[Question] 2+3
[Answer] 5
[Question] 2-3
[Answer] -1
[Question] 2*3
[Answer] 6
[Question] 2/3
[Answer] 0.6&
“See what they’ve done here? They’ve established a symbol for ‘question,’ and another for ‘answer.’ And they’ve also established a symbol for a decimal place, and a symbol for repeating indefinitely, which I’ve shown as that ‘and’ thingy.”
“Ampersand,” said Don, helpfully.
She gave him an I-knew-that scowl, and went on. “Next up, they give us a symbol for ‘the relationship between,’ which I’ve shown as a colon, and that lets us get a bunch of other concepts.” She made this appear:
[Question] 2/3 : 0.6&
[Answer] =
[Question] 5 : 3
[Answer] >
[Question] 9 : 1
[Answer] >>
[Question] 3 : 5
[Answer]
[Question] 1 : 9
[Answer]
[Question] 1 : -1
[Answer] [opposite]
“See?” she said. “We’re getting into judgment calls. Nine is judged to be not just greater than one but much greater than one, and one, in turn, is much less than nine. Next they give us their symbols for correct and incorrect.” This appeared on screen:
[Question] 2+5
[Answer] 7 [correct]
[Question] 3*3
[Answer] 9 [correct]
[Question] 8-3
[Answer] 6 [incorrect]
“And then,” said Sarah, “things get really exciting.”
“I can hardly contain myself,” Don said.
She whapped him lightly on the arm, and nibbled at her own piece of pizza before changing the screen. “This came later in the message. Look.”
[Question] 8/12
[Answer 1] 4/7 [incorrect]
[Answer 2] 4/6 [correct] [alpha]
[Answer 3] 2/3 [correct] [beta]
“See what they’re saying there? I’ve assigned Greek letters to the two new symbols they’re establishing. Can you puzzle out what alpha and beta mean?”
To his credit, he stopped shoveling cheese and pepperoni into his mouth and studied the screen carefully.
“Welllll,” he said at last, “both answer two and answer three are correct, but, um, well, answer three is more correct, right? ’Cause, I mean, they’ve reduced the fraction.”
“Bravo! That’s exactly right! Now, think about that: they’ve just given us a way to express some very powerful concepts.” She touched a key, and the terms alpha and beta were replaced with words:
[Question] 8/12
[Answer 1] 4/7 [incorrect]
[Answer 2] 4/6 [correct] [bad]
[Answer 3] 2/3 [correct] [good]
“That is, they’ve given us a term for distinguishing between an answer that, while technically correct, isn’t preferable from one that is preferable—distinguishing a bad answer from a good one. And, just to drive home the point that they are making that distinction—that these terms should be translated as polar opposites—they give us this.”
[Question] [bad] : [good]
[Answer] [opposite]
Sarah translated. “What is the relationship between ‘bad’ and ‘good’? Why, they’re opposites, just like one and negative one, as we saw before. They’re saying these terms should be treated as actual opposites, in a way that ‘right’ and ‘more right,’ which would have been the other possible way of translating alpha and beta, aren’t.”
“Fascinating,” he said.
She touched her mouse, and a new display appeared. “Now, what about things that aren’t clear-cut? Well, try this. What does gamma mean?”
{3 5 7 11 13 &} = [gamma]
“Odd numbers?” he said. “Every other number?”
“Look again. There’s no nine.”
“Oh, right. Oh, and, um, hey, there’s that ‘and’ thingy again.”
“Ampersand,” said Sarah, imitating Don’s helpful tone from earlier. He grinned. “Right,” she said, “but I’ll give you a hint—something I gleaned from other examples. When the ampersand is right up against another digit, it means that digit is repeated forever. But if there’s a space before it—a little gap in the transmission, as there is here—I think it means that this sequence goes on forever.”
“Three, five, seven, eleven, thirteen…”
“I’ll give you another hint. The next number in the sequence would be seventeen.”
