Dr. Waters's smile brightened. "Have you ever heard of the Paradox of the Infinite Hotel?" he asked.

"No," said Mihalik impatiently.

"Time travel is a mother lode of paradoxes," said Waters. "Have a fondness for them, myself. Kind of a hobby of mine. Studied them all in the future. Don't pretend to understand them all the way they do centuries from now. They have them all sorted out there. But the Hotel, now, I do comprehend. Imagine that there's a hotel with an infinite number of rooms."

"What does this have to do with getting Cheryl and me home?" Mihalik said. There was a kind of animal snarl in his voice.

Dr. Waters ignored him. "And there's a guest in every room in the place, get it? Now a convention comes in late in the day. Big convention. Even an infinite convention, with no reservations in advance.

They're all tired from traveling. People want to go up to nice clean rooms, wash up, take a nap, go out for dinner. Maybe find some girls."

"What's the point?" shouted Mihalik.

"So the desk clerk is a little upset because all his rooms are taken, and he has to deal with all these grumpy salesmen or whatever they are. Then he has a brilliant idea. He goes to Room 1 and knocks on the door and takes the guest from that room and puts him in Room 2. Then he puts the original Room 2 guest in Room 4. He puts the Room 3 guest in Room 6. See? What he's doing, he's putting all the old guests in all the even-numbered rooms. There's an infinite number of even numbers, so it's no problem.

They'll fit. Then he takes the infinite number of new convention people, and puts them in the now vacant odd-numbered rooms. It all works out very well unless too many of them call down to the desk for early wake-up calls. And they better not all want ice at the same time, either."

Mihalik was furious. He wanted to grab Dr. Waters the way he had grabbed Smith's shirt, but he restrained himself. "You're saying that every Frank and Cheryl in all the infinite possible universes just moved over one, like playing musical chairs."

"Something like that," said Dr. Waters. "Gratified you can see my meaning. You're not real, not by the standards of this universe."

"I wonder if all the Franks and Cheryls are having this problem," said Mihalik. He shivered as he glimpsed the vast array of Mihaliks, all lost in this same terrible vision.

"Many of them are settling down comfortably in whatever situation they find themselves," said Dr.

Waters. "As you should. Accept resettlement."

"No," said Mihalik. "We're going to find our way home."

Dr. Waters thought for a moment. "Why don't you and Cheryl come with me? I have something to show you. It might change your thinking about our world."

Mihalik only grunted; Cheryl came toward the desk. "If you can help us get home," she said, "we'll do anything you ask."

"You should be learning," said Dr. Waters, "that you can't choose among alternate realities as if you were looking at tomatoes in a grocery store."

"We know that," said Cheryl. "But why can't you just reverse whatever process brought us here in the first place?"

"Come with me," said Dr. Waters. He smiled at both of them.

A Small Token of Our Esteem It was getting late. Mihalik's watch had stopped, but he had heard bells somewhere tolling twenty-one o'clock. He was sitting with Cheryl and Dr. Waters at a table in a large hall. There were other decorated tables around them; Mihalik turned to see how large the crowd was, and he realized that he couldn't see the far end of the room. There must have been thousands of people, all seated at small round tables made festive with vases of mixed blue and white carnations. There was a head table with a rostrum set up, and a small, elderly, pink-haired woman was speaking into a microphone. She was extremely nervousbecause of the presence of Dr. Waters.

"It's been absolutely marvelous working for the Agency all these years," she said. She glanced around at the people at the head table. "I want to thank my supervisor, and my foreman, Mr. Sokol, and I want to thank all the other men and women who worked with me in the Delitescence Section for making it so pleasant. I love you, and I'm going to miss you all." Tears began to stream down her face.

Another woman, younger and wearing the Agency uniform, stood up and joined her. "Thank you, Diota," she said. "I'm sure they'll all miss you, too. Go sit down, dear, that's it. Hurry up, now. Next I'd like to introduce Captain Telek Shalcross, who is retiring after nearly thirty-eight years in the Second Squad. Captain Shalcross was recruited in 1874, and spent most of his years with us policing the settlements of the sixth and seventh centuries. He has chosen for his retirement home a day he visited twice in the line of duty, September 23, 681 a.d. Let's have a nice hand for Captain Shalcross."

