Galaxy Magazine (December 1956) by Galaxy

Author:Galaxy
Language: eng
Format: mobi
Published: 1956-12-08T16:00:00+00:00

GALAXY SCIENCE FICTION

sack.'"If a man invents a time machine," he said carefully, "and then goes back to kill his grandfather when a boy, then he couldn't have been born, could he?"

"Hardly."

"Then if he hadn't been born, he couldn't invent a time machine in the first place. But if he hadn't invented it, he couldn't have killed his grandfather, so he would have been born anyway." Herman drew a deep breath. "So he didn't kill his grandfather at all. Right?" He looked anxiously at the other man.

"Near enough." Onslow knew better than to labor the point. "If he was born, then his grandfather

couldn't have been killed when a boy, so all that about going back and killing the old man doesn't really enter into it."

"That's what I said," lied Herman. "Mary kept trying to tie me in knots, but I made her see sense in the end." He hesitated. "Got any more?"

"Paradoxes?" Onslow looked surprised. "Sure, if you're interested."

«TJ

I'm interested." Herman glanced through the office windows. The night was a bad one, cold, wet, miserable, a night most people would choose to stay indoors. "May as well talk as read or listen to the radio. More interesting, anyway."

"How about this one?" Onslow helped himself to a cigarette and hunched closer to the stove. "An old Greek named Zeno dreamed it up and it's a good one. Achilles was going to race a tortoise. The tortoise was placed halfway down a measured strip — it doesn't matter how long — and Achilles stood at the starting line. You got the idea?"

"Sure, the tortoise was given a big start."

"It was halfway down the strip," said Onslow. "So the gun went off and the race started. Now before Achilles could catch up with the tortoise, he had to cover half the distance between them. Right?"

H

ERMAN frowned, then nodded. "Sure, of course. He had to reach the halfway mark between them."

"Yes, but by the time he had reached that halfway mark, the tortoise had moved on a bit further. So Achilles had to cover half that distance, by which time the tortoise had moved on still more. So Achilles had to cover

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half that distance and then half the next distance and so on." Onslow leaned back. "How did Achilles ever catch up with the tortoise?"

"Uh?" Herman looked blank. "By running faster, of course. Nothing to it."

YOU GO

"Isn't there?" Onslow reached for paper and pencil. "Look at it this way." He made swift sketches. "First he had to cover half the first distance, then half the second, then the third and all the rest. Look at it that way and he could never have caught up because, no matter how short the distance, he had always to cover a half of it, by which time the tortoise had moved on."

"I see," said Herman glumly. This was one time when he couldn't dazzle Mary with his superior knowledge. It wasn't much good taking home a problem to which he didn't know the answer.

Onslow took pity on him. "No one can really work it out the way it's stated.

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