Orlando held these three negations in his mind at once. The hyperal plane was clearly defined by his anatomy, so long as he remembered that it was perpendicular to all three of his body's axes.
One vaguely cruciform constellation lay almost flat in the hyperal plane: every one of the four stars shared roughly the same altitude above the horizon, and the same left-right azimuthal bearing, and yet they were not bunched together in the sky; the hyperal directions kept them as far apart as the stars of the Southern Cross. Orlando struggled to attach labels to them: sinister and dexter for the quadral pair, gauche and droit for the quintal. It was completely arbitrary, though, like assigning compass points to a fictitious map drawn on a circular piece of paper.
Several degrees away to the left-up-dexter-gauche he could see another four stars; these lay in the lateral plane, the plane of the "ordinary" sky. Mentally extending the two planes and visualizing their intersection was a very peculiar experience. They met in a single point. Planes were supposed to intersect along lines, but these ones refused to oblige. A quadral line running between the sinister and dexter stars of the Hyperal Cross pierced the vertical plane at right angles to both arms of the Vertical Cross… but so did the quintal line. There were four lines in the sky—or in his head—that were all mutually perpendicular.
And the sky still looked flat.
Nervously, Orlando let his gaze drop. Stars were visible below the horizon—not through the ground, but around it, as if he was standing on a narrow, jutting cliff, or a sharp pillar. He'd chosen to have no power to twist his head or body out of the usual three dimensions of the scape, though his eyes bulged literally out of his skull, hyperally, to capture a broad swath of extra information. He pictured a vertical Flatlander with two eye-circles, one above the other, suddenly made spherical, their axes still confined to swivel within the planar world but their lenses, their pupils, their field of view, protruding beyond it. As well as being a ludicrous anatomical impossibility, this compromise was now beginning to induce a giddy mixture of vertigo and claustrophobia. The Island had negligible width in the extra dimensions, and he could see clearly that the slightest hyperal movement of his body would send him plummeting into space like a drunken cosmic stylite. At the same time, the physical confinement that prevented this made him feel like he was wedged between two sheets of glass, or afflicted by some bizarre neurological disease that robbed him of the ability to move in certain directions.
"Restore me."
His visual field collapsed to a relative pinhole, and for a moment he felt so infuriatingly diminished that he shook his head wildly, trying to cast off the blinkers. Then abruptly his vision seemed gloriously normal, and the macrosphere's wide sky was like a fading memory of a disorienting optical illusion.
He wiped the sweat from his eyes. It was a start. A small taste of reality. Maybe he'd work up the courage eventually to wander a fully five-dimensional scape wearing a five-dimensional anatomy. Apart from the alarming possibility of glancing down and catching a glimpse of his own internal organs—like a Flatlander who twisted vis head out of the plane—unless he added two dimensions to his simulated flesh—he'd have the balancing skills of a paper doll, once he was free to fall quadrally and quintally.
But even gaining the anatomy and instincts to navigate five dimensions would only be scratching the surface. There'd always be more to adapt. In the flesh, he'd been scuba-diving dozens of times, but he'd barely been able to communicate with amphibious exuberants. The Transmuters had been here for at least a billion years or a roughly comparable period of macrosphere time, in terms of the rates of the most likely biochemical or cybernetic processes. Of course, they were sentient creatures in control of their own destiny, not beached fish required to have the right mutations in order to survive. They might not have changed at all. They might have clung like good realists—or good abstractionists—to simulations of the old world.
But over the eons, they might easily have decided to acclimatize to their new surroundings. And if they had, communication could prove impossible, unless someone, in the expedition was prepared to meet them halfway. Unless someone was prepared to bridge the gap.
The Flight Deck was crowded, making it a perfect environment in which to practice negotiating unpredictable obstacles, but Orlando found himself spending most of his time transfixed by the view. One entire wall of the penteractal scape was given over to a giant window, and the magnified image of Poincare behind it offered a perfect excuse to do nothing but stand and stare. Moving about in public 5-scapes still made Orlando intensely self-conscious, less out of any fear of falling flat on his face than from a strong sense that he could take no credit for the fact that he didn't. His 5-body came equipped with numerous invaluable reflexes, as any real macrospherean body almost certainly would, but relying on these alien instincts made him feel like he was operating a telepresence robot programmed with so many autonomous responses that any instructions he gave it would be superfluous.
He glanced down at the bottom of the window. The most trivial details in a 5-scape could still be hypnotic; the tesseract of the window met the tesseract of the floor along, not a line, but a roughly cubical volume. That he could see this entire volume all at once almost made sense when he thought of it as the bottom hyperface of the transparent window, but when he realized that every point was shared by the front hyperface of the opaque floor, any lingering delusions of normality evaporated.
With Poincare, delusions of normality were untenable from the start; even its outline confounded his old world notions of curvature and proportion. Orlando could see at a glance that the star's four-dimensional disk filled only about one third of the tesseract he imagined framing it—far less than a circle inscribed within a square—and this made some ill-adapted part of him expect it to sag inward as it arced between the eight points of contact with the tesseract. It didn't, of course. And since the polis had come close enough for the star's continents to he resolved, he'd been bedazzled. The borders of these giant floating slabs of crystallized minerals were intricate beyond the possibilities of three-dimensional nature; no wind-carved landscape, no coral reef could have been as richly convoluted as this silhouette of dark rock against glowing magma.
"Orlando?"
He moved slowly, consciously, thinking it through, following his body's suggestions but refusing to act on autopilot. Paolo was to his rear-left-dexter-gauche, and he turned first in the horizontal plane, then the hyperal. Orlando was blind to signatures, but his visual cortex had been rewired to grant five-dimensional facial cues the same significance as the old kind, and he recognized the approaching four-legged creature immediately as his son.
Bipeds in the macrosphere would have been even less stable than pogo sticks on Earth; with sufficient resources devoted to dynamic balancing, anything was possible, but no one in C-Z had opted for such an unlikely 5-body. Quadrupeds on a four-dimensional hypersurface had just one degree of instability; if the left and right pairs of feet defined orthogonal lines in the hyperal Plane, it created a kind of cross-bracing, leaving only the problem of swaying forward or backward—no more than bipeds faced on two-dimensional ground. Six-legged macrosphereans would be as stable as Earth's quadrupeds, but there was some doubt as to whether they could mutate into an upright species with two arms; eight limbs seemed to allow an easier transition. Orlando was more interested in the choices available to the Transmuters than the dynamics of natural selection, but like Paolo he'd opted for four arms and four legs. No centaur-like extensions to their trunks had been required; the hyperal space around their hips and shoulders provided more than enough room for the extra joints.