Sean at Cosmic Variance wonders why we can’t visualize more than three dimensions. I find it both hard to imagine how you could visualize four dimensions and hard to imagine what biological feature of our brains prevents us from doing so.
Ars Mathematica
Dedicated to the mathematical arts.
I have thought about this problem; To me it seems with effort we should be able to visualize in 4-d but the result is kind of spooky. Since we can depict 3-dobjects on a 2-d piece of paper we should be able to build a 3-d sculpture that depicts 4-d objects. We need to do the math and get the angles correct; the next problem seems to be that since we live in 3-space, objects that will not block or cross others in 4 space will do so in 3-space. Now the whole thing about only being able to see sections of a 4-d object seems to me only to apply if somehow one somehow introduced a 4-d object into 3-space. If one is just visualizing one should be free of this problem. Does this make sense; I have been trying to think of a art project that would build stuff that be 3-space sculptures of 4-space objects. If thios is interesting please reply. We do all sorts of things not designed into us by nature or whatever. Thanks and Have Fun, Sends Steve