by Jerry
“When you want to construct a four dimensional counterpart of any particular geometrical figure, all you have to do is figure out how you would construct a corresponding three dimensional article from two dimensional units and your problem solves itself.
“For instance, if you want to build a cube you can do it by piling together a large number of squares of the same size cut out of paper until you have a pile as high as one edge of your original square. Likewise, if you wish to construct a four dimensional cube—which, by the way, is called a tesseract—you can do it by combining three-dimensional cubes.
“Take another example. To make a cylinder out of two dimensional units, all you have to do is combine a large number of pieces cut in the shape of a circle. Hence a four dimensional cylinder would be composed of the three dimensional counterparts of the circles, namely solid spheres.
“To steer our flyer into hyperspace by means of our rocket principle it is necessary to construct tubes having extension in the fourth dimension. If you were a Flatlander and wanted to make a pipe out of tinfoil, how would you do it?”
“That’s easy,” said Berglin. “I’d make a roll out of it.”
I knew at once that this was not the answer the Professor was fishing for and I couldn’t help smiling just a wee bit at the look of disapproval which Berglin’s common-sense suggestion brought to Banning’s face.
“That’s wrong!” he shouted. “The minute you bend a roll of tinfoil you get completely out of your two dimensional environment. What I mean is, how could you build a pipe by combining a large number of articles, all of which must be absolutely flat and extremely thin?”
“Oh, I see what you mean now. They’d have to be in the form of rings or washers.”
“Exactly! Now you’re beginning to grasp the idea. Suppose for the sake of convenience we call your rings or washers hollow circles. Now what sort of units shall we require for building our four dimensional pipe?”
“Hollow spheres, I suppose.”
“Precisely. And that’s how we made our four dimensional rocket tubes. We combined a large number of hollow spheres in such a way as to make a continuous passageway, through which currents of gases resulting from the combustion of our fuel can be projected, either into or away from hyperspace.
“This sounds simple enough but in actual practice it requires a knowledge of certain principles of higher mathematics which cannot be comprehended except by a person who has spent years in studying them. The difficult thing is to know just how to group the hollow spheres together. You can readily understand that they cannot be placed one in front of the other, one beside the other or one on top of the other, since that would mean merely producing additional extension in either length, width or height. Instead, they have to be placed THROUGH each other and in such a way that the hollow spaces combine to make one continuous hole through which the gases can pass. Do you understand what I mean?”
“I guess I do, but when you talk about sticking together a lot of hollow balls in such a way that gas can pass through the hollow spaces, you’re getting way ahead of me.”
“That’s very simple if you think of these balls as being open in the direction of the fourth dimension, just as a washer or ring is open in the third dimension.
“To a two-dimensional being it would be as impossible to put anything inside a ring as for us to do the same thing to a hollow ball. Yet one of us can easily pick up a small article from qptside and drop it inside the ring. In the same way, by moving through the fourth dimension, you could pick up a pebble and place it inside a tennis ball without making any opening in the rubber. It is also possible to combine hollow spheres in such a way as to form a gas-tight tube.”
“That’s mighty interesting, even though I’m afraid I don’t grasp it completely,” Berglin responded. “Your explanation is entirely different from the conception of the fourth dimension I had before. Somehow or other I got the idea that the fourth dimension is time. I remember reading a book called “The Time Machine.” It’s about a contraption which was supposed to be able to travel in the fourth dimension. With it a man could either go clear back into the days of ancient history or could travel ahead and see how the world is going to be thousands of years in the future.”
To which the Professor replied, “Fantastic tales like that are not intended to be taken seriously. They make interesting yarns but couldn’t possibly be true. I don’t mean to deprecate the so-called scientific fiction stories as a class. Many of them, like ‘Twenty Thousand Leagues Under the Sea,’ which were originally written as the wildest and most impossible imaginative fiction have already been made real through modern inventions. But when you try to conceive of seeing events long before they actually happen, common sense tells us that even the most marvelous of scientific discoveries could never make such a thing possible.”
HERE I took the liberty of butting in on the dialogue.
“Excuse me, Professor,” I ventured. “But doesn’t Einstein’s theory of relativity regard time as a fourth dimension?”
“In one sense, perhaps, but that’s a mere matter of terminology,” he continued. “The essential idea behind the principle of relativity is that every object in the universe is moving. There’s no such thing as absolute rest. And since objects move at different speeds, it is impossible to obtain an accurate measure of the distance between two objects unless we know the speed with which each of the objects, as well as the observer, is traveling.
“There’s where the time element enters in, and it is sometimes referred to, rather loosely, as the fourth dimension. The term ‘separation interval’ is a much better word in my opinion, since that suggests both time and distance.
“I don’t believe that even Einstein would presume to believe that time is a dimension like length, along which one can travel either forward or backward and at varying speeds.
“On the other hand, the geometrical fourth dimension which I have just explained to you has nothing to do with time. It is a real spacial extension, of exactly the same character as length, width and thickness.
