Don't mind if I do!
I approached the problem with the mind of a photographer. I got my BFA in Photography and Media Arts and have worked as a freelance photographer for almost a decade, in addition to teaching photography on occasion so I'm no stranger to looking at bad images. When I first saw the original viral image, I immediately pegged it as a poorly exposed, mis-white-balanced image of a white and gold dress. And despite all the explanations I've seen to the contrary (including yours), I've never been able to see it otherwise.
Now, there's no denying that in the original image there is, in fact, blue present in the dress. But I submit that the actual dress isn't blue and only appears to be because of the problems inherent in the low quality sensors and image processors you find in the average cell phone. When I'm touching up and correcting images in a professional context, the first step is always to make sure the white balance is correct. Every light source in a setting affects the overall color temperature of the image, so unless you're working with direct sunlight or controlled studio lighting then your camera is going to have to rely on its best guess and often it's not quite right. Here's that phenomenon in action:
So these blinds are supposed to be white, but they don't appear to be quite white-white, right? If you have a properly calibrated display, then it should appear to have a very slight blue veneer over the expected white. That's because the light source in the room is a different temperature than the light shining through the blinds from the outside. When I correct the white balance in Lightroom, I end up with this:
Without the benefit of a
balance card, that's probably as close as I can get it without wasting my whole afternoon. So while not perfect, it certainly appears to be closer to the actually present white than it did in the original image.
Here's another example that might be clearer:
We all know snow is white, but if you make an image of snow not being hit by direct sunlight, it's probably gonna appear to be a little blue. The original image of the dress faces similar challenges: the actual dress appears to not be directly lit, but the background is very bright which further exacerbates the poor white balance and exposure (quick side lesson: try photographing someone standing in front of a bright window. you can either correctly expose your model, or correctly expose the outside of the window, but not both). So when I apply the same white balancing techniques to that image, I get this:
Once I had all that figured out, I thought I had put the matter to rest until I started seeing images that purported to be the dress and I begin to wonder if I was somehow going completely insane.
Were people honestly convinced that these were the same dresses? Why can't my mind accept it? I thought that perhaps maybe it was just a matter of complicated lighting and I tried to conceive of what that scenario would look like in practice. Because even if something's black, it would still have some capacity for refection, especially if it were a shiny piece of fabric. If you had a bright enough amber colored light right next to the dress, then it could feasibly result in the black part appearing to be gold in a badly exposed image. And then one night while I was driving, I saw the phenomenon in action. A local bar's sign, comprised of sparse white text and a big black square was being illuminated by the gross orange/amber glow of a street light, and sure enough the highlighted portions of the black did appear to be golden. But the problem was, the white letters also appeared to be golden.
There's simply no scenario where a light powerful enough to make a solid black piece of fabric look golden would also make an adjacent blue piece of fabric appear white. It totally flies in the face of all the practical knowledge I have of photography and studio lighting practices. As for the actual parties involved insisting that the dress is black and blue, I dunno what to tell ya. Maybe there was some sort of miscommunication somewhere that snowballed out of control and/or maybe there's some trolling aspect to it. All I can say is that there's no way a dress can melt steel beams.