For any collection of Schubert conditions on lines in projective space
which generically determine a finite number of lines, we show there exist
real generic conditions determining the expected number of real lines. This
extends the classical Schubert calculus of enumerative geometry for the
Grassmann variety of lines in projective space from the complex realm to the
real. Our main tool is an explicit description of rational equivalences
which also constitutes a novel determination of the Chow rings of these
Grassmann varieties. The combinatorics of these rational equivalences
suggests a non-commutative associative product on the free abelian group on
Young tableaux. We conclude by considering some enumerative problems over
other fields.