The Doctor has seen a lot.
Really, he has. A body of thirty-seven years old plays host to a brain which has seen out a full thousand, and a unique biological formula which, before it was systematically exterminated, had survived, and would survive, a million. In his top pocket, there is a sonic screwdriver, engraved with High Gallifreyan a billion years old, built on technology passed down through races born with time itself.
And yet, in all his years, he has never seen this man before.
Taking that into account, it's quite something that when he speaks, it's articulate and confident, if a little questioning. "The Doctor, hm? Doctor … who, exactly?"
"Well, exactly," the other Doctor (?) chuckles. "Doctor who? But no. Just the Doctor." He waves a hand. "People have called me other things, but I call myself the Doctor. I'm sorry, Doctor Smith, I must seem so egotistic."
"No, no," the Doctor says slowly, gazing at him for a few seconds. Then he blinks, and his usual smile jumps back into place. "So, Doctor, what is it you do around here?"
"Oh," the other waves a hand, "I'm a theorist, you could say. Just a dabbler in physics. It's fun juggling so many variables," he says. "Alpha, beta, gamma, qoppa …"
Qoppa. Now that one has a meaning. "Exotic energy?" the Doctor prompts.
The other smiles distantly. "Yes. Yes, you might say that. Quite exotic indeed." Some sense of immediacy grasps him and he comes back to earth. "It's brilliant stuff, Doctor Smith. Look," he says, reaching into his shirt. The Doctor avoids tensing, but the other one simply pulls out a piece of vaguely aged paper, tied with string, obviously folded and refolded many times.
"This is the kind of calibre we're working at," he explains proudly. "Have a look."
The Doctor unties the string and unfolds the paper, which turns out to be a document dated three years ago, local time. It seems to be a mimeograph of a piece of paper torn from a binder, itself stamped [classified], and it details an extremely complicated and incomplete piece of theory in very small font.
Which, of course, is child's play to the Doctor.
Because he recognises the structure of the problem. A few variables and paragraphs have been reworded and changed, but the overarching problem remains the same, and he's had occasion to solve it once before, many years ago. Something troubles him … but despite that, this should be fun.
He pulls a pencil from inside his coat. The other one looks slightly alarmed, but at the Doctor's query: "Do you mind?" the other Doctor simply nods mutely.
So the Doctor begins to annotate, reword, retheorise, tie up and solve, assuming a few of these variables and those figures, in the slightly messy printing he uses for these kinds of things. One minute and eighteen seconds later, the problem is solved, and he turns it around and hands it back to the other, who now appears more than slightly alarmed.
"You know," he says after a moment, and seems to hesitate, "you know, that's a problem that your standard Nobel laureate in physics typically takes several hours to solve." He thumbs over his shoulder. "Professor Ratzenberger would know."
The Doctor shrugs. "Oh well, I must have got lucky."
"Lucky," the other murmurs, staring at him. "Yes. Yes, perhaps. Anyway, Doctor Smith," he says, and interrupts himself to call, "I'm going to need someone's help, sorry," – "anyway, Doctor Smith, it has been an absolute pleasure. It's really been marvellous," he says hurriedly, pulling a coat around his shoulders that wasn't there before. "But I have to go."
"So soon?" the Doctor says, a little taken aback.
"Mm," the other mutters out of his thick black bundle, "so soon." Rina walks up to assist him, and the two of them manage to wobble out of the bar, but not before the departing man throws a wondering gaze back at the one at the bar.
The one at the bar has already turned away, troubled.
The problem with that problem, as it were, was that the Doctor recognised it. He's not too familiar with the exotic energy mathematics of twenty-third-century Earth, but he is familiar with the ancient texts of the Academy, having had occasion to read them and reread them many times over.
That problem is very uniquely Gallifreyan. It certainly backs up this Doctor's claim to Doctorhood, but it raises two much more troubling problems in turn.
Why will the Doctor decide to task humans with solving a problem whose answer they cannot possibly be prepared for?
And, as a future incarnation, why will he be so surprised when he himself solves it?
