What if you woke up one day and all the things that looked red to you before going to sleep suddenly looked green, with the entire color spectrum shifted accordingly?
Welcome to the "inverted spectrum argument," a critical piece of philosophical lore (dating back to John Locke, more widely known for his theory of natural rights) with implications for the meaning of human consciousness and, of course, that problematic dress that set the internet ablaze Thursday night.
The thought experiment is meant to prove that there is such a thing as what something looks like that is separate from the question of what it is. An identical .JPG file, for example, can look one way to some of us and another way to others. These things — the blackness you see or the goldness I see — are called qualia (quale is the singular) in the philosophical literature.
One common line of argument about qualia is that their existence and importance shows that crucial matters of consciousness cannot be reduced to a mere biophysical understanding of how the brain operates. In his famous 1974 essay "What Is It Like To Be a Bat," Thomas Nagel asks us to consider the qualia induced by navigating the world via echolocation. We can, through physical examination, come to understand a great deal about bats. But we cannot understand what it feels like to be a bat:
We describe bat sonar as a form of three-dimensional forward perception; we believe that bats feel some versions of pain, fear, hunger, and lust, and that they have other, more familiar types of perception besides sonar. But we believe that these experiences also have in each case a specific subjective character, which it is beyond our ability to conceive.
This is more or less why the dress dispute was so vehement and so captivating. I can look at the photo of the dress. And I can image a black and blue dress. But I can't understand what it's like to see that very dress as a black and blue dress. Common sense indicates that the disagreement must have to do with screen brightness settings or background color or monitor tilt — some physical property of the image. When it turns out that two people can look at an identical image on an identical screen and see different things, it seems like someone has gone insane.
Mind and body
To many philosophers, these qualia issues demonstrate that the conscious human mind cannot be reduced to the physical and biological processes of the brain. Other philosophers dispute this (it is philosophy after all) and propose various theories to reconcile the presumption that the whole world is physical with the lived reality of subjective experience and qualia.
Another approach entirely was taken by Tufts University professor Daniel Dennett in his 1988 article "Quining Qualia". It's a pun based on the name of W.V.O. Quine, a philosopher from the previous generation who was widely known for vehemently denying the existence of many things posited by common sense. Dennett's argument is that, despite their distinguished lineage in the philosophical literature, nobody can give a consistent account of what qualia are. It's easy to get freshman philosophy students to believe in them with a couple of thought experiments, but they're not a normal word of everyday language because they're really just a flight of fancy philosophers dreamed up to deny the truth of materialism. Normal people would just go to church and talk about souls.
The fault is in our eyes
The fact that nobody yet seems to have devised a conclusive account of how the dress puzzle arose inspires speculations about qualia and consciousness. But the direction that investigations are going in tends to suggest a more Dennett-style approach. Our eyes contain many different rods and cones that perceive light and color, and even though human eyes are all broadly similar, a whole range of factors are going to lead one person's set of rods and cones to differ from another person's.
Through some miraculous happenstance, this particular washed-out photo of dress seems to have hit onto a dividing line where one large fraction of the population sees it one way and another large fraction sees it another way. But just because people see things differently doesn't mean there's no physicalist explanation of that fact. Things that look blurry to me seem sharp to people with 20/20 vision, and that's because of the shape of my eyeball. Until someone explains in detail exactly what physical differences lead some people to see the gold parts of the dress as black, we're going to keep arguing with each other.
But it's extremely likely that an explanation will be forthcoming. It's not so much that our subjective experiences are incomprehensible to one another, but our eyes just function very slightly differently in a way that happens to be relevant to the perception of one viral photo.
That doesn't mean the consciousness argument will be solved in Nagel's favor, of course, since he still has the bats to fall back on. The awful thing about philosophy is that unlike internet riddles, its big problems never get resolved.