“With one of our four dimensional rocket tubes we shall be able to travel into hyperspace as far as we please, and then, by shooting discharge through the other tube we can just as easily direct our flyer back to three dimensional space.
“You already have some idea of the main purpose behind all this. My object is to use our four dimensional steering apparatus to release us quickly from the grip of gravitation when we want to escape from the earth’s pull. On the other hand, we can always return to three dimensional space and to the gravitational fields of the earth or moon whenever such attractive forces will be of any use to us. Is that all clear?”
“I—I—guess so,” was Berglin’s hesitating response.
CHAPTER IV
The Space Flyer Is Named
IN addition to the four dimensional steering device, our space flyer had another unique and distinctive feature, namely the external lubricating system. This was simply a mechanical device for beating lubricating oil into millions of tiny bubbles and distributing them through small tubes to the exterior of the machine. By imposing rolling, oily contacts between the air and the outside surface of the flyer, this system cut down atmospheric resistance substantially and made it possible to travel through the earth’s gaseous envelope at speeds which would otherwise have produced a terrific amount of friction and heat—more than sufficient to annihilate any conveyance which was not protected by this lubricating envelope.
The cabin, of course, had double walls, heavily insulated.
As our task neared completion I began to cudgel my brains for a fitting name with which to christen our mechanical baby. The only cognomens I could think of were either too trite or too commonplace—names like “The Hyphen” because it was to join the moon and the earth, “Excelsior” and “The Spirit of Luna” were discarded because they were too reminiscent of other aircraft which had won fame in bygone days.
One morning I entered the hangar
to discover that the name question had been settled without any help from me. Under the direction of Professor Banning, a painter was just putting the finishing touches to the word: “AMUNDSEN.”
“What do you think of it?” the Professor asked me. “It certainly is an appropriate name. If Amundsen were alive today, he’d be just the kind of man who would endorse a trip like the one we are going to take. No one who ever lived is more worthy of the honor of having your flyer named after him.”
“That’s the way I feel about it. I consider your famous countryman as the greatest of explorers—the man who discovered the north magnetic pole and the northwest passage, the first man to reach the South Pole, and the only man so far who has seen one pole and has visited the other one in person. But great as these achievements were, they fade into insignificance when compared to his final voyage into the great unknown, when he sacrificed his life in an effort to save a man whom he considered an enemy.
“That’s why I am proud to name my flyer after Captain Roald Amundsen!”
CHAPTER V
The Trial Flight
WHEN the Amundsen was almost completed, Professor Banning sent a wire to Colonel Berglin, who was then in Washington attending to his engrossing duties as head of the newly created department of aviation. Two days later Berglin arrived in his famous “air office.”
It was decided first to test the Amundsen as a terrestrial flyer without making any attempt to leave the earth’s atmosphere or gravitational field. For this reason the four dimensional tubes were not to be used and it was not considered necessary for me to go along. Naturally I was on hand at the time scheduled for the trial flight and I observed the performance from the ground.
Professor Banning and Colonel Berglin entered the cabin and a few minutes later I heard a hissing sound which told me that the rocket tubes were in operation. Evidently only a small amount of power was being used at the start. For several minutes the machine taxied around the field making a series of short low hops. Suddenly, without warning, there shot out of the rear a blast which sent up a great cloud of gravel, and the Amundsen leaped heavenward, at a terrific pace. In a few seconds it had reached an altitude of several thousand feet. It then began the most preposterous series of stunts that have ever been witnessed. It looped and it side-slipped; it rolled like a barrel and spun like a top. It ended up by flying upside down in a wide circle, while at the same time it fluttered like a falling leaf, losing altitude at a terrific rate.
| I stood rooted to the spot in helpless horror! A terrible accident was about to occur before my eyes! So certain did this seem that I even had a momentary mental picture of the mangled bodies of my two dearest friends lying amid a nightmare vision of twisted steel.
I closed my eyes to shut out the gruesome sight. I held my breath and waited for the crash.
Nothing happened.
When I could stand the strain no longer, I opened my eyes. At first I could see nothing in the air and I concluded that in some inexplicable way the flyer had crashed without making a noise loud enough for me to hear.
But the handful of mechanics and airdrome officials who had gathered to watch the hop-off were all still looking at the sky.
With the aid of my field glasses I was able to discern the unique outlines of the Amundsen, sailing majestically upward and onward and apparently under perfect control.
I learned later that the erratic behavior of the Amundsen had been due to a slight defect in the adjustment of the mechanism for controlling the blasts through the eight steering tubes. The wild antics performed in midair were due to Berglin’s attempts to find out what was wrong. He had finally located the trouble just in time to prevent a serious crash. By manipulating the joy stick carefully in such a way as to make allowance for the defective adjustment, he had gotten the flyer under control and thereafter had no difficulty in making it do just what he wished.
