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The starting point for study of mind has to be experiential. This is where our primary data come from. Moreover, while I disagree radically with most of Descartes' conclusions, I shall accept his position that the existence of mind is axiomatic: it is logically inoconsistent for ME to postulate the non-existence of mind because without mind there is no me (see Cottingham, 1992). But we can, and usually are, deluded about the nature of mind -- indeed this is one of the first realisations that come from the practice of meditation.
Concerning the nature of mind, then, it is entirely possible that mind is a derivative concept, reducible to some sort of physical mechanism. If, however, I acknowledge that the existence of mind is the primary aspect of our experience, then it seems unnatural to derive mind from physics, because this would be to trying to explain something obvious and immediate (mind) from something (physics) that is an indirect construction of mind. So for me it seems a more fruitful method not to derive mind from physics but to reconcile the experience of mind with the world description of physics.
In trying to reconcile mind with physics, I start from the fact that, in one sense, I actually know a lot about mind. This knowledge is, however, fundamentally different in its nature from the knowledge that I have of the objects investigated by physics. To use the terminology of Alexander (to which I will turn shortly) my knowledge of mind is the knowledge of ``enjoying'', whereas my knowledge of physical objects is that of ``contemplating''. One could characterise these as knowledge from within and from without. The philosophical problems of mind stem from this fundamental difference.
By the phenomenology of mind, I mean the exploration of mind from within. (The term `phenomenology', from psychology, is perhaps unfortunate since it means something quite opposite to the physicist.) I want to ask, from this point of view, what is the phenomenology of ``position in space'': in particular, what items in our mental world have such position?
This mental world, the world of our awareness, comprises a mass of different thoughts, which can segregate into various categories -- percepts, feelings, judgements, volitions and so on. I want to suggest that the majority of these have little to do with Euclidean space.
Certainly, Euclidean space has a role in visual and proprio-motor percepts, and to some extent in hearing. (One of the triumphs of modern psychology is the unravelling of the contributions of these different senses to our spatial perception.) In addition, many of our feelings, of anger, fear and so on, have important links with parts of the body and hence indirectly with space; but it would be hard to claim that this was the aspect of them that was uppermost in normal awareness. Other aspects of our mental world, I would claim, have no direct link with Euclidean space at all.
Neither, however, are these thoughts linked to any generalised space;
because there are no spatial concepts at all that apply to most of
them. Except in a purely poetic way, would it make sense, for example,
to say that my realisation that 
is irrational is ``between''
my feeling annoyed with my secretary and my hearing an indistinct
roaring noise from the central heating? All that can be said is that
these various thoughts are buzzing around with some kind of
togetherness, but without any sort of betweenness, nearness, or any
other spatial relation to each other.
Another way of appreciating this is through the practice of meditation. In normal awareness we are dominated by visual percepts -- and these are precisely the ones that do happen to be linked to space. But even in the very first exercises of (some forms of) meditation, one quickly strips away these visual components by shutting the eyes and turning inwards, and one can then pay attention to a world that is entirely non-spatial.
One counter argument comes from the fact that there is a spatial component to many non-waking states of consciousness. Dreaming and shamanic travel certainly manifest some sort of spatial organisation which suggests that there might be some kind of fundamental generalised mental space manifesting itself here. But to argue in this way is to treat the dream or shamanic reality in too simplistic a way. Theirs is usually a non-standard, fluid space with quite different properties to Euclidean space. Just as the visual forms of dream objects are the superficial manifestations of archetypal realities, so too is the space in which these objects are located: it is a temporary presentational device, not a basic structural aspect of the underlying reality.
The situation is confused by the way in which in our awareness the spatial is entangled with the non-spatial, sometimes giving the impression that everything is located in space. We need to make an effort to segregate the spatial from the non-spatial. In ordinary states of consciousness, the spatial thoughts are essentially all percepts -- impressions on me of something that is not me. All other thoughts, I would argue, are intrinsically non-spatial, though they may derive some spatiality through being associated with percepts. This distinction is not clear-cut: there is no such thing as a pure percept, but every percept is bound to some concept (the percept of a chair is bound to the concept of ``chair'') and that bound concept is given a secondary spatial location.
All our conscious thoughts, both spatial and non-spatial, are, as noted earlier, in some sense compresent. They have a degree of togetherness, though this may often be qualified: we should not assume that the content of consciousness is completely well defined, with an unambiguous dividing line between conscious and non-conscious, and with everything that is conscious clearly experienced as together. It is in describing this qualified togetherness that there may be a role for the most degenerate sense of ``space'', namely in fuzzy set theory. A fuzzy set (there are various possible formal definitions) is marked by a criterion that can be satisfied to varying degrees: a standard example is ``the set of long streets'', where we would agree that a 10m street with one house is out, and a 10km street with 1000 houses is in, with some sort of gradation in between. It could then plausibly be argued that the togetherness of thoughts is a fuzzy relation, and that the set of conscious thoughts is a fuzzy subset of the ``space'' of all thoughts furnished with this relation. (See Zadeh, 1975, for a survey of different aspects of fuzziness.)
This is, however, so far from the sort of thing envisaged by most people who think of mind as being in some kind of many-dimensional space that the term ``space'' is misleading. A further argument for disallowing, as confusing, the term ``space'' for this sort of mental togetherness relation is the fact that it operates independently of space in the Euclidean sense. My consciousness of a distant star is mentally together (compresent) with my consciousness of the nearby trees even though they are Euclideanly far apart.
Even though we may qualify the ``togetherness'' aspect of consciousness by some stucture distantly related to spatial ideas, and even though spatial and non-spatial aspects of thoughts are tangled together, this should not obscure the primary distinction between the Euclideanly spatial aspect of (at least visual) percepts, and the non-spatial togetherness of all thoughts considered as parts of the contents of my mind, whether or not those thoughts are linked to a Euclidean spatial position. Except for percepts, or thoughts that in dreams or trance clothe themselves with the form of percepts, neither space in the Euclidean sense, nor space in almost any of the derived senses, is present in our awareness.
This suggests that the spatial aspect of percepts derives entirely from outside the mind, from the physical world, and that mind is in its nature non-spatial but in perception can become compresent with spatial things.
To conclude this section, I should return to the seminal work of S. Alexander (1920). He argued that all experience is spatial, even if only vaguely so. There was thus a mental space, as well as a physical space. The distinction between the two was the distinction of subject and object already referred to: mental space is enjoyed, while physical space is contemplated. Yet enjoyed space and contemplated space, he claimed, match. There is a precise correspondence between the space of experience and the space of the physicist.
Reading Alexander, one observes that all his examples of thoughts are visual ones. Here is a writer who is dominated by visual images, and who therefore ignores the preeminence of non-spatial thoughts in our awareness. As a result, he is led to postulate two spaces with a correspondence between them. A fuller appreciation of the range of our thoughts shows that space only comes from percepts. If we take this into account, the alternative picture arises in which enjoyed space is actually derivative from contemplated space.
This formulation raises one interesting philosophical footnote. If enjoyed space, in which we place things, is derived from percepts and from contemplated space, then percepts are not only percepts of things in space, but are at the same time percepts of space. Thus we reach a view that is opposed to that of Kant, who held that space was mental in origin, being the a priori form under which external objects were perceived.