Q-space

Let us refer to the notion of property space which I have defined earlier as P-space (P = property; or equally, P = physical). Now, I want to define another space, which I shall christen Q-space (Q is for qualia.)

Essentially, P-space models a physical universe as a set of point particles, spatiotemporally arranged, each having various numerical physical properties. Q-space, by contrast, models a universe of experience, a stream of qualia which may be experienced by an individual.

Let us consider a simple example. Imagine that sight was our only sense. Let us assume furthermore that we are trichromats, and capable of depth perception. So, at every temporal moment t, we are perceiving a certain visual field, which is organized two-dimensionally. Each point in that visual field can be described by four numbers: three dimensions in colour space, and one dimension of depth. The colour space might be, for instance, CIE L*a*b*. As in the case of P-space, there are certain geometric constraints — for any given combination of x, y, t, there can only be one possible value of L*, a*, b* or z.

An observer, then, can be identified with a region of Q-space.

We can define two different observers, being identical in their temporal parts, as regions of Q-space which in some temporal subregion are fully overlapping. Whereas, cases of non-identical observers having the same experiences, the regions are only partially overlapping, or non-overlapping yet transformable.

An objection: Some people are dichromats; possibly, some people are also tetrachromats. Can we define this Q-space in a way which does not depend on chromatacy? Well: we define colour spaces in terms of differing spectral power distributions which all produce the same qualia (or, equally, are reported to produce the same qualia). Obviously, dichromats and trichromats report differently. But what is the relationship between dichromatic qualia and trichromatic qualia? Since, invariably, an individual will be one or the other for their whole life, or, if they were to change between them, it would likely be either a gradual process, or even if an abrupt process, a non-repeatable one, so it would be difficult for an individual which was to so change to make a judgement as to the identity or non-identity of qualia of different chromatacy. But, suppose through some advanced technology, one had the ability to reconfigure one’s retina at will. (Suppose, due to blindness, one has been given an artificial retina, which, due to technological advances, is identical in behaviour to a natural one; but, even better than a natural one, is adjustable at will, so that one can change the effective number of cone cells, or their response curves, as one wishes.) One might then experiment, by switching frequently between different levels of chromatacy, and even different response curves within a single chromatacy, while keeping constant the spectral power distribution to which one was exposed. One would then be able to form a judgement, as to the relationship between the qualia spaces constructed by different chromatacies. Thus, we could potentially move beyond a Q-space linked to a single vision system, to a generic Q-space which encompasses vision systems with a multitude of different parameters.

Three questions:

— Is the Q-space of generic vision bounded?

— Is the Q-space of generic vision finite-dimensional?

— Is the Q-space of generic vision discrete?

I feel, the answer to all these questions must be “Yes”, up to humanoid beings. For, any humanoid being has an intelligence less than some finite upper bound. And yet, if any of these three questions was false, then the a being capable of such vision would need to perform a potentially infinite amount of computation within its visual systems. Thus, even if, at our present level of knowledge of cognitive science, we do not understand the properties of the Q-space of generic vision, we can conclude that, up to humanoid beings, it is bounded, discrete and finite-dimensional.

An objection: At best, all you have modelled is vision. Indeed, that is true. There are some number of senses (I am not sure, at present knowledge, if we can precisely enumerate them.) They all share a common dimension of time. Although, we may not be able to devise Q-spaces for all of them, with our current knowledge, I feel confident in claiming that they all have Q-spaces, which are bounded, finite-dimensional and discrete, waiting to be discovered. At least some of them, have spatial dimensions; if the Q-spaces of two senses both have spatial dimensions, should we treat the spatial dimensions of each as identical or equivalent (i.e. common), or as distinct? It seems, that the answer to that question is most likely to be an arbitrary choice of modelling, as opposed to an actual question of fact. We can then construct a model, of some number of Q-spaces, with a common dimension of time, and some subset of those Q-spaces also sharing common spatial dimensions. Now, we can construct an overarching combination Q-space, incorporating all those separate Q-spaces. Let us have dimensions of time, of qualia type, of space, and of property. For non-spatial qualia types, we fix the spatial dimensions at an arbitrary value, say origin. The various qualia types have differing applicable properties; for a point at a given qualia type, we can fix the value of the non-applicable property dimensions at an arbitrary point. Thus, as well as the geometrical constraints of the individual Q-spaces, we also have geometrical constraints deriving from their combination into a single overarching combination Q-space. And, if the individual Q-spaces be bounded, finite-dimensional and discrete, and if the number of qualia types be finite, then the combination Q-space must be bounded, finite-dimensional and discrete.

A soul can be bound to a region of combination Q-space, which (1) obeys the inherent geometrical constraints of Q-space; (2) obeys the consistency criteria. Every region of Q-space, which meets both sets of criteria, can potentially be bound to a soul; and yet, it seems, not every such candidate region is so bound. Indeed, I would argue, that the proportion of regions so bound must be greater than none but less than all. We might call this last requirement a third requirement, but it applies over the set of all actual bindings, not over any individual one.

A fourth requirement, again one ranging over all bindings, is anti-solipsism; in other words, the bindings must be as such that there exist the qualia of a belief in the falsehood of solipsism; and the bindings must be as such as there to be other associate qualia which would justify the belief constituted by the former qualia.

P-Space and Q-Space

P-Space is an essentially observer independent notion. Q-Space is essentially observer dependent. However, in constructing subregions of P-Space, I have appealed to observer dependent criteria, which I feel ultimately justifies us in preferring the concept of Q-space. I feel that, Q-space is a better model of the ultimate nature of reality; whereas, P-space, represents a class of models, which while not as good at explaining ultimate reality, are still pragmatically useful. Physical laws, expressed in terms of constraints on the shape of P-space, are ultimately constraints on the shape of the atom-bindings in Q-space; but, it is easier to reason about them in terms of P-space than Q-space. But, I don’t think we should accept the scientist idea that ease of notation = truth. Ease of notation is simply that, ease of notation.