There was a nice hand, and Shalcross came to the microphone. He was tall and broad-shouldered, with a military bearing that made him seem even larger. "I have only one regret," he said. "I wish I could take this uniform with me. I've worn the silver and blue for most of my life, and it will be strange to dress as a civilian again. Especially in seventh-century clothes." For an instant a smile touched his lips, then disappeared. "It is an honor and a privilege to serve the Agency, and all the difficult times and hardships I've known have been repaid tonight, just to glimpse Dr. Waters here with us. That's all I have to say.

G.o.d bless you all."

"See?" said Dr. Waters. "They all love the Agency. All happy about being resettled. All these wonderful people, loyal workers and friends, retiring tonight. They don't have to worry about what the future will hold. If their old age will be lonely and wretched. They know exactly what their declining years will be like, because they've picked their resettlement sites themselves. They've searched through extensive catalogues of pleasant, halcyon times and chosen the very perfect sort of day. Whatever their preferences. Most people go for June or September. Have a number of winter enthusiasts, however.

Makes no difference. We've preselected the years for prosperity, peace, and health conditions. I think it's wonderful."

"If they had anything bad to say about the Agency," said Cheryl, "they wouldn't be here, because the Second Squad would have arrested them this afternoon."

"A valid point," admitted Waters. "Unlikely, though, that any such person would have stayed on with us until retirement age."

One senior employee after another spoke his thanks into the microphone, and then was hustled out of the spotlight. Everyone seemed animated with antic.i.p.ation; no one seemed particularly anxious. It all tended to bear out Waters's words.

"Do these people know what happens after they're abandoned on their chosen day?" asked Mihalik.

"Do they know they can't go anywhere because at midnight they'll be whisked back to their precise point of arrival? Every day starts at the same place, wherever they may have traveled during the previous hours. And they can't acquire anything because at midnight, when the next repet.i.tion of the day starts, all they've gathered disappears. Their only permanent possessions will be just what they take with them from the present. That means they have to go out each morning and find food or medicine or whatever they might need. They can't put up a supply for a few days. They can't afford to get sick or injured. And none of the things they do will have any effect on the past; when the day starts over, none of the true local inhabitants will remember the previous version of the day. Broken things will be magically mended. New friends will be strangers again. There isn't the slightest sense of continuity. It can drive a person insane."

"I know, I know," said Dr. Waters. "And these people understand that. A difficulty, I agree.

Preferable, even with all that, to the over-crowded, starving world we had before. Flaws in the system.

We're not perfect, never claimed to be. But we take precautions. All these retiring men and women are settled near a good food source. As you say, each midnight everything returns to the condition it was in when the resettlee arrived. Means the food supply is inexhaustible. They cannot go hungry. Same is true for most of their needs. We do our best."

Suddenly Cheryl sat up very straight. "That captain," she said. "He visited his resettlement day twicein the line of duty. And the Second Squad -- I never made the connection before. They have no problem at all traveling through time, backward or forward. Time travel has been perfected. You don't need to strand these folks on isolated days in the past. It doesn't have to be that way at all. You're doing it for other reasons, something you're not telling us."

"Of course," said Dr. Waters reasonably. He smiled.

"What are you hiding, then?" asked Mihalik.

"Not going to tell you. Tried persuasion, showed you how nice we can be. Showed you all these marvelous people. Just didn't dent your thick skulls. Now we'll have to try threats and ugliness. Hate to do it. You're so much like Frank and Cheryl, my friends whose places you've taken. But you've forced me. We have other catalogues, you know. Catalogues of particularly gruesome days, in years so bad they've become legendary. We could throw you down anywhere we choose. There are some days in America in 1968 that would make the French Reign of Terror seem like a field trip to the zoo. My favorite is 1361 a.d. A Black Death year. Some perfectly horrendous weeks to choose from right here in England. All we have to do is show a holofilm of one of those days, and criminals confess anything. But we won't bother entertaining you with films. Just pluck one of the worst dates in recorded history out of the hat, and kick your contumacious a.s.ses into the middle of it."

Mihalik cleared his throat. It was very obviously time to regain control of the situation. He gave Dr.

Waters his cool, devastatingly calm smile. "Thank you for everything," he said, "but I believe that once again it's time for Cheryl and me to be going." He got slowly to his feet. Cheryl looked at him, wondering what he was planning. She pushed her chair back and stood up, also.

"You're going nowhere," said Dr. Waters, still seated. "The Second Squad--"

"The Second Squad can't touch us," said Mihalik, "or they would have by now. We're invisible to them because we're not of your world and we just don't exist in your future."