After climbing to an altitude of over 50,000 feet in about ten minutes, Berglin coasted back to earth at an abrupt angle. He could easily have gone higher, but that was hardly necessary since the performance of the Amundsen was sufficient to prove its fitness for its destined task.
On the downward journey the Amundsen approached the airdrome at a tremendous speed. It looked as if it could never land without being carried off the field by its own momentum. But when it was about five hundred feet from the ground, the forward pointing rocket tubes were brought into play. With marvelous rapidity the acceleration was diminished until the machine seemed almost to be suspended in mid air. Then it slowly floated down to earth, settling as softly and noiselessly as a dandelion seed.
CHAPTER VI
Off for the Moon
THE trouble with the Amundsen’s steering mechanism was quickly remedied and a second trial flight demonstrated that the space flyer was thoroughly fit and ready for its crucial journey to the moon. At this time we also tried out the four dimensional steering device and it proved to be a wonderful success.
After everything had been made ready for the hop-off, Banning timed our departure so that it came when the moon was in its first quarter and was trailing the earth in its journey around the sun. While this was not an essential condition of a successful flight to the moon, it made possible a substantial increase in our speed and a saving of fuel, since it enabled us to take advantage of the motion of the moon itself.
Except for the unusual care which we took in checking over all our supplies and equipment, our take-off was uneventful. Only our assistants and most intimate friends knew about our plans. In order to avoid publicity, we embarked in the small hours of the morning.
The instant we were off the ground, Berglin pointed the nose of our flyer upward at a steep angle and so rapidly did we climb that it took us but a few minutes to reach the highly rarefied portions of the earth’s atmosphere.
We were then ready to execute our famous hairpin turn, by means of which we borrowed a tremendous amount of momentum from mother earth and at the same time took advantage of the speed with which the moon was hurtling through space in its journey around the sun.
Following Professor Banning’s instructions, Berglin headed the flyer in such a way that it pointed in the same direction that the earth itself was moving.
“Now give her a shot into hyper-space!” the Professor commanded, and I directed a current of exploding radatomite through one of the four dimensional rocket tubes.
Under the circumstances one might naturally expect a violent shock or jar but nothing of the sort happened. Instead we experienced a most peculiar twisting sensation like the skidding of an automobile on a slippery pavement.
For a few seconds we were projected into hyperspace, then Professor Banning said, “By this time we must be pretty well out of the gravitational field of the earth. So you may as well turn the ship about, Colonel.” Following these orders, Berglin operated the rocket tubes in such a way as to make a wide U turn, bringing the nose of the flyer around so it pointed straight toward the moon and in the opposite direction from that in which the earth was moving.
Perhaps an analogy will make the purpose of this maneuver clear.
Imagine a boy on skates being towed across a frozen lake by a horse traveling at the rate of twenty miles per hour, and being followed at some distance by his dog who is running at exactly the Same speed as the horse; that is, twenty miles per hour.
The boy lets go of the tow rope and, without making any effort to increase his speed, executes a hairpin turn so that he faces toward the dog. It is apparent that he will now be approaching the dog at a speed equal to the dog’s velocity added to the original velocity of the horse, or with a total speed of forty miles per hour. Naturally he will lose some momentum in making the turn and also in coasting after the turn, but it will require only a relatively small amount of effort on his part to make up for this loss of momentum.
In our case, the earth took the part of the horse, the space flyer was the boy, and the moon was the dog. The tow rope which fastened us to the ear
th was the force of gravitation. When we projected ourselves into hyperspace, we virtually cut the rope. After making the hairpin turn, we found ourselves speeding toward the moon while the satellite was rushing toward us. And since, by that time, we had reached the interplanetary space where there was no atmosphere to create friction or resistance, our momentum was practically equal to that with which the earth was traveling around the sun.
“You may as well shut off the power now,” Professor Banning directed. “We can easily coast most of the way. With no atmosphere to retard us, our present momentum should continue indefinitely. Suppose we make a rough estimate of our velocity. At the time we shot off into hyperspace our flyer was making a speed of about a thousand miles an hour. We were also traveling with the earth in its orbital flight at the rate of approximately 66,600 miles per hour. That makes our total speed pretty close to 67,600 miles per hour. At the same time the moon is now rushing toward us a trifle faster than 66,600 miles per hour. We are therefore approaching the moon at the rate of something like 134,000 miles per hour, so we ought to be able to cover the 238,851 miles between us and the moon in less than two hours.
“Of course we could increase our speed still more by using our rocket tubes, but I consider our present rate of progress quite satisfactory. What do you boys think about it?”
“Suits me,” said Berglin.
“Me, too,” I chimed in.
AS we had hopped off when it was still dark, we were in the shadow of the earth for several minutes. It wasn’t long, however, before one edge of the huge spheroid behind us became visible, and a moment later the great blazing orb of the sun peeped at us from behind the earth.
