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CHAPTER 4
Prime Numbers
Now the pulses were washing against a warm world, blue and white, spinning against the backdrop of the stars.
The first pulses in the train of radio waves insinuated themselves through the atmosphere and clouds, struck the landscape and were partially reflected back to space. As the Earth turned beneath them, successive pulses arrived, engulfing not just this one planet but the entire system. Very little of the energy was intercepted by any of the worlds. Most of it passed effortlessly onward—as the yellow star and its attendant worlds plunged, in an altogether different direction, into the inky dark.
They had carefully monitored hundreds of little sectors of the sky within the constellation Hercules at a billion separate frequencies, and they had heard nothing.
The computers turned the telescopes to follow the stars in Lyra from starrise to starset, accumulated the radio photons, monitored the health of the telescopes, and processed the data in a format convenient for their human operators.
“As you can see, nothing much. There was a pointing glitch—at least that’s what it looked like—in forty-nine,” he said, waving vaguely toward the window. “The quasar bunch freed up the one-tens and one-twenties about an hour ago. They seem to be getting very good data.” “Yeah, I heard. They don’t understand . . .” His voice trailed off as an alarm light flashed decorously on the console in front of them. On a display marked “Intensity vs. Frequency” a sharp vertical spike was rising. “Hey, look, it’s a monochromatic signal.” Another display, labeled “Intensity vs. Time,” showed a set of pulses
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“Those are numbers,” Willie said faintly. “Somebody’s broadcasting numbers.”
“Mom, really, I’ve gotta go. We’ve caught some kind of bogey.” “Bogey?” “You know, Mom, something that might be a signal. We’ve talked about it.”
“Evening, Willie, Steve. Let’s see the data. Good. Now where did you tuck away the amplitude plot? Good. Do you have the interferometric position? Okay. Now let’s see if there’s any nearby star in that field of view. Oh my, we’re looking at Vega. That’s a pretty near neighbor.”
“Look, it’s only twenty-six light-years away. It’s been observed before, always with negative results. I looked at it myself in my first Arecibo survey. What’s the absolute intensity? Holy smoke. That’s hundreds of janskys. You could practically pick that up on your FM radio.
“Okay. So we have a bogey very near to Vega in the plane of the sky. It’s at a frequency around 9.2 gigahertz, not very monochromatic: The bandwidth is a few hundred hertz. It’s linearly polarized and it’s transmitting a set of moving pulses restricted to two different amplitudes.”
“It’s being received by 116 individual telescopes. Clearly it’s not a malfunction in one or two of them. Okay, now we should have plenty of time baseline. Is it moving with the stars? Or could it be some ELINT satellite or aircraft?”
“Okay, that’s pretty convincing. It’s not down here on Earth, and it probably isn’t from an artificial satellite in a Molniya orbit, although we should check that. When you get a chance, Willie, call up NORAD and see what they say about the satellite possibility. If we can exclude satellites, that will leave two possibilities: It’s a hoax, or somebody has finally gotten around to sending us a message. Steve, do a manual override. Check a few individual radio telescopes—the signal strength is certainly large enough—and see if there’s any chance this is a hoax; you know, a practical joke by
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“If any of you can think of any other explanation besides extraterrestrial intelligence, I want to hear about it,” she said, acknowledging their presence.
“There’s no way it could be Vega, Dr. Arroway. The system’s only a few hundred million years old. Its planets are still in the process of forming. There isn’t time for intelligent life to have developed there. It has to be some background star. Or galaxy.” “But then the transmitter power has to be ridiculously large,” responded a member of the quasar group who had returned to see what was happening. “We need to get going right away on a sensitive proper motion study, so we can see if the radio source moves with Vega.”
“Of course, you’re right about the proper motion, Jack,” she said. “But there’s another possibility. Maybe they didn’t grow up in the Veg...
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Willie, who had been talking on the phone at an adjacent console, was displaying a wan smile. “Well, I got through to a Major Braintree at NORAD. He swears up and down they have nothing that’ll give this signal, especially not at nine gigahertz. ’Course, they tell us that every time we call. Anyway, he says they haven’t detected any spacecraft at the right ascension and declination of Vega.”
“Interferometry now rules out a Molniya-type orbit, Dr. Arroway.”
“Better and better. Now let’s take a closer look at those moving pulses. Assuming that this is binary arithmetic, has anybody converted it into base ten? Do we know what the sequence of numbers is? Okay, here, we can do it in our heads . . . fifty-nine, sixty-one, sixty-seven . . . seventy-one . . . Aren’t these all prime numbers?”
