Apparently I am wrong, the dress is blue and black. Now this would not bother me, but apparently lots of people, perhaps the majority see it as black and blue, where as some see it as white and gold.
So I took different segments of the dress in isolation and performed and analysis of the colour composition of each portion. In HSV terms this comes up with an average colour of bright drab violet (RGB B9,AD,C4) and medium faded orange (RGB 7A,63,48). So the image of the dress is correctly very light purple and gold. It is certainly not black and blue as there are huge amounts of orange in the image the darkest part of the "black" portion is (RGB 42,42,42) which I believe most people would call grey, and that is the absolute darkest part in the shadow of the left side of the dress!
It is very interesting that peoples optical filters can have such a dramatic effect. So if you see white and gold you are largely correctly identifying the colours out of the context, however, if you are seeing black and blue you are somehow adjusting to the correct context of the photo's horrific white balance.
Interestingly I have read that some people have changed their minds after looking at the photo on a different occasion, I wonder what is required to achieve switching. I have tried adjusting my focal point, but the best I can manage is light purple and dark orange which is roughly what the pixels are.