Diaspora

On Earth, though, there was a growing consensus that Kozuch's whole model had to be abandoned. The six extra dimensions which allowed the wormhole mouths their diversity were already being described as "the mathematical fiction that misled physicists for two thousand years," and theorists were urging each other to adopt a more "realistic" approach with all the puritanical vigor of scourge-wielding penitents.

Blanca accepted that it was possible that all of Kozuch Theory's successful predictions were due to nothing but the "mirroring" of the logical structure of wormhole topology in another system altogether. The motion under gravity of an object dropped down a borehole passing through the center of an asteroid obeyed essentially the same mathematics as the motion of an object tied to the free end of an idealized anchored spring—but pushing either model too far as a metaphor for the other generated nonsense. The success of Kozuch's model could be due to the fact that it was just an extremely good metaphor, most of the time, for some deeper physical process which was actually as different from extra-dimensional wormholes as a spring was different from an asteroid.

The trouble was, this conclusion fitted the prevailing mood in C-Z far too well: the recriminations over the failure of wormhole travel, the backlash against the other polises' continuing retreat from the physical world, and the increasingly popular doctrine that the only way to avoid following them was to anchor C-Z culture firmly to the rock of direct ancestral experience, and dismiss everything else as metaphysical indulgence. In that climate, Kozuch's six extra dimensions could never be more than the product of a temporary misunderstanding of what was really going on.

Blanca had originally pla

Ve ran vis Kozuch avatar; an image of the long-dead flesher appeared in the scape beside ver. Kozuch had been a dark-haired woman, shorter than most, sixty-two years old when she'd published her masterpiece—an anomalous age for spectacular achievement in the sciences, in that era. The avatar wasn't sentient, let alone a faithful re-creation of Kozuch's mind; she'd died in the early years of the Introdus, and no one really knew why she'd declined to be sca

"Half the circumference of the standard fiber." The avatar, not unreasonably, injected a hint of impatience into Kozuch's voice. And though it paraphrased inventively, the answer was always the same: about five time ten-to-the-minus-thirty-five meters.

"The standard fiber?" The avatar gave ver something approaching a look of exasperation, but Blanca pleaded stubbornly, "Remind me." Ve had to go back to the foundations; ve had to re-examine the model's basic assumptions and find a way to modify them that made sense of the Distance Problem, but left the fundamental symmetries of the wormhole mouths intact.

The avatar relented; in the end it always cooperated, whether Kozuch herself would have or not. "Let's start with a two-dimensional spacelike slice through a Minkowski universe—flat and static, the simplest possible toy to play with." It created a translucent rectangle, about a delta long and half a delta wide, then bent it around so that the two halves were parallel, a hand's width apart, one above the other. "The curvature here means nothing, of course; it's necessary in order to construct the diagram, but physically it has no significance at all." Blanca nodded, feeling slightly embarrassed; this was like asking Carl Friedrich Gauss to recite multiplication tables.

The avatar cut two small disks out of the diagram. one in the top plane and the other directly beneath it. "If we want to co

It erased the hourglass-shaped tu

"So you expressed it by adding extra dimensions. If Einstein's equations in four dimensions can't pin down the structure of space-time on the smallest scale, then every 'fixed point' in the classical model must have some extra degrees of freedom."

"Exactly." The avatar gestured at the diagram, and it was subtly transformed: the translucent sheet became a mass of tiny bubbles, each one an identical perfect sphere. This was a heavily stylized view—rather like drawing a cylinder as a long line of adjoining circles—but Blanca understood the convention: every point in the diagram, though fixed in the two dimensions of the sheet, was now considered to be free to position itself anywhere on the surface of its own tiny sphere. "The extra space each point can occupy is called the 'standard fiber' of the model; it's not long and fibrous, I know, but the term is a legacy of mathematical history, so we're stuck with it. I started with a 2-sphere for the standard fiber; I only changed it to a 6-sphere when it became clear that six dimensions were needed to account for all the particles."

The avatar created a fist-sized sphere floating above the main diagram, and covered it with a palette of colors that varied smoothly over the whole surface. "How does giving every point a 2-sphere to move in get around the singularity? Suppose we approach the center of the wormhole from a certain angle, and let the extra dimensions change like this." The avatar drew a white line down the sphere from the north pole toward the equator, and a colored line appeared simultaneously on the main diagram: a path leading straight into the top cone of the wormhole. The path's colors came from the line being sketched on the sphere; they signified the values of the two extra dimensions being assigned to each point.