Ve bid them farewell until next time. They gamboled around ver, protesting noisily and pleading with ver to stay, but Blanca knew they wouldn't miss ver for long.
Back in vis homescape, Blanca admitted to verself that ve'd actually enjoyed the visit. A brief dose of the Puppies' relentless enthusiasm always helped shake up vis perspective on vis own obsession.
Vis current homescape was a fissured, vitreous plain beneath a deep orange sky. Mercurial silver clouds just a few delta from the ground rose in updrafts, sublimated into invisible vapor, then re-condensed abruptly and sank again. The ground suffered quakes induced by forces from the clouds that had no analogue in real-world physics; Blanca was beginning to get a feel for the patterns in the sky that presaged the big ones, but the precise rules, complex emergent properties of the lower-level deterministic laws, remained elusive. This world and its seismology were just decoration and diversion, though. The reason ve'd elected to experience time on the voyage at all zig-zagged for kilodelta across the scape—and the trail of discarded Kozuch diagrams, failed attempts to solve the Distance Problem, would soon constitute the most significant feature of the plain, out-classing the fissures produced by even the strongest quakes.
Blanca hovered at the fresh end of the trail, taking stock of vis recent dismal efforts. Ve'd spent the last few megatau trying to patch an ugly system of "higher-order corrections" onto Kozuch's original model, infinite regresses of wormholes-within-wormholes which ve'd hoped might sum to arbitrarily large, but finite, lengths, hundred-billion-kilometer fractals packed into a space twenty orders of magnitude smaller than a proton. Before that, ve'd tinkered with the process of vacuum creation and annihilation, trying to get the space-time in the wormhole to expand and contract on cue as the mouths were repositioned. Neither approach had worked, and in retrospect ve was glad that they hadn't; these ad hoc modifications were far too clumsy to deserve to be true.
After being used to create the antihydrogen to fuel the Diaspora, the Forge had been reclaimed by the small group of particle physicists in Earth C-Z not terminally disillusioned by the failure of its original purpose. Their experiments had now probed every known species of particle down to the Planck-Wheeler length, and so long as no traversable wormholes were produced the results remained perfectly consistent with Kozuch Theory. To Blanca, this strongly suggested that Kozuch's original identification between particle types and wormhole mouths was correct, and whatever else needed to he overhauled or thrown out, that basic idea should remain intact as the core of a revised theory.
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 welclass="underline" 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."