Factoring Humanity

  He nodded, conceding the point. “So twenty-eight hundred tiles make up how many bigger squares?”

  “Forty-eight.”

  “And what are you going to do with the resulting squares?”

  “Assemble them into cubes—and then assemble those cubes into an unfolded tesseract.”

  “Really? Wow.”

  “Yes.”

  “Well, do you want the finished thing big enough so that you can crawl inside of one of the cubes?”

  “No, that won’t be—”

  She stopped dead.

  No scale specified. Nowhere in any of the messages did there seem to be anything suggesting a size for the construct.

  Make it any size, the aliens seemed to be saying.

  Make it your size.

  “Yes, yes—that would be perfect! Big enough to go inside.”

  “Well, okay—sure. We can build the substrate tiles, no problem. How thick should they be?”

  “I don’t know. As thin as possible, I guess.”

  “I can make them one molecule thick if that’s what you want.”

  “Oh, not that thin. They’ll have to hold together. A millimeter or two, maybe.”

  “No problem. We’ve got a machine all set up to turn out plastic building panels for the School of Architecture; I could modify it easily enough to turn out the tiles you need. Do you want them to have smooth edges or would you like a tongue-and-groove arrangement, so they can snap together?”

  “You mean so they form a big solid piece?”

  Komensky nodded.

  “That would be great.”

  “What about the painting on of the other chemical?”

  “I figured I’d have to do that by hand,” said Heather.

  “Well, you could, but we’ve got programmable microsprayers that can do it for you, assuming the substance has a low enough viscosity. We use the sprayers to paint patterns onto the panels we make for the architecture students—you know, little outlines of bricks, or little dots to represent rivets, stuff like that.”

  “That’d be perfect. How soon can you do it?”

  “Well, during the school year, we’re usually pretty backed up. But in summer, we’ve got lots of free time. We can get at it right away. We’ve still got a couple of grad students hanging around; I’ll have one of them look into manufacturing those chemicals. As I say, at first glance they look simple enough, but we won’t know for sure until we actually try to synthesize them.” A pause. “Who’s going to pay for this?”

  “What’ll it cost?” asked Heather.

  “Oh, not much. Robots are so cheap these days, we no longer amortize their cost over manufacturing runs like we used to. Maybe five hundred dollars for the material.”

  Heather nodded. She’d find some way to explain it to her department head later, once he got back from vacation. “That’s fine. Charge it to Psych; I’ll sign the requisition.”

  “I’ll e-mail you the paperwork.”

  “Terrific. Thank you. Thank you very much.”

  “You’re very welcome.” He smiled and held her with his eyes.

  14

  There was a bleep at Kyle’s office door. He pushed the button that caused it to slide open. A middle-aged Asian woman in an expensive-looking gray suit was standing in the curving corridor, the atrium with its tumbling tapestries visible behind her.

  “Dr. Graves?” she said.

  “Yes?”

  “Brian Kyle Graves?”

  “That’s right.”

  “I wish to talk to you, please.”

  Kyle rose and motioned for her to come in.

  “My name is Chikamatsu. I wish to speak to you about your research.”

  Kyle indicated another chair. Chikamatsu took it, and Kyle sat back down.

  “I understand you have had some success with quantum computing.”

  “Not as much as I’d like. I ended up with egg on my face a couple of weeks ago.”

  “So I heard.” Kyle’s eyebrows went up. “I represent a consortium that would like to contract for your services.” She pronounced consortium “consorsheeum.”

  “Oh?”

  “Yes. We believe you are close to a breakthrough.”

  “Not judging by my current results.”

  “A minor problem, I am sure. You are trying to use Dembinski fields to inhibit decoherence, are you not? They are notoriously tricky.”

  Kyle’s eyebrows climbed again. “That they are.”

  “We have monitored your progress with interest. You are doubtless very close to a solution. And if you do find a solution, my consortium may be prepared to invest heavily in your procedure, assuming, of course, that you can convince me that your system works.”

