Dimensionality vs mediality

Reading Geoffrey’s posting on the inaugural talk given by Eric Champion and his mention of the dimension of ‘soundscape’ that seems to have been relevant even for the first cave paintings (these paintings tend to be in a spot that is acoustically prominent in terms of echo effects etc.) I wonder whether it wouldn’t make sense to think of media channels as dimensions. In other words, 3D – which we nowadays automatically equate with topographical three-dimensionality – could actually also be visual 2D + sound, touch, smell, time, etc.. Doesn’t an image take on a new dimensionality when it is enhanced by either of these? Why restrict the notion of ‘dimension’ to the visual axes in the first place?