Convergent Series

by Charles Sheffield

  "Just who is Max Perry? Why is he important?"

  He had asked that question during his first briefing, as soon as the planetary doublet of Dobelle became more than a name to him. For Dobelle was an insignificant place. Its twin planetary components, Opal and Quake, orbiting a second-class star far from the main centers of the local spiral arm, were almost as poor as Teufel.

  Scaldworld, Desolation, Teufel, Styx, Cauldron—sometimes it seemed to Rebka that poverty was their only bond, the single link that held the Phemus Circle worlds together and separated them from their richer neighbors. And from the records, Dobelle was a worthy member of the club.

  The records on Perry were transmitted to him, too, to be scanned at his leisure. Typically, Hans Rebka reviewed them at once. They made little sense. Max Perry had come from origins as humble as Rebka's own. He was a refugee from Scaldworld, and like Rebka he had made his way rapidly upward, apparently bound for a job at the very top of Circle government. As part of the general grooming process for future leaders, he had been sent for a one-year tour of duty on Dobelle.

  Seven years later he had still not returned. When promotions were offered, he refused them. When pressures were exerted to encourage him to leave the Dobelle system, he ignored them.

  "A large investment," whispered the distant voice beyond the stars. "We have trained him for many years. We want to see that investment in him repaid . . . as you repaid it. Determine the cause of his difficulties. Persuade him to return, or at least to tell us why he refuses to do so. He ignores a direct order. Opal and Quake desperately need people, and Dobelle law prohibits extradition."

  "He won't tell me anything. Why should he?"

  "You will go to Dobelle as his supervisor. We have arranged for a senior position to be created within the ruling oligarchy. You will occupy it. We agree that Perry will not reveal his motives as the result of a simple inquiry. That has been tried. Use your own strengths. Use your subtlety. Use your initiative." The voice paused. "Use your anger."

  "I am not angry with Perry." Rebka asked more questions, but the answers offerd no enlightenment. The assignment still made no sense. The central committee of the Phemus Circle could waste its resources if it so chose, but it was a stupid mistake to waste Rebka's talents—he lacked false modesty—where a psychiatrist seemed more likely to succeed. Or had that already been tried, and failed?

  Hans Rebka swung his legs off the bunk and walked over to the window. He stared up. After a three-day trip through five Bose Network nodes and a subluminal final stage, he had finally landed on the Starside hemisphere of Opal. But Starside was a bad joke—even before dawn there was not a star to be seen. At that time of year, close to Summertide, cloud breaks on Opal were rare. Approaching the planet, he had seen nothing but a uniform, shining globe. The whole world was water, and when Dobelle swung in at its closest to its stellar primary, Mandel, the summer tides reached their peak and the oceans of Opal never saw the sun. Safety lay only on the Slings, natural floating rafts of earth and tangled vegetation that moved across Opal's surface at the prompting of winds and tides.

  The biggest Slings were hundreds of kilometers across. The Starside spaceport was situated on one of the largest. Even so, Rebka wondered how it would fare at Summertide. Where would it go, and would it survive when the main tides came?

  If his birthworld of Teufel had been Fire, then Opal was surely Water.

  And Quake, the other half of the Dobelle planetary doublet?

  Hell, from what he had heard of it. Nothing that Rebka had read or had been told in his briefings had had one good word to say about Quake. Events on Opal at Summertide were said to be spectacular and hair-raising—but survivable. On Quake they were deadly.

  He looked up at the sky again and was startled to see that it was light. Opal and Quake were tidally locked to each other, and they spun around their common center of mass at a furious rate. One day in the Dobelle system was only eight standard hours. His morning musings had taken him well past dawn. He would just have time for a quick breakfast; then an aircar would carry him around the planet to Quakeside—and to the most stupid and least productive job of his life.

  Rebka swore, cursing the name of Max Perry, and walked across to the door. He had not yet met the man, but he was ready to dislike him.