Dr. Waters gave a satisfied grin. "Because in a few hours you'll find yourself filed away in some perilous and dreadful year, with other villains just like yourselves locked into days on either side. But unlike prison, you won't be able to communicate with the people in the other cells. All that will exist for you is your own grim, narrow hole in the calendar."

Mihalik let out a deep breath. "Dr. Waters," he said, and then he swung a powerful blow that smashed the Man from Mars in the face. Mihalik grabbed Cheryl's hand and half dragged her away; they ran toward the nearest exit. They didn't stop to see what reaction they had caused, Mihalik could hear the beginning of a loud uproar. He was moving as fast as he could, and Cheryl was not far behind. A woman in an Agency uniform was guarding the exit; Mihalik slashed at her throat with the side of his hand, and the woman collapsed. Then he was through the door and running for the elevators.

"We've got it made," Mihalik called over his shoulder.

"Hope so," gasped Cheryl.

"Second Squad," said Mihalik, punching the elevator b.u.t.ton furiously, "would have prevented that.

No other security people around."

"Then we don't exist in this future."

"Right. Either Dr. Waters will catch us and do what he threatened, or else we're going to escape."

"How?" asked Cheryl.

"Don't know yet." The elevator arrived, and Mihalik pushed Cheryl in ahead of him. The doors closed; the elevator dropped toward the ground floor. For a moment there was peace except for the lilting melodies from the hidden speaker. Mihalik looked at Cheryl; she was a brave little woman, he thought. She's been through so much, and she's still holding up. He gazed into her beautiful green eyes and wanted to hold her, to kiss her moist, sensuous lips. But this was not the time or the place for that.

Twice into the Same River They ran out of the Agency Plaza and down the marble steps. "d.a.m.n this snow!" Mihalik cried. He hated cold weather. It was night, and the pale beams from the streetlamps made the drifts glitter like crushed diamonds. "Where are we going?" asked Cheryl.

"Don't know yet."

"There must be somebody--"

Then Mihalik knew. There was one person in this world who could help them, who would be glad to help them. "Ray," he said.

"But Ray's in New York," said Cheryl.

"Dr. Waters was supposed to be in New York," said Mihalik. "We were supposed to be returned to New York. The project was in New York. But in this world, the project means the Agency, and all of that is here, in London. Ray will be here, too."

"Unless he's been resettled," said Cheryl. "How do we find him?"

Mihalik thought for a few seconds. "Phone book," he said. There were so few buildings nearby, however, where there might be pay phones. "We have to go back into the Agency Building." He grimaced; he didn't like that idea at all. They ran back up the marble steps and into the building. There were several phones against a wall opposite the elevators. There were no phone books, not of the kind Mihalik was familiar with in his own world. The holophones were different, too. For an instant Mihalik was afraid. He wondered how long they had before the pursuit arrived.

"Look," said Cheryl breathlessly, "there's a b.u.t.ton on the phone marked Info."

She punched it and the screen lit up. A synthesized computer voice asked what information they wanted, and Mihalik gave it Ray's name. He murmured a prayer and waited. A few seconds later, a section of a page number. "I'll remember the address," he said. "and you remember the phone number."

"All right," said Cheryl.

The voice asked if there was other information they required. "Can I make a collect call to that number? I don't have any coins."

"Yes, sir," said the voice. "Your name, please?"

"Tell him it's Frank Mihalik."

"Just a moment, please."

And then the screen was filled with Ray's familiar, grinning mug. Ray was more than just Mihalik's backup, the temponaut who would have plunged into the past if Mihalik had turned up lame or with his liver suddenly lilied. Ray was crony and compotator, tennis partner and paraclete. He was the loyal Patroclus to Mihalik's Achilles. Ray was almost as good as Mihalik at everything a time traveler needed to know; Ray was even better at certain things, like being funny at press conferences. Mihalik was often stuck for a good evasive quip on such occasions, though by means of electronic stimulation of the brain Dr. Waters had inserted more than a thousand into Mihalik's memory. Indeed, the primary reason Mihalik had been chosen over Ray -- and this was a fact wholly unsuspected by either man -- was Cheryl. Ray didn't have a girlfriend or even a wife. Some of the project's psych people felt that in an unexpected crisis that might be a disadvantage. They had been correct about that; thoughts of Cheryl had kept Mihalik going when there was little else motivating him to survive.

