  In Calabi--Yau compactifications of the heterotic string there exist
quantities which are universal in the sense that they are present in every
Calabi--Yau string vacuum. It is shown that such universal characteristics
provide numerical information, in the form of scaling exponents, about the
space of ground states in string theory. The focus is on two physical
quantities. The first is the Yukawa coupling of a particular antigeneration,
induced in four dimensions by virtue of supersymmetry. The second is the
partition function of the topological sector of the theory, evaluated on the
genus one worldsheet, a quantity relevant for quantum mirror symmetry and
threshold corrections. It is shown that both these quantities exhibit scaling
behavior with respect to a new scaling variable and that a scaling relation
exists between them as well.