  “Well, it will either work or it won’t.”

  Chikamatsu nodded. “Doubtless so, but we will need to be sure. You would have to factor a number for us. And, of course, I would have to provide the number—just to be sure it is not some trick, you understand.”

  Kyle narrowed his eyes. “What exactly is the nature of your consortium?” He preferred the hard-T pronunciation himself, but matched Chikamatsu’s usage.

  “We are an international group,” she said. “Venture capitalists.” She had a small cylindrical leather purse, with metal end caps. She opened it, removed a memory wafer, and proffered it to Kyle. “The number we wish factored is on this wafer.”

  Kyle took the wafer but didn’t look at it. “How many digits in the number?”

  “Five hundred and twelve.”

  “Even if I can work out the current bugs with my system, it’ll be a while before I can do that.”

  “Why?”

  “Well, for two reasons. The first is a practical one. Democritus—that’s the name of our prototype—is hardware constrained to factor numbers exactly three hundred digits long, no more, no less. Even if I could get it to work properly, I can’t do numbers of any other length—the quantum registers have to be carefully jiggered for the precise total number of digits.”

  Chikamatsu looked disappointed. “And the other reason?”

  Kyle raised his eyebrows. “The other reason, Ms. Chikamatsu, is that I’m not a criminal.”

  “I—I beg your pardon?”

  He flipped the memory wafer over and over in his hand as he spoke. “There’s only one practical application for factoring large numbers—and that’s cracking encryption schemes. I don’t know whose data you’re trying to access, but I’m no hacker. Find yourself another boy.”

  “It is just a randomly generated number,” said Chikamatsu.

  “Oh, come on. If you’d asked me to factor a number whose length fell within a range—between five hundred and six hundred digits, say—and if you hadn’t shown up with your number all picked out, I might have believed you. But it’s pretty damned obvious you’re trying to crack somebody’s code.”

  Kyle went to hand back the wafer, but now its other side was facing up. As he looked down at it, he saw its label, with a single word written on it in pen: Huneker.

  “Huneker!” said Kyle. “Not Joshua Huneker?”

  Chikamatsu reached out to retrieve the wafer. “Who?” she said, sounding innocent but looking visibly flustered.

  Kyle clenched his fist, covering the wafer. “What the hell are you playing at?” he said. “What’s this got to do with Huneker?”

  Chikamatsu lowered her gaze. “I did not think you would know the name.”

  “My wife was involved with him when she and I met.”

  Chikamatsu’s almond-shaped eyes went wide. “Really?”

  “Yes, really. Now, tell me what the hell this is all about.”

  The woman considered. “I—ah, I must consult with my partners first.”

  “Be my guest. Do you need a phone?”

  She extracted one from her funky purse. “No.” She rose, crossed the room, and began a hushed conversation that bounced between Japanese and what sounded like Russian, with only a few recognizable words—“Toronto,” “Gra
ves,” “Huneker,” and “quantum” among them. She winced several times; apparently she was getting a royal chewing-out.

  After a few moments, she folded up the phone and returned it to her purse.

  “My colleagues are not pleased,” she said, “but we do need your help, and our purpose is not illegal.”

  “You’ll have to convince me of that.”

  She tightened her lips and let air escape loudly through her nose. Then: “Do you know how Josh Huneker died?”

  “Suicide, my wife said.”

  Chikamatsu nodded. “Do you have a Web terminal here?”

  “Of course.”

  “May I?”

  Kyle indicated the unit with a motion of his hand.

  Chikamatsu sat down in front of it and spoke into the microphone. “The Toronto Star,” she said. Then: “Search back issues. Words in article text: Huneker and Algonquin. H-U-N-E-K-E-R and A-L-G-O-N-Q-U-I-N.”

  “Searching,” said the terminal in an androgynous voice. Then: “Found.”

  There was only one hit. The article appeared on the monitor screen.

