Countable Infinities
Rory’s been reading too much again, ever the aspiring scientist. “Have you ever heard of David Hilbert?”
The Doctor continues making laps around the console, tweaking buttons and levers with abandon. “Hilbert…Hilbert,” he muses, managing to look twice as distracted as before without so much as pausing in his course. “Ah, yes! Mathematican. Lived in Germany. Wore a rather smashing hat, if I recall….”
“Right,” says Rory slowly, thrown a bit off track. “No, no, forget the hat. You’ve heard of Hilbert’s hotel, then?”
“Mmm, veridical paradox, countable infinities-yes, I believe so.”
“You have an infinite hotel, booked up to capacity, but it’s infinite, so there’s always room for one more?”
“Yes!” The Doctor pauses momentarily, points at Rory, then continues in his circumnavigation of the control room.
“Right, so, is that how the TARDIS works? With the rooms disappearing and reappearing, and new ones popping up all over?”
“I don’t know, actually.” He stops in his tracks, looking thoughtful. “I like that, though. Hear that, old girl? You’re the Hotel Infinity!” He grins, clapping the wall affectionately.
“How do you know the TARDIS is a she?” asks Amy, leaning on the doorway.
The Doctor fixes her with a strange look. “How do you know when it’s daytime?” he asks, finally.
*
Amy can’t sleep. She can’t stop thinking about what the Doctor said and wondering what it means. Because on the TARDIS, you can’t tell that it’s daytime, you just know. There’s no sun or morning, just the simple knowledge that today is starting and you have to run or you’ll miss it.
When she’d poked Rory awake to ask him, he had mumbled something about circadian rhythms, rolled over and gone back to sleep.
She gives Rory a peck on the cheek and pads down the hall. In the console room, the Doctor is still awake, legs dangling over the edge of the upper deck. His whole body is inclined to something she can’t identify, as if he’s listening to sounds above what she can hear.
“What’re you doing?”
He jumps, then turns to face her. “Oh, Amelia, it’s you.”
“Are you listening to the TARDIS?”
His smile seems to come from somewhere far away. “Something like that.”
Amy sits down beside him and lets her feet swing. “What’s she sound like?”
“Telepathy’s not like talking, Amy. There’s nothing to hear.”
“Can you see things?”
“Sometimes. It’s more like touching, though. Or tasting.”
“And what does the TARDIS taste like tonight?”
“Butterscotch,” he says after a moment, seemingly oblivious to the sarcasm in her voice. “And she’s saying,” he adds, taking her hand, “Something like this.”
Amy leans forward to touch the tip of her tongue to the banister. “Just tastes like metal to me.”
“Silly! Of course you can’t do it like that.”
“Right, ‘cause you never lick anything. You’ve never found important information that way.”
He bites his lower lip as it begins to curl into a smile. For a moment, they sit quietly, listening. Amy still can’t hear a thing.