Extremists
Adolf Zeising (1810–1876) may be known to my fellow enthusiasts for the Golden Section. This is the mathematical relation, marvellously irrational, that as Euclid suggested, is “to cut a finite line in the extreme and mean ratio,” or approximately 5 by 8. More precisely it is 8 by 13, or 13 by 21, or 21 by 34, and so on to infinity. Each numerical ratio is more exact than the last, and yet they go on forever.
My wee tiny son (even now only 80 inches high), born with a prejudice towards math and the sciences, told me about this Golden Section when he was small. He said it was a proof of God, though I had not asked for a theological interpretation.
Herr Zeising, a prominent German psychologist in his time, but also a mathematician, proclaimed it to be a universal law, “the paramount spiritual ideal” of both organic and inorganic nature.
I think my son won that competition, with the natural fanaticism of childhood: for nature is so little in comparison to God.
Nature is also arbitrary, which is to say, unnecessarily precise. Zeising was confuted upon further investigations, where even in art the Golden Section was found to be merely approximated. It would yield exactly not what the ratio would specify. Nonetheless Gustav Theodor Fechner (1801-1887), a godless freethinker, made it the foundation of his “experimental aesthetics.”
As a sometime typographer in my own youth, I noticed that Fechner’s obsession had been imposed on the discipline with Teutonic thoroughness. I myself began to see Golden Sections everywhere, while trying to reproduce them.
Legislating what nature should do, on behalf of nature, is a dangerous game. You have to be Piero della Francesca to play it smoothly — that is, to play it without your viewers noticing what you are up to, until you destroy the game (ruin the joke) by pointing it out. Indeed, in his day, the “Early Renaissance” (i.e. Late Mediaeval) artist was better known as a mathematician than as a painter, and his developments in the “science” of perspective were presented as a technological trick. (My father taught me perspective as something from the ratbag of trompe l’œil.)
We live with extremists everywhere today — with commies and perverts under every bed — and throughout our gestapoes of measurement. They try to displace God, but cannot unseat the Creator of sacred geometry.