“No, it’s the same in Japanese.” He rattled off some words in that language.
“Those are the four most common, and they appear in the same inverse ratio.”
“And it’s true for Hebrew, too,” said Anna.
“But what’s really amazing,” said Kuroda, “is that it doesn’t apply just to words. It applies equally well to letters: the fourth most-common in English, which is O, is used one-quarter as much as the first most-common, E. And it applies to phonemes, too — the smallest building blocks of speech — and, again, in all languages, from Arabic to…” He trailed off, clearly trying to think of a language that started with Z.
“Zulu?” offered Caitlin, deciding to be helpful.
“Exactly, thanks.”
She thought about this. It was indeed pretty cool.
“Everything Masayuki said is right,” Anna said, “but you know what’s even more interesting, Caitlin? This inverse ratio applies to dolphin songs, too.”
Well, that was awesome. “Really?” she said.
“Yes,” said Kuroda. “In fact, this technique can be used to determine if there is information in the noise any animal makes. If there is, it will obey Zipf’s law, so that if you plot the frequency of use of the components on a logarithmic scale, you get a line with a slope of negative one.”
Caitlin nodded. “A line going diagonally from the upper left down to the lower right.”
“Exactly,” said Kuroda. “And when you plot dolphin vocalizations you do get a negative-one slope. But if you take, say, the sounds made by squirrel monkeys, you get a slope, at best, of -0.6, because what they make is just random noise. Even the SETI people — Search for Extraterrestrial Intelligence — are doing Zipf plots now, because the inverse-relationship is a property of information, not of any particularly human approach to language.”
All right, all right: it was cool math.
“Now do you see why I like information theory so much?” Kuroda said, his tone suggesting he was still trying to cajole her. “Hey, do you know John Gordon’s old story about the student of information theory on his first day at university?”
Anna said, “Not this one again!” but Kuroda pressed on undaunted.
“Well,” he said, “the student shows up at the departmental office and hears the professors calling out numbers. One would call out, say, ‘74!,’ and all the other professors would laugh. Then another would call out a different number, say, ‘812,’ and again everyone would laugh.”
“Uh huh,” said Caitlin.
“So the student asks what’s going on, and a prof says, ‘We’re telling jokes. See, we’ve all worked together so long, we know each other’s jokes by heart. There are a thousand of them, so, being information theorists, we applied data compression to them, assigning each one a number from zero through 999. Go ahead, try it yourself.’ And so the student calls out a number: ‘63.’ But no one laughs. He tries again: ‘512!’ Nothing. ‘What’s wrong?’ the student asks.
‘Why is no one laughing?’ And the kindly old prof says, ‘Well, it’s not just the joke — it’s how you tell it.’”
Caitlin found herself smiling despite herself.
“But one day,” Kuroda said, “the student was looking at a weather report for the far north and happened to exclaim the temperature: ‘Minus 45!’ And all the professors burst out laughing.”
He paused, and Caitlin said, “Why?”
“Because,” he replied, and she could tell by his voice that he was grinning, “they’d never heard that one before!”
Caitlin laughed out loud, and found herself feeling better, but her father said, “Ahem” — actually saying it as if it were an English word, rather than like a throat-clearing. “Might we get on with it?”
“Sorry,” said Kuroda, but he sounded like he was still grinning. “Okay, here we go…”
He used the technique he’d developed before to send freeze frames of the Jagster data to Caitlin’s eyePod, and from there to her implant. By trial and error, they found the right refresh rate to get what she was seeing to increment by just one step — just one iteration of whatever rule was governing the cellular automata as they changed from black to white or vice versa. She could now watch, frame by frame, at whatever playback speed she wished, as spaceships moved across her field of view, without missing any steps.
Kuroda had no way to filter out just the cellular automata from the Jagster feed, but Caitlin could do it with ease, simply by focusing on only a portion of the background.
“And,” he said, “speaking of Mathematica, Malcolm, do you have it?”
