Qualia are generally also defined to be ineffable (not communicable and not describable even in principle).
The computational theory of mind states that minds are computations and that brains are a type of computer (albeit one that has elements of randomness to its operation).
Many arguments have been put forward, in which qualia feature, which attempt to disprove (or undermine) the computational theory of mind. In this post I shall address the knowledge argument (although my points will work just as well for other common arguments).
Before describing and tackling the knowledge argument, lets first investigate what qualia might be, if they could not be explained computationally.
We have two possibilities for qualia. Firstly qualia might be causally disconnected from physical reality in that qualia could not cause anything to happen in the physical universe.
The most obvious question to ask then is "Why are qualia important?" If qualia do not effect your actions or the actions of others why should we care about qualia? Furthermore if qualia do not interact with reality then all arguments made for the existence of qualia (of this causally disconnected type) would have been made in a universe without qualia (note that this must also be true of all arguments you make inside your own head (as these arguments can in principle effect the world outside your head)). So if qualia are causally disconnected from physical reality then reading an argument for their existence should not convince one of their existence!
Secondly, qualia might be causally connected to physical reality. In this case we may as well redefine physics to include qualia. When we do, we either get a computationally simulable theory or we do not. In the former case we have a computational theory of qualia. In the latter case we have a profound revolution in physics. Although such paradigm shifts have occurred before, dubious thought experiments are really insufficient, to establish massive breakthroughs in science.
Now for the knowledge argument: "Imagine a vision scientist Mary. Mary has colour vision but is kept in a monochromatic room (say blue) for her entire life (the original version is a black and white room but this has some minor loopholes including Mary seeing the colour of her own nose!). Now suppose Mary learns every computational fact about colour vision that there is to know. Then does Mary understand what it is to experience the colour red?
Suppose now that Mary is let out of her room and sees a red telephone box. Would Mary not learn what it is to experience the colour red in that moment? In which case, the computational theory of mind must miss this aspect of experience."
Before giving my response, I need to explain a subtlety of the computational theory of mind.
When we say "describe an experience" what do we mean? We might mean, that you give all relevant pieces of information, about that experience. Or we might mean, that you tell me enough about that experience, for me to be able to imagine it.
To understand the difference, consider a computer. The computer might have a program that displays images and it might have another program that compiles code written in C++. However, if you write some code in C++ and take a photo of it that photo won't be understood by the compiler. Never the less, the photo might contain a complete description of the program. Indeed this is certainly possible. The problem is, that the computer lacks the ability to translate the image into a text file (which is what it needs to be able to compile it).
I now give my response to the knowledge argument. I acknowledge that Mary does learn something new when she sees the telephone box. However, I think this is because her brain lacks the ability to translate verbal and textual data (in which form all her scientific knowledge is represented) into the very complex brain signals which constitute her experience of the colour red.
It is like, you tried to install an operating system onto your computer, by taking photos of all the source code, and saving these photos to the computer's hard drive.
So Mary, may well gasp with awe and say "I never knew that's what postboxes looked like.". However, this does not in any way, undermine the theory that Mary's mind is computational.
Some may think that a computational account of the human mind is depressing in that it reduces our experience to processing information. I prefer to consider it from the opposite perspective. If my beautiful, mesmerizing and profound experiences of the world are formed from highly complex computations then might even more complex computations be even more intoxicatingly vibrant? In the future we may be able to manipulate the brain and give it new forms of input.
If the computational theory of mind is true then it may one day be possible to add entirely new senses to our brains and entirely new experiences to our minds.
What would it be like to be able to see two extra colours?
What would it be like to be able to see in four dimensions?
What would it be like to have sonar vision?