“Okay, let’s see if I can do another quick summary. I’ll do it in the simplest language. Please check if I’ve missed anything. We have an extremely strong, not very monochromatic signal. Immediately outside the bandpass of this signal there are no other frequencies reporting anything besides noise. The signal is linearly polarized, as if it’s being broadcast by a radio telescope. The signal is around nine gigahertz, near the minimum in the galactic radio noise background. It’s the right kind of frequency for anyone who wants to be heard over a big distance. We’ve confirmed sidereal motion of
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“Holy shit!” she whispered.
By bicycle, small truck, perambulatory mailman, or telephone, the single paragraph was delivered to astronomical centers all over the world. In a few major radio observatories—in China, India, the Soviet Union, and Holland, for example—the message was delivered by teletype. As it chattered in, it was scanned by a security officer or some passing astronomer, torn off, and with a look of some curiosity carried into an adjacent office.
ANOMALOUS INTERMITTENT RADIO SOURCE AT RIGHT ASCENSION 18h 34m, DECLINATION PLUS 38 DEGREES 41 MINUTES, DISCOVERED BY ARGUS SYSTEMATIC SKY SURVEY. FREQUENCY 9.24176684 GIGAHERTZ, BANDPASS APPROXIMATELY 430 HERTZ. BIMODAL AMPLITUDES APPROXIMATELY 174 AND 179 JANSKYS. EVIDENCE AMPLITUDES ENCODE SEQUENCE OF PRIME NUMBERS. FULL LONGITUDE COVERAGE URGENTLY NEEDED. PLEASE CALL COLLECT FOR FURTHER INFORMATION IN COORDINATING OBSERVATIONS. E. ARROWAY, DIRECTOR, PROJECT ARGUS, SOCORRO, NEW MEXICO, U.S.A.
CHAP...
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Decryption Algorithm
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.
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.
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 Encyclopaedia Galactica.
By definition, it has to be mighty hard to understand the behavior of a being much smarter than you are. But even so, even so: Why only 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?”
“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 Poincaré spheres; there’s a nice movie of them varying in time.”
“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,
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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 . . .
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.
“The Fuehrer,” he translated slowly, “welcomes the world to the German Fatherland for the opening of the 1936 Olympic Games.”
CHAPTER 6
Palimpsest
As she had done a hundred times before, she peered out the airplane window and imagined what impression the Earth would make on an extraterrestrial observer, at this cruising altitude of twelve or fourteen kilometers, and assuming the alien had eyes something like ours. There were vast areas of the Midwest intricately geometrized with squares, rectangles, and circles by those with agricultural or urban predilections; and, as here, vast areas of the Southwest in which the only sign of intelligent life was an occasional straight line heading between mountains and across deserts. Are the worlds
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For a moment, the President stood ramrod straight, staring out the French doors into the Rose Garden. She turned toward der Heer. “You mean . . . everything?” “Yes. Everything.” “You mean to say, all that crap on television? The car crashes? Wrestling? The porno channels? The evening news?”
The President had turned away from the French doors and was now apparently preoccupied in examining a marble bust of Tom Paine, newly restored from the basement of the Smithsonian Institution, where it had been consigned by the previous incumbent.
“Ms. President, there’s no doubt they’re smart. That was a very weak signal in 1936. Their detectors have to be fantastically sensitive to pick it up. But I don’t see how they could possibly understand what it means. They probably look very different from us. They must have different history, different customs. There’s no way for them to know what a swastika is or who Adolf Hitler was.”
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“Good. Dr. Arroway, we understand you have something new. Would you care to tell us about it?” “Ms. President, sorry to be late, but I think we’ve just hit the cosmic jackpot. We’ve . . . It’s . . . Let me try and explain it this way: In classical times, thousands of years ago, when parchment was in short supply, people would write over an old parchment, making what’s called a palimpsest. There was writing under writing under writing. This signal from Vega is, of course, very strong. As you know, there’s the prime numbers, and ‘underneath’ them, in what’s called polarization modulation, this
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CHAPTER 7
The Ethanol in W-3
The others would then fall silent and she would continue about doped gallium arsenide detectors, or the ethanol content of the galactic cloud W-3. The quantity of 200-proof alcohol in this single interstellar cloud was more than enough to maintain the present population of the Earth, if every adult were a dedicated alcoholic, for the age of the solar system.
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