  ARTIFCT: PARADOX

  UAC#: 35

  Galactic Coordinates: 27,312.443/15,917.902/+135.66

  Name: Paradox Star/planet association: Darien/Kleindienst

  Bose Access Node: 139 Estimated age: 9.112 ± 0.11 Megayears

  Exploration History: It is not known how many times Paradox was discovered, and all knowledge of it then lost. What is known is that in E. 1379 Ruttledge, Kaminski, Parzen, and Lu-lan organized a two-ship expedition to investigate the light-refraction anomaly now known as Paradox.

  Arriving first, Ruttledge and Kaminski recorded on their ship's main computer the intention of entering the Paradox sphere using the exploration pinnace, while the main ship remained well clear. Five days later, Parzen and Lu-lan arrived and found the other ship and its pinnace, both in perfect working condition. Ruttledge and Kaminski were in the pinnace, alive but suffering from dehydration and malnutrition. They were incapable of speech or simple motor movement, and subsequent tests showed that their memories held no more information than the mind of a newborn baby. The data banks and computer memory on the pinnace were wiped clean.

  Following a review of the other ship's records, Parzen and Lu-lan drew lots to decide who would make a second trip inside the Paradox sphere. Lu-lan won and made the descent. No signals were received from him by Parzen, although there had been prior agreement to send a message every four hours. Lu-lan returned, physically unharmed, after three days. His memory was empty of all learned information, though somatic (instinctive) knowledge was unchanged.

  Paradox was declared off-limits to all but trained investigators in E. 1557.

  Physical Description: Paradox is a spherical region, fifty kilometers in diameter. Its outer boundary displays "soap bubble" color shifts across the surface, reflecting or transmitting different wavelength radiation apparently randomly.

  The sphere is opaque in certain spectral regions (1.2-223 meters) and perfectly transparent in others 5.6-366 micrometers). Nothing is known of the appearance of Paradox's interior.

  Paradox's size and appearance are not invariant. Changes in size and color have been reported nine times during its history.

  Physical Nature: Based on transmission through it, Paradox is believed to have a complex interior structure. However, no first-hand information has ever been obtained, because of Paradox's information-destroying nature. Most analysts believe that Paradox is the four-dimensional extrusion in space and time of a body of much higher dimension, perhaps the twenty/three/seven knotted manifold of Ikro and H'miran.

  Intended Purpose: Unknown. However, Scorpesi has conjectured that Paradox is a "cleansing vat" for large Builder intelligent artifacts, such as Elephant (see Entry 859), prior to reuse. Note, however, that this suggestion is inconsistent with the physical dimensions (4,000 x 900 kilometers) of Elephant itself, unless such objects were subjected to multiple passes through the Paradox sphere.

  —From the Lang Universal Artifact Catalog, Fourth Edition.

  CHAPTER 2

  Summertide

  minus thirty-six.

  The second shift of the working day was just beginning, and already it was clear to Birdie Kelly that it was going to be a bad one. The new supervisor might still be half a world away on Starside, but already the boss was brooding over the man's impending arrival.

  "How can someone who has never even visited this system be competent to control travel between Opal and Quake?" Max Perry stared at Birdie with pale, unhappy eyes. Birdie looked back, saw the starved jut of Perry's jaw, and thought how much good it would do if the other man could just eat a square meal and relax for a day or two.

  "Quake traffic is our job," Perry went on. "We've been doing it for
six years. How much does this Rebka, a total stranger, know about that? Not a thing. Do they think at Circle headquarters that there's nothing to it, and any idiot can understand Quake? We know the importance of forbidding access to Quake. Especially now, with Summertide almost here. But do they know it?"

  Birdie listened to Max Perry's stream of complaints and nodded sympathetically. One thing was sure: Perry was a good man and a conscientious boss, but he had his obsessions. And Captain Hans Rebka, whoever he might be, was sure going to make Birdie's own life more difficult.

