I'm not the Doctor, the man says. As though it could possibly be that simple.
The Master has lived in ruined bodies, beautiful bodies, stolen bodies, formless bodies of energy and will. He's lived as a weak and conscience-addled human. He knows the self is a fractal thing, an iteration.
The closer he looks at Jackson Lake, the more he sees the Doctorness. That ubiquitous pattern, commoner than the Fibonacci sequence; sometimes the Master thinks the universe is Doctors all the way down.
And so the Master rewrites. Takes the memories, flattens the recursion into linearity.
Simplicity has its uses.