Yesterday, we started off into the abstract world of 4-space.

The idea is that the domain of a function in 1 variable is actually a number line, or a linear graph. The domain of functions with 2 variables can be thought of as curves, and 3 variables as surfaces.

We then move into level surfaces (sort of like contour maps), a fascinating look at how the domain of a 4-space function can be represented by 3-D curves and surfaces! Amazing!

So at least we can represent 4-D functions in terms of their domains, just as we can represent the domain of 3-D functions using level surfaces, and then think about the z-dimension separately.

*Image source: http://en.wikipedia.org/wiki/Fourth_dimension*