Can you imagine panicking upon learning that the star of your hugely popular TV show is unable to continue because of health issues? You don’t want to cancel it, but how can you possibly hope to convince audiences everywhere that a different actor is the same man? Simple: just explain that your character has the ability to change his appearance to avoid dying.
This is precisely what happened when William Hartnell had to leave Doctor Who after three years in the lead role, and it was up to Patrick Troughton to convince Whovians everywhere that a different man could play the same character. The adjustment was jolting, to be sure–his Doctor was more lighthearted than the First, took himself less seriously and enjoyed his wanderings more. In fact, it would be difficult to imagine two more different personalities between the First and Second Doctors. But then there would be moments where the veil of silliness would fall away, and the audience could glimpse the Time Lord behind the curtain. The presence and command were the same as they always had been–this, indeed, was the same man.
The first time I watched the Second Doctor was in “The Mind Robber” (well, technically it was “The Three Doctors”, but that’s when I also saw Jon Pertwee for the first time), and although his antics often put a smile on my face, I could also see glimpses of the old Doctor. They were faint but present, nonetheless. That’s the story for every regeneration, I think–no matter how different the personality, there’s always that certain something that, once exposed, makes you think, “Yep. He’s still the Doctor.”