It was hard even if you simplified matters by treating each bubble not as a small miracle of fluid dynamics, but as a simple reflecting sphere. At one point, some years previously, one of the engineers at Corporation 9592—a classic liberal-arts-major-turned-coder-so-he-could-make-a-decent-living—had identified this as the Hand met Spiegelende Bol Problem, and had discomfited many of the more hard-core engineers, during a meeting, by flashing up a graphic of the Escher lithograph of the same name. It was a self-portrait depicting the artist reflected in a mirrored sphere supported in his left hand. Escher’s face was in the middle, but a geometrically distorted rendering of his office could be seen around it. In the background of that was a window. This, of course, was gathering in light from at least ninety-three million miles away. The point being that in order to make a faithful 3-D computer graphics rendering of an object as simple as a shiny ball, you would, in theory, have to take into account every object in the universe. The engineer—a new hire named Corvallis Kawasaki—had footnoted his own remarks by mentioning that the mirrored-ball problem reached at least as far back as the German genius and polymath G. W. Leibniz, who had written of it as a way of thinking about monads. At this point in the meeting, the more well-established engineers had shouted him down and Dodge had made a mental note to yank the boy out of whatever branch of the org chart he’d landed in and employ him in Weird Stuff, which was Dodge’s personal department. In any case, the point, in this instance, was that every single bubble on the surface of the bar of soap was at least as complicated as Escher’s ball. Rendering such a scene realistically was completely out of the question. Far from being a source of frustration, this comforted him, and made him happy—perhaps even a little smug—that he lived in a universe whose complexity defied algorithmic simulation.

He closed his eyes while splashing water on his face and then looked back up at the mirror. Now there was a little spot in the middle where he had been dazzled by the brilliant sparks of light from the bubbles. Soon enough the dazzled patch would shrink and be replaced by a correct view of what was really there.

Except that it did not in this case. When Richard closed his eyes again to towel his face, he could still see a little patch of nothing in his visual field. This was a different sort of nothing from the field of red-tinged black that his eyes were seeing simply by virtue of the fact that his lids had closed over them. He knew what this was. The flash of reflected sun, a minute ago, had triggered a thing in his brain called an optical migraine. It was painless and harmless. He got them a few times a year. It was a visual display—“Aura”—caused by a temporary disruption of blood flow to the visual cortex. It always started thus, with a tiny dazzled region that refused to go away. Over the next half hour it would get bigger, making it impossible for him to read. Then it would gradually migrate rightward and mess with his peripheral vision on that side for a little while before disappearing without a trace.