My statement yesterday morning that the 15 points
of the finite projective space PG(3,2) are indivisible
was wrong. I was misled by quoting the powerful
rhetoric of Lincoln Barnett (LIFE magazine, 1949).
Points of Euclidean space are of course indivisible:
"A point is that which has no parts" (in some translations).
And the 15 points of PG(3,2) may be pictured as 15
Euclidean points in a square array (with one point removed)
or tetrahedral array (with 11 points added).
The geometry of PG(3,2) becomes more interesting,
however, when the 15 points are each divided into
several parts. For one approach to such a division,
see Mere Geometry. For another approach, click on the
image below.