"Back so soon?" said Ray jovially. "The good old days not what you expected?"

"Ray," cried Mihalik, "it's great to see you. You have to listen carefully." He sketched the situation briefly, emphasizing that "time was of the essence," that they were being threatened with "a fate worse than death," and that only Ray's presence indicated that Providence had, after all, "fitted the cloud with a silver lining." The project's chief had loaded Mihalik up with cliches, too, because Dr. Waters hated to see so much blank s.p.a.ce in Mihalik's mind just going to waste.

"So it's not you," said Ray thoughtfully. "It just looks like you. And just talking with you could get me thrown away into the trash, on some G.o.dforsaken prehistoric day before the invention of beer. The SS might be coming up the stairs right now."

"The SS?" Mihalik asked.

"The Second Squad," said Cheryl helpfully.

"Is that Cheryl's voice I heard?" asked Ray. "Is that the real Cheryl with you?"

"She seems real enough to me," said Mihalik. "But then, who wouldn't?" Ray shook his head. "Never mind. You say you're in trouble. Tell me where you are, and I'll come get you. Any friend of mine is a friend of Frank's. Even though you've never met him, I'm sure you'd like him. And I'm sure he'd want me to give you a break."

Mihalik didn't try to follow that logic. "We're in the lobby of the Agency Plaza."

"Hiding out under their noses, huh? Very clever," said Ray. He laughed. "Across the street and to the right, about seven blocks, there's a service station. You lock yourself in the men's room, and Cheryl locks herself in the ladies' room. Wait for me; I'll be there in about half an hour."

"All right," said Mihalik. "Ray, you're our only hope."

"I know. You're lucky I'm not jealous or resentful or anything like that, because this would be the perfect opportunity to clean your clock. You're lucky that we're such great pals. Of course, you don't have any idea what our relationship is like in this 1996; you're banking on our friendship in your 1996.

But you always were an intuitive lad."

"Love to chat with you, Ray," said Mihalik, "but we're kind of pressed for time."

"I'm on my way. I'll knock eleven times." Then the holoscreen went blank.

"Eleven?" Mihalik asked Cheryl. She just shrugged.

They found the gas station easily enough, and did as Ray had directed. It was cold in the rest rooms, and the minutes pa.s.sed slowly. At last, as Mihalik was studying his hairline in the mirror, there came twelve knocks on the door. "Ray?" he called.

"That's me."

Mihalik unlocked the door, and felt a great wave of relief when he saw his faithful sidekick. "You knocked twelve times instead of eleven," he said.

Ray hugged Mihalik fiercely, even though, for Ray, it had been only a day since he had seen his friend.

"Then why did you open the door?" he asked.

"Because you said you were you," said Mihalik. "Let's go get Cheryl."

Soon the three climbed into Ray's flashy red car, and headed up the avenue away from the Agency Plaza, toward Minitern. Ray began making frequent turns, as if eluding hypothetical shadowers. In a few minutes Mihalik, at least, had no idea where he was. "Where are we going?"

"Let me know one thing," said Ray. "Where do you want to go?"

"Home," said Cheryl. "Our home. Our own 1996."

"Well," said Ray confidently, "there's only one person who can help you do that. Dr. Waters. You say that he's not very receptive to the idea at the moment. So we'll outthink him."

Mihalik snorted skeptically. "The three of us combined couldn't think in an hour what Dr. Waters can think while he's shaving."

"Frank," said Cheryl, "let's listen to Ray's idea."

"Thanks," said Ray. "Now here's my plan. We're going to bundle you off to the future, centuries from now. The people there perfected time travel then came back to give it to us. That's where Dr. Waters went in 1984 to get a complete education in chronics. When you meet him there, remember that he won't know what's happened here during the last twelve years. He won't know about yesterday or today. He'll be glad to help you, and the people of the future will probably have a simple solution to your predicament."

"That sounds perfect, Ray," said Cheryl. "It's brilliant."

"There's only one hitch," said Ray. "If, in the future, your arrival there or the results of your journey cause some kind of unpleasantness, they'll know about that, too. They'll be in a position to prevent it, unlike our SS. And then, too, you may not go into the future, after all. You may end up stuck back on that day in 1939."

In the silence that followed, the windshield wipers made dull, lonely noises. "I like to hear about the risks in advance," said Mihalik.