There was a time when I could visualize the obverse, and then the reverse. Now I see them simultaneously. This is not as though the Zahir were crystal, because it is not a matter of one face being superimposed upon another; rather, it is as though my eyesight were spherical, with the Zahir in the center.
– Jorge Luis Borges (1949/1962)
In conversation, a couple people have told me that they can visually imagine four spatial dimensions -- a hypercube, for example. (Probably someone has said this in print, too, but I can't recall any instances. Pointers welcome.)
My mental field of vision is larger than the normal one. In the former I appear to see everything from some commanding point of view, which at once embraces every object and all sides of every object.
– a questionnaire respondent in Galton (1880)
I find this rather hard to imagine, and (I confess) believe. But maybe that's just my own narrowness? If there are or could be four actual, physical spatial dimensions, then presumably there are or could be aliens who could see (and thus presumably visually imagine) in all those dimensions. The unpicturability of such imagery by me doesn't imply its impossibility. Maybe the dimensionality of some people's visual imagining outruns the dimensionality of their vision. (I assume here that no human being can actually outwardly see in four dimensions or with such apparently impossible points of view. At least I've heard no such reports.)
Such impossibilities of visual perspective, if they are possible in visual imagination, appear to strain against two common claims about imagery. One is Hume's "faint perceptions" view, according to which images are just faint copies of ordinary sensory impressions. (One needn't of course be a fully orthodox Humean on this point -- even Hume probably wasn't -- to think that visual imagery is very structurally similar, experientially, to visual sensation.) Another is Stephen Kosslyn's view, related to Hume's, that imagery differs from perception mainly in being the activation of visual brain areas and visual representational forms by central cognitive causes rather than from peripheral sensory stimulation. The visual image, Kosslyn says, is a "simulation" or "emulation" of what we visually perceive. Though not perhaps impossible, it would be odd, on such a view, if the imagistic simulation could have radically different perspectival and spatial properties from the perceptions simulated.
So probably: Either visual imagery of such sensory impossibilities is itself impossible, despite some people's reports, or Hume and Kosslyn (and lots of other people) are wrong. Is there a way to go about settling this?