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“How?” asked Caitlin.

“It’s all about conditional probabilities,” said Kuroda. “If you’ve already got a string of information chunks, what’s the likelihood that you can predict what the next chunk will be? If I say, ‘How are,’ you’ve got a really high probability of correctly predicting what the next word will be: ‘you,’ right? That’s what Shannon called third-order entropy: you’ve got a great shot at predicting the third word. In English, Japanese, and most other languages, you actually have a shot — progressively slimmer, but still better than just a random guess — up to the eighth or ninth word, so we say those languages have eighth — or ninth-order Shannon entropy. But after that — after the ninth word — it really is just a random guess what’s coming next, unless the person happens to be quoting poetry or something else that has a fixed form.”

“Cool!” said Caitlin.

There was a black leather couch in the den. Kuroda sat on it, and it made a poof sound. “It is indeed. Mindless communication systems — like the chemical signals employed by plants — have just first-order entropy: knowing the most recent signal gives no clue what the next one might be. Squirrel monkeys show a Shannon entropy of the second or third order: their language, such as it is, has a little predictability, but is really mostly just random noise.”

“What about dolphins?” asked Caitlin, who was now leaning against a bookcase. She loved reading about dolphins, and had already bugged her parents to take her to MarineLand in Niagara Falls as soon as it opened up again in the spring.

“The best studies to date show dolphins have fourth-order entropy — complex, yes, but not as complex as human language.”

“And now, Dad, you’re making one of these plots for the stuff that’s in the background of the Web?”

He still wasn’t used to the fact that she was seeing, Caitlin thought. He could have saved himself a word by just nodding, but instead he said, “Yes.”

“And what’s the scoop?”

“Second-order,” he said.

Kuroda struggled back to his feet and moved over to stand behind him. “That can’t be right.” He peered at the screen. “Show me the formula you’re using.”

Her dad did something, and Kuroda frowned, then waved a finger at the keyboard. “Run it again.”

A few key clicks, then her dad said, “No difference.”

Kuroda turned to face Caitlin. “He’s right: it’s all just second-order stuff. Oh, there’s information there, but it’s not very complex.”

“You’d expect more from the NSA,” said Caitlin, pleased to be able to wield the initials. “No?”

“Well, you know what they say about government intelligence,” Kuroda replied.

“It’s an oxymoron.”

Caitlin laughed.

“Know what’s great about spending time with someone as young as you, Miss Caitlin? Old jokes are new to you. But, yes, you’re right — it’s not what I’d have expected.”

Caitlin was struck by an idea. “What about stuff that’s more complex than human language? Maybe stuff that looks like gibberish to us is really just too complex for us to … to…”

“Parse,” supplied Kuroda. “But, no, even if it didn’t make sense to us, a Shannon analysis would still give it a high score, not a low one, if it really wasn’t gibberish. If the NSA was using a lot of quadruple negatives — ’I did not not not not go to the zoo’ — or if they were employing complex nested clauses and tense changes like, ‘I would have had have had been present, were it not for … ,’ it would still score high — twelfth, fifteenth order, maybe.”

“Hmm, Then maybe it is just random noise,” she said.

“No, no,” said Kuroda. “Remember the Zipf plots we ran? A Zipf plot giving a negative-one slope means it really does contain information. It’s just that, according to the Shannon-entropy score, it’s not complex information.”

“Well,” she said, “maybe the spies are just grunting out monosyllabic orders like, ‘drop bomb’ or ‘kill bad guy.’”

Kuroda lifted his shoulders. “Maybe.”

Chapter 35

LiveJournaclass="underline" The Calculass Zone

Title: No such thing as bad publicity

Date: Tuesday 2 October, 20:20 EST

Mood: Anticipatory

Location: Soon to be on the map of the stars’ homes

Music: Fergie, “Taking Off”

So where is all the media coverage related to me, you might ask? “Gorgeous girl regains sight!” “Blind genius can see!” “The Hoser still hoping for a second date with Calculass!” Where the heck is Oliver Sacks when you need him?

And, most important of all, where are all the offers to buy my life story for millions?

Good questions! Dr. K’s been keeping a lid on things, waiting for some approvals from the University of Tokyo. But he says we can’t hold off going public any longer. I’ve been flocking posts, and y’all are totally cool, of course, but all those kids at school now know that I can see, too, and some of them have been blogging. And so we’re going to have a press conference. Dad’s arranging for it to be at the Mike L Theatre at PI which is a cool place.

Apparently, I’ll have to speak as part of the press conference, so I’m working on my jokes. PI’s full name is the Perimeter Institute for Theoretical Physics, so I thought I’d start off with this, in honor of my own kitty: “Hey, folks, just think: if Schrodinger’s cat had been radioactive, he’d have had eighteen half-lives…”

Then I’m going to use this one, which The Mom came up with a while ago when Dad was grousing about “peer review.” She said whenever she sees the word p-e-e-r, she reads it as “one who pees,” which, she says, makes publish-or-perish a pissing contest…

Oh, and here’s one I like, but I don’t know if I want to tell it in front of my parents: The difference between a geek and a dork is that a geek wonders what sex is like in zero gravity; a dork wonders what sex is like.

Thank you, thank you, I’m here all week!

[And seekrit message to BG4: check your email, babe!]

This other entity existed in a bizarre realm that challenged my thinking at every turn. Most objects I saw were inanimate; they stayed put unless something acted upon them. But some objects were animate, moving apparently of their own volition. This was a staggering concept. That there was one other entity besides myself had been an overwhelming notion, but now there seemed to be countless others: mobile, complex, and varied in form. Their actions were so erratic, so seemingly random, that it only slowly dawned on me that perhaps these were also beings with their own individual thoughts, separate from mine.

There were other odd facts to absorb about this realm that also had no parallels in my world. For instance, there was a force, apparently, pulling things in a specific direction (another arbitrary coinage: down). And objects seemed to be illuminated by a source or sources of light that was usually up. I struggled to make sense of it all.

And yet these physical realities were easy to deal with compared to the complexity of the animate objects. I had real difficulty making out what I was seeing when the datastream showed me one of them. The images were indeed sharp and clear now, but the forms were so elaborate and random I had trouble figuring out the details. There seemed to be four long projections from a central core and one smaller … lump. But the structure of these lumps was constantly changing, not just as the perspective changed, but as the lump itself … did things.

Oh, for the simplicity of a world of just lines and points! Despite my breakthroughs, despite the few things I had figured out, I still often felt utterly, completely lost…

* * *