Transcriber's Note: This e-text was produced from Astounding Science Fiction, June, 1955. Extensive research did not uncover any evidence that the U.S. copyright on this publication was renewed.
AS LONG AS YOU WISH
If, somehow, you get trapped in a circular time system ... how long is the circumference of an infinitely retraced circle?
By JOHN O'KEEFE
Illustrated by van Dongen
The patient sat stiffly in the leather chair on the other side of the desk. Nervously he pressed a coin into the palm of one hand.
"Just start anywhere," I said, "and tell me all about it."
"As before?" Without waiting for an answer, he continued, the coin clutched tightly in one hand. "I'm Charles J. Fisher, professor of Philosophy at Reiser College."
He looked at me quickly. "Or at least I was until recently." For a second his face was boyish. "Professor of Philosophy, that is."
I smiled and found that I was staring at the coin in his hand. He gave it to me. On one side I read the words: THE STATEMENT ON THE OTHER SIDE OF THIS COIN IS FALSE. The patient watched me with an expressionless face; I turned over the coin. It was engraved with the words: THE STATEMENT ON THE OTHER SIDE OF THIS COIN IS FALSE.
"That's not the problem," he said, "not my problem. I had the coin made when I was an undergraduate. I enjoyed reading one side, turning it over, reading the other side, and so on. A fiendish enjoyment like boys planning where to put the tipped-over outhouse."
I looked at the patient. He was thirty-eight, single, medium build, had an M.A. and Ph.D. from an eastern university. I knew this and more from the folder on my desk.
"Eight months ago," he continued, "I read about the sphere found on Paney Island." He stopped, looking at me questioningly.
"Yes, I know," I said. I opened my desk drawer, took out a clipping from the newspaper, and handed it to him.
I read the clipping before putting it back in the drawer.
Manila, Sept. 24 (INS) Archeologists from University of California have discovered in earth fault of recent quake a sphere two feet in diameter of an unidentifiable material.
Dr. Karl Schwartz, head of the group, said the sphere was returned to the University for study. He declined to answer questions on the cultural origin of the sphere.
"There wasn't any more in the newspapers about it," he said. "I have a friend in California who got me the photographs."
He looked at me intently. "You won't believe any of this." He pressed the coin into the palm of his hand. "You won't be able to."
"The photographs," he continued, as if lecturing, "were of characters projected by the sphere when placed before a focused light. The sphere was transparent, you see, imbedded with dark microscopic specks. By moving the sphere a certain distance each time, there was a total projection of three hundred and sixty different characters in eighteen different orderings. Or nineteen different orderings if you count one which was a list of all the characters."
I made a mental note of the numbers. I felt they were significant.
"As I said," he continued, "I obtained the photographs of the characters. Very strange shapes, totally unlike the characters of Oriental languages, but yet that is the closest way to describe them." He jerked forward in his chair, "Except, of course, ostensively."
"Later," I said. I wanted to get through the preliminaries first. There would be time later to see the photographs.
* * * * *
"The characters projected by the sphere," he said, "weren't like the characters of any known language." He paused dramatically. "There was reason to believe they had origin in an unknown culture. A culture more scientifically advanced than our own."
"And the reasons for this supposition?" I asked.
"The material ... the material of the sphere. It could only be roughly classified as ferro-plastic. Totally unknown, amazing imperviousness. A synthetic material, hardly the product of a former culture."
"From Mars?" I said, smiling.
"There were all kinds of conjectures, but, of course, the important thing was to see if the projection of characters was a message. The message, if any, would mean more than any conjecture."
"You translated it?"
He polished the coin on his jacket. "You won't dare believe it," he said sharply.
He cleared his throat and stiffened into a more rigid posture. "It wasn't exactly translation. You see, to us none of the characters had designation. They were just characters."
"So it was a problem of decoding?" I asked.
"As it turned out, no. Decoding is dependent on knowledge of language characteristics—characteristics of known languages. Decoding was tried, but without success. No, what we had to find was a key to the language."
"You mean like the Rune Stone?"
"More or less. In principle, we needed a picture of a cow, and a sign of meaning indicating one of the characters.
