I had now been running around 1105 for quite a while, and I figured it was time to get back to 1204 and let my alter ego know something of what was going on. So I made the shunt down the line and got to the inn at quarter past three on that same long night of Conrad Sauerabend’s disappearance from 1204. My other self was slouched gloomily on his bed, studying the ceiling’s heavy beams.

“Well?” he said. “How goes it?”

“Catastrophic. Come out into the hall.”

“What’s happening?”

“Brace yourself,” I said. “We finally tracked Sauerabend down. He shunted to 1099, and took a cover identity as a tavernkeeper. A year later he married Pulcheria.”

I watched my other self crumble.

“The past has been changed,” I went on. “Leo Ducas married somebody else, Euprepia something, and has two and a half children by her. Pulcheria’s a serving wench in Sauerabend’s tavern. I saw her there. She didn’t know who I was, but she offered to screw me for two bezants. Sauerabend is smuggling goods down the line, and—”

“Don’t tell me any more,” he said. “I don’t want to hear any more.”

“I haven’t told you the good part yet.”

“There’s a good part?”

“The good part is that we’re going to unhappen all of this. Sam and Metaxas and you are going to trace Sauerabend back from 1105 to the moment of his arrival in 1099, and unarrive him, and shunt him back here into this evening. Thus canceling the whole episode.”

“What happens to us?” my other self asked.

“We discussed that, more or less,” I said vaguely. “We aren’t sure. Apparently we’re both protected by Transit Displacement, so that we’ll continue to exist even if we get Sauerabend back into his proper time flow.”

“But where did we come from? There can’t be creation of something out of nothing! Conservation of mass—”

“One of us was here all along,” I reminded him. “As a matter of fact, I was here all along. I brought you into being by looping back fifty-six seconds into your time-flow.”

“Balls,” he said. “I was in that time-flow all along, doing what I was supposed to do. You came looping in out of nowhere. You’re the goddam paradox, buster.”

“I’ve lived fifty-six seconds longer than you, absolute. Therefore I must have been created first.”

“We were both created in the same instant, on October 11, 2035,” he shot back at me. “The fact that our time lines got snarled because of your faulty thinking has no bearing on which of us is more real than the other. The question is not who’s the real Jud Elliott, but how we’re going to continue to operate without getting in each other’s way.”

“We’ll have to work out a tight schedule,” I said. “One of us working as a Courier while the other one’s hiding out up the line. And the two of us never in the same time at once, up or down the line. But how—”

“I have it,” he said. “We’ll establish a now-time existence in 1105, the way Metaxas has done, only for us it’ll be continuous. There’ll always be one of us pegged to now-time in the early twelfth century as George Markezinis, living in Metaxas’ villa. The other one of us will be functioning as a Courier, and he’ll go through a trip-and-layoff cycle—”

“—taking his layoff anywhen but in the 1105 basis.”

“Right. And when he’s completed the cycle, he’ll go to the villa and pick up the Markezinis identity, and the other one will go down the line and report for Courier duty—”

“—and if we keep everything coordinated, there’s no reason why the Patrol should ever find out about us.”

“Brilliant!”

“And the one who’s being Markezinis,” I finished, “can always be carrying on a full-time affair with Pulcheria, and she’ll never know that we’re taking turns with her.”

“As soon as Pulcheria is herself again.”

“As soon as Pulcheria is herself again,” I agreed.

That was a sobering thought. Our whole giddy plan for alternating our identities was just so much noise until we straightened out the mess Sauerabend had caused.

I checked the time. “You get back to 1105 and help Sam and Metaxas,” I said. “Shunt here again by half past three tonight.”

“Right,” he said, and left.

He came back on time, looking disgusted, and said, “We’re all waiting for you on August 9, 1100, by the land wall back of Blachernae, about a hundred meters to the right of the first gate.”

“What’s the story?”

“Go and see for yourself. It makes me sick to think about it. Go, and do what has to be done, and then this filthy lunacy will be over. Go on. Jump up and join us there.”

“What time of day?” I asked.

He pondered a moment. “Twenty past noon, I’d say.”

I went out of the inn and walked to the land wall, and set my timer with care, and jumped. The transition from late-night darkness to midday brightness left me blinded for an instant; when I stopped blinking I found myself standing before a grim-faced trio: Sam, Metaxas — and Jud B.

“Jesus,” I said, “Don’t tell me we’ve committed another duplication!”

“This time it’s only the Paradox of Temporal Accumulation,” my alter ego said. “Nothing serious.”

I was too muddled to reason it through. “But if we’re both here, who’s watching our tourists down in 1204?”

“Idiot,” he said fiercely, “think four-dimensionally! How can you be so stupid if you’re identical to me? Look, I jumped here from one point in that night in 1204, and you jumped from another point fifteen minutes away. When we go back, we each go to our proper starting point in the sequence. I’m due to arrive at half past three, and you aren’t suppose to be there until quarter to four, but that doesn’t mean that neither of us is there right now. Or all these others of us.”

I looked around. I saw at least five groups of Metaxas-Sam-me arranged in a wide arc near the wall. Obviously they had been monitoring this time point closely, making repeated short-run shunts to check on the sequence of events, and the Cumulative Paradox was building up a multitude of them.

“Even so,” I said dimly, “it somehow seems that I’m not correctly perceiving the linear chain of—”

“Stuff the linear chain of!” the other Jud snarled at me. “Will you look over there? There, on the far side of the gate!”

He pointed.

I looked.

I saw a gray-haired woman in simple clothes. I recognized her as a somewhat younger version of the woman whom I had seen escorting Pulcheria Ducas into the shop of sweets and spices that day, seemingly so long ago, five years down the line in 1105. The duenna was propped up against the city wall, giggling to herself. Her eyes were closed.

A short distance from her was a girl of about twelve, who could only have been Pulcheria’s younger self. The resemblance was unmistakable. This girl still had a child’s unformed features, and her breasts were only gentle bumps under her tunic, but the raw materials of Pulcheria’s beauty were there.

Next to the girl was Conrad Sauerabend, in Byzantine lower-middle-class clothes.

Sauerabend was cooing in the girl’s ear. He was dangling before her face a little twenty-first century gimcrack, a gyroscopic pendant or something like that. His other hand was under her tunic and visibly groping in the vicinity of her thighs. Pulcheria was frowning, but yet she wasn’t making any move to get the hand out of her crotch. She seemed a little uncertain about what Sauerabend was up to, but she was altogether fascinated by the toy, and perhaps didn’t mind the wandering fingers, either.

Metaxas said, “He’s been living in Constantinople for a little less than a year, and commuting frequently to 2059 to drop off marketable artifacts. He’s been coming by the wall every day to watch the little girl and her duenna take their noontime stroll. The girl is Pulcheria Botaniates, and that’s the Botaniates palace just over there. About half an hour ago Sauerabend came along and saw the two of them. He gave the duenna a floater and she’s been up high ever since. Then he sat down next to the girl and began to charm her. He’s really very slick with little girls.”