  Our point of departure is the following simple common generalisation of the
Sylvester-Gallai theorem and the Motzkin-Rabin theorem:
  Let S be a finite set of points in the plane, with each point coloured red or
blue or with both colours. Suppose that for any two distinct points A,B in S
sharing a colour there is a third point C in S, of the other colour, collinear
with A and B. Then all the points in S are collinear.
  We define a chromatic geometry to be a simple matroid for which each point is
coloured red or blue or with both colours, such that for any two distinct
points A,B in S sharing a colour there is a third point C in S, of the other
colour, collinear with A and B. This is a common generalisation of proper
finite linear spaces and properly two-coloured finite linear spaces, with many
known properties of both generalising as well. One such property is Kelly's
complex Sylvester-Gallai theorem. We also consider embeddings of chromatic
geometries in Desarguesian projective spaces. We prove a lower bound of 51 for
the number of points in a 3-dimensional chromatic geometry in projective space
over the quaternions. Finally, we suggest an elementary approach to the
corollary of an inequality of Hirzebruch used by Kelly in his proof of the
complex Sylvester-Gallai theorem.
