  The Gardner length scale $\xi$ is the correlation length in the vicinity of
the Gardner transition, which is an avoided transition in glasses where the
phase space of the glassy phase fractures into smaller sub-basins on
experimental time scales. We argue that $\xi$ grows like $ \sim
\sqrt{B_{\infty}/G_{\infty}}$, where $B_{\infty}$ is the bulk modulus and
$G_{\infty}$ is the shear modulus, both measured in the high-frequency limit of
the glassy state. We suggest that $\xi$ might be inferred from stress-stress
correlation functions, which is more practical for experimental investigation
than studying two copies of the system, which can only be done in numerical
simulations. Our arguments are illustrated by explicit calculations for a
system of disks moving in a narrow channel, which is solved exactly by transfer
matrix techniques.
