Most Qualia are rather well understood an example taken from wikipedia "the perceived redness of an evening sky".
You can talk about why they sky has 'redness' but subjectively what's important is the sensors in your eye, and how what happens to the signal. If you look at the research, people have tracked what causes each receptor to fire and then followed colors back though the optic nerve. So, really the subjective feeling is a signal we have tracked what more do you want?
Often when people say science can't explain X, really what they mean is they can't follow the explanation.
I'd just like to point out that by definition, that's not qualia. You're talking about something else—which is fine. You can deny the existence of qualia all you like, and many people do.
Dennett has made a very good case for the term being so abused as to be useless. He argues against its existence and seemingly the existence of anything like it. I don't really agree with him in this extended sense but I can't define exactly what it is I do agree with, so for now I can only say that there is a lot more to learn about consciousness and related phenomena.
Feel free to edit wikipedia, Qualia: individual instances of subjective, conscious experience ... Examples of qualia are the pain of a headache, the taste of wine, or the perceived redness of an evening sky.http://en.wikipedia.org/wiki/Qualia But, I think you might be thinking of something else.
Some people object to saying Subjective Experience the same thing as Brain State. But, I have never seen an argument that does not at some point presuppose the difference. AKA assume a p-zombie exists...
PS: The Chinese room is a thought experiment is a great analogy for consciousness, they only reason to suppose the room is not intelligent is if you presupposes requirements that's the vary existence of such a room disproves. A computer or person following the instructions may not understand Chinese without the instructions but by following them they create something which does understand Chinese. Just as neurons are not by themselves conscious, but together and in the correct arrangement they can create consciousness.
Go back to the 'definitions' section. Dennett went by this (and similar formulations), and made a compelling argument. I would advise reading Quining Qualia if you are interested. I believe that is where he made the case so well. (You can probably find it on the web.)
The Chinese room is a frustrating argument, and I essentially agree with you on that.
however there's no reason to believe 'qualia' aren't explainable. for example, if "consciousness" is a thing, it may be some kind of system or structural artifact induced by the underlying neurology
qualia then would be properly described by their manifestation in that induced system
that doesn't mean that the descriptions of these sorts of things would resemble anything we refer to as "mathematics" or "engineering" or even "science" today. for example, there's no reason to expect that these things are "computable" or decomposable in any sense
however there's no reason to believe 'qualia' aren't explainable
I think there is. 'Qualia' is, in my opinion, a useless term. Even if something is going on of that sort, many of the points in the common definitions distance it from science. The only connection with the outside world people seem to admit is that we are individually aware of it. I'm okay with the possibility that there is something removed from access like that, but I think something very different is going on, which we have a lot of misconceptions about.
You can talk about why they sky has 'redness' but subjectively what's important is the sensors in your eye, and how what happens to the signal. If you look at the research, people have tracked what causes each receptor to fire and then followed colors back though the optic nerve. So, really the subjective feeling is a signal we have tracked what more do you want?
Often when people say science can't explain X, really what they mean is they can't follow the explanation.