  We streamline treatments of the interpretability orders
$\trianglelefteq^*_\kappa$ of Shelah, the key new notion being that of
pseudosaturation. Extending work of Malliaris and Shelah, we classify the
interpretability orders on the stable theories. As a further application, we
prove that for all countable theories $T_0, T_1$, if $T_1$ is unsupersimple,
then $T_0 \trianglelefteq^*_1 T_1$ if and only if $T_0
\trianglelefteq^*_{\aleph_1} T_1$. We thus deduce that simplicity is a dividing
line in $\trianglelefteq^*_{\aleph_1}$, and that consistently, $SOP_2$
characterizes maximality in $\trianglelefteq^*_{\aleph_1}$; previously these
results were only known for $\trianglelefteq^*_1$.
