Your comparisons do not fit. Not only have things flown since pre-human times, it was not deemed impossible by anything more rigorous than "URK I ROCK HEAD GYARR!"...
The layman's term could be easily replaced by 'universe', 'reality', or whatever else would fit the context - I instantly do a double-take whenever I see that word, because I begin looking for math and find none... think this:
I understand that you aren't familiar with the mathematical meaning of the word, but I'd appreciate if you didn't use it because it's unnecessary and obfuscating.
I gave up on the deity thing for similar reasons - I couldn't find one that was coherent, and when it comes down to it I'd much rather have logic than comfort.
Since I prefer math to physics I don't care much for evidence - I enjoy dealing with abstract things more than pretending to care about real-world events, so I look strictly at logical consistency before anything else and that's where I dropped that belief.
Glenn, four-dimensional visualization is... well, I haven't tried hallucinogens, but thanks to math I don't really need to.
Picture it like this... imagine that we have a being (who will be referred to as Larry Lineman) existing only in one-dimensional space (a line), and we want to show Larry a circle. If we were to draw a circle on a piece of paper and look at it by moving it under a narrow slit on another piece of paper, we'd see a point at the top; moving down, we'd see a pair of points that at first grew further away, then stopped, and then came closer together again, until we came to the bottom of the circle and only saw a single point again.
We would then 'demonstrate' a circle to Larry by saying that "well, when we look at this object through your restrictions, displaying its 'part' in one dimension while moving through the second to see the whole thing, it looks like this" and show him a point that gradually splits into two parts that move apart and then back together until becoming a single point again. What have we done? We've taken advantage of movement through time (and a good bit of intelligence on Larry's part) to turn a static image into a 'movie' of sorts, and let the imagination take the rest.
Similarly, if we had Pete Planeman, a similar entity living only in two-dimensional space (say, on a piece of paper) we could show him a sphere by passing a sphere 'through' the plane - he would see a dot, and then a growing circle, and then a shrinking circle, and finally another dot. Again, we display as much of the object as we can in the restricted space, and use the change in the object over time to help 'imagine' what it would look like in higher-dimensional space.
If, then, Harry Hyperspaceman, a four-dimensional being, tried to show us a four-dimensional hypersphere in this way, it would look to us like a point, then a growing sphere, and then a shrinking sphere, and finally a point; if he were to show us a four-dimensional hypercube, we'd see nothing, then a cube popping straight into existence, and nothing again; if we were to be showed a hyperdodecahedron... well, fuck it, he's a total bastard and I'm going to go get a drink. (This was all possibly just paraphrased from somewhere, but I'll be damned if I know where...)
Jeff