I saw Memoirs of a Geisha last Tuesday. It was a pretty average movie. The casting was just terrible because a number of lead actors were very obviously not Japanese. Also Michelle Yeoh had dyed hair and I'm almost certain that during that period, geishas did not have dye their hair in that fashion. She also went without the pancake makeup, a signature of geishas (or apparently what the Japanese term, geikos), in a number of scenes. I was also puzzled by the blues eyes of Sayuri/Chiyo. Anyone with any passing familiarity with genetics would know that's an anomaly in a Japanese. M, who saw the movie with me, suggested that perhaps the girl was albino, something I did not recall from the book. The book and the plot itself, which I'd read many years ago, was interesting enough. However the movie was a little disappointing since I like a certain authenticity in period films.
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I think that was the idea - that she was special because she was unique.
Actually according to this explanation albinos, who have no melanin pigment at all, have red eyes. Brown eyes are the result of melanin pigment. Blue eyes are in between, where there's pigment in the back layer of iris cells but not the front layer. It's possible though rare for Asians to have blue eyes, see for example this thread.