Contact

CHAPTER 5 Decryption Algorithm

The visiting scientists' quarters were now all occupied, indeed overcrowded, by selected luminaries of the SETI community. When the official delegations began arriving from Washington, they found no suitable accommodations at the Argus site and had to be billeted at motels in nearby Socorro. Kenneth der Heer, the President's Science Adviser, was the only exception. He had arrived the day after the discovery, in response to an urgent call from Eleanor Arroway. Officials from the National Science Foundation, the National Aeronautics and Space Administration, the Department of Defense, the President's Science Advisory Committee, the National Security Council, and the National Security Agency trickled in during the next few days. There were a few government employees whose precise institutional affiliations remained obscure.

The previous evening, some of them stood at the base of Telescope 101 and had Vega pointed out to them for the first time. Obligingly, its blue-white light flickered prettily.

“I mean, I've seen it before, but I never knew what it was called,” one of them remarked. Vega appeared brighter than the other stars in the sky, but in no other way noteworthy. It was merely one of the few thousand naked-eye stars.

The scientists were running a continuous research seminar on the nature, origin, and possible significance of the radio pulses. The project's public affairs office—larger than in most observatories because of widespread interest in the search for extraterrestrial intelligence—was assigned the task of filling in the lower-ranking officials. Every new arrival required an extensive personal briefing. Ellie, who was obliged to brief the senior officials, supervise the ongoing research, and respond to the entirely proper skeptical scrutiny being offered with some vigor by her colleagues, was exhausted. The luxury of a full night's sleep had eluded her since the discovery.

At first they had tried to keep the finding quiet. After all, they were not absolutely sure it was an extraterrestrial message. A premature or mistaken announcement would be a public relations disaster. But worse than that, it would interfere with the data analysis. If the press descended, the science would surely suffer. Washington as well as Argus was keen to keep the story quiet. But the scientists had told their families, the International Astronomical Union telegram had been sent all over the world, and still rudimentary astronomical data-basing systems in Europe, North America, and Japan were all carrying news of the discovery.

Although there had been a range of contingency plans for the public release of any findings, the actual circumstances had caught them largely unprepared. They drafted as innocuous a statement as they could and released it only when they had to. It caused, of course, a sensation.

They had asked the media's forbearance, but knew there would be only a brief period before the press would descend in force. They had tried to discourage reporters from visiting the site, explaining that there was no real information in the signals they were receiving, just tedious and repetitive prime numbers.

The press was impatient with the absence of hard news. “You can only do so many sidebars on “What is a prime number? ” one reporter explained to Ellie over the telephone.

Television camera crews in fixed-wing air taxis and chartered helicopters began making low passes over the facility, sometimes generating strong radio interference easily detected by the telescopes. Some reporters stalked the officials from Washington when they returned to their motels at night. A few of the more enterprising had attempted to enter the facility unobserved—by beach buggy, motorcycle, and in one case on horseback. She had been forced to inquire about bulk rates on cyclone fencing.

Immediately after der Heer arrived, he had received an early version of what was by now Ellie's standard briefing: the surprising intensity of the signal, its location in very much the same part of the sky as the star Vega, the nature of the pulses.

“I may be the President's Science Adviser,” he had said, “but I'm only a biologist. So please explain it to me slowly. I understand that if the radio source is twenty-six light-years away, then the message had to be sent twenty-six years ago. In the 1960s, some funny-looking people with pointy ears thought we'd want to know that they like prime numbers. But prime numbers aren't difficult. It's not like they're boasting. It's more like they're sending us remedial arithmetic. Maybe we should be insulted.”

“No, look at it this way,” she said, smiling. “This is a beacon. It's an announcement signal. It's designed to attract our attention. We get strange patterns of pulses from quasars and pulsars and radio galaxies and God-knows-what. But prime numbers are very specific, very artificial. No even number is prime, for example. It's hard to imagine some radiating plasma or exploding galaxy sending out a regular set of mathematical signals like this. The prime numbers are to attract our attention.”

“But what for?” he had asked, genuinely baffled.

“I don't know. But in this business you have to be very patient. Maybe in a while the prime numbers will turn off and be replaced by something else, something very rich, the real message. We just have to keep on listening.”

