Daphne said, “He just rejected the load. But you’re right. There are blind spots here. Thousands of them. I can load it in some places he cannot see.”
The silver mask above her played several lilting notes, and delicately said, “How will you accomplish this, as I am here, watching you?”
Daphne scowled. “You’re going to see it, but you’re not going to believe it. You cannot see your own blind spots.”
“Nor can you, it seems, see yours. It is you who are astonished by what you see, not I. Based on this, which one of us, Phaethon or I, do you think has been fundamentally deceived?”
2.
Daphne’s dream wand was shaped, at the moment, like a dueling pistol, and she drew it from her hip. She pointed at the little mirror upon which Phaethon had called up the four lines of the gadfly virus code, and touched her ramrod to record it. Then she pointed the barrel, aiming with both hands, at the large mirror where the image of the Nothing Machine mind structure swirled like some hungry whirlpool, glistening like a thousand twisted spiderwebs. She was looking for a dark line, one with a low priority, but the strands of the web kept shifting, turning, changing. The darkness kept appearing and disappearing in separate spots, and there seemed no rhythm or reason to it.
When she pulled the trigger, the virus reloaded into the ship-mind, at the line and address indicated on the mirror with her dream wand.
The line affected grew bright and moved immediately toward the empty center of the whirlpool of thoughts, establishing itself as a central and high-priority thought, a question that could not be ignored. There was a very rapid exchange of information packages with other lines of thought, a flurry of rapid questions-and-answers. Then, satisfied, the other lines moved away from this central line, drawing away their time and attention. The central line, ignored, fell into a low priority, darkened, and was forgotten. The core of the Nothing was still blank.
Evidently the Nothing Machine had answers perfectly satisfactory to itself, to whatever questions the gadfly had asked it about its morality and basic assumptions. And Daphne had seen no interruptions, no organized darkness, such as would have signified the appearance of the conscience redactor.
Could there be no redactor, after all? Could this machine actually be deliberately illogical, rationally irrational?
Daphne did not believe it. She raised the pistol and fired again and again at the mirror, trying to hit the sliding chaos of darkness surrounding the spinning image.
It was not working.
3.
Phaethon, with his hand on the mirror, staring as if into the depth of some bottomless maelstrom, whispered aloud, “What did I assume? Where is the error?”
His own face now appeared in the glass, fingers raised and touching his. The maelstrom of the Nothing thought-architecture was still behind the reflection, so his face seemed to wear a halo of spiderwebs and spinning darkness. Phaethon squinted, wondering what was wrong with the reflection. Then, he realized it wasn’t a reflection. His face was bare, his hair was flying free, and he was dressed not in his armor but in a somber black jacket and high white cravat.
The reflection said, “We assumed the universe was rational. What if it is not?”
4.
Phaethon said to his reflection in the mirror: “I don’t believe in you. I could not have been convinced—not honestly convinced—by any argument started from that assumption. It is nonsense.”
The reflection gave a short nod, and said, “Let me rephrase. What we call rational reality is a subset of a larger system. That system includes the conditions which take place inside the event horizon of a black hole, where all our laws of mathematics, our categories of time and space, identity and causality break down. Our Sophotechs, with their mathematics and their logic, could not understand or operate inside a black hole. The Second Oecumene machines could, and can, and do. The reason why the thought-architecture you’re looking at seems to make no sense, is for the same reason that we could not decipher Ao Varmatyr’s thinking, even when we had a noetic reading of him. It is based on irrational mathematics.”
Phaethon shook his head. “If you think the laws of logic are not absolute, then you are not a version of me. Try to build a bridge without believing two plus two support girders equals four support girders, and you’ll see what I mean.”
The reflection said, “Try to build a bridge inside a black hole, where space is so warped that one girder acts like two or three, and uncertainty values are greater than unity, and maybe you can build it. But no, please do not accuse me of betraying my principles. All I have done, now, is apply them consistently. Our idea of logic may be limited to the conditions that obtain in normal timespace, the conditions under which we all evolved, and for which our Sophotechs were built. However, the Nothing Machine was constructed under conditions where our categories of causation and identity do not apply. It was built to serve a moral system which our Sophotechs, by axiom, reject.
What I learned, and the thing that convinced me, was that I found out I was making the same axiomatic assumption as the Sophotechs, but, I realized, I was not consistently applying it. Also, certain basic facts about the Nothing Machine, and about the history of the Second Oecumene, are just dead wrong. There is much more going on here, I’m afraid, than what first appears. Find out the facts before you judge.”
