How is it possible that the Doctor remembers
every single iteration he has had in the castle?
I'm talking about this line:
The Doctor: THAT’S when I remember! Always then. Always...then. Always EXACTLY then. I can’t keep doing this, Clara! I can’t! Why is it always me? Why is it never anybody else’s turn?! Why can’t I just lose?!
[He comes face to face with the blackboard, which has the word NO! written on it; Clara stands with her back to the Doctor]
The Doctor: But I can remember, Clara. You don’t understand. I can remember it all. Every time!
(He's talking about when he sees the word "BIRD" written in the sand).
The Doctor has been dying and being reborn for over 2 billion years. Or maybe not "reborn", but a new copy arrives to do the whole thing all over again. I don't think it makes him 2 billion years old now (the last iteration, the one who didn't die, only aged like two days after the events of "Face The Raven"), but I'm confused about the "remembering" part.
Does The Doctor actually remember
every single time he has done it? Or does he just figure it out every time?
Answer
If the Doctor remembers, that raises the questions of what he remembers, and how.
There's no question of when he remembers. We get a lovely little camera zoom effect to mark that exact moment. The camera zoom is followed by a bit of the Doctor's internal dialogue which confirms that he remembers, well, something.
My first impression of the internal dialogue was that the Doctor was remembering his earlier adventures. There are, of course, countless times throughout his various incarnations that he simply could not afford to surrender and take the easy way out. It would make sense that he remembers those times, and we could interpret his interior dialogue in that manner. However, that interpretation does not survive a second viewing of the episode.
Earlier in the episode, we are reminded that the Doctor possesses a specific ability:
He is psychic.
His telepathy is so strong and so well-developed that he is able to talk a wooden door into unlocking, just by thinking nice thoughts. The Doctor only rarely uses this ability, but we have to acknowledge that he can read minds. This doesn't seem to be an intelligent wooden door, so we should acknowledge that he can read psychic impressions from nearby inanimate objects -- an ability that's apparently triggered by thinking some kind of compatible and relevant thought.
If we accept that as an explanation of how, then we can make a very good guess as to the what.
He's reading the psychic impressions that earlier teleporter instantiations of himself left on the tougher-than-diamond wall. The camera zoom effect marks the moment when he's, well, reading his own mind.
Each iteration lasts at least a day. For all we know, it might take the Doctor a week to reach Room 12. I doubt that the Doctor remembers all of those chunks of time. In every iteration, he has a few scant seconds that he uses to punch the wall. During those few seconds, he is desperate and facing certain death -- an emotional moment that we can easily believe would leave a psychic impression.
Each new copy of himself remembers nothing about earlier iterations until after he reaches Room 12. On the one hand, yes, he just figures it out every time. On the other hand, it's basically the same realization every time -- a compatible and relevant thought. At that point, his mind is flooded with having made that realization over and over again, and with the experience of punching the wall over and over again.
After billions of years of teleporter iterations, those scant seconds add up to mere millions of years.
This would explain why he acts like he remembers nothing about the castle before the camera zoom. He doesn't. Even after the camera zoom, he still doesn't need to remember every thing, but he seems to remember the sum of those scant seconds -- all of it, from every time.
At least, that's the interpretation that survives my second viewing of the episode.
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