Reiterated: the complete short fiction, page 199
“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 communiques?” 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 pom 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.”
Chapter 35
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.
“Caitlin.” Her mom’s voice, very soft. She turned. Her mother was doing something with her head, and . . .
Oh! She was gesturing with it, just as her dad had earlier to Kuroda: she was indicating Caitlin should come with her. Caitlin got up and followed her to the kitchen, on the far side of the intervening dining room, leaving her dad sitting in his favorite chair in the living room.
“Sit down, sweetheart.”
Caitlin did so. She was still just beginning to learn to interpret expressions, but her mother’s seemed . . . agitated, perhaps. “Have I done something wrong?”
“You can’t stare at your father like that.”
“Was I? Sorry. I know it’s not polite—I’ve read that.”
“No, no. It’s not that. It’s—well, you know how he is.”
“How?”
“He doesn’t like to be looked at.”
“Why not?”
“You know. I told you.”
“Told me what?”
“It’s nothing to be ashamed of,” her mom said. “And maybe it’s even why he’s so good at math and things like that.”
Caitlin shook her head a bit. “Yes?”
“You know,” her mom said again. “You know about your father’s . . .” She lowered her voice, and turned her head, perhaps, Caitlin thought, to glance through the door. “. . . condition.”
Caitlin felt her eyes going wide—but, as she’d already discovered, that didn’t really expand her field of view. “Condition?”
“I told you years ago. Back in Austin.” Caitlin racked her brain, trying to recall any such conversation, but—
Oh. “I asked you why Dad didn’t talk much, and you said—at least I thought you said . . . oh, cripes.”
“What?”
“I thought you said he was artistic. I hadn’t known that word then.” She swallowed and found herself looking through the kitchen
doorway, too, making sure they were alone.
“Well, he is artistic. He thinks in pictures, not words.”
Caitlin felt herself go limp in the chair. It made sense, she realized, her heart pounding; it made perfect sense. Her father—the renowned physicist Malcolm Decter, B.Sc., M.Sc., Ph.D.—was autistic.
Shoshana had heated up a couple of sacks of Orville Redenbacher’s in the microwave, and she, the Silverback, Dillon, Maria, and Werner were now seated in the main room of the bungalow, facing the large Apple computer monitor, munching away.
“Okay,” said Shoshana, touching a button on the remote, “here we go.”
She had footage of Dr. Marcuse from earlier projects, including one bit in which he’d done an amazingly protracted yawn. She’d thought about putting that in a circle, with the letters M-G-M above, and the caption “Marcuse Glick Movies” below, but she’d decided not to risk it. Instead, the little video began with white letters over a plain black screen that said, “Ape Makes Representational Art,” followed by the URL of the Marcuse Institute.
Next there was footage of the blank canvas, and then a reverse angle to show Hobo. “This is Hobo,” said Marcuse’s voice over top of the pictures, “a male . . .” There was just the slightest hesitation, Shoshana noticed. She hadn’t been aware of it when they’d recorded the audio; she’d take it out in the final edit. “. . . chimpanzee,” continued Marcuse. “Hobo was born at Georgia State Zoological Park, but was raised in San Diego, California, under the care of primatologist Harl P. Marcuse, who . . .”
The narration continued, and Hobo’s second painting of Shoshana took shape on the canvas. She ate some popcorn and watched the faces of the little audience as much as she watched her video, gauging their reaction. And then came her own big moment: the image divided into a split-screen, with the colored canvas on the left and new footage Dillon had shot on the right: a long pan around her head, and then holding on her in profile, the portrait Hobo had made side-by-side with the genuine article.
“The money shot!” said Dillon. Shoshana threw a little popcorn at him, which he batted out of the air with his hands.
When the video was over, Dillon and Maria clapped politely, and Werner nodded his head in satisfaction. But it didn’t matter what they thought, Shoshana knew. Only the Silverback’s opinion counted. “Dr. Marcuse?” she said, a bit timidly.
He shifted in his chair. “Good work,” he said. “Let’s get it online—and then see what the response is from the Georgia Zoo.”
Chapter 36
And here was the biggest leap of all so far, here was the discovery, the realization, the breakthrough, that was the hardest to make but also, I suspected, the most important.
The other entity looked at many, many things, and I had gathered that they were mostly near to it, but there was this rectangle, this frame, this window that it often looked at that was—
Oh, such a leap! Such a strange concept!
It was a display of some sort, a way of representing things that weren’t actually there. And I could see what was on the display, but only when the entity looked at it.
And, just now, the display was showing something . . . strange. It took me time to work out the recursiveness of it all: the entity was looking at the display, and the display was showing moving images of a being unlike any I’d yet seen, with longer upper projections and shorter lower ones and a lump that was differently shaped. And this abnormal being was making . . .
Yes, yes, yes! The abnormal being was making marks on yet another flat surface: shapes, splashes of color. I watched, baffled, perplexed, and—
And suddenly the display was divided into two parts. On one side, I saw the colored shapes that the strange entity had made, and on the other there was an entity of the type I was more used to seeing. That entity was rotating, and—and—and—
And then it stopped rotating, holding its position, and—
The shapes on one side, the entity on the other: there was a . . . a correspondence between them. The shapes were a—yes, yes! They were a simplified version of the entity on the right. It was a stunning revelation: this was a representation of that!
The simplified representation was two-dimensional, similar to the way I was used to conceptualizing my own reality. I watched, and concentrated, and—
Suddenly it all made sense!
The lump at the top of each entity did have structure, did have components. As I saw them rendered in basic form, I could now discern the parts on the actual entity that had been rendered. The strange being that had made this rendering had exaggerated certain details so that I now saw not only their significance but realized what things differed from lump to lump: the color of the . . . eye, I’d call it. The color of the hair. The color of the rest of the lump. The shape of the nose. The shape of the mouth. The relative size of the ear.
The individual that had been rendered had an odd projection off the back of its lump, possibly part of its hair; as I recalled other lumps I’d seen, I realized that such projections were rare but not unheard of.
It was wonderful! I was clearly discerning the parts of the . . . no, not lump; a lump was a generic mass, and this was a specific, very special form, so it deserved its own coinage: head.
I was still far from fully understanding these creatures, but I was at last making progress!
Caitlin and Dr. Kuroda headed down to their basement workspace. He’d described it in words to her before, and she now saw—saw!—that he’d done a pretty good job. It was indeed unfinished, had a concrete floor (which she’d already known about from walking across it), and it did contain bookcases and an old TV. But she’d had no idea that the bookcases were finished in a pattern of lighter and darker brown swirling together; she guessed that was wood grain, something she’d felt on other pieces of furniture. And the TV was larger than she’d imagined, and had a black housing.
Still, there were so many other things that Kuroda hadn’t mentioned: thousands of details about the walls, the bare lighting fixture, the metal box that had the light switch on it, the curtains on the little window, a cylindrical contraption that she belatedly realized was the water heater, and on and on. How one decided quickly, as he had, which details were important and which were not worth mentioning was still a mystery to her; it all seemed relevant.
The swivel chairs turned out to have dark red upholstery, which was another thing Kuroda had failed to mention. She sat down in one and Kuroda took the other. He was wearing a colorful loose-fitting shirt with an abstract pattern on it.
“You get along well with my dad,” she said to him, once he’d settled in. The two men had actually bantered a bit over dinner; Kuroda seemed to have an instinct for knowing when her dad was trying to be funny and had laughed at things in a way that encouraged him to say more.