“Of course,” he said. “It should be accessible here. Let me…”
Caitlin heard them moving around, then, after a bit, Kuroda said, “Ah, thanks,” to her dad, and then, generally, to everyone, “Okay, let’s run the Zipf-plotting function.” Key clicks. “Of course, we’ll have to try a lot of different ways of parsing the datastream,” he continued, “to make sure we are isolating individual informational units. First, we’ll—”
“There!” interrupted her dad, actually sounding excited.
“What?” said Caitlin.
“Well, that’s it, isn’t it?” said Kuroda.
“What?” she repeated more firmly.
“You’re sure you’re concentrating on just the cellular automata?” Kuroda asked.
“Yes, yes.”
“Well,” he said, “what we’re getting as we plot them flipping from black to white is a lovely diagonal line — from the upper left to the lower right. A negative-one slope all the way.”
Caitlin lifted her eyebrows. “So there is information — real content — in the background of the Web?”
“I’d say so, yes,” said Kuroda. “Malcolm?”
“There’s no random process that can generate a negative-one slope,” he said.
“Le’azazel!” exclaimed Anna; it sounded like a curse word to Caitlin.
“What?” said Kuroda.
“Don’t you see?” Anna said. “A negative-one slope: it’s intelligent content on the Web in a place it’s not supposed to be — intelligence disguised to look like random noise.” She paused as if waiting for one of the men to supply the answer and, when they didn’t, she said, “It’s got to be the NSA.” She paused, letting that sink in. “Or maybe it’s comparable spooks elsewhere — Shin Bet, perhaps — but I’d bet it’s the NSA. We already know, from Hepting, that they muck around with the traffic on the net; it looks like they’ve found a way to package clandestine communications that move in the apparent noise.”
“What sort of content could it be, though?” asked Caitlin.
“Who knows?” said Anna. “Secret communiqués? Like I said, people have tried to use cellular automata before for data encryption, but nobody — at least not anyone who’s gone public — has ever worked out a system. But the NSA scoops up a lot of the top math grads in the US.”
“Really?” said Caitlin, surprised.
“Oh, yes,” said Anna. “It’s a real problem in the field of math academically, actually. Most of the best US grads in math and computer science either go to the NSA, where they work on classified projects, or to private-sector places like Google or Electronic Arts, where they do stuff that’s covered by nondisclosure agreements. God knows what they’ve come up with; it’s never published in journals.”
Kuroda said something that might have been a swearword of his own in Japanese, then: “She may be right. We should tread very, very carefully here, my friends. If this stuff in the background of the Web is supposed to be secret, those in power may take … steps … to ensure that it remains that way. Miss Caitlin, far be it from me to tell you what to do, but perhaps you could be circumspect about this topic in your blog?”
“Oh, no one pays attention to my LiveJournal. Besides, I flock — friends-lock — anything that I don’t want strangers to read.”
“Do what he says,” her dad said, startling her by the sharpness of his voice.
“Th
e authorities could seize your implant and eyePod as threats to national security.”
Caitlin got down off the table. “They wouldn’t do that,” she replied.
“Besides, we’re in Canada now.”
“Don’t think for one second that the Canadian authorities won’t do whatever Washington asks,” her father said.
She wasn’t sure what to make of all this. “Um, okay,” she said at last. “But you guys are going to keep studying it, right?”
“Of course,” Dr. Kuroda said. “But carefully, and without tipping our hand.”
He paused. “It’s a good thing we’re doing a video conference with Anna; if this were text-based IM the authorities would already know what we’ve found. At least for now, video is a lot harder for them to automatically monitor.”
The full impact of what he and Anna were saying was coming to her. She turned her head toward Kuroda. “But what about our paper?”
“Eventually, Miss Caitlin, perhaps. But for now, the better part of valor is discretion.”
