In many of my previous posts, I have indicated the presence of an "imaginary qualia space" which is a counterpart of the real qualia space. The real qualia space corresponds to "real" sensations while the imaginary space corresponds to imagined sensations. Both of these can exist simultaneously at a certain point in the CBS. For example, even though I might be seeing a red object, in my mind I can be imagining it to be blue at the same exact spot. As I had indicated in this post, the imagined qualia can for all practical intent and purposes be compared against other real or imagined qualia and the normal operators associated with qualia apply to them as much as real qualia.
Can I take this a step further and imagine an imagined qualia? I do not count dreams as pure imagination states (since dreams have both real and imagination states and are indistinguishable from the waking state in this regard). So, imagining something in one's dream is the same as imagining something in one's waking state. When I try to imagine a red ball where none exists and try to imagine it being blue, the original red gets replaced by blue. This is unlike the case where I imagine a real red ball being blue. The real hue of red is always there and my imagination of it becoming blue does not change the red that I am perceiving all along.
Basically I am saying that there can exist only one imagination qualia space that can co-exist with the real one. This applies to all qualia (sight, hearing, touch, etc).
If this hypothesis is true, is this some kind of species-specific limitation? In other words, are there other species, or even other extra-terrestrial beings in our universe that can have overlapping imagination spaces? Or is this an arbitrary constraint imposed by the "program" that simulates our universe, something that could easily be changed by the master programmer? Or, is this because of some fundamental mathematical truth that imposes a limit of one imagination space and something that is program-independent ?
If the answer is the third one, then we can possibly club the real and imagination qualia spaces into one complex space, where the real part corresponds to our real qualia and the imaginary part corresponds to our imagined qualia. Since the accesses for both real and imagination states are the same (see this post), there is no reason why this cannot be acheived. Alongside, there exist operators which can act on the real and imaginary parts, or some combination thereof. For example, I can compare the hue of an imagined blue region with that of a real blue wall and decide which one is lighter.
So what are we going to acheive by making our qualia complex values, you may ask. One thing is, we just have one qualia space instead of two. Another way of putting it is, to specify the complete qualia state of a conscious entity at a given time, the dimension of the qualia space required is cut in half.
But this aside, are there any other advantages to doing this that follow from the properties of complex numbers? Let us take the case of conjugate qualia. For example the two states corresponding to imagining touching a hot object and a cold object with my index finger. If I am not actually touching any object at that time, the two states are purely imaginary and conjugates of each other. If on the other hand I am actually touching some hot (or cold) object with that finger, then the two states correspond to complex conjugate values. (Actually, in this example, I have ignored other parts of the CBS that correspond to the rest of the body as well as other sensations - we can always take only the subspaces corresponding to particular sensations and the regions of the CBS within the subspaces that are of interest to us - in this case, only the one corresponding to the index finger).
At this point, it is not apparent if there is anything to be gained out of this. But assuming a theory of qualia ever gets developed, it would be interesting to see if representing qualia as complex values in the above manner is compatible with it (if not encouraged by it).