The Einstein See-Saw

PART IV

Marooned in Hyperspace

"I suppose you realize what he has done?" Miss Bloomsbury inquired.

"Couldn't be too sure, but it looks like plenty. What's the equation for it?" Beneath his jocularity, Phil felt a tremendous sinking within him. It looked serious, despite the fact that he did not understand it at all.

"He has swung us out into hyperspace, or into the fourth dimension, as your newspaper readers might understand it, and has let us hang there. Remember our slip of paper. Suppose X and Y were swung out of the plane of the paper and allowed to remain at an angle with it. We are at an angle with space, out in hyperspace."

There was a period of bewilderment, almost panic, in which they both felt so physically weak that they had to sit down on the concrete and stare at each other mutely. But this passed and their natural courage soon reasserted itself. Their first thought was to take stock of what information they could get on their situation; and their first step was to venture as close as possible to the queer little horizon which lay almost at their very feet. It gave them a frightened feeling, as though they were standing high up on a precipice or tower.

To their surprise, the horizon receded as they walked toward it, always remaining about a dozen feet away from them. At first they walked on concrete and then came to a crumbly edge of it and found themselves stepping on hard, sandy earth. Later there was rock, sometimes granite-like, sometimes black and shiny. But what they saw underfoot was nothing, compared with the glimpses of things they got out in the surrounding emptiness. First there was a vast space in which a soft light shone, and in which there were countless spheres of various sizes, motionlessly suspended. The spheres seemed to be made of wood, a green, sap-filled, unseasoned wood. The scene was visible for a few seconds, and vanished suddenly as they walked on. This astonished them; so they stepped back a pace or two and saw it again; and as they moved on, it disappeared again.

Then there was a great stretch of water in which the backs of huge monsters rolled and from which a hot wind blew for a few instants until they passed on and the scene vanished. There was a short walk with nothing but emptiness, and then there appeared huge, oblique, cubistic looking rows of jagged rocks in wild, dizzy formations that didn't look possible; and farther on, after another interval of emptiness, a tangle of brown, ropey vines with black-green leaves on them, an immense space filled with serpentine swinging loops and lengths of innumerable vines. Several loops projected so near them that they could have reached out and touched them had they wished.

"This is too much for me!" Phil gasped. "Have we gone crazy? Or did he kill us, and is this Purgatory?"

Ione smiled and shook her little head in which she had a goodly store of modern mathematics stored away.

"These must be glimpses of other 'spaces' besides our own space. If we could see in four dimensions we could see them all spread out before us. But we can only perceive in three dimensions; therefore, as we walk through hyperspace, past the different 'spaces' which are ranged about in it, we get a glimpse into such of them as are parallel with our own space. Can you understand that?"

"Oh, yes," groaned Phil. "It sounds just about like it looks. But, don't mind me. Go on, have your fun."

"I've been thinking about those wooden spheres," continued Ione. "I'm sure they must be sections of trees that are cut crosswise by our 'space;' they grow in three dimensions, but only two of them are our dimensions and a third is strange to us. We see only three-dimensional sections of them, which are spheres. There is more of them, that we cannot see, in another dimension."

"Yes, yes. Just as plain as the Jabberwock!"

"Look! There's a real Jabberwock!" exclaimed Ione.

On ahead of them they saw a number of creatures that seemed to be made of painted wooden balls in different colors, joined together.

"Tinkertoys!" exclaimed Phil. "Live ones! Big ones!"

The animals, though they looked for all the world as though they were made of painted wood, moved with jerky motions and clattered and snarled.

"There is probably more to them in another dimension," Ione said.

Suddenly one of the beasts approached them with a leap. There were two big eyes and two rows of teeth that came together with a snap, right on Phil's trouser-leg. He jerked himself away, sacrificing some square inches of trouser-leg, and, whirling around, kicked at the thing with all his force. It almost paralyzed his foot, for the animal seemed to be made of wood or bone. But it disappeared, and, as it did, both of them felt a queer, nauseating jolt. A few more minutes' walk brought them back to the safe without seeing any more spaces; and the sight of its black iron bulk filled them with a home-like relief, which in a moment they recognized as a mockery.

"Are we on a sphere of some sort?" Phil asked.

"Probably on an irregular mass of matter," Ione replied, "part of which is Tony's concrete floor, and part of which comes out of some other dimension. This mass of matter is at one end of a long, bar-like portion of space, the middle of which is pivoted in our world, somewhere in Chicago, and both ends of which are free in hyperspace."

"Then," suggested Phil, "why can't we walk down to the axle on which it is balanced, and step out into Chicago?"

"Because there isn't any matter for us to walk on. We are not able to move about in space, in three dimensions, you know. We can only get around in two dimensions, on the surface of matter."

"Well, let's try another exploration trip at right angles to our first one. After all, these 'spaces' are an interesting show, and I want to see some more."