Chapter 30
Masayuki Kuroda had spent the rest of Saturday, and all day Sunday, working with Miss Caitlin, studying the cellular automata. But it was now Monday, the first day of October. Masayuki had been in Canada a week now. He missed his wife and his own daughter, and felt guilty that Hiroshi was having to cover his classes for him. But, still, he was entitled to a little time off while he was here, no? Besides, there was only so much he could do while Miss Caitlin was at school.
He took another bite of his roast-beef sandwich and looked around the kitchen. He didn’t think he’d ever get used to North American houses. A home this size would be almost impossible to find in Tokyo, and yet there were streets full of them here. Of course, the Decters obviously weren’t hurting for cash, but, still, with only Malcolm working, and with all the expensive equipment Caitlin had, they certainly couldn’t have a lot of disposable income left.
“I want to thank you,” he said. “You’ve been so hospitable.”
Barbara Decter was seated on the opposite side of the square pine table, holding a cup of coffee in two hands. She looked over its brim at him. She was, Masayuki thought, quite lovely: probably closer to fifty than forty, but with large, sparkling blue eyes and a cute upturned nose that almost made her look like an anime character. “It’s my pleasure,” she said. “To tell the truth, I’ve enjoyed having you here. It’s nice to, you know, have someone talkative around. Back in Austin…”
She trailed off, but her voice had become a bit wistful before doing so.
“Yes?” he said gently.
“I just miss Texas, is all. Don’t get me wrong; this place is nice, although I am not looking forward to winter, and…”
Masayuki thought she looked sad. After a time he again said, “Yes?”
She held up a hand. “I’m sorry. It’s just … been particularly difficult coming here. I had friends back in Austin, and I had things to do: I worked every weekday as a volunteer at Caitlin’s old school, the Texas School for the Blind.”
He looked down at the place mat. It was a large laminated photo of a city skyline at night; a caption identified it as Austin. “So why did you move here?”
“Well, Caitlin was pushing to go to a regular school, anyway — she said she’d need to be able to function in normal classes if she were going to go on to MIT, which has been her goal for years. And then Malcolm got this job offer that was too good to pass up: the Perimeter Institute is a dream come true for him. He doesn’t have to teach, doesn’t have to work with students. He can just think all day.”
“How long have you been married, if I may ask?”
Again, the slightly wistful tone. “It’ll be eighteen years in December.”
“Ah.”
But then she gave him an appraising look. “You’re being polite, Masayuki. You want to know why I married him.”
He shifted in his chair and looked out the window. The leaves had started to change color. “It’s not my place to wonder,” he said. “But…”
She raised her shoulders a bit. “He’s brilliant. And he’s a great listener. And he’s very kind, in his way — which my first husband was not.”
He took another bite of his sandwich. “You were married before?”
“For two years, starting when I was twenty-one. The only good thing that came out of that was it taught me which things really matter.” A pause. “How long have you been married?”
“Twenty years.”
“And you have a daughter?”
“Akiko, yes. She’s sixteen, going on thirty.”
Barb laughed. “I know what you mean. What does your wife do?”
“Esumi is in — what do you say in English? Not ‘manpower’ anymore, is it?”
“Human resources.”
“Right. She’s in human resources at the same university I work at.”
The corners of her mouth were turned down. “I miss the university environment. I’m going to try to get back in next year.”
He felt his eyebrows going up. “As … as a student?”
“No, no. To teach.”
“Oh! I, ah—”
“You thought I was June Cleaver?”
“Pardon?”
“A stay-at-home mom?”
“Well, I…”
“I’ve got a Ph.D., Masayuki. I used to be an associate professor of economics.” She set down her coffee cup. “Don’t look so surprised. Actually, my specialty is — was — game theory.”
“You taught in Austin?”
“No. In Houston; that’s where Caitlin was born. We moved to Austin when she was six so she could go to the TSB. The first five years, I did stay at home with her — and believe me, looking after a blind daughter is work. And I spent the next decade volunteering at her school, helping her and other kids learn Braille, or reading them things that were only available in print, and so on.”
She paused and looked through the opening to the large, empty living room.
