Yesterday's APOD presented an interesting point of view.
You know what would be cool? If you could create some glasses (perhaps fed by some sort of camera mounded on your head) that would give your eyes this view all the time. The human brain is adaptable to it's vision field being modified and I think it would adapt to this change too. I'm sure you would start to navigate quiet nicely. And if you removed the glasses after your brain adapted what would you see? In experiments that turn the vision field upside down the subjects report their vision field flips upside down when they remove the glasses that do this to them (and they do regain their normal sense after a bit). So ... would the world appear to be a pie slice of a projective plane if you adapted to this view and then removed your glasses?