We present the underlying theoretical motivation for the recently introduced kinematic variable $n^2$. Scattering amplitudes are considered as functions of $s$ and $n^2$, and asymptotic formulas for $s\to \infty$ at fixed $n^2$ are derived. It is shown empirically that many diffractive reactions appear to scale, i.e., they show little or no energy dependence when considered as functions of $n^2$. The shrinkage of the forward diffraction peak in $\frac{d\sigma }{\mathrm{dt}}$ seen in many reactions at present energies, is predicted to die out with increasing energy. It is shown that $\overline{p}p\to \overline{p}p$ scattering should exhibit antishrinkage. Several reactions are studied: $\mathrm{pp}\to \mathrm{pp}$, $K^{+}p\to K^{+}p$, ${\pi }^{\pm }p\to {\pi }^{\pm }p$, $\gamma p\to \rho p$, $\gamma p\to \phi p$, $\mathrm{pp}\to p{N}^{*}$. Speculative predictions are made for a kind of "superscaling" in inclusive reactions and in deep-inelastic electron scattering.

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