Abstract: By Ramsey's theorem, any system of n segments in the plane has roughly log $n$ members that are either pairwise disjoint or pairwise intersecting. Analogously, any set of n points $p(1),\cdots p(n)$ in the plane has a subset of roughly loglog $n$ elements with the property that the orientation of $p(i)p(j)p(k)$ is the same for all triples from this subset with $i
