“I was just talking to her,” Moke said. “I think she’s been talking to Polk too”
“What about?”
“She said she’d heard you found some maps, Captain. I guess Gladiator told her.”
“No reason why she shouldn’t, but I found those while she was here—she must have seen them. While we were waiting for the first survey parties to come in.”
“You didn’t hide them from her, or anything like that?”
“No, of course not. She just didn’t show much interest in them.” Actually, Daw remembered, he had taken the charts—technically they were star charts rather than maps—to show Helen and had been rather disappointed by her reaction; as an empathist, she had explained, she was much more concerned with things that had not been vital to the ship’s operations than with the things that had.
“Everyone takes what is necessary, Captain,”she had said. “By definition they have to. It’s what is taken that could be left behind that reveals the heart.”
“She wanted to know if any of them showed the inside of the ship,” Moke said.
Daw felt tired. “I’ll talk to her,” he said, and cut Moke off.
He started to adjust his communication for the girl’s band, then thought better of it. His investigation of the command module—if in fact this was the command module—was nearly complete, and it served no purpose for him to stand by and watch Polk tinkering with his instruments. After having Gladiator scan the charts so that duplicates could be made on board for study, he had replaced the originals. Now he gathered them again.
It was the first time he had been more than two units away from the corner module he and Helen had first investigated, and though he had heard the chambers of the interior modules described by the men he had sent through them, and had seen the pictures they had taken, it was a new and a strange experience to plunge through tube after tube and emerge in chamber after chamber, each so huge it seemed a sky around him, each seeming without end.
The tubes, like those of his own ship, were circular in section; but they were dim (as Gladiator’s were not) and lined with shimmering, luminous pastels he felt certain were codes but could not decipher. His years in space had taught him the trick of creating the thing called up and down in his mind, changing them when it suited him, destroying them with the truth of gravitationless reality when he wished. In the tubes he amused himself with them, sometimes diving down a pulsing pink well, sometimes rocketing up a black gun barrel, until at last he found that he was no longer master of these false perceptions, which came and went without his volition.
Entering each module was like being flung from a ventilation duct into the rotunda of some incredible building. The walls of most were lined with enigmatic machines, the centers cobwebbed with cables spanning distances that dwarfed the great mechanisms they held. Light in the modules—at least in most—was like that in the first Daw had examined—bright, shadowless), and all-surrounding; but some were dim, and some dark. In these his utility light showed shapes and cables not greatly different from those he had seen in other modules, but in the dancing shadows it cast to the remote walls, it sometimes seemed to Daw that he saw living shapes.
At last, when he had become almost certain he had lost his way and was cursing himself (for his religious beliefs permitted any degree of self-condemnation, though they caviled at the application of the same terms to any soul except his own) for a fool and a damned fool, he saw the flicker of other lights in one of the half-lit modules and was able, a moment later, to pick out Helen Young-meadow’s suit with his own beam and, a half-second afterward, the suits of the sailors he had sent with her. At almost the same instant he heard her voice in his phones: “Captain, is that you?”
“Yes,” he said. Now that he had found her, he discovered that he was unwilling to admit that he had come looking for her. Everyone, notoriously, fell in love with empathists—the reason they were invariably assigned as married couples. In retrospect he realized how foolish it had been for him to allow her to accompany him at all, despite the rationalizations with which he had defended the decision to himself; and he found that he was anxious that neither she nor the men with her should think that he had come here for her sake. “I understand you were asking my second about charts, Mrs. Youngmeadow,” he said, deliberately bringing his voice to the pitch he used in delivering minor reprimands. “I want to make it clear to you that if you have found any such documents they should be submitted to me for scanning as soon as possible.”
“We haven’t found any maps,” the girl said, “and if we did, of course I’d turn them over to you, though I don’t suppose you could read them either.”
The fatigue in her voice made Daw despise himself. Softening the question as much as he could, he asked, “Then why were you questioning Mr. Moke?”
“I knew you had found some. I was hoping they showed this ship and could tell us where my husband might be.”
“They’re star charts, Mrs. Youngmeadow. You saw them when I found them.”
“I wasn’t paying much attention then. Do you think they’re important?”
“Very important,” Daw said. “They could easily be the key to understanding—well, the entire system of thought of the people who built this ship. Naturally Gladiator can’t stay here—”
“Can’t stay here until my husband’s found?”
“We aren’t going to abandon your husband, Mrs. Youngmeadow.”
“I don’t suppose I could stop you if you wanted to.”
“We don’t.”
