Free Rollback by Robert J. Sawyer

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