* * *

“Time travel was discovered at a period when the Chorite Heresiarchy was breaking up,” said Kelm, in the lecture hall. “You’ll study the details later; for now, take my word that it was a turbulent age, when commercial and genetic rivalry was a tooth-and-claw matter between giant combines; anything went, and the various governments were pawns in a galactic game. The time effect was the by-product of a search for a means of instantaneous transportation, which some of you will realize requires infinitely discontinuous functions for its mathematical description…as does travel into the past. I won’t go into the theory of it—you’ll get some of that in the physics classes—but merely state that it involves the concept of infinite-valued relationships in a continuum of 4N dimensions, where N is the total number of particles in the universe.

“Naturally, the group which discovered this, the Nine, were aware of the possibilities. Not only commercial-trading, mining, and other enterprises you can readily imagine—but the chance of striking a deathblow at their enemies. You see, time is variable; the past can be changed—”

“Question!” It was the girl from 1972, Elizabeth Gray, who was a rising young physicist in her own period.

“Yes?” said Kelm politely.

“I think you’re describing a logically impossible situation. I’ll grant the possibility of time travel, seeing that we’re here, but an event cannot both have happened and not happened. That’s self-contradictory.”

“Only if you insist on a logic which is not Aleph-sub-Aleph-valued,” said Kelm. “What happens is like this: suppose I went back in time and prevented your father from meeting your mother. You would never have been born. That portion of universal history would read differently; it would always have been different, though I would retain memory of the ‘original’ state of affairs.”

“Well, how about doing the same to yourself?” asked Elizabeth. “Would you cease existing?”

“No, because I would belong to the section of history prior to my own intervention. Let’s apply it to you. If you went back to, I would guess, 1946, and worked to prevent your parents’ marriage in 1947, you would still have existed in that year; you would not go out of existence just because you had influenced events. The same would apply even if you had only been in 1946 one microsecond before shooting the man who would otherwise have become your father.”

“But then I’d exist without—without an origin!” she protested. “I’d have life, and memories, and…everything…though nothing had produced them.”

Kelm shrugged. “What of it? You insist that the causal law, or strictly speaking the conservation-of-energy law, involve only continuous functions. Actually, discontinuity is entirely possible.”

He laughed and leaned on the lectern. “Of course, there are impossibilities,” he said. “You could not be your own mother, for instance, because of sheer genetics. If you went back and married your former father, the children would be different, none of them you, because each would have only half your chromosomes.”

Clearing his throat: “Let’s not stray from the subject. You’ll learn the details in other classes. I’m only giving you a general background. To continue: the Nine saw the possibility of going back in time and preventing their enemies from ever having gotten started, even from ever being born. But then the Danellians appeared.”