  To improve our understanding of orbital instabilities in compact planetary
systems, we compare suites of $N$-body simulations against numerical
integrations of simplified dynamical models. We show that, surprisingly,
dynamical models that account for small sets of resonant interactions between
the planets can accurately recover $N$-body instability times. This points
toward a simple physical picture in which a handful of three-body resonances,
generated by interactions between nearby two-body mean motion resonances,
overlap and drive chaotic diffusion, leading to instability. Motivated by this,
we show that instability times are well described by a power law relating
instability time to planet separations, measured in units of fractional
semi-major axis difference divided by the planet-to-star mass ratio to the
$1/4$ power, rather than the frequently adopted $1/3$ power implied by
measuring separations in units of mutual Hill radii. For idealized systems, the
parameters of this power-law relationship depend only on the ratio of the
planets' orbital eccentricities to the orbit-crossing value, and we report an
empirical fit to enable quick instability time predictions. This relationship
predicts that observed systems comprised of three or more sub-Neptune-mass
planets must be spaced with period ratios $P \gtrsim 1.35$ and that tightly
spaced systems ($P \lesssim 1.5$) must possess very low eccentricities ($e
\lesssim 0.05$) to be stable for more than $10^9$ orbits.
