Hemineglect is among the more bizarre neurological conditions (which is also to say, devastating to the patient). In brief, the patient ignores one or the other half of space, right or left, up to and including his or her own body. They won't register stimuli on the neglected side and will even ignore their own bodies on that side, sometimes claiming that their limbs aren't their own: if you hold their arm up in front of them and ask them whose arm it is, they'll often insist it's a family member who's hiding nearby. (Yes, really.) A neurologist related to me that these patients will even sometimes request to be moved to a new bed in the hospital because there's someone else laying in bed with them (as in, the neglected half of their own body. Yes, really.) To these patients, a circle has only 180 degrees. The neglected half of space might as well be the fourth dimension.
Needless to say, natural experiments like these cases are a rich substrate for neurophilosophy. One aspect of neglect syndromes that I find interesting is that some of this behavior apparently amounts to a delusion, in the strict sense of a steadfast false belief. Neglect patients will sometimes complain that the hospital isn't feeding them enough, and of course when the nurse or physician comes into the room, they see a plate of food that's exactly half-eaten. So they turn the plate 180 degrees - and the patient grumbles "Good," and continues eating. See the disconnect here? If I were at dinner and said "Wow that green curry was good but I wish there were more," and my dining companion was able to magically produce more curry out of the fourth dimension before my eyes like some kind of a 3D chef visiting Flatland, of course I would be utterly amazed - but I haven't heard of such a reaction in the anecdotal reports I've heard from neurologists so far (I have not yet interacted with a neglect patient).
I'll do my best to put myself in the neglect patient's place again. Most of us believe that we have exactly 2 arms and 2 legs, and would react incredulously if a researcher told us that no, in fact we had four arms and four legs, but we were only using two of each. The researcher says to me "Fine, I can prove it." In an empty room with just her and me, she holds up an arm in front of me that looks just like me other two arms - skin color, size, etc. - and says it's my arm. I can't feel it or move it, and somehow I'm unable to see what it connects to, and it seemed to appear out of thin air (just like the green curry). But having four arms is ridiculous! Yet I trust this researcher; she seems incredibly earnest, she can reproduce this trick any time I ask with no preparation, and as I soon discover, so can anyone else I ask, including people with no possible connection to the researcher. All of them can hold up in front of me one or two arms that look like my own arms.
In such a position, I would be forced to conclude, as bizarre as it seems, that the evidence points to some kind of a perceptual defect on my part. As strange as it is, and as much as I absolutely cannot understand where this arm is coming from or how it connects to me, I eventually have to accept the incredible truth (after many, many trials) that I and everybody else has four arms, and that there's something strange about my perception that keeps me from seeing them. And even if I remain incredulous, certainly I would at least want to know how they were doing this amazing trick. But severe neglect patients not only avoid curiosity about things that could disturb their limited perception of space, they make up impossible stories about where their limb is coming from if it's presented to them. Clearly the deficit that produces their inability to fully represent space is neurological, rather than psychogenic. But isn't this part of the behavior arguably delusional?