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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.