“Um, ah…”
“They’re primes,” she said. “Gamma is their symbol for prime numbers.”
“Ah. But why start with three?”
She was grinning broadly now. “You’ll see. This is the beauty part.” She darted her mouse around. “There’s a little more set theory, which I won’t bore you with, that establishes a symbol for ‘belongs to this set,’ and then we get this…”
[Question] 5 [belongs to] [prime numbers]
[Answer] [correct]
“Does five belong to the set of prime numbers—or, more colloquially, the question is ‘Is five a prime number?’ And the answer is yes; indeed, five was one of the sample numbers we used in naming the set ‘prime numbers.’”
She made another similar Q&A pair appear:
[Question] 4 [belongs to] [prime numbers]
[Answer] [incorrect]
“Is four a prime number?” said Sarah, interpreting. “No.” She rotated her mouse’s wheel again:
[Question] 3 [belongs to] [prime numbers]
[Answer] [correct]
“Is three prime? Yup, sure is. And what about two? Ah, well, let’s have a look.” More mouse movements, and this appeared:
[Question] 2 [belongs to] [prime numbers]
[Answer 1] [correct] [good]
[Answer 2] [incorrect] [good]
[Answer 3] [delta]
“Huh?”
“My precise reaction,” said Sarah, smiling.
“So what’s delta?” Don said.
“See if you can figure it out. Look at answer one and answer two for a moment.”
He frowned. “Hey, wait. They can’t both be good answers. I mean, two is a prime number, so saying that it isn’t can’t be a good answer.”
She smiled cryptically. “They give exactly the same three answers for the number one,” she said, scrolling the screen.
[Question] 1 [belongs to] [prime numbers]
[Answer 1] [correct] [good]
[Answer 2] [incorrect] [good]
[Answer 3] [delta]
“Again, that’s gibberish,” he said. “One either is or isn’t prime. And, well, it is, isn’t it? I mean, a prime is a number that’s only evenly divisible by itself or one, right?”
“Is that what they taught you at Humberside Collegiate? We used to define one as a prime; you’ll see it called such in some old math books. But these days, we don’t. Primes are generally thought of as numbers that have precisely two whole-number factors, themselves and one. One has only one whole-number factor, and so isn’t a prime.”
“Seems rather arbitrary,” said Don.
“You’re right. It is a debatable point. One is definitely an oddball as primes go. And two—well, it’s not an odd-ball; it’s an even-ball. That is, it’s the only even prime number. You could just as arbitrarily define the set of primes as all odd numbers that have precisely two whole-number factors. If you did it that way, then two isn’t a prime.”
“Ah.”
“See? That’s what they’re conveying. Delta is a symbol that means, I think, ‘It’s a matter of opinion.’ Neither answer is wrong; it’s just a matter of personal preference, see?”
“That’s fascinating.”
She nodded. “Now, the next part of the message is really interesting. Elsewhere, they established symbols for ‘sender’ and ‘recipient’—or ‘me,’ the person sending the message, and ‘you,’ the person receiving it.”
“Okay.”
br />
“And with those,” said Sarah, “they get down to the nitty gritty. Look at this.” Her display changed:
[Question] [good] : [bad]
[Answer] [sender] [opinion] [good] >> [bad]
“See? The question is, what’s the relationship between good and bad. And the response from the sender, who had said previously, when discussing factual matters, that good is the opposite of bad, now says something quite a bit more interesting: good is much greater than bad—a significant philosophical statement.”
“‘Does not your sacred book promise that good is stronger than evil?’”
Sarah felt her eyes go wide. “You’re quoting the Bible?”
“Um, actually, no. That’s Star Trek. Second season, ‘The Omega Glory.’” He shrugged sheepishly. “‘Yes, it is written: good shall always destroy evil.’”
Sarah shook her head in loving despair. “You’ll be the death of me yet, Donald Halifax.”
–-- Chapter 11 --–
“MCGAVIN ROBOTICS,” SAID a crisp, efficient female voice. “Office of the president.”
