The secret life of toddlers

In the morning I eavesdrop on the small boys via the baby monitor. They are two and four years old, so their conversations are mostly incoherent or downright silly. Not this morning, though. Today's dialogue is profound and slightly disturbing:

"I'm not Harry Potter; you're Harry Potter!"
"No, I'm not Harry Potter; you're Harry Potter!"
"You're Harry Potter; I'm Harry Houdini."
"You're not Harry Houdini; I'm Harry Houdini!"

I will be sorting this out all day. Who would I rather be? A magician or an escape artist? And how do my children even know about these people? Why are they arguing about it? Help me out here.