however simple, leads to the same conclusion; a curve must bend at every point, and yet not bend at any point; it must be nowhere a straight line, and yet be a straight line at every part. The blacksmith, passing an iron bar between three rollers to make a tire for a wheel, bends every part of it infinitely little, so that the bending shall not be perceptible at any one spot, and shall yet in the whole length arch the tire to a full circle. It may be that in this paradox lies an additional charm of the curved outline. The eye
