[bluesbassman]

I don't know how much math you've studied, but in linear algebra and other topics of mathematics, 4 dimensional or higher vectors are common. You can think of a vector as an "arrow" which has a length and a direction. So a 2-dimensional vector can be represented by this figure on your monitor: --->

A 3-dim vector can be thought of as an "arrow" pointing in a room. We can just as easily mathematically define 4-dimensional and higher vectors, which are "arrows" in 4-dimensional or higher space. The math is a natural, straightforward extension of 3-dimensions, however yes, they can be difficult to physically visualize. I try to imagine 4-dimensional vectors "extending" in an "extra" dimension I can't quite see.

In much of my work, I play around with mathematical objects called quaternions, which can be represented for some calculations by 4-dimensional vectors. So after a while, this becomes more natural and intuitive, even if I can't quite "see" it.