Hi Mattb-
If we dissect your brain, we can never find a chemical that equates to "the experience of seeing a green patch". nor is it possible to locate a single memory trace, because we store ideas holomorphically - spread through out a collection of related experiential traces and neuronal linkages. (Right Doc? It's been 30+ years since grad school.)
Thus, there is a lively argument about the relationship of the inner person as a "thinking thing" (Descartes' "chose pensante") and uncertainty about material vehicle in which the person rides (Descartes expressed this as wax that had no form and might be deceptively molded into any form), as opposed to the material nature of the person as a collection of causal linkages within a purely mechanistic system with total determinism of stimulus and response.
My opinion is very radical, in that I deny the material world as primal, and suggest that it is only an appearance that is superimposed over probability fields (those abstract wave mechanical quantum level things that physicists talk about) and that these, in turn, are simply innate emergences from emptiness. For me, the universe is totally and completely mapped, but also emergent anew at every instant (which is why I study topology to understand it). Our portion is not to create, but to choose a path through which to move the "viewpoint" (what the Tibetans call the Knower, and what astral travellers experience as their location) through the fixed pathways, much in as if walking through a city by selecting this or that sidewalk.
Without getting ever more obscure, I'd suggest that the choices we make and the pathways along which we move are material, chemical, fixed and determined. But the motion of the individual viewpoint, eg. the part that I call "Me", is, just as it feels when we do it, a matter of choosing this or that pathway, which is from a perspective external to and superordinal to the material locations and structures, but which arises from a position defined by its location in determined mechanical space, because that's how we are able to retain fixed definitions, and without matter and its totally determined nature, we are unable to have anything with absolute limits by which to create a definition.
The closest formal philosophy I have encountered is Madhyamika Prasangika in Buddhism, although Shankara's Crest Jewel of Discrimination" sets out roughly similar ideas.
If that isn't adequately confusing, stay tuned - maybe I can make it worse next time!

dave