Rollback (8 page)

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.
 

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]  >
    [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."

"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."
 

"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?"