“But now, I’m going to talk to UW and Laurier — that’s the other university in town — about picking up some sessional work, at least. I couldn’t do any this term because my Canadian work permit hasn’t come through yet.” She smiled a bit ruefully. “I’m a bit rusty, but you know what they say: old game theorists never die, we just lose our equilibrium.”
He smiled back at her. “Are you sure you don’t want to come to Toronto for the show?”
“No, thanks. I’ve seen Mamma Mia. We all went back in August. It’s great, though. You’ll love it.”
He nodded. “I’ve always wanted to see it. I’m glad I was able to get a ticket on such short notice, and—” Yes, yes — of course!
“Masayuki?”
His heart was pounding. “I am an idiot.”
“No, no, lots of people like ABBA.”
“I mean Miss Caitlin’s software. I think I know why she was able to see the lightning, but not anything else in the real world. It’s related to the delta modulation: the Jagster feed is already digital, but the real-world input from her retina starts out as analog and is converted to digital for processing by the eyePod — and that must be where I screwed up. Because when she saw the lightning, that was a real-world signal that already had only two components: bright light and a black background. It was essentially digital to begin with, and she could see that.” He was thinking furiously in Japanese and trying to talk in English at the same time. “Anyway, yes, yes, I think I can fix it.” He took a sip of coffee. “Okay, look, I’m not going to be back from Toronto until after midnight tonight. And Caitlin will be in bed by then, won’t she?”
“Yes, of course. It’s a school night.”
“Well, I don’t want to wait until tomorrow after school to test this; I mean, it probably won’t work right the first time, anyway, but, um, could you do a favor for me?”
“Of course.”
“It should just be a small patch — nothing as elaborate as downloading a complete software update to
her implant, like we did before. So I’m going to queue up the patch code to be sent automatically to her eyePod next time she switches to duplex mode. That’ll mean taking the Jagster feed offline, but I’ll leave instructions for Caitlin on how to reinstate it if she wants it later tonight. Anyway, when she gets home, ask her to switch to duplex, and have her tell you what difference, if any, it makes.”
Barb nodded. “Sure, I can do that.”
“Thanks. I’ll leave instructions for rolling back to the old version of software, too, in case something goes wrong. As I say, the patch probably won’t work the first time, but my server will still record her eyePod’s output based on the patched code, so tomorrow while she’s at school, I’ll be able to go back and examine the datastream from tonight, see if the encoding has been improved at all, and then I can make any further tweaks that are required. But if we don’t get the first test done tonight, I’ll lose a whole day before I can refine it.”
“Sure, no problem.”
He gobbled the last bite of his sandwich. “Thank you.” He glanced at the clock on the microwave — he’d never get used to digital clocks that showed a.m. and p.m. instead of twenty-four-hour time. “I want to get an early start into Toronto this afternoon; I’m taking you at your word that it would be crazy to try to drive into downtown there in rush hour. So, if you’ll excuse me, I’m going to get that patch set up.”
Chapter 31
Mr. Struys had started off today’s chemistry class by reading aloud from The Globe and Mail. The lab bench Caitlin shared with Bashira was halfway to the back of the room, but she could easily hear the rustling newsprint followed by his voice intoning, “‘Initial reports out of China’s Shanxi province had put the death toll at between 2,000 and 2,500 from the natural eruption of carbon dioxide gas there on September 20. Beijing is now admitting that as many as 5,000 people have died, and some unofficial estimates are putting the body count at double that.’“ He paused. “So, who did their homework over the weekend? What’s this news story reminiscent of?”
An interesting thing about being blind, Caitlin thought, was that you never knew how many people were putting up their hands. But either she was usually the only one or else Mr. Struys liked her, because he often called on her. She liked him, too. It pleased her to know his first name, which was Mike. She’d heard another teacher call him that; it seemed to be a popular choice here in Waterloo. After all the “Dr. Kuroda” and “Professor Decter” stuff at home, it was nice to hear a teacher slip up in front of students and call a colleague by his first name.
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