In The Asylum of the Daleks, The Doctor says that he is immune to nanogenes, but in The Doctor Dances, the burn on his hand is healed by nanogenes.
How is this possible?
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Well, first, it’s only speculated that he’s immune:
RORY: Just give me your arm. Let me put this on you. Just give me your arm!
AMY: Don’t touch me! (She is already wearing a wristband.)
RORY: It’s the Doctor’s. When you were sleeping
AMY: That Time Lord. What’s the betting he doesn’t even need it.
He was wearing the wristband for a time, so it’s possible that he’s not really immune but merely wasn’t exposed to the nanogenes for a long enough period.
But what if Amy’s right, and he really doesn’t need the wristband?
Well, we know that nanogenes can be resisted:
RORY: Fair point. Love this plan. What about Amy?
DOCTOR: Keep her remembering, keep her focused. That’ll hold back the conversion.
Presumably this ties into the innate mental powers that every being has, to some extent or another, on Doctor Who. As mentioned elsewhere, this might be why Constantine was able to resist the nanogene transformation in “The Empty Child.” Since Time Lords have prodigious psychic abilities, it is indeed quite possible that the Doctor is able to resist the transformation by will alone. He did something similar in “Nightmare in Silver”, when he resisted an attempt by highly advanced Cybermen to convert him.
DOCTOR: Stop rummaging in my mind.
C-DOCTOR: Just you try and stop me. Ooo, who’s Clara. Why are you thinking about her so much?
C-DOCTOR: Fascinating. A complete mental block. Highly effective.
By contrast, when the nanogenes work on him in “The Doctor Dances,” they’re doing something positive:
DOCTOR: Sub-atomic robots. There’s millions of them in here, see? Burned my hand on the console when we landed. All better now. They activate when the bulk head’s sealed. Check you out for damage, fix any physical flaws. Take us to the crash site. I need to see your space junk.
As such, there would be no reason for him to resist the nanogenes (consciously or otherwise).