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Jenny.  "And what about my arithmetic, Sir?  Is that a similar thing?"
    "It's related, yes.  The way we understand it, you kind of "see languages whole."  There's this deeply layered, fixed structure in your brain ready to soak up any language.  You hear pieces of the language and the fixed structure sorts it all out, quickly figuring out the rules.  It appears your brain has worked out how to use this structure to solve arithmetic puzzles too."  He turned to Séamus.  "Things like multiplying two five-digit numbers together, taking the square root of a seven-digit number, dividing a three-digit number into a nine-digit number, etcetera."
    There was a brief silence, then Jenny asked, "So how are you going to use me?"  As she spoke, she looked at Séamus, even though the question seemed directed at Wilkie.  Séamus found her look curious and questioning, but not aggressive.
    The Professor smiled. "You, and three other girls with similar gifts to you, will invent a new language.  And it will be a very unusual language.  It won't be spoken, because it will be made up entirely of numbers.  If this language really works in the way that I hope, it will be of immeasurable importance to humanity."
    Jenny looked uncertain.  "You're going to show us how to invent a language?  All I've done is copy languages so far."
    Wilkie turned to Alice. "My Dear, how would you answer that one?"
    Alice hesitated, then said, "Jenny, I had real difficulty learning even a second language.  Also, though maths is my profession, almost everything I do involves symbols, not numbers. So I can't imagine what it's like to have your gifts.  But the Professor's studies of people like you, and even people with fewer gifts but stuck in situations where they share no language with the people around them, has led him to believe that you will be able to generate such a language almost instinctively.  In other words, it will happen without you really trying. 
    "But the bigger challenge is restricting you to using numbers only.  It's never been tried before.  We've designed a room where we think you'll have the best tools to do it, but to be honest none of us are sure it can actually be done.  And we don't know how to instruct you on it, except tell you to go with your own instincts.  You and the other girls are the real experts, not us."
    The girl nodded thoughtfully.  "My mother told me she'd received your first payment, thank you," she said to all of them. "I understand the guaranteed payments, and the bonus if this project succeeds.  So I suppose that success is developing this number language so it can work like any other language.  And it might take us a few months, or more than a year?"
    "We've no idea," Wilkie said.  "If it's looking hopeless after twelve months, for certain we'll abandon it.  But even as you're struggling to get the language working, there's a good chance we'll be getting something useful out of you – isn't there, Alice?"
    Alice smiled. "Now at last we are in my area of competence.  My computer programs will be analyzing all your efforts.  We're hoping we can work out clues to how your brain processes language.  If we see enough useful patterns, we may even be able to leap ahead of you and complete the job.  On the other hand, it's possible you may have reached a working language and we just need you to keep going on for quite a while, simply because we need to shake out more patterns. But by that time, you'll have earned your bonus.  Any extra time we require you to stay on, we'll be paying you more on top of that."
    Jenny giggled a little. "In that case, you can have me as long as you need me. At this rate, I'll have my parents off my back and be set for life."
    The conversation continued another half-hour, then Séamus showed Jenny back to her room.  As she stepped inside, she asked, "Can you and I go for a walk a bit later?  I would like to see more of the countryside here."  Surprised, Séamus said he