  One of the most important and useful examples in discrete geometry is a
finite sequence of points on the moment curve $\gamma(t)=(t,t^2,t^3,\dots
,t^d)$ or, more generally, on a {\it strictly monotone curve} in $\mathbb R^d$.
These sequences as well as the ambient curve itself can be described in terms
of {\it universality properties} and we will study the question: "What is a
universal sequence of oriented and unoriented lines in $d$-space''
  We give partial answers to this question, and to the analogous one for
$k$-flats. Given a large integer $n$, it turns out that, like the case of
points the number of universal configurations is bounded by a function of $d$,
but unlike the case for points, there are a large number of distinct universal
finite sequences of lines. We show that their number is at least $2^{d-1}-2$
and at most $(d-1)!$. However, like for points, in all dimensions except $d=4$,
there is essentially a unique {\em continuous} example of a universal family of
lines. The case $d=4$ is left as an open question.
