“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.”
CHAPTER 6
Palimpsest
And if the Guardians are not happy, who else can be?
As the plane reached cruising altitude, with Albuquerque already more than a hundred miles behind them, Ellie idly glanced at the small white cardboard rectangle imprinted with blue letters that had been stapled to her airline ticket envelope. It read, in language unchanged since her first commercial flight, “This is not the luggage ticket (baggage check) described by Article 4 of the Warsaw Convention.” Why were the airlines so worried, she wondered, that passengers might mistake this piece of cardboard for the Warsaw Convention ticket? Why had she never seen one? Where were they storing them? In some forgotten key event in the history of aviation, an inattentive airline must have forgotten to print this caveat on cardboard rectangles and was sued into bankruptcy by irate passengers laboring under the misapprehension that this was the Warsaw luggage ticket. Doubtless there were sound financial reasons for this worldwide concern, never otherwise articulated, about which pieces of cardboard are not described by the Warsaw Convention. Imagine, she thought, all those cumulative lines of type devoted instead to something useful—the history of world exploration, say, or incidental facts of science, or even the average number of passenger miles until your airplane crashed.
If she had accepted der Heer's offer of a military airplane, she would be having other casual associations. But that would have been far too cozy, perhaps some aperture leading to an eventual militarization of the project. They had preferred to travel by commercial carrier. Valerian's eyes were already closed as he finished settling into the seat beside her. There had been no particular hurry, even after taking care of those last-minute details on the data analysis, with the hint that the second layer of the onion was about to unpeel. They had been able to make a commercial flight that would arrive in Washington well before tomorrow's meeting; in fact, in plenty of time for a good night's sleep.
She glanced at the telefax system neatly zipped into a leather carrying case under the seat in front of her. It was several hundred kilobits per second faster than Peter's old model and displayed much better graphics. Well, maybe tomorrow she would have to use it to explain to the President of the United States what Adolf Hitler was doing on Vega. She was, she admitted to herself, a little nervous about the meeting.
She had never met a President before, and by late-twentieth-century standards, this one wasn't half bad. She hadn't had time to get her hair done, much less a facial. Oh well, she wasn't going to the White House to be looked at.
What would her stepfather think? Did he still believe she was unsuited for science? Or her mother, now confined to a wheelchair in a nursing home? She had managed only one brief phone call to her mother since the discovery over a week ago, and promised herself to call again tomorrow.
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 squared, 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 of more advanced civilizations totally geometrized, entirely rebuilt by their inhabitants? Or would the signature of a really advanced civilization be that they left no sign at all? Would they be able to tell in one swift glance precisely which stage we were in some great cosmic evolutionary sequence in the development of intelligent beings?
What else could they tell? From the blueness of the sky, they could make a rough estimate of Loschmidt's Number, how many molecules there were in a cubic centimeter at sea level. About three times ten to the nineteenth. They could easily tell the altitudes of the clouds from the length of their shadows on the ground. If they knew that the clouds were condensed water, they could roughly calculate the temperature lapse rate of the atmosphere, because the temperature had to fall to about minus forty degrees Centigrade at the altitude of the highest clouds she could see. The erosion of landforms, the dendritic patterns and oxbows of rivers, the presence of lakes and battered volcanic plugs all spoke of an ancient battle between land-forming and erosional processes. Really, you could see at a glance that this was an antique planet with a brand new civilization.
Most of the planets in the Galaxy would be venerable and pretechnical, maybe even lifeless. A few would harbor civilizations much older than ours. Worlds with technical civilizations just beginning to emerge must be spectacularly rare. It was probably the only quality fundamentally unique about the Earth.
Through lunch, the landscape slowly turned verdant as they approached the Mississippi Valley.
There was hardly any sense of motion in modern air travel, Ellie thought. She looked at Peter's still sleeping form; he had rejected with some indignation the prospect of an airline lunch. Beyond him, across the aisle, was a