For once, Don wished he did have a picture phone; for all he knew, he was talking to a robot. “I’d like to speak to Cody McGavin, please.”
“Mr. McGavin is unavailable. May I ask who’s calling?”
“Yes. My name is Donald Halifax.”
“May I ask what this is about?”
“I’m the husband of Sarah Halifax.”
“Ah, yes. The SETI researcher, no?”
“That’s right.”
“What can I do for you, Mr. Halifax?”
“I need to talk to Mr. McGavin.”
“As you might imagine, Mr. McGavin’s schedule is very full. Perhaps there’s something I can help you with?”
Don sighed, beginning to get it. “How many layers deep am I?”
“I’m sorry?”
“How many layers between you and McGavin? If I give you a message, and you decide it’s worth passing on, it doesn’t go to McGavin, does it?”
“Not normally, no. I’m the receptionist for the president’s office.”
“And your name is?”
“Ms. Hashimoto.”
“And who do you report to?”
“Mr. Harse, who is the secretary to Mr. McGavin’s secretary.”
“So I have to get through you, then the secretary’s secretary, then the secretary, before I get to McGavin, is that right?”
“We do have to follow procedures, sir. I’m sure you understand that. But of course things can be escalated quickly, if appropriate. Now, if you’ll just tell me what you need…?”
Don took a deep breath, then let it out. “Mr. McGavin paid for my wife and me to undergo rejuvenation treatments—you know, rollbacks. But it hasn’t worked for my wife, only for me. The doctor from Rejuvenex says nothing can be done, but maybe if she had a request directly from Mr. McGavin. Money talks. I know that. If he indicated he was dissatisfied, I’m sure—”
“Mr. McGavin has had a full report on this.”
“Please,” Don said. “Please, my wife…my wife is going to die.”
Silence. His words were probably more brutally honest than the receptionist to the secretary to the secretary to the president was used to hearing.
“I am sorry,” Ms. Hashimoto said with what sounded like genuine regret.
“Please,” he said again. “Surely whatever report he’s seen came from Rejuvenex, and they’ve doubtless put a spin on it. I want him to understand what we—what Sarah—is going through.”
“I’ll let him know you called.”
No, you won’t, he thought, you’ll just pass it on to the next layer. “If I could just talk to Mr. McGavin, just for a minute. I just…” He hadn’t begged for anything for decades—not since…
It hit him, just then. It hit him like a sucker punch to the gut.
Forty-five years ago. The oncology ward at Princess Margaret. Dr. Gottlieb talking about experimental therapies, about things that were new and untested.
And Don begging her to try them on Sarah, to try anything that might save her. The details were lost to time, but he did now recall the interferon treatment, not approved for use in the States. Gottlieb might have agreed to try it because of his begging, his insistent demands that she do everything that might help.
The experimental treatment had failed. But now, four decades on, its lingering effects were blocking another treatment, all—he swallowed hard—because of him.
“Mr. Halifax?” said Ms. Hashimoto. “Are you still there?”
Yes, he thought. Yes, I’m still here. And I’ll still be here for years to come, long after Sarah’s gone. “Yes.”
“I do understand that you’re upset, and, believe me, my heart goes out to you. I’ll flag this double-red. That’s the best I can do. Hopefully someone will get back to you shortly.”
JUST AS HE had all those many years ago, when Sarah had been trying to translate the first Dracon message, Don stopped by from time to time to see how she was faring with decrypting the current one. But instead of working at the university, she was struggling with this one in the study—the upstairs room that had once been Carl’s.
The Dracons’ original message, the one picked up in 2009, had been divided into two parts: a primer, explaining the symbolic language they were using, and the meat of the message—the MOM, as it rapidly came to be known—which used those symbols in baffling ways. But eventually Sarah had figured out the purpose of the MOM, and a reply had been sent.