This was the hardest part to explain to the press, that the signals had essentially no content, no meaning—just the first few hundred prime numbers in order, a cycling back to the beginning, and again the simple binary arithmetic representations: 1, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31… Nine wasn't a prime number, she'd explain, because it was divisible by 3 (as well as 9 and 1, of course). Ten wasn't a prime number because 5 and 2 went into it (as well as 10 and 1). Eleven was a prime number because it was divisible only by 1 and itself. But why transmit prime numbers? It reminded her of an idiot savant, one of those people who might be grossly deficient in ordinary social or verbal skills but who could perform mindboggling feats of mental arithmetic—such as figuring out, after a moment's thought, on what day of the week June first in the year 11,977 will fall. It wasn't for anything; they did it because they liked doing it, because they were able to do it.

She knew it was only a few days after receipt of the message, but she was at once exhilarated and deeply disappointed. After all these years, they had finally received a signal—sort of. But its content was shallow, hollow, empty. She had imagined receiving the Encyclopedia Galactica.

We've only achieved the capacity for radio astronomy in the last few decades, she reminded herself, in a Galaxy where the average star is billions of years old. The chance of receiving a signal from a civilization exactly as advanced as we are should be minuscule. If they were even a little behind us, they would lack the technological capability to communicate with us at all. So the most likely signal would come from a civilization much more advanced. Maybe they would be able to write full and melodic mirror fugues: The counterpoint would be the theme written backwards. No, she decided. While this was a kind of genius without a doubt, and certainly beyond her ability, it was a tiny extrapolation from what human beings could do. Bach and Mozart had made at least respectable stabs at it.

She tried to make a bigger leap, into the mind of someone who was enormously, orders of magnitude, more intelligent than she was, smarter than Drumlin, say, or Eda the young Nigerian physicist who had just won the Nobel Prize. But it was impossible. She could muse about demonstrating Fermat's Last Theorem or the Goldbach Conjecture in only a few lines of equations. She could imagine problems enormously beyond us that would be old hat to them. But she couldn't get into their minds; she couldn't imagine what thinking would be like if you were much more capable than a human being. Of course. Nor surprise. What did she expect? It was like trying to visualize a new primary color or a world in which you could recognize several hundred acquaintances individually only by their smells…. She could talk about this, but she couldn't experience it. By definition, it has to be mighty hard to understand the behavior of a being much smarter than you are. Buy even so, even so: Why only prime numbers?

The Argus radio astronomers had made progress in the last few days. Vega had a known motion—a known component of its velocity toward or away from the Earth, and a known component laterally, across the sky, against the background of more distant stars. The Argus telescopes, working together with radio observatories in West Virginia and Australia, had determined that the source was moving with Vega. Not only was the signal coming, as carefully as they could measure, from where Vega was in the sky; but the signal also shared the peculiar and characteristic motions of Vega. Unless this was a hoax of heroic proportions, the source of the prime number pulses was indeed in the Vega system. There was no additional Doppler effect due to the motion of the transmitter, perhaps tied to a planet, about Vega. The extraterrestrials had compensated for the orbital motion. Perhaps it was a kind of interstellar courtesy.

“It's the goddamnedest most wonderful thing I ever heard of. And it's got nothing to do with our shop,” said an official of the Defense Advanced Research Projects Agency, preparing to return to Washington.

As soon as the discovery had been made, Ellie had assigned a handful of the telescopes to examine Vega in a range of other frequencies. Sure enough, they had found the same signal, the same monotonous succession of prime numbers, beeping away in the 1420 megahertz hydrogen line, the 1667 megahertz hydroxyl line, and at many other frequencies. All over the radio spectrum, with an electromagnetic orchestra, Vega was bleating out prime numbers.

“It doesn't make sense,” said drumlin, casually touching his belt buckle. “We couldn't have missed it before. Everybody's looked at Vega. For years. Arroway observed it from Arecibo a decade ago.

Suddenly last Tuesday Vega starts broadcasting prime numbers? Why now? What's so special about now?

How come they start transmitting just a few years after Argus starts listening?”

“Maybe their transmitter was down for repairs for a couple of centuries,” Valerian suggested, “and they just got it back on-line. maybe their duty cycle is to broadcast to us just one year out of every million.

There are all those other candidate planets that might have life on them, you know. We're probably not the only kid on the block.” But Drumlin, plainly dissatisfied, only shook his head.

