At length he found the youngest of them, Katharina, a girl of perhaps eight or nine, of at least seven and at most eleven, softly singing a song to herself in the so-called Music-Making Room amid the clutter of old instruments there, many of which, he saw, were glockenspiels, most of which, in fact, he realized, were glockenspiels, and actually all of which, on closer inspection, were glockenspiels, the instruments were all glockenspiels without exception, “Basically it was just a room full of glockenspiels,” of various shapes and sizes and states of disrepair, all of them heaped together, piled on top of one another, there was something gruesome about this glockenspiel pile, this big heap of hundreds if not thousands of glockenspiels, the millions of metal bars of which flashed splintered reflections of little Katharina’s unkempt blonde braid as it swung to and fro behind her head. She sat cross-legged on the floor. He stood outside the doorway and listened to her sing. Her voice, while untrained, was lovely, the tune lilting, but the tale it told, of a “little pink pig” trying to evade slaughter at the hands of a “big black-bearded butcher,” began to perturb the astronomer. At first, as the little pink pig “pops out” of the big butcher’s arms and “pops through” a hole in the fence, he thought: She’s singing one of those wily-barnyard-animal songs beloved by children the world over; and he expected, needless to say, that the pig would emerge victorious from the encounter; but shortly thereafter the butcher “catches that little pink pig by her pink little leg” and “chops it off with his big shiny axe.” The refrain, “appallingly, to my mind,” spoke of the pig’s survival: “But did she go down? No she did not go down, no she did not go down, no she did not go down!” The astronomer marveled: “The song wishes this to be heard as a message of resilience.” The pig escapes again, is instantly caught again. In the second, third, and fourth verses, as the astronomer eavesdropped and Katharina’s braid swung to and fro, the butcher chops off the pig’s second, third, and fourth legs. “But did she go down? No she did not go down, no she did not go down, no she did not go down!” By now, the astronomer noted, one was praying for the pig to go down, at last to die. Instead she escapes again, the butcher catches her again and chops off her head, then chops her in half, “But did she go down? No she did not go down, no she did not go down, no she did not go down!” The butcher chops the pig into quarters, into eighths, into sixteen pieces, into thirty-two, still the pig doesn’t die, but that fact was actually becoming—as the song went on—less and less appalling and more and more abstract, his revulsion subsided, “The song,” he realized, “had taken a mathematical turn,” it seemed to be no longer about the brutality of the butcher but the perplexities of the infinite, the pig endures in sixty-four pieces, in one hundred and twenty-eight pieces, “the characters were receding, the numbers were coming to the fore,” two hundred fifty-six, five hundred twelve, and at this point the astronomer realized that if he did not intervene the song would actually not come to an end, not ever, or at least not until she lost interest in singing it, “and small children as I’ve since established time and time again, Herr Leibniz, do not naturally lose interest in singing songs,” it is an empirical fact, he noted, that children are instinctually drawn to infinitely long, infinitely iterative songs, we all sing such songs throughout our childhood, and it is only at a certain stage of our maturation, a stage evidently not yet reached by Katharina, that we abruptly stop singing such songs and subsequently sing only finitely long songs. One might, of course, postulate that Princess Katharina’s powers of computation would impose their own limit on the length of the song, which required its singer to multiply by two larger and larger figures, but the astronomer could already intuit, and would soon confirm, that this little girl’s mental abilities were of no common sort. So he tiptoed in, picked up one of the many mallets littering the floor, and at the moment she reached once again the refrain he struck on a glockenspiel the corresponding note.