The Adventure of the Determined Detective
Sherlock had rejected the idea of simply tackling him, as he might have done other objects of investigation. Oh, certainly he could throw himself at the fellow and bring him down, and plant drugs or some other sort of evidence on him, then use his connections in the police, or even Mycroft, to have him detained while he located the blue 'telephone box', and –
Wait. This was probably the sort of theorising that John kept on complaining about. John might possibly have a point. This wasn't the sort of thing that would necessarily create an atmosphere of goodwill, unless he could plausibly claim innocence later and maybe exploit the Doctor's gratitude for helping get him out of police custody, and then . . .
The whole thing was so damned irritating. Fascinating, but irritating.
Pictures. He had plenty of pictures of the 'Doctor', culled from online sources, library microfiches, newspaper articles, and even a few hand-drawn works or woodcuts. The same faces kept on coming up, again and again. A slender blond man at Cranleigh Manor in the twenties, in a woodcut from the seventeenth century, in a security photograph at Heathrow Airport. A gloomy fellow in a leather jacket in the publicity photos of the Titanic, and then in a CCTV snapshot of a London laundry a couple of years ago. A white-haired man standing outside an old phone box at Totters' Lane Junk Yard.
If time travel was impossible, then it was all a fraud. A grand, glorious fraud, carefully inserted into the documentation over centuries – or could it have been drawn up as a snare for him? Designed and put together to attract his attention. Possibly.
But if time travel was possible . . .
Well. Wouldn't that be interesting.
Mycroft has tried to warn him off. More than once. This has worked about as well as Mycroft's attempts normally do. Mycroft then tried to borehim off by pretending it wasn't important. That didn't work either.
Mycroft has interesting connections to something called Torchwood which Sherlock suspects is linked to the 'Doctor'. However, stepping over that line would be a declaration of war. Sherlock isn't quite prepared for that yet.
Perhaps he could send John to one of the known sites where the 'Doctor' has shown up in the past, and see if it roused any attention. The 'Doctor' has a known habit of responding to the sincere and serious-minded, such as teenagers, idiots, and worthy virtuous individuals with no sense of self-preservation. But then the 'Doctor' might wander off with John, and that wouldn't do at all.
(A link to the old stories of elves and changelings? Something to investigate.)
It'd be almost too easy to have time travel be real, and to have the 'Doctor' be some sort of secret organization involved in it. That'd be far too simple an explanation. Sherlock wants something more interesting. More fascinating. Something that he can get his teeth into.
But first he wants the 'Doctor'. He has so many questions to ask him.
The need for answers is its own disease, and one that John has no idea about; John has no notion of its scope, of how it fevers the blood and the brain, or how far it can push the sufferer. John would no doubt think that it could be cured. It can't be. It can't even be immunised against. Each new variety of the disease bursts on Sherlock in a new assault, and frets him waking and sleeping. This particular one, this 'Doctor', is chronic, though every new scrap of information makes it acute.
He must know.
He wonders if the 'Doctor' himself would understand that: would understand how far the need to know, the urge to investigate, can drive a man. Is he curious? Is he fascinated by the little things? Is he driven to probe into the larger ones?
There's a photo of the 'Doctor' from the Eighties: a cheery fellow with a hat and long scarf, with a wide smile and with utterly insane eyes that stare out of the photograph as if he's not convinced of its reality.
That's fair enough. Sherlock often has issues with reality himself. He hopes the 'Doctor' will understand how far he's prepared to go to get his answers.
And if he doesn't?
Well, one can always apologise afterwards.