The exhibit said, "These diagrams show the pure gravitational potential, which always produces an attractive force." A disembodied hand appeared and placed a small test particle at the edge of each well, with predictable consequences: both particles fell straight in. "Starting from rest, a collision is unavoidable. But if there's any sideways motion, that alters the dynamics completely." The hand placed a particle on the rim of the first well, but this time gave it a flick that sent it into an elliptical orbit around the central weight.

"The best way to see what's really going on is to follow the body along its orbit." The surface's grid pattern began to spin, tracking the particle, and as it did the shape of the well changed dramatically: the center of the funnel inverted into a tall, steep spike, raising the weight above the surrounding surface. "In a rotating reference frame, the centrifugal force for a given amount of angular momentum acts like an inverse-cube repulsion." Inverse-cube conquered inverse-square for small distances, so centrifugal force won out over gravity near the center; the star or planet from the bottom of the well was now high on a summit. The outer region of the funnel continued to slope down, though, so there was a circular trench around the spike where this initial fall in the surface reversed into a climb.

The patches of floor on which they were standing began to circle the table, tilting as necessary to keep them from overbalancing. Orlando groaned at the gimmick, but seemed amused in spite of himself. They caught up with the rotating reference frame, leaving the particle apparently moving only along a fixed, radial line. It rolled back and forth in the trench, cradled and confined by this hollow in the energy surface, the extremes of its elliptical orbit now revealed as nothing more than the farthest points it could reach as it tried to climb either the central spike or the gentler slope of the outer wall.

When the ride stopped, the exhibit offered them three chances to flick a particle into orbit around the second gravity well. Orlando accepted. The first two particles he launched spiraled down to a collision, and the third went skidding off the rim of the table. He muttered something about wishing he was deaf, dumb, and blind.

The exhibit transformed the surface to show the effect of centrifugal force. The inverse-fourth-power attraction of gravity was stronger than inverse-cube repulsion near the center, so even when the reference frame began to spin, the well remained a well. But further away, centrifugal force took over and turned the downward slope of the approach into an ascent. And where the ascent reversed and the surface plunged, in place of the first well's circular trench there was a circular ridge. Compared to the three-dimensional universe, the entire potential energy surface was upside-down.

The exhibit spun them around with the reference frame. Then, its disembodied hand moving with them, it placed a particle on the outer slope of the ridge; unsurprisingly, it fell directly away from the center. A second particle, placed on the inner slope, fell straight into the well.

"No stable orbits." Orlando picked up the particle that was rolling away and tried to balance it precisely on the ridge, but he couldn't position it accurately enough. Paolo saw a flash of fear in his eyes, but he said wryly, "At least that means no Lacertas. Everything that's going to fall together would have done it long ago."

They walked on to the next exhibit, a model of the macrosphere's cosmological evolution. As matter clumped together under mutual gravitational attraction from the initial quantum fluctuations of the early macrosphere, rotational motion either cut in at some point and blew the condensing gas cloud apart, or the process "crossed over the ridge" and the collapse continued unchecked. Star systems, galaxies, clusters and superclusters, all stabilized by orbital motion, were impossible here. But the fractal distribution of the primordial inhomogeneities meant that the end products of the collapse process had a wide spectrum of masses. Ninety percent of matter ended up in giant black holes, but countless smaller bodies were predicted to form, sufficiently isolated to survive for long periods, including hundreds of trillions with a stability and energy output comparable to stars.

Orlando turned to Paolo. "Stars without planets. So where will the Transmuters be?"

"Orbiting a star, maybe. They could stabilize an orbit with light sails."

"Built out of what? There'll be no asteroids to mine. Maybe they created a lot of raw materials with the singularity when they first crossed through, but for anything new they'd have to mine the star itself."

"That's not impossible. Or they could live on the surface, if they chose. That's where any native life is expected to be found."

Orlando glanced back at the model, which included something like a Hertzsprung-Russell diagram, plotting the evolving distribution of stellar temperatures and luminosities. "I wouldn't have thought many stars would he cool enough. Except for brown dwarves, and they'd freeze completely in no time at all."

"You can't really compare temperatures. We're used to nuclear reactions being orders of magnitude hotter than chemical ones, making them inimical to biology. But in the macrosphere they both involve similar amounts of energy."

"Why?" Orlando's gestalt still betrayed a sense of unease, but he was clearly hooked now. Paolo gestured at an exhibit further along, beneath a rotating banner reading PARTICLE PHYSICS.

The macrosphere's four-dimensional standard fiber yielded a much smaller set of fundamental particles than the ordinary universe's six-dimensional one. In place of six flavors of quarks and six flavors of leptons there was just one of each, plus their antiparticles. There were gluons, gravitons, and photons, but no W or Z bosons, since they mediated the process of quarks changing flavor. Three quarks or three antiquarks together formed a charged "nucleon" or "antinucleon," similar to an ordinary proton or antiproton, and the sole lepton and its antiparticle were much like an electron and positron, but there was no combination of quarks analogous to a neutron.

Orlando scrutinized the table of particles. "The lepton is still much lighter than the nucleon, the photon still has zero rest mass, and the gluons still act like gluons… so what shifts the chemical energy closer to the nuclear?"

"You saw what happened with the gravity wells."

"What's that got to do with it? Ah. Same thing happens in an atom? Electrostatic attraction also goes from inverse-square to inverse-fourth, so there are no stable orbits?"

"That's right."

"Hang on." Orlando screwed his eyes shut, no doubt dredging ancient memories of his flesher education. "Doesn't the uncertainty principle keep electrons from crashing into the nucleus? Even if there's no angular momentum, the attraction of the nucleus can't squeeze the electron's wave too tightly, because confining its position just increases its momentum."

"Yes. But increases it how much? Confining a wave spatially has an inverse effect on the spread of its momentum. Kinetic energy is proportional to the square of momentum, making that inverse-square. So the effective 'force,' which is the rate of change of kinetic energy with distance, is inverse-cube."

Orlando's face lit up for a moment with the sheer pleasure of understanding. "So in three dimensions, a proton can't ever make an electron crash, because the uncertainty principle is just as good as centrifugal force. But in five dimensions, that's not good enough." He nodded slowly, as if coming to terms with the inevitability of it. "So the lepton's wave shrinks down to the size of the nucleon. Then what?"

"Once the lepton's inside the nucleon, it's kink—pulled inward by the portion of the charge that's closer to the center than it is itself, which is roughly proportional to the fifth power of the distance from the center. That means the electrostatic force stops being inverse-fourth-power, and becomes linear. So the energy well isn't bottomless; outside the nucleon it's too steep for the lepton to 'brace itself' against the sides, the way an electron does in three dimensions, but inside the nucleon the sides curve together and meet in a paraboloid."