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“It’s official,” she says, not looking up. “They’re announcing the new Product Management today.” She keeps refreshing and refreshing and refreshing; I think her battery is going to die before noon.

I alternate pages of The Guide to Central Park Birds (purchased at the JFK bookstore) with furtive glances through Mat’s binoculars.

Here’s what I see:

As the pitch of the city rises and traffic starts to pick up on Fifth Avenue, a lone figure comes trotting up the opposite sidewalk. It’s a man, middle-aged, with a fuzz of brown hair that’s blowing in the wind. I fiddle with the focus on the binoculars. He has a round nose and fleshy cheeks that are glowing pink in the cold. He’s wearing dark pants and a tweedy jacket that fit him perfectly; they’ve been tailored to the swell of his belly and the slope of his shoulders. He bounces a little as he walks.

My spider-sense is operational, because sure enough, Round Nose stops at the Unbroken Spine’s front door, wiggles a key in the lock, and steps gingerly inside. Twin lamps in small sconces on either side of the door come to life.

I tap Kat’s shoulder and point to the glowing lamps. Neel narrows his eyes. Penumbra’s train will pull into Penn Station at 12:01 p.m. and until then, we watch and we wait.

* * *

Following Round Nose, a thin but steady trickle of incredibly normal-looking New Yorkers passes through the dark doorway. There’s a girl in a white blouse and a black pencil skirt; a middle-aged man in a drab green sweater; a guy with a shaved head who looks like he would fit in at Anatomix. Can these all be members of the Unbroken Spine? It doesn’t feel right.

Neel whispers, “Maybe they target a different demographic here. Younger. Sneakier.”

There are many more New Yorkers who don’t pass through the dark doorway, of course. The sidewalks on both sides of Fifth Avenue are full of them, a flux of humanity, tall and short, young and old, cool and uncool. Clots of pedestrians drift past us and block my view. Kat is agog.

“It’s so small but there are so many people,” she says, watching the human flow. “They’re … it’s like fish. Or birds or ants, I don’t know. Some superorganism.”

Neel cuts in: “Where did you grow up?”

“Palo Alto,” she says. From there to Stanford to Google: for a girl obsessed with the outer limits of human potential, Kat has stayed pretty close to home.

Neel nods knowingly. “The suburban mind cannot comprehend the emergent complexity of a New York sidewalk.”

“I don’t know about that,” Kat says, narrowing her eyes. “I’m pretty good with complexity.”

“See, I know what you’re thinking,” Neel says, shaking his head. “You’re thinking it’s just an agent-based simulation, and everybody out here follows a pretty simple set of rules”—Kat is nodding—“and if you can figure out those rules, you can model it. You can simulate the street, then the neighborhood, then the whole city. Right?”

“Exactly. I mean, sure, I don’t know what the rules are yet, but I could experiment and figure them out, and then it would be trivial—”

“Wrong,” Neel says, honking like a game-show buzzer. “You can’t do it. Even if you know the rules — and by the way, there are no rules — but even if there were, you can’t model it. You know why?”

My best friend and my girlfriend are sparring over simulations. I can only sit back and listen.

Kat frowns. “Why?”

“You don’t have enough memory.”

“Oh, come on—”

“Nope. You could never hold it all in memory. No computer’s big enough. Not even your what’s-it-called—”

“The Big Box.”

“That’s the one. It’s not big enough. This box”—Neel stretches out his hands, encompasses the sidewalk, the park, the streets beyond—“is bigger.”

The snaking crowd surges forward.

* * *

Neel gets bored and walks down the street to the Met, where he intends to snap reference photos of marble breasts from antiquity. Kat composes short urgent messages to Googlers with her thumbs, chasing down rumors of the new PM.

At 11:03 a.m., a stooped figure in a long coat totters up the street. My spider-sense tingles again; I believe I can now detect a certain strain of weirdness with lab-grade precision. The stooped totterer has a face like an old barn owl, with a furry black Cossack’s hat pulled down over wiry eyebrows that stick out into space. Sure enough: he ducks into the dark doorway.

At 12:17 p.m., it’s finally beginning to rain. We’re shielded beneath tall trees, but Fifth Avenue is quickly darkening.

At 12:29 p.m., a taxi stops in front of the Unbroken Spine, and out steps a tall man in a peacoat, pulling it close around his neck as he leans down to pay the driver. It’s Penumbra, and it’s surreal to see him here, framed by dark trees and pale stone. I’ve never even imagined him anywhere other than the inside of his bookstore. They’re a package deal; you can’t have one without the other. But here he is, standing in the middle of the street in Manhattan, fiddling with his wallet.

I hop up and sprint across Fifth Avenue, dodging slow-moving cars. The taxi pulls away like a yellow curtain, and, ta-da! There I am. First Penumbra’s face is blank, then his eyes narrow, then he smiles, and then he tips his head back and barks a loud laugh. He keeps laughing, so then I start laughing, too. We stand there for a moment, just laughing at each other. I’m also panting a bit.

“My boy!” Penumbra says. “You might just be the strangest clerk this fellowship has seen in five hundred years. Come, come.” He ushers me up onto the sidewalk, still laughing. “What are you doing here?”

“I came to stop you,” I say. It sounds strangely serious. “You don’t have to—” I’m huffing and puffing. “You don’t have to go in there. You don’t have to get your book burned. Or whatever.”

“Who told you about burning?” Penumbra says quietly, raising an eyebrow.

“Well,” I say, “Tyndall heard it from Imbert.” Pause. “Who heard it from, uh, Monsef.”

“They are wrong,” Penumbra says sharply. “I have not come here to talk of punishment.” He spits it out: punishment, as if it’s something far beneath him. “No. I have come to make my case.”

“Your case?”

“Computers, my boy,” he says. “They hold the key for us. I have suspected it for some time, but never had proof that they could be a boon to our work. You have provided it! If computers can help you solve the Founder’s Puzzle, they can do much more for this fellowship.” He makes a thin fist and shakes it: “I have come prepared to tell the First Reader that we must make use of them. We must!”

Penumbra’s voice has the timbre of an entrepreneur pitching his startup.

“You mean Corvina,” I say. “The First Reader is Corvina.”

Penumbra nods. “You cannot follow me here”—he waves his hand back toward the dark doorway—“but I would speak to you after I am finished. We will have to consider what equipment to purchase … which companies to work with. I will need your help, my boy.” He lifts his gaze to look over my shoulder. “And you are not alone, are you?”

I look back across Fifth Avenue, where Kat and Neel are standing, watching us and waiting. Kat waves.

“She works at Google,” I say. “She helped.”

“Good,” Penumbra says, nodding. “That is very good. But tell me: How did you find this place?”

I grin when I tell him: “Computers.”

He shakes his head. Then he tucks a hand into his peacoat and pulls out a skinny black Kindle, still activated, showing sharp words against a pale background.