So here is what is now an everyday example of representing multidimensional data on a two dimensional surface.

The critical factor is that the illusion of depth is created on a flat or two dimensional surface.

The 5-sphere, or hypersphere in six dimensions, is the five dimensional surface equidistant from a point.

The illusion of three dimensions on a two dimensional surface can be created by providing each eye with different visual information.

Two dimensional surfaces are a good representation for most objects, though they may be non-manifold.

Alternatively, canvases may be altered by losing their flatness and assuming a three dimensional surface.

The reason is, simply put, that solutions to such systems are asymptotic to a two dimensional surface and therefore solutions are well behaved.

Area is the amount of space a two dimensional (flat) surface takes up.

The 6-sphere or hypersphere in seven dimensions is the six dimensional surface equidistant from a point, e.g. the origin.

The model can be compared to a slowly vibrating string, or a two dimensional surface obeying the wave equation.