  Birdie sighed and leaned back in his wicker chair. Perry's office stood on the top floor of Opal's highest Quakeside building, a four-story experimental structure that had been built to Perry's own specifications. Birdie Kelly still felt uncomfortable inside it. The foundation extended down through layers of mud and a tangle of dead and living roots, right on past the lower basement of the Sling to the brackish waters of Opal's ocean. It was buoyed by a hollow chamber just below the surface, and the hydrostatic lift from there carried most of the load.

  Even such a low building did not feel safe to Birdie. The Slings were delicate; without firm foundations, most buildings on Opal were held to one or two stories. For the past six months this Sling had been tethered in one spot, but as Summertide approached that would be too dangerous. Perry had ordered that in eight more days the Sling should be released to move at the mercy of the tides—but was that soon enough?

  The communicator sounded. Max Perry ignored it. He was leaning back in his reclining chair, staring up at the ceiling. Birdie rubbed at his threadbare white jacket, leaned forward, and read the crude display.

  He sniffed. It was not a message likely to put Max Perry in a better mood.

  "Captain Rebka is closer than we thought, sir," he said. "In fact, he left Starside hours ago. His aircar should be ready to land in a few minutes."

  "Thanks, Birdie." Perry did not move. "Ask the Slingline to keep us posted."

  "I'll do that, Commander." Kelly knew he had been dismissed, but he ignored it. "Before Captain Rebka gets here you should take a look at these, sir. As soon as you can."

  Kelly laid a folder on the plaited-reed tabletop that lay between them, sat back, and waited. Max Perry could not be rushed in his current mood.

  The ceiling of the room was transparent, looking directly up into Opal's normally cloudy skies. The location had been carefully chosen. It was close to the center of Quakeside, in a region where atmospheric circulation patterns increased the chance of clear patches. At the moment there was a brief predusk break in the overcast, and Quake was visible. With its surface only twelve thousand kilometers from the closest point of Opal, the parched sphere filled more than thirty-five degrees of the sky like a great, mottled fruit, purple-gray and overripe, poised ready to fall. From that distance it appeared peaceful, but already the dusky limb of the planet showed the softening of edges that spoke of rising dust storms.

  Summertide was just thirty-six days away, less than two standard weeks. In ten days' time Perry would order the evacuation from Quake's surface, then monitor that evacuation personally. In every exodus for the past six years he had been the last man or woman to leave Quake, and the first to return after Summertide.

  It was a compulsion with Perry. And regardless of what Rebka might want, Birdie Kelly knew that Max Perry would try to keep it that way.

  Already night was advancing on the surface of Opal. Its dark shadow would soon create the brief false-night of Mandel eclipse on Quake. But Perry and Kelly would not be able to see that. The break in the overcast was closing, eaten away by swirls of rapidly moving cloud. There was a final flash of silver from far above, light reflected from the glittering knot of Midway Station and the lower part of the Umbilical; then Quake faded rapidly from view. Minutes later the roof above their heads showed the starred patterns of the first raindrops.

  Perry sighed, leaned forward, and picked up the folders. Kelly knew that the other man had registered his earlier words without really hearing them. But Perry knew that if his right-hand man said he ought to look at the folder at once, there was a good reason for it.

  The green covering held three long message summaries, each one a request for a visit to the surface of Quake. There was nothing very unusual in that. Birdie had been ready to give routine approval pending examination of travel plans—until he saw the source of the requests. Then he knew that Perry had to see them and would want to study them in detail.

  The communicator buzzed again as Perry began to concentrate on the contents of the folder. Birdie Kelly took one look at the new message and quietly left the room. Rebka was arriving, but Perry did not need to be on the airstrip to welcome him. Birdie could do that. Perry had quite enough to worry about with the visit requests. Every one had come from outside the Dobelle system—outside, in fact, the worlds of the Phemus Circle. One was from the Fourth Alliance, one from a remote region of the Zardalu Communion, so far away that Birdie Kelly had never heard of it; and one, oddest of all, had been sent by the Cecropia Federation. That was unprecedented. So far as Birdie knew, no Cecropian had ever come within light-years of Dobelle.