“But if you do, Captain, you’ll have to abandon me too, I’m not going back to our ship until we find out what happened to him, and if he’s still alive; you say that a person can live indefinitely in one of these suits—all right, I’m going to do that. Even if your ship leaves they’ll still send out another one from Earth to investigate this, with cultural anthropologists and so forth on board; and when they get here they’ll find me.”
One of the crewmen muttered, “Tell him!” under his breath; Daw wondered if the man realized it had been picked up by his helmet mike. To the girl he said, “They’ll find me too, Mrs. Youngmeadow. This ship is much too valuable a discovery for us to leave before someone else comes—but when they do come—this is what I was trying to say when you interrupted me—we’ll have to go. They’ll have equipment and experts; we are primarily a fighting ship. But it should be possible for you to arrange a transfer at that time.”
“Captain . . .”
After a moment had passed, Daw said, “Yes?”
“Captain, can these men hear us?”
“Of course.”
“Would you send them away? Just for a minute?”
“They could still hear us, if we stay on general band. If you have something private you wish to say, switch to my own band.”
He watched as she fumbled with the controls cm the forearm of her suit. One of the crewmen glided skillfully toward her to help, but she waved him away. Her voice came again. “Have I got you, Captain?”
“Yes.”
“I just wanted to tell you that I’m sorry I said what I did. You’ve been a friend to my husband and me, I know. I’m very tired.”
Daw said, “I understand.”
“Captain, I’ve been thinking. Will you mind if I ask some questions? I realize it may be silly, but if I don’t at least try—”
“Certainly.”
“That cyberneticist—Lieutenant Polk. You asked him to find out—” She hesitated. Then, “I’m sorry, I can’t think of the words.”
“I asked him to find out for me what the numbers in the operating registers of this ship’s computer were. To put it another way, I asked him to find out the answer—in raw form at least—of the last computation they performed.”
“Is that possible? I would think their numbers would be all different—like Roman numbers or something, or worse. I asked him about it—a few hours ago when you went back to Gladiator—and he explained to me that whatever he
found would just be ones and zeros—”
“Binary notation,” Daw said.
“Yes, binary notation, because it isn’t really numbers, you can’t have real numbers inside a machine because they’re not physical, but just things turned on or off; but I don’t see what good knowing it—just one, one, one, zero, zero, zero, like that—will do you if you don’t know how they’d be used when they came out of the machine. Captain, I know you must think I don’t know what I’m talking about, but I did have to take some mathematics . . . even if I wasn’t very good at it.” The transmission ended in a whisper of despair.
“I know you’re worried about your husband,” Daw said. “We’re looking for him, as you know. I’ve got parties out. I shouldn’t have included him among the searchers— that was a mistake, and I’m—”
“No!” Helen Youngmeadow jerked at the cable she was holding, swinging herself toward him until their faceplates touched and he could hear her voice, conducted through the metal, like an echo to the sound in his earphones. “You should have sent him. That’s just it. At first, when we were waiting and waiting and the others came back I talked to them and listened to them, and, my God, they didn’t know anything, they hadn’t seen anything, and I thought just wait, just wait, Mr. Captain Daw, my man will show you what an empathist can do! Then when he didn’t come I started to blame you, but that isn’t right. I’m an empathist, my profession is supposed to be understanding cultures—every culture, when most people don’t even comprehend their own. Now you’ve got these men staying with me to watch out for me—to watch out for me!—and do you know what they are? I asked them, and one is a plastics engineer and the other’s a pharmacist’s mate.”
“They’re good men,” Daw said. “That’s why I sent them with you, not because I thought they could assist you professionally.”
“Well, you were wrong,” the girl said in a much calmer voice. “We found a dingus of some sort floating loose in that last module we were in, and your plastics engineer looked at it for a while and then told us what he thought it was and how it had been made: he said they had used a four-part mold, and showed me where they had squirted in the melted stuff. So he understands his part of them, you see, but I don’t understand mine. Now you’re implying that you understand their math, or at least something about it. Can’t you explain it to me?”
“Certainly,” Daw said, “if you’re interested. I’m afraid, though, that I don’t see that it has any immediate bearing on locating your husband.”
“A computer will answer anyone, won’t it? I mean normally.”
“Unless some sort of privacy provision has been made in the program.”
“But there isn’t much chance they’d do that on a ship like this; you said when we opened the hatch to get in that no one worried about burglars in space, so I doubt if they’d be worried about snoopers aboard their own ship either. And if their computer is like Gladiator, meant to run everything, it will know where my husband is—all we have to do is learn how to turn it on and ask it.”
“I see what you mean,” Daw told her, “but I’m afraid that’s going to be a good deal more complicated than what I’ve got Polk trying to do.”
“But it’s the first step. Show me.”
