“Originally existence was without spatial dimension as such, or to put it another way, each particle in existence introduced a new dimension. The configuration of existence was that of a stupendous simplex, made up of an infinite number of particles all equidistant from one another and all receding at the standard rate—through ‘recession’ here becomes a rarefied concept, since there were no such entities as time or distance to measure velocity by. The Simplex, as this primordial state is called, still exists, but it had become flawed. Through causes unknown a small part of it has collapsed into three dimensions, and this flattened ‘facet’ constitutes our universe.
“It is postulated that there may be other flattened facets on the Simplex. If a means of entering the Simplex could be found we could presumably travel to these other universes. Not only that, but a route through the Simplex would make all points in our local universe equally accessible, since the Simplex does not recognise relative distances. So far this old scientific dream has resisted all efforts to bring it to reality.
“The forces of nature that make our universe what it is are all consequent on the collapse of matter into three dimensions. Particles that have to share dimensions occlude one another and break the recessional relationship between other particles. A degree of fragmentary disunity then begins to occur in nature.
“The arising of relative velocities below the standard recessional rate is the first result to flow from this. The situation for a material body in the three-dimensional realm is that it is surrounded, at the limit of its Hubble sphere, by an opaque shell of particles receding from it at the standard absolute rate, the velocity of light. But any other body lying within the Hubble sphere will eclipse a part of the circumferential shell, so that each body will receive fewer recession lines from that part of its general environment in which the other lies. The asymmetric distribution of recession lines produces an opposition among them, ending in a modification of the apparent rate of recession between the bodies themselves. Seemingly the bodies recede at a slower rate in proportion to the deficiency in recession lines. In reality, of course, it is the space between them that is altered.
“If the bodies are sufficiently close—as close as the galaxies of our local group, for instance—the recessional pressure of the Hubble shell prevents them from receding at all. Instead, it begins to push them towards one another. This phenomenon we know as gravitation, the first of what are sometimes called the ‘attractive forces,’ though it is really only a screening effect. For reasons which will be covered later, the induced motion becomes an acceleration instead of a velocity, and the strength of the effect follows the law of perspective.
“At very close range, the recessional pressure is magnified to become the nuclear binding force. This also will be covered later in the course.
“A second major area of effects arises as a by-product of what has just been described. What happens to those recession lines connecting particles whose recession has slowed or been reversed? All particles lying within the Hubble sphere are attempting to recede from one another at the standard rate but are constrained from doing so. Recession lines joining these particles are undergoing strain; they respond by acquiring a compensating lateral component. These ‘strain lines’ form their own special kind of space, the space of electric charge.
“So we see that our three-dimensional realm really consists of a hierarchy of interpenetrating three-dimensional spaces. First there is absolute or inertial space consisting of a single standard velocity; this space is exuded by the Hubble shell. Within that relative space arises, containing a range of velocities. And as a by-product of relative space, interwoven with inertial space, is the strain space of electromagnetism, a space independent enough to create its own particles consisting solely of electric charge.
“Our introduction now is ended and we are ready to go into the subject in more detail. Please indicate which aspect interests you most: the historical, the mathematical, or the philosophical.”
Hesper, however, gave no answer. She had fallen asleep.
Mo was considerate enough not to rouse her. She woke two hours later, and feeling refreshed, decided to see more of the city.
After leaving the apartment she began to ascend. Early evening had turned to late dusk. Light had come on all over the moving city: shaded pastel light in the sidewalk eateries and drinkeries, sharp light that blazed on the tessellated plazas, pillars of light that rose up and down the moulded yellow towers. Up Hester went; up moving helter-skelter rampways, up slowly climbing city squares that were gradual elevators, up the gentle slopes of flying boulevards, avoiding, in her eagerness for new impressions, the fast lifts that could have lofted her in seconds, until she found a place where the panorama of Mo and its changing landscape were displayed below.
Pleasant it was to sit on an overhanging terrace, protected by a balustrade of genuine carved oak, sipping the drink that was brought her, enjoying the cool air and taking in that panorama. She had ignored the talk that was all around her as she climbed, being more interested in the smells of various foods from the grills of countless establishments as the Mohists flocked to their evening repast. But now, as she relaxed, she sensed among the others sharing the terrace with her a feeling of anticipation, almost of dread. The feeling seemed incongruous in a people so placid and good-natured, and for that reason alone it filled her with foreboding. She was about to speak to an elderly man at the next table when the cause of their dread appeared on the horizon.
At first it could, perhaps, have been another moving city, but soon it bulked too large for that and could only have been a peculiarly arc-shaped mountain of a yellow-puce colour. And then, as the time inexorably passed, it became too huge for any mountain.
The moon was rising. It was the moon.
Up it came, and up, more and more of it. It had closed the remaining distance to Earth in an amazingly short time. A hush fell over the moving city, a hush that lasted for hours while gradually the moon rose and became a vast plate that covered the world like a lid—though Hesper, an experienced space traveller, easily discerned its sphericity. No one spoke or moved, except to sip at the drinks that continued to be served by the dutiful waiters, both robot and human. Instead, everyone’s gaze and consciousness became transfixed by the new, solid sky that passed over.
The sun illuminated the-face of the satellite throughout from below the horizon, its light filtering round the atmosphere, though the moon’s disk eventually darkened towards the centre. The yellowishness of its early approach quickly vanished and it became first dazzlingly white then greyish and grained. Easily visible were the great craters gaping upside down, the ancient splashes of lighter dust that rayed out from many of them, and the vast flat plains. Visible too, were signs of the past works of man: furrows from mining operations, fine lines that were transport networks.
By midnight the entire disk had lifted itself clear of the landscape, a satellite ceiling hanging so low it was as if one could reach up and touch it, and leaving only a narrow rim of blackness to all points of the compass. Hesper realised it was so close it must be grazing Earth’s upper atmosphere. But how could this be? Long before now its approach should have heaved up such tides in sea, land and air as utterly to destroy everything upon the planet. Not only that, the satellite should be beginning to break up as a result of even greater tidal stresses induced in it by the larger body. It was a long way inside Roche’s limit.