by Gene Wolfe
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 on 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 the 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 give in.”
“Worse than that,” Daw admitted, “we don‘t—or at least we didn’t—know whether they ran their fingers 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 e
asy. 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.”
“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.”
“I could guess some of them myself, I think. You’ve already told me that the horizontal mark is a one, so since the equals sign isn’t two it must be the S-shaped thing.”
“You’re right,” Daw said, “how did you know?”
“Because it looks like our two, only backward; and ours is a cursive mark for what used to be two horizontal lines—it used to look like a Z. From the shape of their S sign I’d say it started out as two lines slanted.” She smiled.
“It is interesting, isn’t it?” Daw said.
“Very interesting. But now will you tell me what you’re going to learn when you can read whatever number the people who built this place left in their computer?”
“We don’t know, really; but from the nature of the number we may be able to guess what it was. What I’m hoping for is the heading they took when they abandoned the ship.”
“Did they abandon this ship?”
Daw was nonplussed. “We’ve been all through it.”
“Even through the path assigned my husband?”
“Of course; the first thing I did when he failed to return was to send a party to retrace his route.”
“And they did it?”
“Yes.”
“And came back and reported?”
“Yes.”
“Captain Daw, could we do it? I mean, I know you’re needed to direct things, even if I’m not, but could we do it? I don’t have your logical mind, but I have a feeling for situations, it’s part of my stock-in-trade. And I think the two of us might find something where no one else would.”
Daw thought for a moment. “Good administrative practice,” he said. “I see what you mean.”
“Then tell me, because I don’t myself.”
“Just that since this is our biggest problem I should give it my personal attention; and you should come too, because you are the one who wants it settled most and will have the greatest dedication to the job. You realize though, don’t you, that you are—we are—almost in the center of your husband’s route now.”
Even as he made this last small protest Daw felt himself carried away by the attraction of the idea. He would lose a certain amount of face with the men he had assigned to guard Helen, but, as he told himself, he could afford to lose some face. Addressing them, he said: “Mrs. Youngmeadow and I are going to retrace her husband’s search path through this vessel in person. You may return to your duty.”
The two saluted, and Daw saw—incredibly—a new respect in their expressions, and something like envy as well. “Dismissed!” he snapped.
When they had gone Helen Youngmeadow said: “You really like it, don’t you, going off by yourself? I should have known when we went alone to board this ship.”
“No,” Daw said. “I should be on Gladiator.”
“That’s the voice of conscience. But this is what you like.” The girl launched herself from the cable she had been holding and gave half-power to her backpack rockets, doing a lazy wingover to avoid the next wire.
“Where are you going?” Daw called.
“Well, we’re going to retrace the way my husband came, in the same direction he did, aren’t we? So there’s no use going back to the beginning that way; but if we take the modules next to his we might find something.”
“Do you think your husband would have deviated from the assigned route?”
“He might have,” said Helen’s voice in Daw’s ear. He could see her now, far ahead in the dimness, ready to dive into the pale, circular, lime-green immensity of a tube. “He was a funny person, and I guess maybe I may not have known him as well as I thought I did.”
Daw put on a burst of speed and was up with her before she had gone a thousand yards into the tube. “You’re right,” he said, “this is what I like.”
“I do too—maybe my husband liked it too much. That would be in harmony with his personality profile, I think.” Daw did not answer, and a few seconds later she asked in a different tone, “Do you know what I was thinking of, while you were telling me about those charts? Stones. Little pebbles. Do you get it?”
“No,” Daw said. The tube was bent just enough here for the ends to be invisible to them. They sailed through a nothingness of pale green light.
“Well, I may not know a lot of math but I know some etymology. You were talking about calculations, and that word comes from the Latin for a stone: calculus. That was the way they used to count—one stone for one sheep or one ox. And later they had a thing like an abacus except that instead of rods for the counters it had a board with cup-shaped holes to put stones in. Those numbers you figured out were little stones from a world we’ve never seen.”
Daw said, “I think I understand.” He could make out the end of the tube now, a region of brighter light where vague shapes floated.
“The thing I wonder about is where are they now, those first stones? Ground to powder? Or just kicking around Italy or Egypt somewhere, little round stones that nobody pays any attention to. I don’t really think anything would happen if they were destroyed—not realty—but I’ve been wondering about
it.”
“Your sense of history is too strong,” Daw told her. He nearly added, “Like Wad’s,” but thought better of it and said instead, “For some reason that reminds me—you were going to tell me why you were talking to Wad, but you never did.”
“Wad is the boy that looks like you? I said I would if you’d tell me about him.”
“That’s right,” Daw said, “I didn’t finish.” They were leaving the tube now, thrown like the debris from an explosion through an emptiness whose miles-distant walls seemed at first merely roughened, but whose roughness resolved into closely-packed machines, a spininess of shafts and great gears and tilted beams—all motionless.
“You told me about the midshipmen,” Helen reminded him. “I think I can guess the rest, except that I don’t know how it’s done.”
“And what’s your guess?”
“You said that you were Wad—at least in a sense. In some way you’re training yourself.”
“Time travel? No.”
“What then?”
“Future captains are selected by psychological testing when, as cadets, they have completed their courses in basic science. Then instead of being sent to space as junior officers, they go as observers on a two-year simulated flight—all right on Earth. The advantage is that they see more action in the two years of simulation than they’d get in twenty of actual service. They go through every type of emergency that’s ever come up at least once, and some more than once—with variations.”
“That’s interesting; but it doesn’t explain Wad.”
“They have to get the material for the simulations somewhere. Sure, in most of it the midshipman just views, but you don’t want to train him to be a detached observer and nothing else. He has to be able to talk to the people on shipboard, and especially the captain, and get meaningful, typical replies. To get material for those conversations a computer on every navy ship simulates a midshipman whom the captain and crew must treat as an individual.”
“Do they all look like you?”
“They have to look like someone, so they’re made to look—and talk and act—as the captain himself did during his midshipman days. It’s important, as I said, that the captain treat his midshipman as a son, and that way there’s more—” Daw paused.