A chat with myself, or Gmail Autochat

They need to fix the thing where you can chat with yourself. I saw a green dot on the message I'd just written to my brother Alex that said "Reply by chat to", and thought, "cool, I'll chat him for kicks". The absence of a name didn't clue me in.

And then I noticed that whatever I said was echoed back to myself with an empty name. Huh, how strange, I wonder if Alex will see it twice. Then I noticed that he (my correspondent, who was Alex, of course?) was typing. Also strangely, he seemed to stop typing repeatedly and never actually send a message. He must be typing me a real epistle.

And how is this that he's typing to me when I open up the quick contacts and it says he's offline?

Oh wait.

Note: presumably this odd use case is possible for me because send my Gmail messages with my custom platte.name address in the From.