Suppose you're walking to a common destination with someone, and you enter your building, and you know that the two of you generally part ways at this point, because you have different rooms to go to. So, naturally, you wind down the conversation, wrap up the topic, and say your see-you-laters (because if you didn't do this, then you'd have to stop at the parting points and hurriedly bring the conversation to a close). The two of you part ways, and all of a sudden, the other person decides to turn around and follow you, and catches up with you.

What do you do now?

You can't just stand there with this person you were speaking with three seconds ago standing silently next to you. And you wound down the conversation, so starting it up again would be clumsy and unnecessary: the topic had been concluded. Where do we go with this?

Perhaps what you could talk about is what compelled the other person to about-face and follow down your path. Were there some intricate graph-theory algorithms that passed through this person's head and led them to calculate a better route to reach their destination? Or perhaps their elevator simply wasn't working? Regardless, you're in tough luck, because you just got yourself into another ASS (Awkward Social Situation).