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recent years has been because of the excessive demands on his time required to care for a disabled child.”

That had been removed thirteen days ago. The change log gave only an IP address, not a user name. The IP address was the one for the Decter household; the change could have been made (among other possibilities) by Caitlin, her parents, or that other man—Dr. Kuroda, I now knew—that I had often seen there.

The deletion might have been made because Caitlin had ceased to be blind.

But…

But it seemed more likely that this text was cut because someone—presumably Caitlin herself—didn’t like what it said.

But I was merely inferring that. It was possible to more directly study Caitlin—and so I did.

In short order, I read everything she’d ever put publicly online: every blog post, every comment to someone else’s blog, every Amazon.com review she’d written. But—

Hmm.

There was much she had written that I could not access. Her Yahoo mail account contained all the messages she had received, and all the messages she had sent, but access was secured by a password.

A nettlesome situation; I’d have to do something about it.

LiveJournal: The Calculass Zone

Title: Changing of the Guard

Date: Saturday 6 October, 00:55 EST

Mood: Astonished

Location: Waterloo

Music: Lee Amodeo, “Nightfall”

I got a feeling I’m going to be pretty scarce for the next little while, folks. Things they be a-happenin’. It’s all good—miraculous, even—but gotta keep it on the DL. Suffice it to say that I told my parents something el mucho grande tonight, and they didn’t freak. Hope other people take it as well as they did…

Even though she was exhausted, Caitlin updated her LiveJournal, skimmed her friends’ LJs, updated her Facebook page (where she changed her status to “Caitlin thinks it’s better to give than to receive”), and then checked her email. There was a message from Bashira with the subject, “One for the math genius.”

When she’d been younger, Caitlin had liked the sort of mathematical puzzles that sometimes circulated through email: they’d made her feel smart. These days, though, they mostly bored her. It was rare for one to present much of a challenge to her, but the one in Bashira’s message did. It was related to an old game show, apparently, something called Let’s Make a Deal that had starred a guy named Monty Hall. In it, contestants are asked to pick one of three doors. Behind one of them is a new car, and behind each of the others is a goat—meaning the odds are one in three that the contestant is going to win the car.

The host knows which door has the car behind it and, after the contestant picks a door, Monty opens one of the unchosen ones and reveals that it was hiding a goat. He then asks the player, “Do you want to switch to the other unopened door?”

Bashira asked: Is it to the contestant’s advantage to switch?

Of course not, thought Caitlin. It didn’t make any difference if you switched or not; one remaining door had a car behind it and the other had a goat, and the odds were now fifty-fifty that you’d picked the right door.

Except that that’s not what the article Bashira had forwarded said. It contended that your chances of winning the car are much better if you switch.

And that, Caitlin was sure, was just plain wrong. She figured someone else must have written up a refutation to this puzzle before, so she googled. It took her a few minutes to find what she was looking for; the appropriate search terms turned out to be “Monty Hall problem,” and—

What the hell?

“…When the problem and the solution appeared in Parade, ten thousand readers, including nearly a thousand Ph.D.s, wrote to the magazine claiming the published solution was wrong. Said one professor, ‘You blew it! Let me explain: If one door is shown to be a loser, that information changes the probability of either remaining choice—neither of which has any reason to be more likely—to 1/2. As a professional mathematician, I’m very concerned with the general public’s lack of mathematical skills. Please help by confessing your error and, in the future, being more careful.’ ”

The person who had written the disputed answer was somebody called Marilyn vos Savant, who apparently had the highest IQ on record. But Caitlin didn’t care how high the lady’s IQ was. She agreed with the people who said she’d blown it; she had to be wrong.

And, as Caitlin liked to say, she was an empiricist at heart. The easiest way to prove to Bashira that vos Savant was wrong, it seemed to her, would be by writing a little computer program that would simulate a lot of runs of the game. And, even though she was exhausted, she was also pumped from her conversations with Webmind; a little programming would be just the thing to let her relax. She only needed fifteen minutes to whip up something to do the trick, and—

Holy crap.

It took just seconds to run a thousand trials, and the results were clear. If you switched doors when offered the opportunity to do so, your chance of winning the car was about twice as good as it was when you kept the door you’d originally chosen.

But that just didn’t make sense. Nothing had changed! The host was always going to reveal a door that had a goat behind it, and there was always going to be another door that hid a goat, too.

She decided to do some more googling—and was pleased to find that Paul Erdos hadn’t believed the published solution until he’d watched hundreds of computer-simulated runs, too.

Erdos had been one of the twentieth century’s leading mathematicians, and he’d co-authored a great many papers. The “Erdos number” was named after him: if you had collaborated with Erdos yourself, your Erdos number was 1; if you had collaborated with someone who had directly collaborated with Erdos, your number was 2, and so on. Caitlin’s father had an Erdos number of 4, she knew—which was quite impressive, given that her dad was a physicist and not a mathematician.

How could she—let alone someone like Erdos?—have been wrong? It was obvious that switching doors should make no difference!

Caitlin read on and found a quote from a Harvard professor, who, in conceding at last that vos Savant had been right all along, said, “Our brains are just not wired to do probability problems very well.”

She supposed that was true. Back on the African savanna, those who mistook every bit of movement in the grass for a hungry lion were more likely to survive than those who dismissed each movement as nothing to worry about. If you always assume that it’s a lion, and nine times out of ten you’re wrong, at least you’re still alive. If you always assume that it’s not a lion, and nine times out of ten you’re right—you end up dead. It was a fascinating and somewhat disturbing notion: that humans had been hardwired through genetics to get certain kinds of mathematical problems wrong—that evolution could actually program people to be incorrect about things.

Caitlin felt her watch, and, astonished at how late it had become, quickly got ready for bed. She plugged her eyePod into the charging cable and deactivated the device, shutting off her vision; she had trouble sleeping if there was any visual stimulation.

But although she was suddenly blind again, she could still hear perfectly well—in fact, she heard better than most people did. And, in this new house, she had little trouble making out what her parents were saying when they were talking in their bedroom.

Her mother’s voice: “Malcolm?”

No audible reply from her father, but he must have somehow indicated that he was listening, because her mother went on: “Are we doing the right thing—about Webmind, I mean?”

Again, no audible reply, but after a moment, her mother spoke: “It’s like—I don’t know—it’s like we’ve made first contact with an alien lifeform.”

“We have, in a way,” her father said.