Although his nature was the opposite of conspiratorial, Valerian thought he had caught an undercurrent in Drumlin's last question: could all this be a reckless, desperate attempt by Argus scientists to prevent a premature closing down of the project? It wasn't possible. Valerian shook his head. As der Heer walked by, he found himself confronted by two senior experts on the SETI problem silently shaking their heads at one another.

Between the scientists and the bureaucrats there was a kind of unease, a mutual discomfort, a clash of fundamental assumptions. One of the electrical engineers called it an impedance mismatch. The scientists were too speculative, too quantitative, and too casual about talking to anybody for the tastes of many of the bureaucrats. The bureaucrats were too unimaginative, too qualitative, too uncommunicative for many of the scientists. Ellie and especially der Heer tried hard to bridge the gap, but the pontoons kept being swept downstream.

This night, cigarette butts and coffee cups were everywhere. The casually dressed scientists, Washington officials in light-weight suits, and an occasional flag-rank military officer filled the control room, the seminar room, the small auditorium, and spilled out of doors, where, illuminated by cigarettes and starlight, some of the discussions continued. But tempers were frayed. The strain was showing.

“Dr. Arroway, this is Michael Kitz, Assistant Secretary of Defense for C3I.”

Introducing Kitz and positioning himself just a step behind him, der Heer was communicating…

what? Some unlikely mix of emotions. Bemusement in the arms of prudence? He seemed to be appealing for restraint. Did he think her such a hothead? “C3I”—pronounced cee-cubed-eye—stood for Command, Control, Communications, and Intelligence, important responsibilities at a time when the United States and the Soviet Union were gamely making major phased reductions in their strategic nuclear arsenals. It was a job for a cautious man.

Kitz settled himself in one of the two chairs across the desk from Ellie, leaned forward, and read the Kafka quote. He was unimpressed.

“Dr. Arroway, let me come right to the point. We're concerned about whether it's in the best interest of the United States for this information to be generally known. We were not overjoyed about your sending that telegram all over the world.”

“You mean to China? To Russia? To India?” Her voice, despite her best effort, had a discernible edge to it. “You wanted to keep the first 261 prime numbers secret? Do you suppose, Mr. Kitz, the extraterrestrials intended to communicate only with Americans? Don't you think that a message from another civilization belongs to the whole world?”

“You might have asked our advice.”

“And risk losing the signal? Look, for all we know, something essential, something unique might have been broadcast after Vega had set her in New Mexico but when it was high in the sky over Beijing.

These signals aren't exactly a person-to-person call to the U. S. of A. They're not even a person-to-person call to the Earth. It's station-to-station to any planet in the solar system. We just happened to be lucky enough to pick up the phone.”

Der Heer was radiating something again. What was he trying to tell her? That he liked that elementary analogy, but ease up on Kitz?

“In any case,” she continued, “it's too late. Everybody knows now that there's some kind of intelligent life in the Vega system.”

“I'm not sure it's too late, Dr. Arroway. You seem to think there'll be some information-rich transmission, a message, still to come. Dr. der Heer here”—he paused to listen to the unexpected assonance—”Dr. der Heer says you think these prime numbers are an announcement, something to make us pay attention. If there is a message and it's subtle—something those other countries wouldn't pick up right away—I want it kept quiet until we can talk about it.”

“Many of us have wants, Mr. Kitz, she found herself saying sweetly, ignoring der Heer's raised eyebrows. There was something irritating, almost provocative, about Kitz's manner. And probably hers as well. “I, for example, have a want to understand what the meaning of this signal is, and what's happening on Vega, and what it means for the Earth. It's possible that scientists in other nations are the key to that understanding. Maybe we'll need their data. Maybe we'll need their brains. I could imagine this might be a problem too big for one country to handle all by itself.”

Der Heer now appeared faintly alarmed. “Uh, Dr. Arroway. Secretary Kitz's suggestion isn't all that unreasonable. It's very possible we'd bring other nations in. All he's asking is to talk about it with us first. And that's only if there's a new message.”

His tone was calming but not unctuous. She looked at him closely again. Der Heer was not a patently handsome man, but he had a kind and intelligent face. He was wearing a blue suit and a crisp oxford shirt. His seriousness and air of self-possession were moderated by the warmth of his smile. Why, then, was he shilling for this jerk? Part of his job? Could it be that Kitz was talking sense?

