Then Heinrich said: “For these and all my sins I am very sorry.” He added: “It sounds stupid when I say it. When I say anything.” Since the world was his the Prince was obviously doing something completely crazy, truly stupid, and entirely contradictory whenever he opened his mouth to say anything to anyone, Heinrich noted. “And in any case I haven’t infiltrated my own turret disguised as a priest in order to forgive myself my sins such as they are but in order to teach myself about triangles, yes, triangles! So, then, Father,” said Prince Heinrich, and he burst into laughter, then looked frightened, and at last went still: “Speak. Teach me. I am all yours.”

And the astronomer took off his hood and set down his staff and taught the Prince about triangles.

And he found—“and this tells us something about the nature of mathematics”—that despite his being clearly completely crazy Heinrich’s aptitude for trigonometry was undiminished.

And when the delegation of the Electors arrived a few days later the Prince with extraordinary skill and the ardor of a genuine pursuer of truth estimated the distance from Earth of the New Star, and when the Electors departed each for his own dominion all seven were persuaded beyond doubt of the young man’s sanity, and thus his fitness for his father’s office, the astronomer told Leibniz, putting an empty eye socket to the eyepiece of his telescope, picking up his quill, and writing down a long string of numbers. And even though Prince Heinrich was found dead the next day in the privy protruding from his turret, slain, it seemed, by his own hand, it could not be denied that he had learned about triangles, and the grief-stricken Emperor assured his Imperial Astronomer that he intended to honor the edict he had signed.

FOUR

THE REST OF THE STORY spans half a century, but is swiftly told—and must be swiftly told, said the astronomer, according to Leibniz, for the Moon will interpose herself between us and the Sun exactly twenty-four minutes from now, “neither more nor less.”