“No, no. Coins! Do you have coins?”

“In a jar on my dresser.” She was saving to go see Lee Amodeo with Bashira when she came to Centre in the Square.

“Great, great. Do you mind if I go get it?”

“I can do it. It’s my house.”

“No, you take the time to look at the Web, see if you can make out any more detail in the background. I’ll be right back.”

Kuroda could never sneak up on anyone. She heard the sounds of his return long before he actually arrived. She then heard a great jangling as he dumped the coins on their worktable, and more noise as he shuffled them around — perhaps sorting them. “All right. Here’s a bunch of coins. Can you arrange them in the pattern you’re seeing? Put one down for each light spot, and leave a coin-sized space for each dark spot.”

Caitlin shooed Schrodinger out of her lap, and swung her chair to face the table. “I told you. They keep changing.”

“Yes, yes, but…” He made a noisy sigh. “I wish there were some way to photograph it, or at least to slow down your perception, and—” His voice brightened. “And there is! Of course there is!”

She heard him moving about, then soft key clicks. “What are you doing?” she asked.

“I’m halting your reception of the datastream from Jagster, and just passing on the last iteration of it over and over again, so it’ll keep coming down the pike without changing, sort of like—”

“A freeze-frame!” she said as the image ceased to move. She was delighted to be able to apply another concept she’d only ever read about before.

“Exactly. Now, can you make a pattern with the coins that matches what you’re seeing in a portion of the background?”

“A very small portion,” she said. And she started moving the coins around; he’d given her a bunch of dimes. After a moment, she pushed one off to a corner of the desk. “American,” she said; all those years of reading Braille made it easy to tell Queen Elizabeth from FDR.

She built up a grid of dimes and dime-sized empty spaces, counting the coins automatically as she deployed them. “Done,” she announced. “Eight dollars and ninety cents.”

“Completely random,” Kuroda said, sounding disappointed.

“No, it’s not. Not quite. See this group of five dimes here?” She had no trouble keeping track of the pattern she’d made, and touched the appropriate coins. “It’s the same as this group here, except turned ninety degrees to the right.”

“So it is,” he said, excitedly. “It looks like the letter L.”

“And this one’s the same, too,” she said, “turned upside down.”

“Excellent!”

“But what does it mean?” she asked.

“I’m not a hundred-percent sure,” he said. “Not yet. Here, focus your attention again on the same spot in your vision. I’m going to update the data going to your implant, just once … and done.”

“Okay. It’s completely different.”

“Can you make it for me with the coins?”

“I’m not even sure I’m looking at the same spot anymore,” she said. “But here goes.” She rearranged the dimes, and, just to underscore that not only the pattern but also the number of light and dark squares had changed, she added, “Six dollars and twenty cents.” She paused. “Ah! Three sets of that five-coin pattern this time.”

“And in different places,” he said.

“But what does it mean?”

“Well,” said Kuroda, “this may sound crazy, but I think they’re cellular automata.”

“Who in the what now?”

“Hey, I thought you were the daughter of a physicist,” he said, but his tone was one of gentle teasing.

She smiled. “Sue me. And besides, if they’re cellular, I’d need to be a biologist’s daughter, no?”

“No, no — they’re not biological cells; they’re cells in the computer-science sense of the word: a cell is the basic unit of storage in computer memory, holding a single unit of information.”

“Ah.”

“And an automaton is something that behaves or responds in a predictable, mechanical way. So cellular automata are patterns of information units that respond in a specific way to changes in their surroundings. For example, take a grid of black and white squares — each square is a cell, okay?”

“Yes.”

“And on a chessboard that goes on forever, each square has eight neighbors, right?”

“Right.”

“Well, suppose you say to each square something like, okay, if you’re already black and three or more of your neighbors are white, then turn white yourself. An instruction like that is called a rule. And if you keep applying the rule over and over again, strange things happen. I mean, yes, if you just focus on one individual square, all you’d see is it flipping back and forth between black and white. But if you look at the overall grid, patterns of squares can seem to move across it — cross shapes, maybe, or hollow squares, or L shapes like we have here, or clusters of cells that change shape in set stages and, after a fixed number of steps, return to their original shape, but have moved somewhere else in the process. It’s almost as though the shapes are alive.”

She heard the chair groan as he shifted in it.

“I remember when I first encountered cellular automata in Conway’s Game of Life as an undergrad,” he said. “What’s fascinating about all this is that they’re representations of data that are interpreted as being special by an observer. I mean, those L-shaped things — they’re called ‘spaceships,’ by the way, these patterns that retain their cohesion and fly across the grid — well, spaceships don’t really exist; nothing is actually moving and the spaceship you see on the right side of the grid is completely different in composition from the one you originally saw on the left side. And yet we think of it as the same one.”

“But what are they for?”

“Besides making undergrads go ‘ooooh,’ you mean?”

“Yeah.”

“Well, in nature—”

“These occur in nature?”

“Yes, in lots of places. For instance, there’s a kind of snail that makes the pattern on its shell in direct response to a cellular-automata rule.”

“Really?”

“Yes. It has a row of spigots that spit out pigment, or not, based on what the neighboring spigots on either side are doing.”

“Cool!”

“Yes, it is. But what’s really cool is that there are cellular automata in brains.”

“Really?” she said again.

“Well, they’re in lots of kinds of cells, actually. But they’ve been studied particularly in neural tissue. The cytoskeletons of cells — their internal scaffolding — is made up of long strings called microtubules, and each component of a microtubule, a little piece of protein called a tubulin dimer, can be in one of two states. And those states go through permutations as though they were cellular automata.”

“Why would they do that?”

“No one knows. Some people, though, including — hey, maybe your father knows him? Roger Penrose? He’s a famous physicist, too, and he and his associate, a guy named Hameroff, think that those cellular automata are the actual cause of consciousness, of self-awareness.”

“Sweet! But why?”

“Well, Hameroff is an anesthesiologist, and he’s shown that when people are put under for surgery their tubulin dimers fall into a neutral state — instead of some being black, say, and some being white, they all sort of become gray. When they do that, consciousness goes off; when they start behaving as cellular automata again, consciousness comes back on.”

She made a mental note to Google this later. “But if the snail has spigots, and the brain has these whatchamacallits—”

“Tubulin dimers,” said Kuroda.

“Okay, well if these tubulin dimers are the actual things that are flipping in the brain, what’s flipping in the background of webspace?”

She imagined him shrugging; it would have gone naturally with his tone of voice. “Bits, I guess. You know: binary digits. By definition, they’re either on or off, or one or zero, or black or white, or however you want to visualize them. And maybe you’re visualizing them as squares of two different colors, just at the limit of your mental resolution.”