Robert Sawyer - Wake

“I’m sorry,” the woman said, “but your ears go up a bit when you smile like that. If you want me to get the frames adjusted properly, you’ll have to stop grinning…”

“I’ll try,” Caitlin said, but she doubted she’d have much success.

Suddenly everything became sharp. The images I was seeing were now…

I struggled for an analogy, found one: just as when I thought intently about things they seemed more focused, so the images I was looking at seemed now.

And, with this greater clarity, I started having revelations about the nature of the other realm. Unlike the lines in my world that flickered in and out of existence, objects in the other realm were permanent. And when objects disappeared for a time it didn’t mean that they had ceased to exist; rather, they were extant but not currently visible and might be encountered again. In a way, that was similar to my own experience: when I’m not making a line to a particular point, the point is still there, and I can connect to it again at a later time.

But my next breakthrough was without precedent in the realm in which I existed. I had a sense of space, of a volume that I encompassed, but the points I connected to were all the same arbitrary distance away, or whole multiples of that same distance. I could link directly to a point, meaning it was one unit away, or get to it through intermediate points, putting it two or more units away. But in this other realm objects could recede in infinitely fine increments, becoming apparently smaller in size, a fact I only belatedly recognized after originally thinking they were actually shrinking. And objects could pass behind each other. Most were opaque, but some were transparent or translucent — and those had been instrumental in letting me at least start to figure out what was going on.

Bit by bit, I was learning to decode this other universe.

When Caitlin, her mom, and Dr. Kuroda returned from the mall, they saw that Caitlin’s father’s car was here, meaning he’d come home surprisingly early on a weekday. Caitlin hurried into the house to see him — to really see him. She came to the open den doorway, Kuroda behind her, while her mom went off to do something else. Blondie’s “Heart of Glass” was playing on his stereo.

The detail Caitlin was perceiving now was overwhelming, and her father’s face was … harder now that she saw it crisply. “Hi, Dad,” she said.

He was sitting at his desk, looking at his LCD monitor. He didn’t meet her eyes. “Hi.”

Still, he’d come home early from work, presumably to see Caitlin, and that made her happy. “Um, whatcha doin’?”

He tilted his head. Caitlin didn’t know what to make of it, but Kuroda seemed to think it was an invitation to come see. He tapped her on the shoulder, urging her to move into the room. She did so, and was pleased that she could make out the characters on the monitor clearly from several feet away, although she still couldn’t read the text.

“I had an idea,” her dad said, “so I came home to check it out.”

“Yes?” said Caitlin.

He didn’t look at Kuroda, but he did address him: “This is more your field than mine, Masayuki,” he said. “I thought I’d look again at the data set we did the Zipf plots on.”

“The secret spook communiqués?” said Caitlin, hoping to get a rise from her dad.

But her father shook his head. “I don’t think that’s what they are anymore.”

He gestured at the monitor.

Kuroda moved in and peered at the screen. “Shannon entropy?”

Caitlin smiled. Sounds like the name of a porn star. “What’s that?”

Kuroda looked at her father, as if giving him first chance to explain, but he said nothing, so Kuroda did: “Claude Shannon was the father of information theory. He came up with a way of gauging not just whether a signal contained information — which is what Zipf plots show — but how complex that information is.”

“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.”