The inverted spectrum is the hypothetical concept of two people sharing their color vocabulary and discriminations, although the colors one sees — one's qualia — are systematically different from the colors the other person sees.
The concept dates back to John Locke. It invites us to imagine that we wake up one morning, and find that for some unknown reason all the colors in the world have been inverted. Furthermore, we discover that no physical changes have occurred in our brains or bodies that would explain this phenomenon. Supporters of the hypothesis of qualia as non-physical entities argue that, since we can imagine this happening without contradiction, it follows that we are imagining a change in a property that determines the way things look to us, but that has no physical basis. In more detail:
The argument thus states that if we find the inverted spectrum plausible, we must admit that qualia exist (and are non-physical). Some philosophers find it absurd that an "armchair argument" can prove something to exist, and the detailed argument does involve many assumptions about conceivability and possibility, which are open to criticism. Perhaps it is not possible for a given brain state to produce anything other than a given quale in our universe, and that is all that matters.
|"||...there are more perceptually distinguishable shades between red and blue than there are between green and yellow, which would make red-green inversion behaviorally detectable. And there are yet further asymmetries. Dark yellow is brown (qualitatively different from yellow), whereas dark blue is blue[..] Similarly, desaturated bluish-red is pink (qualitatively different from saturated bluish-red), whereas desaturated greenish-yellow is similar to saturated greenish-yellow. Again, red is a "warm" color, whereas blue is "cool" -- and perhaps this is not a matter of learned associations with temperature.||"|
Vincent Conitzer has illustrated the possibility of an inverted spectrum using the following scenario. Someone is observing a simulated reality through a VR headset, and is not aware that she is wearing a headset or that what she is observing is a simulation. Conitzer argues that the code responsible for the physics of the simulation can be separated from the code that determines in which colors the simulation is displayed by the headset (as well as determining which perspective in the simulation to display). So, it would be possible to change that additional code, inverting the displayed colors, without changing anything about the simulated physics. Hence, which (real-world) colors are displayed is a further fact over and above the facts of the simulated physics.
In his book I Am A Strange Loop, Douglas Hofstadter argues that the inverted spectrum argument entails a form of solipsism in which people can have no idea about what goes on in the minds of others--contrary to the central theme of his work. He presents several variants to demonstrate the absurdity of this idea: the "inverted political spectrum", in which one person's concept of liberty is identical to another's concept of imprisonment; an inverted "sonic spectrum" in which low musical notes sound like "high" ones and vice versa (which he says is impossible because low sounds can be felt physically as vibrations); and a version in which random, complex qualia such as riding a roller coaster or opening presents are reversed, so that everyone perceives the world in radically different, unknowable ways.