  Chikamatsu stood up. “Have a look,” she said.

  Kyle took the seat she’d vacated. The article was dated February 28, 1994. The words “Algonquin” and “Huneker” were highlighted everywhere they appeared in red and green respectively. He read the whole thing, telling the screen once to page down as he did so:

  ASTRONOMER TAKES OWN LIFE

  Joshua Huneker, 24, was found dead yesterday at the National Research Council of Canada’s radio telescope in Algonquin Park, a provincial park in northern Ontario. He had committed suicide by eating an apple coated with arsenic.

  Huneker, who was studying for a Ph.D. at the University of Toronto, had been snowed in alone at the radio telescope for six days.

  He had been working in Algonquin Park on the international Search for Extraterrestrial Intelligence (SETI) project, scanning the sky for radio messages from alien worlds. Because Algonquin is so far from any city, it receives little radio interference and is therefore ideally suited for such delicate listening.

  Huneker’s body was found by Donald Cheung, 39, another radio astronomer, who was arriving at the telescope facility to relieve Huneker.

  “It’s a great tragedy,” said NRC spokesperson Allison Northcott, in Ottawa. “Josh was one of our most promising young researchers and he was also a real humanitarian, very active with Greenpeace and other causes. However, judging by his suicide note, he apparently had personal problems related to his romantic involvement with another man. We will all miss him.”

  When he was finished, Kyle swiveled the chair around to face the woman. He hadn’t know the details of Josh’s death before; the whole thing seemed rather sad.

  “His story remind you of anyone’s?” asked Chikamatsu.

  “Sure. Alan Turing’s.” Turing, the father of modern computing, had committed suicide in 1954 in the same way, and for the same reason.

  She nodded grimly. “Exactly. Turing was Huneker’s idol. But what the spokesperson did not mention was that Josh left two notes, not one. The first was indeed about his personal problems, but the second . . .”

  “Yes?”

  “The second had to do with what he had detected.”

  “Pardon?”

  “Over the radio telescope.” Chikamatsu closed her eyes, as if wrestling for one final moment about whether to go on. Then she opened them and said softly, “The Centaurs were not the first aliens we made contact with; they were the second.”

  Kyle creased his forehead skeptically. “Oh, come on!”

  “It is true,” said Chikamatsu. “In nineteen ninety-four, Algonquin picked up a signal. Of course it was not from Alpha Centauri—you cannot see that star from Canada. Huneker detected a signal from somewhere else, apparently had no trouble decoding it, and was stunned by whatever it said. He burned all the original computer tapes, encrypted the only remaining record of the message, and then killed himself. To this day, nobody knows what that alien message said. They closed down the Algonquin Observatory immediately thereafter, citing budget cuts. What they really wanted to do was disassemble everything to see if they could determine which star the signal had come from; Huneker had been scheduled to survey over forty different stars during the week he was alone up there. They tore that place apart, but never figured it out.”

  Kyle digested this, then: “And Huneker used—what? RSA encryption?”

  “Exactly.”

  Kyle frowned. RSA is a two-key method of data-encryption: the public key is a very large number, and the private key consists of two prime numbers that are factors of the public key.

  Chikamatsu spread her hands, as if the problem was plain. “Without the private key,” she said, “the message cannot be decoded.”

  “And there were five hundred and twelve digits in Huneker’s public key?”

  “Yes.”

  Kyle frowned. “So it would take conventional computers trillions of years to find its factors by trial and error.”

  “Exactly. We have had computers working full time on it since just after Huneker killed himself. So far, no luck. But, as you say, that is with conventional computers. A quantum computer—”

  “A quantum computer could do it in a matter of seconds.”

  “Precisely.”

  Kyle nodded. “I can see why leaving an encrypted message behind might appeal to a Turing fan.” Turing had been pivotal in defeating the Nazis’ Enigma encoding machine in World War II. “But why should I agree to do this for you?”

