The geometricians do not attempt to refer to it by this number; they give it a letter, e.
Is this line imaginary? Not at all; you may see the catenary frequently. It is the shape taken by a flexible cord when held at each end and relaxed; it is the line that governs the shape of a sail filled out by the wind. All this answers to the number e.
What a quantity of abstruse science for a bit of string! Let us not be surprised. A pellet of shot swinging at the end of a thread, a drop of dew trickling down a straw, a splash of water rippling under the kisses of the air, a mere trifle, after all, becomes tremendously complicated when we wish to examine it with the eye of calculation. We need the club of Hercules to crush a fly.
Our methods of mathematical investigation are certainly ingenious; we cannot too much admire the mighty brains that have invented them; but how slow and laborious they seem when compared with the smallest actual things! Shall we never be able to inquire into reality in a simpler fashion? Shall we be intelligent enough some day to do without all these heavy formulæ? Why not?
Here we have the magic number e reappearing, written on a Spider’s thread. On a misty morning the sticky threads are laden with tiny drops, and, bending under the burden, have become so many catenaries, so many chains of limpid gems, graceful chaplets arranged in exquisite order and following the curve of a swing. If the sun pierce the mist, the whole lights up with rainbow-colored fires and becomes a dazzling cluster of diamonds. The number e is in its glory.
Geometry, that is to say, the science of harmony in space, rules over everything. We find it in the arrangement of the scales of a fir-cone, as in the arrangement of a Spider’s sticky snare; we find it in the spiral of a snail-shell, in the chaplet of a Spider’s thread, as in the orbit of a planet; it is everywhere, as perfect in the world of atoms as in the world of immensities.
And this universal geometry tells us of a Universal Geometrician, whose divine compass has measured all things. I prefer that, as an explanation of the logarithmic curve of the Nautilus and the Garden Spiders, to the Worm screwing up the tip of its tail. It may not perhaps be in agreement with some latter-day teaching, but it takes a loftier flight.