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sun, in which there was embedded the flaw, the pearl, for Johannes Kepler to find.
    But the world had not been created in order that it should sing. God was not frivolous. From the start he held to this, that the song was incidental, arising naturally from the harmonious relation of things. Truth itself was, in a way, incidental. Harmony was all. (Something wrong, something wrong! but he ignored it.) And harmony, as Pythagoras had shown, was the product of mathematics. Therefore the harmony of the spheres must conform to a mathematical pattern. That such a pattern existed Johannes had no doubt. It was his principal axiom that nothing in the world was created by God without a plan the basis of which is to be found in geometrical quantities. And man is godlike precisely, and only, because he can think in terms that mirror the divine pattern. He had written: The mind grasps a matter so much the more correctly the closer it approaches pure quantities as its source. Therefore his method for the task of identifying the cosmic design must be, like the design itself, founded in geometry.
    Spring came to Graz and, as always, took him by surprise. He looked out one day and there it was in the flushed air, a quickening, a sense of vast sudden swooping, as if the earth had hurtled into a narrowing bend of space. The city sparkled, giving off light from throbbing window panes and polished stone, from blue and gold pools of rain in the muddied streets. Johannes kept much indoors. It disturbed him, how closely the season matched his present mood of restlessness and obscure longing. The Shrovetide carnival milled under his window unheeded, except when a comic bugle blast or the drunken singing of revellers shattered his concentration, and he bared his teeth in a soundless snarl.
    Perhaps he was wrong, perhaps the world was not an ordered construct governed by immutable laws? Perhaps God, after all, like the creatures of his making, prefers the temporal to the eternal, the makeshift to the perfected, the toy bugles and bravos of misrule to the music of the spheres. But no, no, despite these doubts, no: his God was above all a god of order. The world works by geometry, for geometry is the earthly paradigm of divine thought.
    Late into the nights he laboured, and stumbled through his days in a trance. Summer came. He had been working without cease for six months, and all he had achieved, if achievement it could be called, was the conviction that it was not with the planets themselves, their positions and velocities, that he must chiefly deal, but with the intervals between their orbits. The values for these distances were those set out by Copernicus, which were not much more reliable than Ptolemy's, but he had to assume, for his sanity's sake, that they were sound enough for his purpose. Time and time over he combined and recom-bined them, searching for the relation which they hid. Why are there just six planets? That was a question, yes. But a profoun-der asking was, why are there just these distances between them? He waited, listening for the whirr of wings. On that ordinary morning in July came the answering angel. He was in class. The day was warm and bright. A fly buzzed in the tall window, a rhomb of sunlight lay at his feet. His students, stunned with boredom, gazed over his head out of glazed eyes. He was demonstrating a theorem out of Euclid -afterwards, try as he might, he could not remember which -and had prepared on the blackboard an equilateral triangle. He took up the big wooden compass, and immediately, as it always contrived to do, the monstrous thing bit him. With his wounded thumb in his mouth he turned to the easel and began to trace two circles, one within the triangle touching it on its three sides, the second circumscribed and intersecting the vertices. He stepped back, into that box of dusty sunlight, and blinked, and suddenly something, his heart perhaps, dropped and bounced, like an athlete performing a miraculous feat