And he recounted to the Emperor the pitiable state in which he had found his son, how he had looked and how he had smelled and the threats he had made, and the bowl and the unicorn horn fell to the floor as the Emperor buried his face in his hands. “Then Matthias is right,” he moaned between his fingers, “my madness has reached full flower in him, my boy is beyond redemption! He, too, is dead and damned, we’re all dead and damned in this family.” And scurrying to return to the Emperor the bowl and the horn, the Court Chamberlain insisted, with some desperation, that Matthias was wrong, that the Prince was much less mad than he appeared, that in his nakedness and agitation, in his smearing on his own body of his own effluence—“a calculated smearing!”—the Prince was obviously playacting the role of a madman, to secure for himself the solitude he had always sought, for he had never wanted to be emperor and that’s what would make him such a good one. It is a performance, he insisted, a cliché albeit quasi-convincing performance of a mad prince! And the Emperor kept moaning: “A dead and damned family, full of dead and damned family members!” And the astronomer, in order to intensify the chaos which, so he claimed to Leibniz, he had instigated intentionally, chimed in intermittently with: “Not suited for a trigonometry tutorial.” And the Emperor howled: “Dead and damned!” And the Chamberlain insisted: “An act! A pantomime! A performance!”

Only when the havoc had reached its highest pitch did the astronomer put forward the proposal he had formulated.

There is, he said, one condition under which he might consider risking life and limb to enter Prince Heinrich’s turret and teach him the mathematics of triangles.

And peering through his fingers the Emperor murmured: “What is it?”

And the Court Chamberlain hissed: “Speak, man!”

The condition, the astronomer declared, was this: he required a written guarantee that, if he succeeded, he would receive carte blanche funding from the Imperial Treasury for the production of his tubes—not within reason, so to speak, but without, not bound by common sense but unbound by it, funding constrained by nothing but the demands of his own eyes. “That is my condition,” the astronomer said, and no sooner had he said it than the Emperor had drawn up an edict to this effect and signed it.