Saturday, April 21, 2007

Operators in qualia space

Perception of qualia would be of no use if operations on them don't exist. For example, one can perform relational operators on qualia - for example, one could decide which light is brighter of two, or which sound is louder. One could also perform things like ordering pitches or hues. A tribal who has never come across printing or painting would still instinctively classify orange as being "between" red and yellow. What he does is apply an averaging function in the qualia space of hues.

However there is a fundamental limitation to operations on qualia whose result is qualia. This limitation is what I term "access limitation". This essentially states that the resultant qualia can sometimes be "out of bounds" for the access of a particular brain.

I will give two examples. The first one has to do with intensity. Intensity is the magnitude of different senses (vision, hearing, smell, pain, etc). At lower intensities, one can perform relational operations quite easily. (By performing operations, I mean, ordering sources according to different intensities, or even imagining or dreaming two sources of different intensities.) But at higher and higher intensities, the sense organs become saturated that further relational operations is not possible. Now one can dismiss this as just the limitation of the physical sense organs. But according to my previous post the limitation is built into the access pathway in the brain itself, and with a different brain architecture, a potentially infinite dynamic range can be realized for most, if not all, senses. This is the reason why we cannot even imagine or dream or hallucinate a greater dynamic range than our everyday experience.

The second limitation is even more illustrative. When I mentioned an averaging operator in the space of hues, the assumption was that the individual is not color blind. If an individual cannot experience an eigenhue (see this post for what I mean by it), then no relational or any other operation on the hues he perceives would give rise to that eigenhue. This is why soemtimes color blind people cannot even imagine the color they are missing. This is again an example of access limitation. This is not about intensity, but about the hue.

I will give another example of the second limitation that affects everyone. Take the sense of pitch. Now pitches corresponding to two frequencies which differ from each other by the twelfth root of two are adjacent notes. In fact, one can easily figure out the succeeding note from the current one. This is the basis of music theory. What we do is keep applying the same operator in qualia space ("one note above") starting from a low base note and we very soon find ourselves at the upper end of the hearing range. We can also go down as "one note below", and would then find ourselves at the lower end. In fact, when one crosses the limits (either lower or upper), one cannot even imagine notes beyond these. This is quite unusual because in pitch qualia space where neighboring notes are so beautifully related over several octaves with great consistency, the breakdown seems almost implausible. For in an abstract qualia space of pitches, it would seem that we should be able to carry out the determination of successive notes (either ascending or descending) ad nauseum. A platonic model of pitches should correspond to an infinite number of octaves. Logical reasoning dictates that. And yet that isn't the case. We should blame it on the access part of our brains. Our access is closed to pitches below 20Hz or beyond 20KHz (roughly).

I wish to reiterate that when I mean "access" I don't mean the ability to just sense such qualia (which can be tied to the ability of the sense organs). It means the ability of the mind to construct the qualia under question as a function of some operation in qualia space. In the pitch example given above, the ability of people to determine a pitch which is an octave higher than a pitch sounded to them is the access of the higher pitch. Most people would succeed if the sounded pitch were 1KHz. They would fail when the sounded pitch is 15KHz.

As I had mentioned earlier, the platonic space of qualia (which is post Cartesian theater) is ultralinear (infinite dynamic range), and the vagaries of the access limitations are due to the physical workings of the brain. It is possible that the brains of some other species of animals have different access limitations and may or may not overlap the regions reachable by the human brain.