Authors: Robert J Sawyer
They decided to put a lens with an identical prescription in the right side, even though Caitlin was still blind in that eye. Lenses for myopia tended to shrink the appearance of eyes, and this way they’d both look the same, the saleswoman said.
Her mom was usually a tough up-sell, but she said yes, yes, yes to everything the clerk offered: antiglare, antiscratch, anti-UV, the whole nine yards; Caitlin suspected if the clerk had rattled off an extra hundred bucks for antediluvian, she’d have coughed up for that, too.
Caitlin knew LensCrafters’ slogan from the ubiquitous commercials: glasses in about an hour. She thought it would be the longest hour of her life. She felt her Braille watch as she, Kuroda, and her mom walked through the mall to the food court—for the first time, without the use of her white cane. Everything was still blurry, and that was giving her a headache. Still, in a way, it was relaxing. To see the people coming toward her! To not bump into things! She hadn’t realized it until now, but she’d always used to walk with her shoulders tensed, preparing for an impact. But now—well, now she had a bounce in her step, something else she’d never thought could happen literally.
Still, all the visual input was disorienting, and she found herself taking a look, then closing her eyes for five or six paces, then looking again. When they got to the food court, Kuroda went to the sushi place—which, Caitlin suspected, would disappoint him—and she and her mom went to Subway. Caitlin was amazed to see how colorful the sandwich fillings were, and, somehow, seeing the food made it taste even better.
The three of them sat together at a little red table with chairs attached to it. Dr. Kuroda used chopsticks to dip a piece of sushi in sauce.
Caitlin couldn’t resist. “Do they tell you in Japan that it’s raw fish?”
Kuroda smiled. “Do they tell you what’s in the special sauce on a Big Mac?”
She laughed. At last the hour was up and they headed back to LensCrafters. Caitlin took a seat on the stool, and the nice woman placed the glasses on her face—
And Caitlin didn’t wait. She got up, and turned around, and looked—really looked—at her mother.
“Wow,” Caitlin said. She paused, trying to come up with a better word, but couldn’t. Her mother’s face was so detailed, so alive! “Wow!”
“Here, let me adjust how they sit...” said the clerk.
Caitlin sat back down and swiveled to face her.
“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.”
“Well,” she said, “maybe the spies are just grunting out monosyllabic orders like, ‘drop bomb’ or ‘kill bad guy.’”
Kuroda lifted his shoulders. “Maybe.”
LiveJournal: 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...
* * * *
Caitlin couldn’t stop looking at her father, thinking that it might prompt him to look back at her. But he never did. He just looked away, or, as he was doing now, he stared out the living-room window at the gray sky and the trees, which were now losing their leaves.
She had hoped that when she finally saw him, his face would be ... animated, that was the word; that he would smile frequently, that his eyebrows would move up and down as he spoke, that she might even see that he was affectionate toward her mother, touching her forearm at odd moments, maybe, or even stroking her hair.