“Arecibo is designated prime, isn’t it? But there are backups, and—oh, wait. Something’s going up on the Web page.”
“I see it, too.”
“Damn holograms—ah, here it is: ‘No technical malfunction at receiving end. Apparently no message was sent.’ ”
“That can’t be the end of the transmissions,” said Salme. “There has to be a key.”
“Maybe they got tired of waiting for us to reply,” said Heather. “Maybe they won’t send again until we do reply.”
“Or maybe—”
“What?” asked Heather.
“Drake equation, final term.”
Heather was quiet for a moment. “Oh,” she said softly.
The Drake equation estimated the number of radio-broadcasting civilizations in the galaxy. It had seven terms:
R* fp ne fl fi fc L
The rate of star formation, times the fraction of stars with planets, times the number of those planets that are suitable for life, times the fraction of such planets on which life actually appears, times the fraction of life forms that are intelligent, times the fraction of such life forms that actually develop radio, times…
Times big L: the lifetime of such a civilization.
A civilization that had radio probably also had nuclear weapons, or other equally dangerous things.
Civilizations could be wiped out in a matter of moments—certainly in less than a single thirty-one-hour day.
“They can’t be dead,” said Salme.
“They’re either dead, or they voluntarily stopped, or the message is complete.”
There was a knock at the door. Heather covered the mouthpiece. “Come in!”
The departmental assistant stuck his head in. “Sorry to bother you, Professor Davis, but the CBC is on the phone. They want to talk to you about what happened to the aliens.”
10
Kyle’s lab was crowded. The dean leaned against one wall, the department chair had his butt perched on the shelf jutting out of the bottom of Cheetah’s console, a lawyer from the university’s patent unit sat in Kyle’s usual chair, and the five grad students who worked on Kyle’s quantum-computing team were milling around as well.
“Okay,” said Kyle to the group. “As you know, there’s been a technique available since nineteen ninety-six for producing simple quantum-logic gates; that technique was based on using nuclear magnetic resonance to measure atomic spins. But it was hampered by the fact that as you added bits, the output signal got exponentially weaker: a thirty-bit quantum computer based on that principle produces output only one-billionth as strong as that from a one-bit computer based on the same technique.
“Well, the method we’re going to demonstrate today is, we believe, the long-sought-after breakthrough: a quantum computer that, in theory, can employ an unlimited number of bits with no reduction in output quality. For our demo today, we’re going to try to factor a randomly generated three-hundred-digit number. To do that on the department’s ECB-5000 would take approximately one hundred years of constant calculation. If we’re right—if this works—we’ll have an answer about thirty seconds after I commence the experiment.”
He moved across the room.
“Our prototype quantum computer, which we call Democritus, has not just thirty registers, but one thousand, each of which consists of a single atom. The results will be a series of interference patterns, which another computer—that one over there—will analyze and reduce to a numeric readout.” He looked from face to face. “All set? Let’s go.”
Kyle walked over to the simple black console containing the Democritus computer. For the sake of drama, they’d built a large knife switch, worthy of Frankenstein’s lab, into the side of the cabinet. Kyle pulled it down, its blade touching the metal contacts. A bright red LED came on and—
— and everyone held their breath. Kyle kept watching Democritus, which, of course, was operating absolutely silently. Part of him missed the old days of clicking relays. Others were watching the digital clock mounted next to the red EXIT sign on the curving wall.
Ten seconds went by.
Then ten more.
Then a final ten.
And then the LED went dark.
Kyle let out his breath.
“Done,” he said, heart pounding.
He gestured for everyone to follow him across the room. There, another computer was analyzing the output from Democritus.
“It’ll take about five minutes to decode the interference pattern,” said Kyle. He allowed himself a smile. “If you’re thinking that that’s a lot longer than it took to produce the pattern, you’re right—but we’re now dealing with a conventional computer.”
“How many computations would it take to factor a number that big?” asked the dean, her voice clearly intrigued.
“Approximately ten to the five hundredth,” said Kyle.
“And there’s no way to do it in fewer steps?” she asked. “This isn’t a case of Democritus taking a shortcut?”
Kyle shook his head. “No, it really does take ten to the five hundredth steps to factor a number that big.”
“But Democritus didn’t do that many steps.”
“This Democritus didn’t—in fact, it performed only one calculation, using a thousand atoms as the stones in its abacus, so to speak, to do so. But if all went well, 10500 other Democrituses in other universes will also each have done one calculation—involving, of course, a total of a thousand times 10500 atoms, which is 10503 atoms. And that, my friends, is a very significant number.”
“How so?” asked the department chair.
“Well, the precise value isn’t important. What is important is how it relates to the number of atoms in our entire universe.” Kyle smiled, waiting for the inevitable question.
“And how many atoms are there in our universe?” asked the dean.
“I called up Holtz over in the McLennan Physical Labs and asked her,” said Kyle. “The answer, plus or minus a couple of orders of magnitude, is that there are ten to the eightieth atoms in the universe.”
A few jaws dropped.
“Do you see?” said Kyle. “In that thirty-second period, to factor our test number, Democritus must have accessed many trillions of times more atoms than there are in our entire universe. Other, earlier quantum-computing demonstrations have never involved enough bits to actually exceed the quantity of atoms available to them in our universe, leaving open some doubt as to whether they’d actually accessed parallel worlds, but if this experiment works, the only answer will be that our Democritus worked in tandem with computers in other universes.”
The conventional computer they were standing in front of beeped and one of its monitors came to life. Precisely two strings of numbers appeared on the screen, each dozens of digits long.
“Are those the first two factors?” asked the lawyer, clearly anxious to start notarizing things.
Kyle felt his heart sink. “Ah, no. No.” He swallowed; his stomach was roiling. “I mean, yes, certainly, they are doubtless factors of our source number, but—but. . .”
One of Kyle’s grad students looked at him and then said the words that, at that moment, Kyle himself couldn’t get out. “The display shouldn’t have appeared until all the factors are ready. Unless by some miracle, the source number has only two factors, then the experiment didn’t work.”
The department head loomed in at the screen and placed his index finger on the last digit of the second number; it was a four. “That’s an even number, so there have got to be smaller factors that aren’t displayed.” He straightened up. “What went wrong?”