Moved by some democratic impulse he did not bother to analyze, Daw switched back to the general communication band before spreading one of file charts—without gravity or air currents it hung like smoke in the emptiness—to illustrate what he was about to say; then for the benefit of the crewmen he explained: “This is one of their star charts—we found it in the first module we entered. In a rough way you could consider it a map of this part of the galaxy, as seen from above.”
The girl said: “I don’t understand how you can talk about seeing a galaxy from above or from below, except by convention—or how you know those dots on the chart are stars at all without being able to read the language. And if they are stars, how do you know they represent the region we’re in? Or is that just a guess?” Her voice was as controlled as it might have been during a dinner-table discussion on board Gladiator, but Daw sensed tension that held her at the edge of hysteria.
“To begin with,” he said, “the galaxy’s not a shapeless cloud of stars—it is disk-shaped, and it seems pretty obvious that anyone mapping any sizable portion of it would choose to look at things from one face or the other. Which face is chosen is strictly a matter of convention, but there are only two choices. And we’re pretty certain these things are star charts, because Gladiator measured the positions of the dots and ran a regression analysis between them and the known positions of the stars. The agreement was so good that we can feel pretty sure of the identities of most of the dots. What’s more, if you’ll look at the chart closely you’ll see that our friends have used three sizes of dots.”
Daw paused and one of the crewmen asked, “Magnitude, Captain?”
“That’s what we thought at first, but actually the three sizes seem to symbolize the principal wavelengths radiated—small dots for the blue end of the spectrum, medium for yellow stars like Sol, and large for the red giants and the dark stars.”
Helen Youngmeadow said, “I don’t see how that can help you read the numbers.”
“Well, you’ll notice faint lines running from star to star, with symbols printed along them; it seems reasonable to assume that these are distances, and of course we know the actual distances.”
“But you don’t know what sort of squiggle they use for each number, or what units the distances are given in.”
“Worse than that,” Daw admitted, “we don’t—or at least we didn’t—know whether they ran their figures from left to right or from right to left—or whether they were using positional notation at all. And of course we didn’t know what base they were using, either. Or which symbol took the place of our decimal point.”
“But you were able to find all that out, just from the chart?”
“Yes. The base was fairly easy. You probably remember from your own math that the number of numerals a system needs is equal to the number of the base. Our decimal notation, for example, uses ten—zero through nine. If you’ll look at these numbers you’ll see that a total of thirteen symbols are used—”
“Base thirteen?”
Daw shook his head. “We doubt it very much. Thirteen is a prime number, divisible only by one and itself, and as such an almost impossible base. But if we assume that one of the symbols is a position indicator like our decimal point, that leaves twelve; and twelve is a very practical base. So the question was which symbol divided the wholes—of whatever unit they were using—from the fractional parts.”
Helen Youngmeadow leaned toward the chart, and Daw sensed, with a happiness he had hardly known himself capable of, that some portion of her despair was fading. “You could try them one by one,” she said. “After all, there are only thirteen.”
“We could have, but there turned out to be a much quicker way. Remember, these numbers represent stellar distances, and we felt that we knew what most of the stars were. So we programmed a search routine to look for a star whose distance from one of the base stars on the chart was twelve times that of some other, closer star. In positional notation—and we had to assume for the time being that they were using a positional notation, since if they weren’t they wouldn’t need an analogue to the decimal point—when you shift the symbol, or group of symbols, at the front of a number up by one position, it has the effect, roughly, of multiplying the number by the base. So we had our program determine the ratio nearest twelve, the closer the better; and when we had located our stars we looked for a symbol that hadn’t changed position in the larger number. Here”—he indicated two lines of print on the chart—”see what I mean?”
“No,” the girl said after a moment. “No, I don’t. There are eight symbols in one expression and nine in the other, but the one on the right looks like an equation—the thing like a fish with a spear through it is equal to one group minus another.”
&nb
sp; “Yes, it does,” Daw admitted, “but the thing that resembles an equals sign is their mark for seven, and the ‘minus’ is a one. The vertical mark that looks like our one is their decimal point, and the numbers are read from right to left instead of left to right.”
“How did you get the values of the numerals?”
“Do you really want to hear about all this?”
“Yes, I do, but I don’t know why. Captain, is there actually a chance we might be able to get the computer on this ship working, and ask it where my husband is? And it would answer—just like that? That’s what I’m trying to believe, but sometimes it slips. Maybe I’m just interested because you are, and I empathize; it’s a fault of mine.”
Daw was suddenly embarrassed, and conscious as he had not been for some time of the empty ship around him. “Gladiator could explain this as well as I could,” he said. “Better.”
Orbit 11 - [Anthology] Page 3