Phaethon said angrily to his reflection, “I cannot believe you let me be convinced by this monster! He tried to steal my ship! He’s trying to steal it now! What in the world could convince you?”
The reflection said, “He was trying to steal it from you only to give it to you.”
“More nonsense!”
“No, listen. It was meant to make you the hero of the Second Oecumene, just like Ao Varmatyr said. And if that had been you there on the bridge then, you would have been convinced by Ao Varmatyr. He wanted to reason with you. Instead, Atkins slaughtered him.”
“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 nonidentity 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 ensure 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 counter-balanced 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 spacetime 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. Finding 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-1. And see. The Nothing Philanthropotech can guide us. Give him control of the ship.”
5.
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.”
Daphne, who had been silent, watching him, now leaned from her throne, and said, “Darling, you are really creeping me out talking to yourself that way. You know it is just a fraud! If you are going to talk to the Nothing Machine, talk to the other illusion, the one with the wild hair. At least it looks dead and unnatural and has a fashionable tailor. Not to mention background music. But don’t think those are your words just because they are coming out of what looks like your mouth!”
A ring of chimes accompanied the soft words issuing from the silver mask. The feathery antennae nodded. “The image is accurate. Phaethon, should he consent to hear the evidence, and learn the facts, will, without any outside interference, be convinced.”
Phaethon looked over at her. He pointed at the mirror showing the thought-diagram of the Nothing Mind, the whirlpool. “I don’t know why the gadfly virus did not do anything. Maybe the irrational mathematics somehow can work, or . . . or something. There is something wrong with what we are seeing, but I don’t know what it is. . . .”
Daphne said, “Snap out of it! There is no paradox! There has to be a core logic. It is just hidden. I’m making a data-ferret, and loading it. I’ll find the damn thing. That conscience redactor has to be in there somewhere. There has to be a command-level core logic running this whole thing, and the redactor will have access to it. Keep talking! We just have to hit a topic that the conscience redactor will react to! Once it shows itself, we win!”
“But what if—” Phaethon started.
“What if the Nothing is right after all?” Phaethon’s reflection finished.
The silver mask said mildly, “My thoughts are open for your inspection. There is no deception here.”
Daphne was listening to the conversation between Phaethon and Phaethon.
Perhaps she was thinking of her old vocation, because Daphne uttered a word that referred to horse droppings. Then she said, “Just keep talking! If he convinces you, then he convinces you—fine. We’ll both turn into monsters and go kill off our family and friends, and then jump down a b
lack hole!”
“At least we will be together, my dear,” said Phaethon’s reflection said to her.
“Will you shut him up?!” Daphne scowled, frowning at the mirror in front of her, and unfolding an old-fashioned command-easel from her throne arm. She muttered, “Doesn’t even sound like you. . . .”
Daphne was startled to see her own face appear in the mirror.
6.
“Oh, no! Not you, too!” She pointed an angry finger at the reflection. “Don’t you start with me! Switch off !”
The reflection ignored the command. Instead she said, “You’ve never turned your back on truth before, no matter how it hurt. Do that now, and you are just like Daphne Prime! And you’re not like her! And deciding not to listen to what I have to say before you hear me say it, well, that’s just another type of drowning. And that’s just not the way you are! I should know!”
Daphne looked skeptical. “And just how many simulations of me did he have to run before, by chance, he found one who was convinced? A thousand? Ten thousand?”
The reflection seemed to lean forward, as if she were able to come blazing out of the glass by sheer force of conviction. “Don’t you dare talk to me that way! I do not change my mind for little things and I do not let people tell me what to do! Not even me. Or you. Or whatever. Listen. Are you going to listen?”
“Who? Me? Trapped onboard a sunken ship with a monster and my fiancé ex-husband who is slowly going mad? Where am I going? Talk yourself blue in the face. But I’m looking to see how many simulations he ran.”
Daphne called up the information on the simulation runs and frowned. There was something odd here.
She slowly turned and stared at her reflection.
“Just . . . what . . . did . . . he . . . say?”
“You mean, what did he say to convince me in one try . . . ?” The mirror image smiled Daphne’s private smile, the one she only used in looking glasses, when she was very pleased with herself. “Something wonderful! Listen: What is the one thing we are afraid of?”