I came across an interesting question while reading the blog of Scott Aaronson today. The question was as follows:

In the world of the colour-blind, how could I prove that I could see colour?

I’m presuming, to make the discussion more life-like and less cheaty, that this civilisation hasn’t discovered that light comes in wavelengths, or that it has but it can’t distinguish very well between wavelengths (so that all coloured light falls into the same bucket of 100nm to 1000nm, for instance). The challenge is to design an experimental protocol to confirm or deny that I have access to information that the colour-blind do not. This question is much harder than the corresponding question in the world of the blind, because having vision tells you so much more than having colour vision (simply set up a flag two miles away, have someone raise it at a random time, note down the time you saw it raised, and compare notes).

Oh. That’s unfortunate. This protocol works perfectly well to determine colour, too - I just need to provide two flags of different colour, present them for inspection so that the experimenters verify that they look identical to them, mark the base of the flagpoles A and B in some way that the colour-blind can detect (etching?), note down which colour corresponds to which flag, walk a hundred metres, have the experimenter wave one of the flags at random, write down which flag was waved, repeat to taste.

How about a proof that I could hear when no-one else knew what hearing was? I would need to find something that I could hear that no-one else could detect - perhaps the dropping of a vase fifty metres away - and, while blindfolded, raise my hand when I heard the vase drop. I would, of course, have to remember to explain that there could be a time delay over long distances.

Stereo sound (the ability to detect where something is by the sound it makes)? I shut my eyes, someone walks around me and claps once; I point to that person.

Smell? Easy - simply uncork a test tube of water or hydrogen sulphide. I can identify which was used.

Taste? Again, we could dissolve sugar and salt separately into water.

Proprioception? It seems odd to me that any physical being could have managed to evolve language and not proprioception, but I could at least demonstrate the ability to exercise fine control over my body by pulling the spring of a Newton meter with a toe, finger, mouth, etc. This should be good evidence that I know how much strength I am exerting. I could also do this blind (although my results would be more rough, because I’m not a good proprioceptor), and I could also not see the scale of the Newton meter. To test awareness of where my body parts are, I could place both hands behind my back and have someone move one of them (with me blindfolded); I would then touch the moved hand with my other hand.

Language (the fact that “the sounds I am making convey information”)? This would require two people who spoke the same language, of course. We could be placed in separate booths, with a row of pictures in front of us. Someone would point to a picture in one booth, the person in the relevant booth would describe it, the other person would point to the corresponding picture.

This discussion turned out to be less interesting than I would have liked. Anyway, it would appear to imply that if someone did indeed have extra senses, that person would easily be able to convince me of this fact. For instance, in the world of the colour-blind, I would present two items, saying “These items differ in a property which I can sense and which you cannot; show me one and I will tell you which it was”. If the experiment were repeated and I were consistently able to say which item was shown, then I think this should count as proof that I can see colour. Of course, any limitations on my power (“I can’t necessarily distinguish between any two items, but I can distinguish between these two”, or “I can only distinguish between two items when it’s a full moon in three days and when I’ve received a blood sacrifice and when the experimenter has sufficient faith in my abilities”) should be declared up front, so that they can’t be used to explain away failure (so, for instance, we could in advance find someone very credulous). Parallels to the Randi prize fully intended.