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 planned to spend no more than twenty or thirty megatau on the problem, then sleep for the rest of the voyage, satisfied that ve'd struggled long and hard enough to understand exactly how difficult it would be to find a solution. Ve'd guarded against investing too much hope in the prospect of helping Gabriel out of his post-Forge depression, despite fanciful visions of greeting him when he woke with the news that his soul-destroying "failure" had been transformed into the key to the physics of the next two thousand years. But the fact remained that Renata Kozuch had invented a universe of unsurpassed elegance, ruled by a set of economical and harmonious laws—and the bulletins from Earth were beginning to portray this marvelous creation as some kind of hideous mistake, as disastrous as the Ptolemaic epicycles, as wrong-headed as phlogiston and the aether. Blanca felt that ve owed Kozuch herself a spirited defense.

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 scanned. But the software had access to her published views on a wide range of topics, and it could read between the lines to some degree and extract a limited amount of implicit information. Blanca asked, for the thirty-seventh time, "How long can a wormhole he?"

"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 connect these circles with a wormhole, there are two ways of doing it." It pasted a thin rectangular strip into the diagram, joining a small part of the top hole's rim to the matching segment of the bottom rim. Then it extended this tentative bridge all the way around both holes, spinning it out into a complete tunnel. The tunnel assumed an hourglass shape, tapering to a waist but never pinching closed. "According to General Relativity, this solution would appear to have negative energy in some reference frames, especially if it was traversable. The two mouths could still have positive mass, though, so I pursued some tentative quantum-gravity versions of this for a while, but in the end I could never make it work as a model for stable particles."

It erased the hourglass-shaped tunnel, leaving the two holes disconnected again, then pasted a narrow strip between the left-hand side of the top rim and the right hand side of the bottom rim. As before, it extended the strip all the way around both circles, always connecting opposite sides of the rims, creating a pair of cones meeting at a point between the wormhole mouths. "This solution has positive mass. In fact, if GR held true at this scale, it would just be a pair of black holes sharing a singularity. Of course, even for the heaviest elementary particles the Schwarzschild radius is far smaller than the Planck-Wheeler length, so quantum uncertainty would disrupt any potential event horizons, and perhaps even smooth away the singularity as well. But I wanted to find a simple, geometrical model underlying that uncertainty."

"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.