CONVERSATION WITH A GEOMETRICIAN.
It sometimes happens that a man has no answer to make, and yet is not persuaded. He is overthrown without the feeling of being convinced. He feels at the bottom of his heart a scruple, a repugnance, which hinders him from believing what has been proved to him. A geometrician demonstrates to you, that between a circle and a tangent, you may thread a number of curves, and yet cannot get one straight line to pass. Your eyes, your reason, tell you the contrary. The geometrician gravely answers you, that it is an infinitesimal of the second order. You stare in stupid silence, and quit the field all astonished, without having any clear idea, without comprehending anything, and without having any reply to make.
Consult but a geometrician of more candor, and he explains the mystery to you.
"We suppose," says he, "what cannot be in nature, lines which have length without breadth. Naturally and philosophically speaking, it is impossible for one real line to penetrate another. No curve, nor no right line can pass between two real lines that touch one another. These theorems that puzzle you are but sports of the imagination, ideal chimeras. Whereas true geometry is the art of measuring things actually existent."
I was perfectly well satisfied with the confession of the sensible mathematician, and, with all my misfortune, could not help laughing on learning that there was a quackery even in that science, which is called the sublime science. My geometrician was a kind of philosophical patriot, who had deigned to chat with me sometimes in my cottage. I said to him:
"Sir, you have tried to enlighten the cockneys of Paris, on a point of the greatest concern to mankind, that of the duration of human life. It is to you alone that the ministry owes its knowledge of the due rate of annuities for lives, according to different ages. You have proposed to furnish the houses in town with what water they may want, and to deliver us at length from the shame and ridicule of hearing water cried about the streets, and of seeing women inclosed within an oblong hoop, carrying two pails of water, both together of about thirty pounds weight, up to a fourth story. Be so good, in the name of friendship, to tell me, how many two-handed bipeds there may be in France?"
THE GEOMETRICIAN.—It is assumed, that there may be about twenty millions, and I am willing to adopt this calculation as the most probable, till it can be verified, which it would be very easy to do, and which, however, has not hitherto been done, because one does not always think of every thing.
THE MAN OF FORTY CROWNS.—How many acres, think you, the whole territory of France contains?
THE GEOMETRICIAN.—One hundred and thirty millions, of which almost the half is in roads, in towns, villages, moors, heaths, marshes, sands, barren lands, useless convents, gardens of more pleasure than profit, uncultivated grounds, and bad grounds ill cultivated. We might reduce all the land which yields good returns to seventy-five millions of square acres; but let us state them at fourscore millions. One cannot do too much for one's country.
THE MAN OF FORTY CROWNS.—How much may you think each acre brings in yearly, one year with another, in corn, seeds of all kinds, wine, fish-ponds, wood, metals, cattle, fruit, wool, silk, oil, milk, clear of all charges, without reckoning the tax?