They started out in the selected direction, and after a short walk got a glimpse of a vast space dotted with stars and nebulae, with two bright moons sailing overhead. A few steps farther on was a wall of solid granite, near enough to touch with their hands. Again, there was an intensely active mass of weaving bright stripes and loops and circles, seeming to consist of light only, and making them dizzy in a few seconds. Ione wondered if it might not be something like an organic molecule on a large scale. Again, odd, queer, indescribable shapes and outlines would appear and disappear, obviously three-dimensional sections of multi-dimensional things, cut by space. Once they passed a place of intense cold and terrific noise and escaped destruction or lunacy only because it took them the merest instant to get past.

They arrived back at the safe, very much fatigued from the strain, their minds woefully confused. Hunger and thirst were beginning to thrust up their little reminders; and for the first time the terrors of their position, flung out into hyperspace on a small, barren piece of matter, began to seem real.

After a rest they started out again. As Phil had touched, in kicking it, a creature from another "space," perhaps they might find water and even food somewhere. They retraced their first steps to the spot where they had at first seen water. They found it again and were able to dip their hands into it. It was warm, and too salty to drink. They came to the place with the creepers or vines, and Phil reached out and seized one of them. It was heavy, rubbery, and elastic, stretching readily as he pulled it.

"These little lurches that we feel must be the snapping back of the space-puckers as expressed by tensors," Ione remarked. "Every time matter goes in or out of space, the nature of space is altered."

"Well," observed Phil, releasing the vine, "I'd better be careful. If one of these things hauls me off here, our last bond with home is gone. I don't want to get lost in some other space."

As he released the vines they snapped back to their places, and the forest of them dimmed a little and reappeared.

They made the round again, dodging cautiously past the point where they had previously found the "Tinkertoy" animals, and succeeded in getting past their snapping teeth. But no promise of food or water did they find anywhere.

"Looks like we're sunk," observed Phil, as they dropped down on the concrete to rest, leaning their backs against the safe.

How time counted in hyperspace, neither Phil nor Ione could tell; Phil knew that his watch was running. He knew that it was ages and ages that he sat with his back against the safe, reviewing all the events of his put life, and thinking of this ignominious end to a lively career! He swore half aloud; then suddenly looked at Ione, ready to apologize. He found her weeping silently.

"I should never have let you come into the building with me," he stammered in confusion at her tears.

"Oh, what do I care what becomes of me!" she exclaimed angrily. "But who will take care of poor daddy? He doesn't even know when it's time to eat." And she burst into a fresh fit of weeping.

Phil bent his head in the dumbness of profound despair.

PART V

The Reversible Equation

Despair, however, is a luxury. Necessity is a stimulus. With the parchings of thirst and the gnawings of hunger, the two young people ceased swearing and weeping. Phil got up and paced about and sat down again. Ione's tears stopped and dried, and she sat and thought.

In the back of her mind there had been forming a vague sort of an idea, which had signalled ahead of itself that there was hope. She sat there and desperately drove her reason to its utmost efforts, to find that idea and bring it to the surface of consciousness. Hand to hand fights with wild animals, battles between ships of the line, vicious duels between ace-aviators in the clouds are tense fights; but they cannot compare in anxious difficulty with the struggle to bring up an unformed idea out of the subconscious mind – especially when one knows that the idea is there, and that it must be found to save one's life.

"Ione!" exclaimed Phil. It was the first time he had used the name. "What is the matter? You are as tense as a – "

"Ah!" cried Ione, springing up. "Tense! Tensors! I have it!"

Phil gazed at her in alarm. She laughed; at first it was a strained laugh, but gradually it melted into her sunny one.

"No, I'm not crazy. I knew there was a way out, and I've been trying to reason it out. How simple. You remember the little jolts when you pulled at the vines and when you kicked the funny animal? Tensors. Matter and space are so closely interrelated that you can't move matter in or out of space without causing disturbance, recoils, and tremors in space. Those bits of matter were small, and produced only a slight disturbance. It takes about a hundred pounds of lead to swing this segment – "

"Oho! Got you!" exclaimed Phil. "Not so dumb! The safe!"

"Yes. The safe!" Ione cried.

"Throw it off and watch us swing, eh? What would happen?"

"I might calculate it if I knew the weight of the safe."

"No calculating when I'm around," Phil said. "It couldn't make things any worse. Try it first and calculate afterwards."

They got behind the safe and pushed, and their combined strength against it was about as effective as it would have been in moving the Peoples' Gas Building. They sat down again in despair.

"Suppose we could budge it," Ione said. "All we could do would be to push it around, this piece of matter we are on. That wouldn't help. We've got to get it out of space. We can't push it hard enough to do that. It's got to be shot out suddenly – "

"And we haven't got a gun handy," Phil remarked droopingly.

"Not exactly a gun. A sort of sling – "

Phil leaped to his feet.

"A sling. Why! To be sure! The vines!"

Without another word, both of them got up and ran. They hastened in a direction opposite to the one they had at first taken on their trip of exploration, and this brought them first past the "space" of the Tinkertoy-like animals. As they went by, several of these beasts darted at them, one of them snapping at Ione's heels. She uttered a scream, causing Phil to turn about and kick right and left among them. He drove them back and escaped from them, rejoining Ione.

