“He means he thinks they’re just a random by-product of something else,” Kuroda said gently. “Like foam, which is an epiphenomenon of waves: it doesn’t mean anything; it just occurs.”
She got it: her dad was saying, hey, see, nothing here worth fighting about; if the cellular automata are meaningless, there’s probably nothing of value to patent anyway. But that hardly excused Kuroda even thinking about making a buck—a yen!—off something that she was doing. Yes, yes, his hardware was feeding her the signals, but it was her brain that was interpreting them. Websight wasn’t just hers, it was her.
“You may be right, Malcolm,” said Anna Bloom, over the webcam link from Haifa. Caitlin was still fuming, and wondered if Anna really knew the mood here. She was seeing a very limited view through the camera, no doubt, and the crappy computer mike probably wasn’t picking up subtlety of tone.
Anna went on: “One bit does affect the next, at least in copper wire; the magnetic fields do overlap, after all. So maybe some sort of…I don’t know, constructive interference, perhaps…could accidentally give rise to cellular automata.”
“But they would still just be noise,” her dad said.
“You’re probably right,” Kuroda replied. “But um, what is it you like to say, Miss Caitlin? You’re ‘an empiricist at heart.’”
He was trying to cajole her, to include her, she knew, but she remained angry. Kuroda worked with computers all day long, for crying out loud—didn’t he know that information wants to be free?
Caitlin was still leaning against the worktable. The street-hockey game continued outside: someone just scored.
“Miss Caitlin?” said Kuroda. “Testing what your father just suggested will involve some cool math…”
“Like what?” she said, her tone petulant.
“Perhaps a Zipf plot…”
Caitlin didn’t know what that was, either, but to her great surprise her father said a very enthusiastic, “Yes!” That was enough to make her curious, but she wasn’t ready to give in just yet. “Is there empty room on this table?” she said, patting its surface. “And do you think it’ll hold me?”
“Sure,” said Kuroda after a pause, presumably to give her father a chance to answer first. “Everything to the left—your left—of the computer is clear.”
Caitlin boosted herself up onto the table, the folding legs groaning slightly as she did so, and she sat cross-legged on it. “Okay,” she said, her tone still not very cheery. “I’ll bite. What’s a Zipf plot?”
“It’s a way of finding out if there’s any information in a signal, even if you can’t decode the signal,” Kuroda said.
Caitlin frowned. “Information? In the cellular automata?”
“Could be,” said Kuroda in a tone that sounded like it should be accompanied by a shrug.
“But, um, can cellular automata contain information?” Caitlin asked.
“Oh, yes,” said Anna. “In fact, Wolfram wrote a paper about encoding information into them for cryptographic purposes as far back as, um, 1986, I think. And a bunch of people have tried to develop public-key cryptography systems using them.”
“Anyway,” Kuroda said, “George Zipf was a linguist at Harvard. In the 1930s, he noticed something fascinating: in any language, the frequency with which a word is used is inversely proportional to its rank in a table of the frequency of use of all words in the language. That means—”
You don’t have to spoon-feed Calculass! “That means,” she said, “the second most-common word is used one-half as often as the first most-common, the third most-common is used one-third as often as the first most-common, the fourth most-common is used one quarter as often, and so on.” She frowned. “But is that really true?”
“Yes,” said Kuroda. “In English, the most-common word is ‘the,’ then ‘of,’ then ‘to,’ then…um, I think it’s ‘in.’ And, yes, ‘in,’ or whatever it is, is used one-quarter as often as ‘the.’”
“But surely that’s just a quirk of English, isn’t it?” said Caitlin, shifting slightly on the table.
“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 i
mplant. 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.” Keyclicks. “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. “The 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 videoconference 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.”
thirty
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 bri
lliant. 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.”
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