  Stranger yet, every visitor wanted to be on the surface of Quake at Summertide.

  When Birdie Kelly returned he did something that he reserved for emergencies. He knocked on the door before he came in. The action guaranteed Perry's instant attention.

  Kelly was holding yet another folder, and he was not alone. Behind him stood a thin, poorly dressed man who stared about with bright dark-brown eyes and was apparently more interested in the room's meager and tattered furnishings than in Perry himself.

  His first words seemed to bear out that idea. "Commander Perry, I am pleased to meet you. I am Hans Rebka. I know that Opal is not a rich planet. But your position here would surely justify something better than this."

  Perry put down the folder and followed the other man's inquisitive eyes as they surveyed the room. It was a sleeping chamber as well as an office. It held no more than a bed, three chairs, a table, and a desk, all battered and well used.

  Perry shurgged. "I have simple needs. This is more than enough."

  The newcomer smiled. "I agree. All men and women would not."

  Regardless of whatever other feelings his smile might hide, part of Rebka's approval was quite genuine. In the first ten seconds with Max Perry he was able to dispose of one idea that had come to him after reading the other's history. Even the poorest planet could provide great luxury for one person, and some men and women would stay on a planet because they had found wealth and high living there, with no way to export it. But whatever Perry's secret, that could not be it. He lived as simply as Rebka himself.

  Power, then?

  Hardly. Perry controlled access to Quake, and little else. Permits for offworld visitors went through him, but anyone with real clout could appeal to a higher authority in the Dobelle system council.

  So what was the driving force? There had to be one; there always was. But what was it?

  During the official introductions and the exchange of meaningless courtesies on behalf of the government of Opal and the General Coordinators' office for the Phemus Circle, Rebka turned his attention to Perry himself.

  He did it with real interest. He would rather be exploring Paradox, but despite his contempt for the new assignment he could not turn off his curiosity. The contrast between Perry's early history and his present position was just too striking. By the time Perry was twenty years old he had been a section coordinator in one of the roughest environments the Circle could offer. He had been subtle in handling problems, and yet he had been tough. The final assignment for one year to Opal was almost a formality, the last tempering of the metal before Perry was judged ready for work in the Coordinators' office.

  He had come. And he had stuck. In one dead end job for all those years, unwilling to leave, lacking all his old drive. Why?

  The man himself gave no clue as to the source of the problem. He was pale-faced
and intense, but Rebka could see as much pallor and intensity just by looking in the mirror. They had both spent their early years on planets where survival was an achievement and thriving was impossible. The prominent goiter in Perry's neck spoke of a world where iodine was in short supply, and the thin, slightly crooked legs suggested an early case of rickets. Scaldworld's tolerance of plant life was grudging. At the same time Perry appeared in excellent health—something that Rebka could and would check in due course. But physical well-being only made it clearer that there must be mental problems. They would be harder to examine.

  The inspection was not one-sided. While the formal exchanges of government greetings were taking place, Rebka knew that Perry was making his own assessment.

  Did he hope that the new supervisor would be a man burned out from previous service or excesses, or perhaps some lazy pensioner? The Circle government had its share of people looking for sinecures, idlers willing to let Perry and others like him run the operation any way they wanted to, provided that the boss was not asked to do any work.

  Apparently Perry wanted to find out whom he was dealing with and would waste no time in doing so, for as soon as the final courtesies had been exchanged he asked Kelly to leave and gestured Rebka to one of the chairs. "I assume that you will take up your duties here very soon, Captain?"

  "More than soon, Commander. My duties on Opal and Quake have begun. I was told that they commenced at the moment the ship touched down on Starside Port."

  "Good." Perry held out the green folder plus the fourth and latest document that Kelly had handed to him. "I was in the middle of reviewing these. I would appreciate it if you would take a look and give me your opinion."