The doctor looked up, and it seemed to take her eyes a moment to focus. “Sorry,” she said. “I just—well, I just never thought I'd end up having to apologize for giving someone another sixty or seventy years of life."
Don crouched down next to his seated wife. How excruciating doing that would have been just a short time ago—and yet it gave him no pleasure now to be able to do it with ease. “I am sorry, honey,” he said. “I am so sorry."
But Sarah was shaking her head. “Don't be. It's going to be all right. You'll see."
How could it be all right? he wondered. They'd spent their lives in synch, born the same year, growing up with the same events in the background. Both remembered precisely where they were when Neil Armstrong set foot upon the moon during the year they'd each turned nine. Both had been teenagers when Watergate happened; in their twenties when the Berlin Wall fell; in their thirties when the Soviet Union collapsed; in their forties for the first detection of alien life. Even before they'd met, they'd been marching through the stages of life together, jointly aging, and improving, like two bottles of wine of the same vintage.
Don's head was swimming, and so, it seemed, was his vision. Sarah's face appeared blurred, the tears in his eyes doing what Rejuvenex's sorcery couldn't, erasing her wrinkles, smoothing out her features.
* * * *
Chapter 10
Like most SETI researchers, Sarah had worked late many nights after that first alien transmission had been received back in 2009. Don had come to see her in her office at the University of Toronto on one of those evenings, after he'd finished his work at the CBC.
"Anybody home?” he'd called out.
Sarah had swung around, smiling, as he came through the door carrying a red-and-white Pizza Hut box. “You're an angel!” she crowed. “Thank you!"
"Oh,” he said. “Did you want something, as well?"
"Pig! What did you get?"
"A large Pepperoni Lover's ... ‘cause, um, I like pepperoni, and we're lovers..."
"Awww,” said Sarah. She actually preferred mushrooms, but he couldn't stand them. Coupling that with his dislike for fish had given rise to the little speech she'd listened politely to him give on numerous occasions, a pseudo-justification that he thought was witty for his eating choices: “You should only eat food that's as evolved as you are. Only warm-blooded animals—mammals and birds—and only photosynthesizing plants."
"Thanks for coming by,” she said, “but what about the kids?"
"I called Carl, told him to order a pizza for him and Emily. Said he could take some money out of my nightstand."
"When Donald Halifax parties, everybody parties,” she said, smiling.
He was looking around for somewhere to set the pizza box. She leapt to her feet and moved a globe of the celestial sphere off the top of a filing cabinet, setting it on the floor. He placed the box where the globe had been and opened its lid. She was pleased to see some steam rising. Not too surprising; the Hut was just up on Bloor Street.
"So, how's it going?” he asked. This wasn't the first time he'd brought food to her office. He kept a plate, knife, and fork in one of the office cupboards, and he got them now. Sarah, meanwhile, pulled out a piece of pizza, severing the cheesy filaments with her fingers.
"It's a race,” she said, sitting down in the chair in front of her workstation. “I'm making progress, but who knows how it compares to what everyone else is achieving? I mean, sure, there's a lot of sharing of notes going on online, but I doubt anyone is revealing everything yet."
He found the other office chair—a beat-up folding one—and sat next to her. She was used to the way her husband ate pizza, but couldn't actually say she liked it. The crust wasn't part of his diet—of course, the greasy Pizza Hut deep-dish crust probably shouldn't be part of anyone's diet, although she found it impossible to resist. He got the toppings off with a fork, swirling it in the molten cheese almost as though he were eating spaghetti. He also ate sandwiches a similar way, digging out the fillings with cutlery while leaving the bread behind.
"Anyway, we'd always expected that math would be the universal language,” Sarah continued, “and I guess it is. But the aliens have managed something with it that I wouldn't have thought possible."
"Show me,” Don said, moving his chair closer to her workstation.
"First, they establish a pair of symbols that everybody working on this agrees serve as brackets, containing other things. See that sequence there?” She pointed at a series of blocks on her computer screen. “That's the open bracket, and that one there"—pointing at another place on the screen—"is the closing bracket. Well, I've been doing a rough-and-ready transliteration of everything as I go along—you know, rendering it in symbols we use. So, here's what the first part of the message says.” She flipped to another window. It was displaying this:
* * * *
{ } = 0
{ * } = 1
{ ** } = 2
{ *** } = 3
{ **** } = 4
{ ***** } = 5
{ ****** } = 6
{ ******* } = 7
{ ******** } = 8
{ ********* } = 9
* * * *
"See how clever they are?” said Sarah. “The brackets let us tell at a glance that there's nothing in the first set. And see what they're doing? Establishing digits for the numbers zero through nine—the aliens are using base-ten, which may mean they've got the same number of fingers we have, or it might just mean that they've decoded some of our TV, and have seen that that's how many fingers we've got. Oh, and notice that this chart gives us their equals sign, too."
He got up and helped himself to another slice; when you skipped the crust, you went through pizza awfully quickly.
"Anyway,” she continued, “they immediately give us the basic mathematical operators. Again, I've rendered them in familiar notation. She rotated the wheel on her mouse, and this scrolled into view:
* * * *
[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] (right angle bracket)
[Question] 9 : 1
[Answer] (right angle bracket) (right angle bracket)
[Question] 3 : 5
[Answer] (left angle bracket)
[Question] 1 : 9
[Answer] (left angle bracket) (left angle bracket)
[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 odd-ball 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."
"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] (right angle bracket) (right angle bracket) [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 Industries,” 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.
Analog SFF, October 2005 Page 7