  We study Jang's equation on a one-parameter family of asymptotically flat,
spherically symmetric Cauchy hypersurfaces in the maximally extended
Schwarzschild spacetime. The hypersurfaces contain apparent horizons and are
parametrized by their proximity to the singularity at $r = 0$. We show that on
those hypersurfaces sufficiently close to the singularity, every radial
solution to Jang's equation blows up. The proof depends only on the geometry in
an arbitrarily small neighborhood of the singularity, suggesting that Jang's
equation is in fact detecting the singularity. We comment on possible
applications to the weak cosmic censorship conjecture.
