What exactly makes our experience of sight different from, say, our experience of smell? What gives rise to these as distinct types of qualia? If vision, olfaction and the rest are each a dimension of qualia, how many such dimensions are possible? Are there any organizing principles that relate all possible dimensions of qualia to each other? (apart from nonduality, which goes even further and transcends the very distinction between subject and object)
The difference is that they generate sufficiently different forms of qualia that it is worth us including words in our language to describe them as different things. There are plenty of situations where the lines between them break down. In my opinion, the most spectacular is Synesthesia, where the clear distinctions break down dramatically.
As for "how many dimensions are possible," you must ask yourself whether your qualia are the same as a qualia of another. This is an open ended question, which suggests there are at least 5 senses * 7 billion = 35 billion dimensions to qualia.
Since this is usually not a satisfactory answer for people, we do tend to develop organizing principles to relate these dimensions. We make the assumption that, if we can identify an organ primarily responsible for a qualia, and people are generally comfortable using the same word to describe the same situation, then those dimensions are probably highly correlated. This is the process we used to collapse the qualia into the "5 senses."
There is not a universal agreement on 5 senses. The wikpedia page on senses points out that the 5 senses are "traditional" and widely accepted, but also goes into some of the alternative definitions that have been suggested.
An accepted estimate of the number of senses that each human possesses is along the lines of 21. Though we are certainly no conscious of all of them, they seemingly produce different kinds of qualia:
- Blood Pressure
- Blood Oxygen Content
- Spinal fluid pH level
- Lung Inflation
I believe that the differences between them are simply due to the fact that they stimulate different parts of the brain. As a naturalist, I don't believe in a concept of a soul or an entity apart from the brain that generates consciousness or feeling, but of course one is free to believe otherwise and I welcome discussion pertaining to it.
I don't believe 'dimensions' is the correct word to use for different qualias, but rather that they are simply different and evoke different emotions or physiological responses by stimulated different regions of our brain. We know that encoding memories in the brain, especially long-term, stimulates the auditory cortices of the brain and encodes it as audition.
I'm not sure if this answers your questions, but let me know if there's more that I can discuss!
Unfortunately, the answer to all these questions seems to be "we don't know".
there are various notorious problems with qualia; one is that many people deny its existence completely (famous e.g. Dennett, Minsky), another is that many who do acknowledge it confuse it with a lot of other phenomena such as perception, psychology, memory, etc., and finally, and most importantly it is impossible to describe it.
there is simply no way to convey its existence beyond saying silly things such as it is the way things feel, or it is how red looks like, or it is that thing which computers may never have, or that it is the only thing that surely exists, and finally by getting mysteriously mad at people who just don't get what on earth you are talking about.
in particular you cannot describe qualia to someone by saying it is the width or pitch, or color of something, or that it has width or pitch or color as attributes, or that it is that thing which conveys these attributes.
in analogy, what you are asking is arguably like trying to classify the light (qualia) in a room (your brain) by the attributes of the objects in the room; for example by suggesting there are various dimensions to light, such as the width and height of the bed, or the number of drawers in the open closet, etc...
so, I believe it is better to ask which kinds of perceptions seem to have associated qualia, and what are the relationships between these different kinds of perceptions.
since we cannot describe qualia, we cannot know its attributes, and therefore, the answer to your questions is still "we don't know".
There may very well be, see Nagels essay on what it is to be like a bat; but it's a condition of our finite existence that we cannot transcend our conditions of sense; hence we can only imagine them, or speculate on them.
This leads to a pointed question: suppose there was an animal one of whose senses wasn't contiguous with ours - ie it had an additional sense - how could we determine it?
The senses are qualitatively different by definition
That's exactly what makes a sense: receive stimuli that are qualitatively different.
If we look at two example stimuli that are detected by the same sense, we would say they are not qualitatively different.
If two stimuli detected by different senses are said to be qualitatively different.