"Wait," he said, when they reached the vines. "Remember those wooden balls. If I could get a few to throw at those critters – "

In a moment they were off, and finally arrived at the point from which they first saw the balls. Odd it seemed, how they hung suspended in space, thousands of them, all sizes. Phil reached out and grasped one about the size of a baseball and drew it toward himself. He felt a dizzy lurch and heard Ione scream.

"Let go!" she screamed again.

When he suddenly realized what was going on, he found himself prostrate on the ground, with Ione across him, her arms about his knees.

"Do you realize," she panted, disentangling herself, "that you were pulling yourself out of this space into that one?"

"Thanks!" said Phil. "Never say die. More careful this time, and a smaller one."

He reached out and grasped a ball smaller than a golf-ball, and pulled carefully, keeping an eye upon Ione. There was resistance to his pull, but gradually the ball came. It seemed heavy. There was a crack as of breaking wood, and he fell backward, with a wave of nausea sweeping strongly over him. He gazed in amazement at a heavy wooden stick that he held in his hands. The only thing about it that suggested the ball for which he had reached was its diameter.

"Can't understand it, but appreciate it just the same," he said. He broke the stick in two, and had two excellent clubs.

"Simple," Ione replied. "The balls are cross-sections of these trees or sticks which grow in a 'space' at right angles to our own; and we only see their three-dimensional cross-sections."

"Yes," said Phil. "Cabbages and kings. I'm for you and the party."

A short walk brought them to the "space" of the vines. After testing the matter out carefully, they found that they could each pull two of them at a time. The vines stretched amazingly when they found those whose far ends were fixed firmly in the tangle, permitting them to carry their own ends along with them toward the safe. Phil wound his vines around his left arm and stuck one club through his belt. The other he got ready for the wooden animals.

He needed it. The size of the pack was doubled, and he rapped them till his hand was numb before he and Ione got by. Their vines drew out thin, but held until they were firmly tied about the safe. They went back after four more.

"I should judge," said Phil, "that by the time we get thirty or forty, the elastic pull will be strong enough to drag the safe back with them as they snap back home."

Trip after trip they made, fighting the wooden animals with their clubs each time. Their clothes were torn, and their legs bleeding; their throats were dry and lips cracked. The hard animals seemed to have a persistent, mechanical ferocity that was undismayed by hammering with the clubs and by repeated repulses. Phil could not seem to hurt them; he merely knocked them away. Finally, on the ninth trip, Ione collapsed when she reached the safe. As she fell, the elasticity of the vines began slowly to drag her back with them. Phil was forced to sit across her knees while he tied his own vines about the safe. Then he released her and added her vines to the great cable about the safe.

An overbold hard animal rattled up and snapped at her. Goaded to fury, Phil swung at it with his club and hurled it through the air. He could feel the lurch as it left his space and entered another. Then he pushed with his mightiest effort against the safe. It budged, and slid a few inches. He used his stick as a lever. It moved again, a little faster. Ione struggled to her feet and tried to help, but her efforts were ineffectual.

With one arm about her, Phil pried again under the safe, knowing that another trip after vines was out of question. Another animal snapped at their heels. For a while, it was kick backwards, then a shove at the safe. Each time the safe moved. The sight of its movement revived Ione, so that she was able to push also. Gradually it acquired a steady motion, pulled by the contraction of the vines; its progress soon became faster and faster. Phil was about to follow it and give it another push, when Ione drew him back.

Suddenly they experienced a sinking sensation and a fearful vertigo. The snapping animals faded. Ahead of them was the forest of vines, and they saw the safe hurled into it, crashing, plunging into the tangled mass. The whole view crumpled and moved upwards like a swirl of leaves in a wind, and then vanished with a snap.

They were sick and dizzy, but tremendously curious to see everything. The water, the cubistic cliffs, the vast space full of balls, all curiously blurred, appeared in succession. There were blank spaces and then blurred sights of things which they did not recognize, never having seen them before. Then the dizziness and the nausea abated, and ahead of them was a vast yellow blue, a huge nebula, and in it were double-colored suns and ringed planets with swarms of moons; this glorious sight remained for many seconds, as they gazed at it in panting astonishment, half reclining on the concrete; and then it faded. Again the nausea came on; again the succession of blurred views. Eventually the myriad spheres, the water with the leviathans, the forest of vines, each succeeding scene grew more blurred. Their nausea was correspondingly increased, till they were forced to lie down on the ground from illness.

When their giddiness abated, there were blurring views again. There was an impression as though the speed of a train were decreasing as one looks out of the window. And how one view held for several seconds, a vast and wild mountain-range with glaciers and snow peaks by moonlight. When this faded gradually, the scenes began to flick by, more and more rapidly, and grew blurred. Phil and Ione were attacked by nausea until, again, they had to lie down. After that came the familiar succession: the wooden animals, the tangle of vines, the vast sea, the spheres, and more blurred scenes. Then came a pause, with the nebula and the glorious suns swinging into view once again.