What often strikes me as I read about higher spatial dimensions is the potential relationship between the mathematicians' conception of the fourth spatial dimension and the physicists' conception of time as the fourth dimension in a space-time continuum. In Flatland, as we discussed in class, A Square's impression of A Sphere as A Sphere moves through flatland is not that of a creature moving in a spatial direction, but rather of someone (a priest, in fact) moving through time; he appears first as a point, or an infant, grows in size to that of an adult Circle, then shrinks, as if an old man withering. Thus, to the 2-dimensional observer, it is as though this visitor is progressing through time, rather than through a form of space. Likewise, it could be that many phenomena in our own experience may be explained by motion in higher dimensions; the bizarre behavior of particles described but not quite explained by quantum mechanics may be better accounted for by motion through the fourth dimension, or, on the other side of the university, angels, spirits or ghosts may be creatures who have achieved the ability to travel through the fourth dimension.
I have a crazy idea that our own motion through time is actually directed motion through a fourth spatial dimension; that is, time is the same as the other dimensions but our motion through it is not under our control. As an analogy, imagine the following: at a moment in Flatland, freeze time. Take this flat sheet of time and set it on a table somewhere. Then, at the next moment, freeze time again. Everything that has moved should have shifted slightly. Take this slab of time and place it neatly on top of the first one. Continue this process until you have a nice tall stack. It will look like a number of prisms: triangular, pentagonal, etc. twisting and curving upwards. This motion upwards, which is simply a spatial direction to us as we examine our new sculpture, is actually time in Flatland. A good demonstration of this concept is the claymation shorts they used to show on Pee-Wee 's Playhouse, where a carefully constructed slab of clay would be cut away a slice at a time to reveal the frames of an animated story.
We, then, would be living in a three-dimensional space projected forward by some force (the big bang, it would seem) through the fourth dimension; to an observer in 4-space, we would be cutting a swath across their universe as we, in our own perception, move through time. Naturally, if this sort of thing could be true, there exists the potential to step outside of our three-space and come back in a different time, as if we were to take A Square out of his space and stick him back in further up or further down the time axis. Or, like Superman spinning the earth around backwards, we could slow down our entire universe's motion through time and send it back the other way...