OK, then I should have worded it like this: I can visualize a 4 dimensional vector space over the reals. Even if the 4th dimension in your particular setting is

OK, then I should have worded it like this: I can visualize a 4 dimensional vector space over the reals. Even if the 4th dimension in your particular setting is not time, I can still visualize it as such. Also, visualizing an n dimensional vector is not very interesting. A vector indicates a point, and a point looks the same in any number of dimensions.