Which Alice?

The Red King's Theory
After watching them for a while, Alice turned to the Red King, who
was by now thoroughly awake.
"You must be Alice!" said the King.
"Why, yes," Alice replied, "only how did you know?"
"Oh," replied the King, "I just had the strangest dream! I
dreamed that I was walking through the woods with Tweedledee
and Tweedledum, and we came across a girl who looked exactly like
you, curled up fast asleep against a tree. 'Who is that?' I asked.
'Why, that is Alice,' said Tweedledee, 'and do you know what she is
dreaming about?' I replied, 'How could anyone know what she is
dreaming about?' 'Why, she is dreaming about you! he replied.
Then both brothers tried to convince me that I had no independent
existence of my own but that I was only an idea in your mind and
that if you were to wake up, I'd go out—bang!—just like a candle!
"So now," continued the King, "I'm certainly glad to see you
awake and to see that I have not gone out—bang!—just like a
candle!"
"How utterly extraordinary!" cried Alice. "Why, the very same
thing happened in reverse the first time I ever saw you: You were
asleep, I was with Tweedledee and Tweedledum, and they told me
that you were dreaming about me and that if you were to awaken, I
would no longer exist but go out—bang!—like a candle!"
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