Hardy beamed. “That is the miracle. You see, at the far end of the tube there is a force field. The frog is compelled to jump towards it by the heat. The effect of the field is to reduce animal tissue to its proximity. The frog is made smaller the farther he goes.”
“Why?”
“It’s the only way the jumping span of the frog can be reduced. As the frog leaps he diminishes in size, and hence each leap is proportionally reduced. We have arranged it so that the diminution is the same as in Zeno’s paradox.”
“But where does it all end?”
“That,” Hardy said, “is the question to which we are devoted. At the far end of the tube there is a photon beam which the frog would pass through, if he ever got that far. If he could reach it, he would cut off the field.”
“He’ll reach it,” Grote muttered.
“No. He’ll get smaller and smaller, and jump shorter and shorter. To him, the tube will lengthen more and more, endlessly. He will never get there.”
They glared at each other. “Don’t be so sure,” Grote said.
They peered through the window into the tube. The frog had gone quite a distance up. He was almost invisible, now, a tiny speck no larger than a fly, moving imperceptibly along the tube. He became smaller. He was a pin point. He disappeared.
“Gosh,” Pitner said.
“Pitner, go away,” Hardy said. He rubbed his hands together. “Grote and I have things to discuss.”
He locked the door after the boy.
“All right,” Grote said. “You designed this tube. What became of the frog?”
“Why, he’s still hopping, somewhere in a sub-atomic world.”
“You’re a swindler. Some place along that tube the frog met with misfortune.”
“Well,” Hardy said. “If you think that, perhaps you should inspect the tube personally.”
“I believe I will. I may find a trap door.”
“Suit yourself,” Hardy said, grinning. He turned off the gas and opened the big metal door.
“Give me the flashlight,” Grote said. Hardy handed him the flashlight and he crawled into the tube, grunting. His voice echoed hollowly. “No tricks, now.”
Hardy watched him disappear. He bent down and looked into the end of the tube. Grote was half-way down, wheezing and struggling. “What’s the matter?” Hardy said.
“Too tight….”
“Oh?” Hardy’s grin broadened. He took his pipe from his mouth and set it on the table. “Well, maybe we can do something about that.”
He slammed the metal door shut. He hurried to the other end of the tube and snapped the switches. Tubes lit up, relays clicked into place.
Hardy folded his arms. “Start hopping, my dear frog,” he said. “Hop for all you’re worth.”
He went to the gas cock and turned it on.
It was very dark. Grote lay for a long time without moving. His mind was filled with drifting thoughts. What was the matter with Hardy? What was he up to? At last he pulled himself on to his elbows. His head cracked against the roof of the tube.
It began to get warm. “Hardy!” His voice thundered around him, loud and panicky. “Open the door. What’s going on?”
He tried to turn around in the tube, to reach the door, but he couldn’t budge. There was nothing to do but go forward. He began to crawl, muttering under his breath. “Just wait, Hardy. You and your jokes. I don’t see what you expect to –”
Suddenly the tube leaped. He fell, his chin banging against the metal. He blinked. The tube had grown; now there was more than enough room. And his clothing! His shirt and pants were like a tent around him.
“Oh, heavens,” Grote said in a tiny voice. He rose to his knees. Laboriously he turned around. He pulled himself back through the tube the way he had come, towards the metal door. He pushed against it, but nothing happened. It was now too large for him to force.
He sat for a long time. When the metal floor under him became too warm he crawled reluctantly along the tube to a cooler place. He curled himself up and stared dismally into the darkness. “What am I going to do,” he asked himself.
After a time a measure of courage returned to him. “I must think logically. I’ve already entered the force field once, therefore I’m reduced in size by one-half. I must be about three feet high. That makes the tube twice as long.”
He got out the flashlight and some paper from his immense pocket and did some figuring. The flashlight was almost unmanageable.
Underneath him the floor became warm. Automatically he shifted, a little up the tube to avoid the heat. “If I stay here long enough,” he murmured, “I might be –”
The tube leaped again, rushing off in all directions. He found himself floundering in a sea of rough fabric, choking and gasping. At last he struggled free.
“One and a half feet,” Grote said, staring around him. “I don’t dare move any more, not at all.”
But when the floor heated under him he moved some more. “Three-quarters of a foot.” Sweat broke out on his face. “Three-quarters of one foot.” He looked down the tube. Far, far down at the end was a spot of light, the photon beam crossing the tube. If he could reach it, if only he could reach it, if only he could reach it!
He meditated over his figures for a time. “Well,” he said at last, “I hope I’m correct. According to my calculations I should reach the beam of light in about nine hours and thirty minutes, if I keep walking steadily.” He took a deep breath and lifted the flashlight to his shoulder.
“However,” he murmured, “I may be rather small by that time. . . .” He started walking, his chin up.
Professor Hardy turned to Pitner. “Tell the class what you saw this morning.”
Everyone turned to look. Pitner swallowed nervously. “Well, I was downstairs in the basement. I was asked in to see the Frog Chamber. By Professor Grote. They were going to start the experiment.”
“What experiment do you refer to?”
“The Zeno one,” he explained nervously. “The frog. He put the frog in tube and closed the door. And then Professor Grote turned on the power.”
“What occurred?”
“The frog started to hop. He got smaller.”
“He got smaller, you say. And then what?”
“He disappeared.”
Professor Hardy sat back in his chair. “The frog did not reach the end of the tube, then?”
“No.”
“That’s all.” There was a murmuring from the class. “So you see, the frog did not reach the end of the tube, as expected by my colleague, Professor Grote. He will never reach the end. Alas, we shall not see the unfortunate frog again.”
There was a general stir. Hardy tapped with his pencil. He lit his pipe and puffed calmly, leaning back in his chair. “This experiment was quite an awakener to poor Grote, I’m afraid. He has had a blow of some unusual proportion. As you may have noticed, he hasn’t appeared for his afternoon classes. Professor Grote, I understand, has decided to go on a long vacation to the mountains. Perhaps after he has had time to rest and enjoy himself, and to forget –”
Grote winced. But he kept on walking. “Don’t get frightened,” he said to himself. “Keep on.”
The tube jumped again. He staggered. The flashlight crashed to the floor and went out. He was alone in the enormous cave, an immense void that seemed to have no end, no end at all.
He kept walking.
After a time he began to get tired again. It was not the first time. “A rest wouldn’t do any harm.” He sat down. The floor was rough under him, rough and uneven. “According to my figures it will be more like two days, or so. Perhaps a little longer. . . .”
He rested, dozing a little. Later on he began to walk again. The sudden jumping of the tube had ceased to frighten him; he had grown accustomed to it. Sooner or later he would reach the photon beam and cut through it. The force field would go off and he would resume his normal size. Grote smiled a little to himself. Wouldn’t Hardy be surprised to —
He stubbed his toe and fell, headlong into the blackness around him. A deep fear ran through him and he began to tremble. He stood up, staring around him.
Which way?
“My God,” he said. He bent down and touched the floor under him. Which way? Time passed. He began to walk slowly, first one way, then another. He could make out nothing, nothing at all.
Then he was running, hurrying through the darkness, this way and that, slipping and falling. All at once he staggered. The familiar sensation: he breathed a sobbing sigh of relief. He was moving in the right direction! He began to run again, calmly, taking deep breaths, his mouth open. Then once more the staggering shudder as he shrank down another notch; but he was going the right way. He ran on and on.