Great question and one I have often thought about 🙂
I’m not sure that there is anyway to tell this, because if we both look at the same shade of ‘blue’ we have both learnt to call it ‘blue’ and so would say we are seeing that. I don’t think we know if our brains are interpreting the colour in exactly the same way.
I guess the question “what is blue” is more of a philosophical question!
From a technical point of view our eyes have different receptors (cones) for different wavelengths of light. Some people have problems with certain cones, making them less receptive to light of certain wavelength (color blind). So, different people have (slightly) different working cones, but the brain translates their signals to what we all agree on is “blue”. It would be interesting if you could transfer the cones from one person to another (keeping the same brain) and see what their brain makes from those (different) signals and still tell you it’s blue you’re looking at.
Just to add to what Cees said – this is an unsolved philosophical problem, how we tell whether the things that we sense (feelings, visions) actually represent the things that exist in the physical world.
You might also be interested (since you chose the colour blue) in the Blue-Green problem (http://en.wikipedia.org/wiki/Distinguishing_blue_from_green_in_language). It turns out that lots of languages use similar words to describe both blue and green, while others separate them quite clearly. Language is a key factor in how we understand the world!
EDIT – I was listening to the latest edition of the excellent science podcast RadioLab today, and it’s all about questions like this! You might be interested: http://www.radiolab.org/2012/may/21/
I think it depends in exactly how the light receptor cells in your eyes are and what genes they express? For instance with colour blindness there are certainly some colours that colour blind people cannot see but they see something else instead. So I wonder whether we might all just see things in a slightly different shade?
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