I think this thread may be my fault – here’s the post where I brought up Mary. I think I’ve said most of what I would say here there, so I’ll just lazily copy:
The classic example is, of course, Mary the colour scientist. I believe that one reason it seems so convincing is the mismatch in bandwidth between visual and textual modes of information gathering: Our visual system gathers tons of bits effortlessly, while reading – implicitly the way Mary avails herself of ‘all the physical information about seeing colours’ – conveys relatively little information in an instant. Indeed, one could posit that the way information is processed in the brain depends on the speed that information is presented to it; then, it would indeed be possible for Mary to ‘read’ all about colour, yet learning something new about colour upon seeing it for the first time, without this having any deleterious consequences to physicalist explanations. But I don’t think even this is necessary.
Tale a variation on Mary: Marv, who is, through unknown means, confined to a two-dimensional world. One could argue analogously that there is no way for him to imagine his experiencing a three-dimensional world, as there is no way for a linear combination of two dimensional vectors – which is all he has in his repository to build representations of the world from – to be three dimensional. However, this conclusion we know to be wrong – it is hard, though not impossible, to teach yourself to visualize four dimensions – at least well enough to conceivably not be confronted with something ‘fundamentally new’ when suddenly exposed to a four-dimensional reality. (French mathematician Étienne Ghys has a page where you can learn to do visualizations of four dimensions.)
The difference between Mary and Marv is, I think, only one of quantity, not of quality. While it is just barely possible to imagine that Marv might succeed in visualizing the third dimension, the problem is just so much more intractable in Mary’s case that we are easily persuaded to call it impossible. But if Marv can succeed, Mary just might, too, though we perhaps can’t begin to imagine how.
The thought experiment of Mary succeeds due to the trick of presenting as a sharp divide what is actually a far more fuzzy gradation – generating new experiences from old ones. If the way you need to go to produce a new experience is short, we do not think of it as difficult – you can, say, often predict how a dish you make for the first time will taste, or you can imagine a scenery from a prediction in a book well enough in order to recognize it when confronted with it in actuality. These are easy cases – you directly possess the building blocks necessary to ‘assemble’ the ‘new’ experience. It gets harder in Marv’s case, where the building blocks you possess – two dimensions – don’t suffice to generate a three-dimensional manifold. And in Mary’s case, it seems that there does not exist any way to reassemble the known to create or infer the unknown – colours can only be thought of in terms of colours. But of course, when it comes right down to the fundamentals, everything in the mind is composed of the same fundamental building blocks – information, encoded in neuron firings. It’s very hard to create the ‘what it is like’ of colour vision from these building blocks; but there is no reason to think it should be impossible.