# Differences

*Differences* between values are distinct from those values
themselves. For example, *n-dimensional points* can be related
using an *affine space*; whilst the *difference between these
points* is better represented as a *vector space*. The
crucial difference is that vectors have a special, distinguished
“origin” (the 0 vector, representing
“no difference”), whilst affine spaces don’t need to distinguish any
points as being more “special” than others.

A good example of this is a 1-dimensional line, which we often model
as a “number line” with entirely artificial labels for both position and
magnitude. In fact, the “number line” is a more abstract space: of
*differences between 1-dimensional points*. The relationship
between these two spaces is captured algebraically by a torsor