“It's a remote contingency anyway.” Kitz sighed as he got to his feet. “The Secretary of Defense would appreciate your cooperation.” He was trying to be winning. “Agreed?”

“Let me think about it,” she replied, taking his proffered hand as if it were a dead fish.

“I'll be along in a few minutes, Mike,” der Heer said cheerfully.

His hand on the lintel of the door, Kitz had an apparent afterthought, removed a document from his inside breast pocket, returned, and placed it gingerly on the corner of her desk. “Oh yes, I forgot. Here's a copy of the Hadden Decision. You probably know it. It's about the government's right to classify material vital to the security of the United States. Even if it didn't originate in a classified facility.”

“You want to classify the prime numbers?” she asked, her eyes wide in mock incredulity.

“See you outside, Ken.”

She began talking the moment Kitz left her office. “What's he after? Vegan death rays? World blower-uppers? What's this really about?”

“He's just being prudent, Ellie. I can see you don't think that's the whole story. Okay. Suppose there's some message—you know, with real content—and in it there's something offensive to Muslims, say, or to Methodists. Shouldn't we release it carefully, so the United States doesn't get a black eye?”

“Ken, don't bullshit me. That man is an Assistant Secretary of Defense. If they're worried about Muslims and Methodists, they would have sent me an Assistant Secretary of State, or—I don't know—one of those religious fanatics who preside at presidential prayer breakfasts. You're the President's Science Adviser. What did you advise her?”

“I haven't advised her anything. Since I've been here, I've only talked to her once, briefly, on the phone. And I'll be frank with you, she didn't give me any instructions about classification. I thought what Kitz said was way off base. I think he's acting on his own.”

“Who is he?”

“As far as I know, he's a lawyer. He was a top executive in the electronics industry before joining the Administration. He really knows C3I, but that doesn't make him knowledgeable about anything else.”

“Ken, I trust you. I believe you didn't set me up for this Hadden Decision threat.” She waved the document in front of her and paused, seeking his eyes. “Do you know that Drumlin thinks there's another message in the polarization?”

“I don't understand.”

“Just a few hours ago, Dave finished a rough statistical study of the polarization. He's represented the Stokes parameters by Poin-care spheres; there's a nice movie of them varying in time.”

Der Heer looked at her blankly. Don't biologists use polarized light in their microscopes? she asked herself.

“When a wave of light comes at you—visible light, radio light, any kind of light—it's vibrating at right angles to your line of sight. If that vibration rotates, the wave is said to be elliptically polarized. If it rotates clockwise, the polarization is called right-handed; counterclockwise, it's left-handed. I know it's a dumb designation. Anyway, by varying between the two kinds of polarization, you could transmit information. A little right polarization and that's a zero; a little left and it's a one. Follow? It's perfectly possible. We have amplitude modulation and frequency modulation, but our civilization, by convention, ordinarily just doesn't do polarization modulation.

“Well, the Vega signal looks as if it has polarization modulating. We're busy checking it out right now. But Dave found that there wasn't an equal amount of the two sorts of polarization. It wasn't left polarized as much as it was right polarized. It's just possible that there's another message in the polarization that we've missed so far. That's why I'm suspicious about your friend. Kitz isn't just giving me general gratuitous advice. He knows we may be onto something else.”

“Ellie, take it easy. You've hardly slept for four days. You've been juggling the science, the administration, and the press. You've already made one of the major discoveries of the century, and if I understand you right, you might be on the verge of something even more important. You've got every right to be a little on edge. And threatening to militarize the project was clumsy of Kitz. I don't have any trouble understanding why you're suspicious of him. But there's some sense to what he says.”

“Do you know the man?”

“I've been in a few meetings with him. I can hardly say I know him. Ellie, if there's a possibility of a real message coming in, wouldn't it be a good idea to thin out the crowd a little?”

“Sure. Give me a hand with some of the Washington deadwood.”

“Okay. And if you leave that document on your desk, someone'll be in here and draw the wrong conclusion. Why don't you put it away somewhere?”

“You're going to help?”

“If the situation stays anything like what it is now, I'll help. We're not going to make our best effort if this thing gets classified.”

Smiling, Ellie knelt before her small office safe, and punched in the six-digit combination, 314159.

She took one last glance at the document that was titled in large black letters THE UNITED STATES VS. HADDEN CYBERNETICS, and locked it away.

