**2. Colorspace **
While reading a computer graphics textbook, I came across the idea
that all colors lie in a unique point within a three dimensional cube,
on which the three axes are red, green and blue. This is a very
promising idea for graphic representation of higher spaces for me. The
idea that a single pixel onscreen corresponds to a three dimensional
point seems intuitively a strong one; you could do graphs of four
dimensions on a line! There's a lot to explore here, I think.

**3. Alternative Interpretations of Geometry**
There is mention in B3D of a geometry of segments, where in each
segment is drawn with opposite endpoints on two respective coordinate
planes, thus presenting each segment as an object determined by four
variables, namely, the coordinates of its respective endpoints. It is
possible to reinterpret a four dimensional geometry to refer to such
a geometry of segments, by treating the segments as though they were
points. There are lots of other possibilites like this, including
geometries of ellipses, spheres, squares, sine waves, and just about
anything you can think of. The nice thing about them is that they are
of high dimensionality, yet are easily represented in our space. I
think there could be a whole lot of fun to be had here; what
particularly strikes me as promising is the idea of illustrating a
single, demonstrative geometric figure using many different
representations. I would really like to have a go at this one.

Keith_Adams@brown.edu