by Hank Davis
“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.”
“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 ‘2’. 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 really—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 spinniness 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.
“Empathy?” He could hear the fragile smile.
“That’s your word. Sympathy.”
“Before it was corrupted by association with pity; that used to mean what empathy does now.”
A new voice rang in Daw’s headphones” “Captain! Captain!”
“Yes, here.”
“This is Polk, Captain. We didn’t want to bother you, sir, but we’ve got the numbers from the central registers in that corner module, and from the form—well, we think you’re right. It’s a bearing.”
“You’ve got duplicates of the charts, don’t you?” Where were they going?”
“What star, you mean, sir?”
“Yes, of course.”
“It doesn’t seem to be a bearing for any star, Captain. Not on their charts or ours either.”
Helen Youngmeadow interrupted to say: “But it has to point to some star! There are millions of them out there.”
Daw said, “There are billions—each so remote that for most purposes it can be treated as a nondimensional point.”
“The closest star to the bearing’s about a quarter degree off,” Polk told her. “And a quarter of a degree is, well ma’am, a hell of a long way in astrogation.”
“Perhaps it isn’t a bearing then,” the girl said.
Daw asked, “What does it point to?”
“Well, sir—”
“When I asked you a minute ago what the bearing indicated, you asked if I meant what star. So it does point to something, or you think it does. What is it?”
“Sir, Wad said we should ask Gladiator what was on the line of the bearing at various times in the recent past. I guess he thought it might be a comet or something. It turned out that it’s pointing right to where our ship was while we were making our approach to this one, sir.”
Unexpectedly, Daw laughed. (Helen Youngmeadow tried to remember if she had ever heard him laugh before, and decided she had not.)
“Anything else to report, Polk?”
“No, sir.”
She asked, “Why did you laugh, Captain?”
“We’re still on general band,” Daw said. “What do you say we switch over to private?”
His own dials bobbed and jittered as the girl adjusted her controls.
“I laughed because I was thinking of the old chimpanzee experiment; you’ve probably read about it. One of the first scientists to study the psychology of the nonhuman primates locked a chimp in a room full of ladders and boxes and so on—”
“And then peeked through the keyhole to see what he did, and saw the chimpanzee’s eye looking back at him.” Now Helen laughed too. “I see what you mean. You worked so hard to see what they had been looking at—and they were looking at us.”
“Yes,” said Daw.
“But that doesn’t tell you where they went, does it?”
Daw said, “Yes, it does.”
“I don’t understand.”
“They were still here when we sighted them, because we changed course to approach this ship.”
“Then they abandoned the ship because we came, but that still doesn’t tell you where they went.”
“It tells me where they are now. If they didn’t leave before we had them in detection range, they didn’t leave at all—we would have seen them. If they didn’t leave at all, they are still on board.”
“They can’t be.”
“They can be and they are. Think of how thinly we’re scattered on Gladiator. Would anyone be able to find us if we didn’t want to be found?”
Far ahead in the dimness her utility light answered him. He saw it wink on and dart from shadow to shadow, then back at him, then to the shadows again. “We’re in no more danger than we were before,” he said.
“They have my husband. Why are they hiding, and who are they?”
“I don’t know; I don’t even know that they are hiding. There may be very few of them—they may find it hard to make us notice them. I don’t know.”
The girl was slowing, cutting her jets. He cut his own, letting himself drift up to her. When he was beside her she said: “Don’t you know anything about them? Anything?”
“When we first sighted this ship I ran an electronic and structural correlation on its form. Wad ran a bionic one. You wouldn’t have heard us talking about them because we were on a private circuit.”
“No.” The girl’s voice was barely audible. “No, I didn’t.”
“Wad got nothing on his bionic correlation. I got two things out of mine. As a structure this ship resembles certain kinds of crystals. Or you could say that it looks like the core stack in an old-fashioned computer—cores in rectangular arrays with three wires running through the center of each. Later, because of what Wad had said, I started thinking of Gladiator; so while we were more or less cooling our heels and hoping your husband would come in, I did what Wad had and ran a bionic correlation on her.” He fell silent.
“Yes?”
“There were vertebrates—creatures with spinal columns—before there were any with brains; did you know that? The first brains were little thickenings at the end of the spinal nerves nearest the sense organs. That’s what Gladiator res
embles—that first thin layer of extra neurons that was . . . the primitive cortex. This ship is different.”
“Yes,” the girl said again.
“More like an artificial intelligence—the computer core stack of course, but the crystals too; the early computers, the ones just beyond the first vacuum-tube stage, used crystalline materials for transducers: germanium and that kind of thing. It was before Ovshinsky came up with ovonic switches of amorphous materials.”
“What are you saying? That the ship is the entity? That the crew are robots?”
“I told you I don’t know,” Daw said. “I doubt if our terms are applicable to them.”
“But what can we do?”
“Get in touch with them. Let them know we’re here, that we’re friendly and want to talk.” He swung away from her—up, in his current orientation, up six miles sheer before coming to rest like a bat against the ceiling, then revolving the ship in his mind until the ceiling became a floor. The girl hovered five hundred feet above his head as he inspected the machines.
“I see,” she said, “you’re going to break something.”
“No,” Daw said slowly, “I’m going to find something to repair or improve—if I can.”
Several hours passed while he traced the dysfunction that held the equipment around him immobile. From the module where he had begun he followed it to the next, where he found broken connections and fused elements; another hour while he made the connections again, and found, in cabinets not wholly like any he had seen built by men, parts to replace those the overloads had destroyed. When he had finished his work, three lights came on in distant parts of the module; and far away some great machine breathed a sigh that traveled through the metal floor to the soles of his boots, though Helen, still floating above him, did not hear it. “Do you think they’ll come now?” she asked when the lights gleamed. “Will they give him back to us?”
Daw did not answer. A shape—a human shape—was emerging from the mouth of a distant tube. It was a half-mile away, but he had seen it as the girl spoke, a mere speck, but a speck with arms and legs and a head that was a recognizable helmet. In a moment she had followed his eyes. “Darling,” she said. “Darling.” Daw watched. A voice, resonant yet empty, said, “Helen.”