"For me, there was no possibility of finding similarities between the characters and characters of other languages—that would require tremendous linguistic knowledge and library facilities. Nor could I use a decoding approach—that would require special knowledge of techniques and access to electronic computers and other mechanical aids. No, I had to work on the assumption that the key to the sphere was implicit in the sphere."
"You hoped to find the key to the language in the language itself?"
"Exactly. You know, of course, some languages do have an implicit key? For example hieroglyphics or picture language. The word for cow is a picture of a cow."
He looked at the toes of his shoes. "You won't be able to believe it. It's impossible to believe. I use the word impossible in its logical sense.
"In most languages," he continued, looking up from his shoes, "the sound of some words themselves indicates the meaning of the word. Onomatopoetic words like bowwow, buzz."
"And the key to the unknown language?" I asked. "How did you find it?"
* * * * *
I watched him push the coin against the back of his arm, then lift it to read the backward letters pressed into his skin. He looked up at me and smiled.
"I built models of the characters. Big material ones, exactly proportionate to the ones projected. Then—quite by accident—I viewed one of them through a glass globe the size of the original sphere. What do you think I saw?"
"What?" I noticed he had the boyish look again.
"A distortion of the model. But that's not what's important. The distortions, on study, gave specific visual entities. Like when looking at one of those trick pictures and suddenly seeing the lion in the grass. The lines outlining the lion are there all the time, only the observer has to view them as the outline of a lion. It was the same with the models of the characters, except the shapes that appeared were not of lions or other recognizable things. But they did suggest."
He pressed the coin against his forehead, closed his eyes and appeared to be thinking deeply. "Yes, impossible to believe. No one can believe it."
"In addition to the visual response, the distortions gave me definite feelings. Not mixtures of feelings, but one definite emotional experience."
"How do you mean?"
"One character when viewed through the globe gave me a visual image and, at the same time, a strong feeling of light hilarity."
"I take it then that these distortions seemed to connote meanings, rather than denote them. You might say that their meaning was conveyed through a Gestalt experience on the part of the observer."
"Yes, each character gave a definite Gestalt. But, the Gestalt was the same for each observer. Or at least for thirty-five observers there was an eighty per cent correlation."
I whistled softly. "And the translation?"
"Doctor, what would you say if I told you the translation was unbelievable; that it couldn't be seriously entertained by any man? What if I said that it would take the sanity of any man who believed it?"
"I would say that it might well be incorrect."
He took some papers from his pocket and laughed excitedly, slumping down in the chair. "This is the complete translation in idiomatic English. I'm going to let you read it, but first I want you to consider a few things."
He hid the papers behind the back of his chair; his face became even more boyish, almost as if he were deciding on where to put the tipped over outhouse.
"Consider first, doctor, that there was a total projection of three hundred and sixty different characters. The same number as the number of degrees in a circle. Consider also that there were eighteen different orderings of the characters, or nineteen counting the alphabetical list. The square root of three hundred and sixty would lie between eighteen and nineteen."
"Yes," I said. I remembered there was something significant about the numbers, but I wasn't at all sure that it was this.
"Consider also," he continued, "that the communication was through the medium of a sphere. Moreover, keep in mind that physics accepts the path of a beam of light as its definition of a straight line. Yet, the path is a curve; if extended sufficiently it would be a circle, the section of a sphere."
"All right," I said. By now the patient was pounding the coin against the sole of one shoe.
"And," he said, "keep in mind that in some sense time can be thought of as another dimension." He suddenly thrust the papers at me and sat back in the chair.
I picked up the translation and began reading. The patient sat stiffly in the leather chair on the other side of the desk. Nervously he pressed a coin into the palm of one hand.
"Just start anywhere," I said, "and tell me all about it."
"As before?" Without waiting for an answer, he continued, the coin clutched tightly in one hand. "I'm Charles J. Fisher, professor of philosophy at Reiser College."
He looked at me quickly. "Or at least I was until recently." For a second his face was boyish. "Professor of philosophy, that is."
I smiled and found that I was staring at the coin in his hand. He gave it to me. On one side I read the words: THE STATEMENT ON THE OTHER SIDE OF THIS COIN IS FALSE. The patient watched....