“Fill a bottle with dried peas and add a little water. The peas, in swelling, will become polyhedrons by mutual pressure. Even so with the Wasps’ cells. The builders work in a crowd. Each builds at her own will, placing her work in juxtaposition to her neighbours’; and the reciprocal thrusts produce the hexagon.”
A preposterous explanation, which no one would venture to suggest if only he had condescended to make use of his eyes. Good people, why not look into the early stages of the Wasp’s work? This is quite easy in the case of the Polistes, who builds in the open, on a twig of some hedge-plant. In the spring, when the Wasps’-nest is founded, the mother is alone. She is not surrounded by collaborators who, vying with her in zeal, would place partition against partition. She sets up her first prism. There is nothing to hamper her, nothing to impose one form upon her rather than another; and the original cell, free from contact in every direction, is as perfect an hexagonal prism as the rest will be. The faultless geometry of [[237]]the structure asserts itself from the outset.
Look again when the comb of the Polistes or any Social Wasp that you please is more or less advanced, when numbers of builders are at work upon it. The cells at the edge, most of them still incomplete, are free as regards their outer halves. So far as this part is concerned there is no contact with the preceding row of cells; no limit is imposed; and yet the hexagonal configuration appears as plainly here as elsewhere. Let us abandon the theory of mutual pressure: a single glance of the least discernment contradicts it flatly.
Others, with more scientific, that is to say, less intelligible ostentation, substitute for the contact of the swollen peas the contact of spheres which, with their intersections and by virtue of an unseeing mechanism, lead to the superb structure of the Bees. The theory of an order emanating from an Intelligence watchful over all things is, to their thinking, a childish supposition; the riddle of things is explained by the mere potentialities of chance. To these profound philosophers, who deny the geometrical Idea Which rules the forms of things, let us propound the problem of the Snail.
The humble mollusc coils its shell according [[238]]to the laws of a curve known as the logarithmic spiral, a transcendental curve compared with which the hexagon is extremely simple. The study of this line, with its remarkable properties, has long delighted the meditations of the geometricians.
How did the Snail take it as a guide for his winding staircase? Did he arrive at it by means of intersecting spheres, or other combinations of forms dove-tailed one into the other? The foolish notion is not worth stopping to consider. With the Snail there is no conflict between fellow-workers, no interpenetration of similar, adjoining structures. Quite alone, completely isolated, peacefully and unconsciously he achieves his transcendental spiral with the aid of glaireous matter charged with lime.
Did the Snail even invent this cunning curve himself? No, for all the molluscs with turbinate shells, those which dwell in the sea and those which live in fresh water or on land, obey the same laws, with variations of detail as to the conoid on which the typical spiral is projected. Did the present-day builders accomplish it by gradually improving on an ancient and less exact curve? No, for the spiral of abstract science has presided over the scrollwork of their shells ever since [[239]]the earliest ages of the globe. The Ceratites, the Ammonites and other molluscs prior in date to the emergence of our continents coil their shells in the same fashion as the Planorbes[3] of our books.
The logarithmic spiral of the mollusc is as old as the centuries. It proceeds from the sovran Geometry which rules the world, attentive alike to the Wasp’s cell and to the Snail’s spiral.
“God,” says Plato, “is ever the great geometer: Αεὶ ὁ Θεὸς γεομετρεῖ.”
Here truly is the solution of the problem of the Wasps. [[240]]