John Wright - The Golden Transcendence

"Atkins did that because... because of the necessities of war...."

The reflection looked contemptuous. "I'm you. Don't try to fool yourself. That is the same reason why the Nothing pretended to try to steal the ship, and to get you here. To do that he had to make our life a living hell for a short time. The necessities of war. If that excuse applies to Atkins fighting Varmatyr, it applies to the Silent Ones fighting Sophotechs as well. Only their war is a great deal bigger."

"A war against reality! A revolt against reason."

The reflection shook its head. "No. The mathematics of the standard model break down under certain conditions. Right? Our science cannot predict or describe in any meaningful terms the interior conditions of a black hole. Right? But those interior conditions exist; they are real. And reality cannot lack integrity. Right? So the same mathematics must describe both sets of real conditions, both inside and outside, and there must be meta-laws describing the transitions and boundary conditions between them. Look at this."

Lines of mathematical symbols appeared on a nearby mirror, and images from non-Euclidean geometry. The mathematics started from the premise of the noniden-tity of unity, and a unity-to-infinity equivalence.

Phaethon frowned at them. The proofs had an internal self-consistency, granting the absurd premise, and normal mathematics was made a subset of this system by assuming a condition where infinity, by not equaling itself, was finite...

Phaethon turned away, "This is allegedly the irrational mathematics of the Second Oecumene, I suppose? It's nonsense. The whole thing forms a Goedelian null-set. If I numbered the lines of the proof and assign numbers from your number lines to them, by the lemma of your first proof, the proof itself disproves itself, and you get a set with fewer than no members."

The reflection nodded. "Like a geometric solid bigger on the inside than on the outside. How do you think the Silent Ones constructed a nonevaporating microscopic black hole? The ratio of interior volume to exterior volume is not one to one."

"Constructed.... ?" Phaethon, against his will found himself beginning to be interested. Then he drew back sharply. "No! This makes no sense! Nothing can escape from a black hole; no signal can get out; how could anything be built inside of one... ?"

The reflection looked at Phaethon disdainfully. Phaethon wondered if he looked as haughty as that when he disagreed with other people. Perhaps there was a reason why he had few friends within the Golden Oecumene.

The reflection was saying, "You know several ways of transmitting information out from a black hole; you just mentioned them now. Black holes have mass, rotation, and charge; this information, as well as the metric information of position, is transmitted from the interior to the exterior. A ghost machine could transmit virtual particles outside."

"Not and transmit information! The ghost particles would fall outside the light cone of the event-object!"

"If the speed of light and the location of the event horizon were determinable. Quantum uncertainties en-sure that these values are not fixed, except within a small statistical range."

Phaethon said, "But how could you build a machine inside the event horizon? To outside observers, it would take infinite time; tidal forces would destroy you; and the interiors of black holes are homogenous points..."

The reflection said, "You know an 'event horizon' only exists to outside observers. It's not a solid sheet or something. An incoming object can drop through it without noticing anything except weird light effects overhead. Tidal effects only occur for smaller masses"-an equation appeared on the mirror-"and, in any case, can be counterbalanced by establishing a gravity null zone."

A diagram appeared, showing a pyramid on the surface of a Second Oecumene station, its apex pointed toward the black hole. Above the pyramid was a rotating ring, so that a line reaching up from the apex passed through the center.

Phaethon said, "I've seen that before___"

"In the Last Broadcast. The Silent Ones engineered a way to transmit noumenal information down the gravity well without having tidal forces distort the signal. These rings are made of neutronium, and are rotating at nearly the speed of light. The gravitational 'frame drag' from the rotation pulls on the black hole metric and locally distorts it. The event horizon is pushed inward toward the hole, for the same reason that, theoretically, your escape velocity on a moon is less if a large gravitating body is directly overhead. The larger or the nearer the overhead body, the closer the net gravity acceleration acting on you drops to zero. Through these null points, information, even the noumenal information of a coded mind, can pass into the event horizon undistorted."

Other mirrors showed other engineering details. Diagrams appeared, calculations, examples, blueprints.

Phaethon murmured, "But the drop to the event horizon would take infinite time to occur...."

"Only to outside observers. Once inside, time becomes a spatial direction, and does not necessarily point in the direction of increasing entropy. That is a function of the radius."

"But there are no interior conditions, no place to build anything...."

A final diagram appeared, this one of hollow sphere within hollow sphere. "Suppose you have a hollow and even sphere made of homogenous material. The surface gravity is high. What is the interior gravity?"

Phaethon snorted. This was an apprentice question for first-term students. "Zero. Net gravity inside a hollow sphere is always zero."

"The sphere is neutronium. The surface gravity is very high. The escape velocity is near the speed of light. Same result?"

"Of course."

"The escape velocity is greater than the speed of light. By definition, it is a black hole. The interior velocity is still zero, isn't it? And you can build anything you want inside there, can't you? A civilization? A machine intelligence the size of Jupiter? Anything. And if you ran out of 'space,' you can just peel off an even layer of the inside material, ball it up so that its density gives it the proper Schwarzschild metric properties, and pop it into the center, and make another one___The space-time metric is not bound by any particular rational value at that point. It can be bigger on the inside than on the outside, since the radius of the neutronium sphere and the radius of the event horizon are unrelated. You can just make more space. The size of a planet, a Dyson sphere, a galaxy. A universe. More time. Infinite time. World within world, without end. Enough worlds for anyone who wants one...."

Phaethon looked at the image of sphere within sphere, opening endlessly into further and deeper endlessness. His mind was racing, studying the math, studying the diagrams, looking for errors, contradictions. Looking for some reason to disbelieve, binding none. The image of the spheres, darkness within darkness, nothingness within nothingness, drew his gaze, as if he were falling into a well.

The reflection said, "We can go to Cygnus X-l. And see. The Nothing Philanthropotech can guide us. Give him control of the ship."

That snapped Phaethon's head back up. He spoke coldly: "No one is taking my ship. No one. Your Nothing Machine is a monster. How can you agree with anything it says? Look at it! Look at the structure! The very picture of insanity, a mind without a center."

"No, brother." The reflection pointed over his shoulder with his thumb, indicating the swirling maelstrom appearing in the mirror behind him. "This is an image of liberty. Think of the economic process of the free market. Think of the organization you use on your own ship. Each separate element is free to cooperate or not with the common goal; no central hierarchy is needed to impose that goal, no basic logic-structure. All that is needed is a context, a philosophy, to give the cooperative effort a context in which to act. It is a self-organizing and self-regulating chaos. This, this type of mind, this type of community, represents my basic values, my basic view of life. That, more than anything, is what convinced me."