This second message from the aliens also had two parts. But in this case, the beginning was the explanation of how to decrypt the rest, assuming the right decryption key could be provided, and the rest, well, that was anybody’s guess. Because it was encrypted, not even a single symbol that had been established in the original message was visible in the second part of this one.
“Maybe the aliens are responding to one of the unofficial responses,” Don said, late one evening, leaning against the study’s doorway, hands crossed in front of his chest. “I mean, even before you sent the official reply, didn’t thousands of people send their own unofficial responses to the Dracons?”
Sarah looked ancient, almost ghostly, in the glow from her magphotic monitor, her thin white hair backlit from his perspective. “Yes, they did,” she said.
“So maybe the decryption key is something that was in one of those messages,” he said. “I mean, I know you worked very hard on it, but maybe the Dracons weren’t interested in the official SETI-team response. Whoever they intended to have read their latest message might already have done so.”
Sarah shook her head. “No, no. The current Dracon message is a response to our official reply. I’m sure of it.”
“That might just be wishful thinking,” he said gently.
“No, it’s not. We put a special header at the top of the official reply—a long numeric string, to identify that message. That’s one of the reasons we didn’t post the entire reply we sent on the web. If we had, everyone would have the header, which would have defeated its purpose. The header was like an official letterhead, uniquely identifying the response we sent on behalf of the whole planet. And this reply to our response references that header.”
“You mean it quotes it?” he asked. “But, then, doesn’t everybody have it now? Any Tom, Dick, or Harry could send a new message to the Dracons and have it look official.”
Her wrinkled features shifted in the cold glow as she spoke. “No. The Dracons understood that we were trying to provide a way to distinguish official responses from unofficial ones. They obviously grasped that we didn’t want everyone who managed to detect their latest message to know what the header was. So the Dracons quoted every other digit from it, making clear to us that they were responding to the official reply, but without giving away what had distinguished the official reply in the first place.”
“Well, there’s your answer,” Don said, quite pleased with himself. “The decryption key must be the ot
her digits from the header, the ones the Dracons didn’t echo back.”
Sarah smiled. “First thing we tried. It didn’t work.”
“Oh,” he said. “It was just a thought. Are you coming to bed?”
She looked at the clock. “No, I—” She stopped herself, and Don’s stomach knotted. Perhaps she’d been about to say I don’t have time to waste on sleeping. “I’m going to struggle with this some more,” she finished. “I’ll be along in a bit. You go ahead.”
DON CALLED MCGAVIN’S office four more times without any luck, but finally his datacom rang. His ring tone was the five notes from a forgotten film called Close Encounters of the Third Kind, the sort of aliens-come-to-Earth story that seemed quaintly passé now. He looked at the caller ID. It said “McGavin, Cody”—not “McGavin Robotics,” but the actual man’s name.
“Hello?” Don said eagerly, as soon as he’d flipped his datacom open.
“Don!” said McGavin. He was somewhere noisy and was shouting. “Sorry to be so long getting back to you.”
“That’s all right, Mr. McGavin. I need to talk to you about Sarah.”
“Yes,” said McGavin, still shouting. “I’m sorry, Don. I’ve been briefed on all this. It’s just awful. How is Sarah holding up?”
“Physically, she’s okay. But it’s tearing us both apart.”
His tone was as gentle as one’s could be when shouting. “I’m sure.”
“I was hoping you could speak to the people at Rejuvenex.”
“I already have, repeatedly and at length. They tell me there’s nothing that can be done.”
“But there must be. I mean, sure, Rejuvenex has tried all the standard things, but there’s got to be a way to make the rollback work for Sarah if you—”
He stopped talking, which was probably just as well. He’d been about to say, “if you just throw enough money at it.” But McGavin wasn’t listening. Don could hear him saying something to someone else; from the sounds of it, he’d placed a fingertip over his datacom’s mike and was talking to a flunky standing beside him. At last McGavin came back on. “They’re working on it, Don, and I’ve told them to spare no expense. But they’re totally stumped.”