It was a group of about thirty people—technicians and scientists associated with Project Argus, a few senior government officials, including the Deputy Director of the Defense Intelligence Agency in civilian clothes.

Among them were Valerian, Drumlin, Kitz, and der Heer. Ellie was the only woman. They had set up a large television projection system, focused on a two-meter-by-two-meter screen set flush against the far wall. Ellie was simultaneously addressing the group and the decryption program, her fingers on the keyboard before her.

“Over the years we've prepared for the computer decryption of many kinds of possible messages.

We've just learned from Dr. Drumlin's analysis that there's information in the polarization modulation. All that frenetic switching between left and right means something. It's not random noise. It's as if you're flipping a coin. Of course, you expect as many heads as tails, but instead you get twice as many heads as tails. so you conclude that the coin is loaded or, in our case, that the polarization modulation isn't random; it has content…. Oh, look at this. What the computer has just now told us is even more interesting. The precise sequence of heads and tails repeats. It's a long sequence, so it's a pretty complex message, and the transmitting civilization must want us to be sure to get it right.

“Here, you see? This is the repeating message. We're now into the first repetition. Every bit of information, every dot and dash—if you want to think of them that way—is identical to what it was in the last block of data. Now we analyze the total number of buts. It's a number in the tens of billions. Okay, bingo! It's the product of three prime numbers.”

Although Drumlin and Valerian were both beaming, it seemed to Ellie they were experiencing quite different emotions.

“So what? What do some more prime numbers mean?” a visitor from Washington asked.

“It means—maybe—that we're being sent a picture. You see, this message is made of a large number of bits of information. Suppose that large number is the product of three smaller numbers; it's a number times a number times a number. So there's three dimensions to the message. I'd guess either it's a single static three-dimensional picture like a stationary hologram, or it's a two-dimensional picture that changes with time—a movie. Let's assume it's a movie. If it's a hologram, it'll take us longer to display anyway. We've got an ideal decryption algorithm for this one.”

On the screen, they made out an indistinct moving pattern composed of perfect whites and perfect blacks.

“Willie, put in some gray interpolation program, would you? Anything reasonable. And try rotating it about ninety degrees counterclockwise.”

“Dr. Arroway, there seems to be an auxiliary sideband channel. Maybe it's the audio to go with the movie.”

“Punch it up.”

The only other practical application of prime numbers she could think of was public-key cryptography, now widely used in commercial and national security contexts. One application was to make a message clear to dummies; the other was to keep a message hidden from the tolerably intelligent.

Ellie scanned the faces before her. Kitz looked uncomfortable. Perhaps he was anticipation some alien invader or, worse, the design drawings of a weapon too secret for her staff to be trusted with. Willie looked very earnest and was swallowing over and over again. A picture is different from mere numbers. The possibility of a visual message was clearly rousing unexamined fears and fantasies in the hearts of many of the onlookers. Der Heer had a wonderful expression on his face; for the moment he seemed much less the official, the bureaucrat, the presidential adviser, and much more the scientist.

The picture, still unintelligible, was joined by a deep rumbling glissando of sounds, sliding first up and then down the audio spectrum until it gravitated to rest somewhere around the octave below middle C.

Slowly the group became aware of faint but swelling music. The picture rotated, rectified, and focused.

Ellie found herself staring at a black-and-white grainy image of… a massive reviewing stand adorned with an immense art deco eagle. Clutched in the eagle's concrete talons…

“Hoax! It's a hoax!” There were cries of astonishment, incredulity, laughter, mild hysteria.

“Don't you see? You've been hoodwinked,” Drumlin was saying to her almost conversationally. He was smiling. “It's an elaborate practical joke. You've been wasting the time of everybody here.”

Clutched in the eagle's concrete talons, she could now see clearly, was a swastika. The camera zoomed in above the eagle to find the smiling face of Adolf Hitler, waving to a rhythmically chanting crowd.

His uniform, devoid of military decorations, conveyed a modest simplicity. The deep baritone voice of an announcer, scratchy but unmistakably speaking German, filled the room. Der Heer moved toward her.

“Do you know German?” she whispered. “What's it saying?”

“The Fuehrer,” he translated slowly, “welcomes the world to the German Fatherland for the opening of the 1936 Olympic Games.”