Clara followed as the Doctor stalked the wreckage of the building. For the most part, the TARDIS's telepathic field was doing its job and no one was giving them any funny looks as they clambered over charred walls and ducked under caution tape, but Clara could swear she'd periodically see people staring at them out of the corner of her eye only for them to be gone when she turned to look at them. Sure it wasn't her imagination, she decided to interrupt the Doctor's grumbling search.
"So... I'm sure it's just my imagination, but I keep seeing people... I don't know, noticing us? And then when I look again they're gone. What's up with that?" she asked, only half-expecting a reply from him.
"You're right, it's your imagination. But they really are there. Well, only they aren't." His explanation was only leaving her more confused, which must have been apparent on her face, so with a great sigh, he stopped, dropping the piece of rubble he'd surely not been about to lick, and gave her his full attention.
"You remember when I said this was the wrong Lagos?" he asked, pulling a straw from his pocket, "Well, imagine this straw is your Earth. Your 2016, with your Lagos and your Nigeria. Now this," he pulled another straw from his pocket, "is where we are now. A parallel universe. Now, see the bendy part in this straw? At some point, the history of this world went all bendy. Right now, we're bent off to one side, but for some reason our new friend back there, Isaiah, can still see the other bendy bit. So can we, to a certain extent, because we're not even from this straw. We're so far not from this straw that the bendy bit is actually confusing the TARDIS computers to the point where she can't find the hole she came in through."
Clara pondered this for a moment. "Okay. I think I get it. I'm not asking where you're pulling all these straws from, but we jumped from one to the other, and you're trying to figure out where the straw went all bendy and straighten it, right? That way we can get back to the right straw?" When he nodded, she pressed him, "So what are you looking for?"
"Organic matter," he said, pulling the box out of his pocket again, "so I can use this."
"You're gonna make me ask what's in the box, aren't you? It's not a head, is it? Awful small head if it is."
The Doctor knelt, apparently finding what he was looking for. He shoved his arm into a hole near the bottom of a burnt-out wall and pulled it back holding a half-crushed, lightly singed, and certainly very dead rat. Clara cleared her throat uncomfortably as the Doctor knelt, opening the box and placing the rat on the ground next to it. From the box he pulled a large silver scalpel that seemed to have some arcane, indecipherable writing on it.
"It's called a tracking knife. I nicked it from some particularly nasty characters living in a pocket of looped time. They'd use it to dissect living things, garner secrets from their timelines. It harvests biodata. I need an organic connection to this universe so I can track its timeline back to see where the divergence happened. We're looking for a still point in time, something that can be easily manipulated."
"And once we find that, we can go back and fix it? The knife is going to tell you all that by cutting up a dead rat?" Clara was still clearly uncomfortable with the dissection, but understood the reasoning behind it and looked on in interest as little lines of blue light began to appear in the air over the rat's now bisected body.
"I don't particularly feel like walking up to one of these nice people here and asking for a volunteer for a live temporal vivisection. It would be more effective, but it's more Missy's style than mine." The Doctor plucked at several of the strands, and they vibrated curiously. He manipulated the knife with suspicious skill, and several more intersecting strands appeared. "The knife should be able to get enough information for me to compare to the TARDIS databanks. I left the computer collating information from local sources, so we should be able to more accurately track down the bendy bits."
The strands began to coalesce into a single line, small symbols appearing at various points along it. The Doctor made a further cut and a fork appeared in them. "Gotcha," he said, standing and placing the knife gingerly back in the small box, "June 1943. Western Hemisphere, likely East Coast of the United States."
"Well, what are we waiting for then?" Clara asked, turning on her heel. "Let's go save a universe!"