“Wake up, Renn, let’s get down to business!” Mven Mass called to him. The physicist smiled in shy confusion.
A stretch of firm sand between two ridges of rock was turned into a scientific auditorium. Renn Bose, using fragments of seashells, drew and wrote in the sand, in his excitement he fell flat, his body rubbing out what he had written and drawn so that he had to draw it all again. Mven Mass expressed his agreement or encouraged the physicist with abrupt exclamations. Darr Veter, resting his elbows on his knees, wiped away the perspiration that broke out on his forehead from the effort he was making to understand. At last the red-headed physicist stopped talking, and sat back on the sand breathing heavily.
“Yes, Renn Bose,” said Darr Veter after a lengthy pause, “you have made a discovery of outstanding importance.”
“I did not do it alone. The ancient mathematician Geiaenberg propounded the principle of indefiniteness, the impossibility of accurately defining the position of tiny particles. The impossible has become possible now that we understand mutual transitions, that is, we know the repagular calculus[18]. At about the same time scientists discovered the circular meson cloud in the atomic nucleus, that is, they came very near to an understanding of anti-gravitation.”
“We’ll accept that as true. I’m not a specialist in bipolar mathematics,” particularly the repagular calculus which studies the obstacles to transition. But I realize that your work with the shadow functions is new in principle, although we ordinary people cannot properly understand it unless we have mathematical clairvoyance. I can, however, conceive of the tremendous significance of the discovery. There is one thing…” Darr Veter hesitated.
“What, what is there?” asked Mven Mass, anxiously.
“How can we do it experimentally? I don’t think we can create a sufficiently powerful electromagnetic field….”
“To balance the gravitational field and obtain a state of transition?” inquired Renn Bose.
“Exactly. Beyond the limits of the system, space will remain outside our influence.”
“That’s true, but, as always in dialectics, we must look for a solution in the opposite. Suppose we obtain an anti-gravitational shadow vectorally and not discretely.”
“Ah! But how?”
Swiftly, Renn Bose drew three straight lines and a narrow sector with an arc of greater radius intersecting them.
“This was known before bipolar mathematics. Two thousand and five hundred years ago it was called the Problem of the Fourth Dimension. In those times there was a widespread conception of multidimensional space; the shadow properties of gravitation, however, were unknown and people attempted to find an analogy with electromagnetic fields which led them to believe that points of singularity meant that matter had disappeared or had been changed into something that could be named but could not be explained. How could they have had any conception of space with their limited knowledge of the nature of phenomena? But our ancestors could guess — you sec, they realized that if the distance from, say, star A to the centre of Earth along line OA is twenty quintillion kilometres, then the distance to the same star by vector OB will equal zero… in practice, not zero but approaching it. They said that zero time would be achieved if the velocity of motion were equal to the velocity of light. Remember that the cochlear calculus2” has been only recently discovered!”
“Spiral motion was known thousands of years ago,” Mven Mass remarked cautiously, interrupting the scientist. Kenn Bose dismissed the remark disdainfully.
“They knew the motion but not the laws! It’s like this, if the gravitational field and the electromagnetic field are two sides of one and the same property of matter and if space is a function of gravitation, then the function of the electromagnetic field is antispace. The transition from one to the other yields the vector shadow function, zero space, which is known in everyday language as the speed of light. I believe it to be possible to achieve zero space in any direction. Mven Mass wants to visit the planet of Epsilon Tucanae — it’s all the same to me as long as I can set up the experiment! As long as I can set up the experiment!” repeated the physicist, lowering his short white eyelashes wearily.
“You will need not only the outer stations and Earth’s energy, as Mven Mass pointed out, but some sort of an installation as well. Such an installation cannot be simple or easily erected.”
“In that respect we’re lucky. We can use Corr Yule’s installation near the Tibetan Observatory. Experiments for the investigation of space were carried out there a hundred and seventy years ago. There will have to be some adjustments and, as far as volunteers to help me are concerned, I can get five, ten, twenty thousand any time I like. I have only to call for them and they will take leave of absence and come.”
“You seem to have thought of everything. There is only one other consideration, but it is the most important — the danger of the experiment. There may be the most unexpected results; in conformity with the law of big numbers we cannot make a preliminary attempt on a small scale. We must take the extraterrestrial scale from the start.”
“What scientist would be afraid of risk?” asked Renn Bose, shrugging his shoulders.
“I wasn’t thinking of personal risk! I know that there will be thousands of volunteers as soon as they are required for some dangerous and novel enterprise. The experiment will also involve the outer stations, the observatories, the whole system of installations that has cost mankind a tremendous amount of labour. These are installations that have opened a window into the Cosmos, that have put mankind in contact with the life, knowledge and creative activity of other populated worlds. This window is mankind’s greatest achievement: do you think that you, or I, or any other individual or group of individuals has the right to take the risk of closing it, even for a short time? I would like to know whether you feel that you have that right and on what grounds?”
“I have and on good grounds,” said Mven Mass, rising to his feet. “You have been at archaeological excavations — do not the billions of unknown skeletons in unknown graves appeal to us? Do they not reproach us and make demands of us? I visualize billions of human lives that have passed, lives in which youth, beauty and the joy of life slipped away like sand through one’s fingers — they demand that we lay bare the great mystery of time, that we struggle against it! Victory over space is victory over time, that is why I’m sure that I’m right, that’s why I believe in the greatness of the proposed experiment!”
“My feelings are different,” said Renn Bose. “But they form the other side of the same thing. Space still cannot be overcome in the Cosmos, it keeps the worlds apart and prevents us from discovering planets with populations similar to ours, prevents us from joining them in one family that would be infinitely rich in its joy and strength. This would be the greatest transformation since the Era of World Unity, since the days when mankind finally put an end to the separate existence of the nations and merged into one, in this way making the greatest progress towards a new stage in the conquest of nature. Every new step in this direction is more important than anything else, more important than any other investigations or knowledge.”
Renn Bose had scarcely finished when Mven Mass spoke again.
“There is one other thing, a personal one. In my youth I had a collection of old historical novels. There was one story about your ancestors, Darr Veter. Some great conqueror, some fierce destroyer of human life of whom there were so many in the epochs of the lower forms of society, launched an attack against them. The story was about a strong youth who was madly in love. His girl was captured and taken away — ’driven off”“ was the word used in those days. Can you imagine it? Men and women were bound and driven off to the country of the conqueror like cattle. The youth was separated from his beloved by thousands of miles. The geography of Earth was unknown, riding and pack animals were the only means of transport. The world of those days was more mysterious and vast, more dangerous and difficult to cross than Cosmic space is for us today. The young hero hunted for his dream, for years he wandered terribly dangerous paths until he found her in the depths of the Asian mountains. It is difficult to define the impression I had when I was younger, but it still seems to me that I, too, could go through all the obstacles of the Cosmos to the one I loved!”
18
Repagular Calculus — a calculus in bipolar mathematics that deals with moments of transition (repagulum) from one state or condition to another and from one mathematical sign to another (imaginary).