I hit the STOP button.
"Tom, something's been bothering me since you mentioned it a few days ago."
"And what is troubling you, my son?"
"Well, you said that you found out about Conrad's trip to the Middle Ages when you went to the Battle of Chmielnick during the Mongol invasion. You said that the battle you saw had a different outcome than what's written up in the history books. And you said that the investigation teams you sent out came back duplicated. Why weren't you duplicated as well?"
"Well, I was! It was strange, meeting myself. Not because running into yourself is all that odd. With time travel, we do that all the time. But protocol is that the senior self always talks first, and the two of us just stood there, each waiting for the other to speak first, since neither of us remembered being there before. It was quite a while before I asked him why he didn't say something. Eventually, we figured out what happened. Being a sensible person, both of me, I decided to timeshare the management of the place with my other half. We flipped a coin and I got it for this century and he gets it for the next."
"Good Lord!"
"Well, what else could I do? Fight myself? I suppose it would have been more complicated had I been married, but after a bit of youthful insanity, like Conrad, I'm not the marrying kind."
He hit the START button.