  “We have a copy of the Huneker disk—something very hard to get hold of, believe me. My partners and I believe the disk encodes information that may be of great commercial value—and if we can decode it first, we will all make a lot of money.”

  “All?”

  “When I was talking to them on the phone, my partners empowered me to offer you a two-percent share of all proceeds.”

  “And what if there aren’t any?”

  “Sorry, I should have been more explicit: I am prepared to offer you an advance of four million dollars, against a two-percent share of all proceeds. And you keep all rights to your quantum-computing technology; we simply want the message decoded.”

  “What makes you think there’s anything of commercial value in the message?”

  “Huneker’s second handwritten note said simply, ‘Alien radio message—unveil new technology.’ The disk with the encoded transmission—a three-and-a-half-inch floppy, if you remember such things—was found lying on top of that note. Huneker had clearly understood the message and felt that it described some innovative technology.”

  Kyle frowned dubiously and leaned back in his chair. “I’ve spent half my life trying to decipher what students mean when they write something. He could have just been saying that we’d need a new technology, such as quantum computing, to break his encryption.”

  Chikamatsu sounded unduly earnest. “No, it must describe some great innovation—and we want it.”

  Kyle decided not to argue the point with her; she’d clearly devoted way too much time and money to this issue to countenance the thought that it was all a waste. “How did you find out about me?”

  “We have monitored quantum-computing research for years, Professor Graves. We know exactly who is doing what—and how close they are to a breakthrough. You and Saperstein at the Technion are both on the verge of solving the technical difficulties.”

  Kyle exhaled. He hated Saperstein’s guts—had for years. Did Chikamatsu know that? Probably—meaning that she might be baiting him. Still, four million dollars . . .

  “Let me think about it,” he said.

  “I will contact you again,” said Chikamatsu, rising. She held out a hand for the memory wafer.

  Kyle was reluctant to let it go.

  “It only has the public key on it,” said Chikamatsu. “Without the actual alien message, it is useless.”

  Kyle hesitated a moment longer, then handed over the
plastic wafer, now slick with perspiration from his palm.

  Chikamatsu wiped it on a tissue, then returned it to her purse. “Thank you,” she said. “Oh, and a word to the wise—I rather suspect we are not the only ones aware of your research.”

  Kyle spread his arms and tried to sound jaunty. “Then maybe I should simply hold out for the best offer.”

  Chikamatsu was already at the door. “I do not think you will like the sort of offers they make.”

  And then she was gone.

  15

  The phone rang in Heather’s office. She glanced at the call-display readout; it was an internal U of T call. That was a relief: she was getting tired of the media. But then, it seemed, they had gotten tired of her, too; the cessation of the alien messages was already old news, and reporters seemed to be leaving her alone now. Heather picked up the handset. “Hello?”

  “Hi, Heather. It’s Paul Komensky, over at the CAM lab.”

  “Hello, Paul.”

  “It’s good to hear your voice.”

  “Ah, yours, too, thanks.”

  Silence, then: “I, ah, I’ve got those substances ready you asked me to mix up.”

  “That’s great! Thank you.”

  “Yeah. The substrate, it’s unremarkable, essentially just a polystyrene. But the other stuff, well, I was right. It is a liquid at room temperature, but it does dry—into a thin, crystalline film.”

  “Really?”

  “And it’s piezoelectric.”

  “Pi—pi—what?”

  “Piezoelectric. It means that when you put it under stress, it generates electricity.”

  “Really?”

  “Not much, but some.”

  “Fascinating!”

  “It’s not all that unusual, really; it happens a lot in various minerals. But I wasn’t expecting it. The crystals this stuff dries to are actually similar to what we call relaxor ferroelectrics. That’s a special kind of piezoelectric crystal that can deform—that is, change shape—ten times as much as standard piezoelectric crystals do.”

  “Piezoelectric,” Heather said softly. She used her fingertip to write the word on her datapad. “I’ve read something about that—can’t offhand think where, though. Anyway, can you make the tiles now?”