  Discriminating quark jets from gluon jets is an important but challenging
problem in jet substructure. In this paper, we use the concept of mutual
information to illuminate the physics of quark/gluon tagging. Ideal quark/gluon
separation requires only one bit of truth information, so even if two
discriminant variables are largely uncorrelated, they can still share the same
"truth overlap". Mutual information can be used to diagnose such situations,
and thus determine which discriminant variables are redundant and which can be
combined to improve performance. Using both parton showers and analytic
resummation, we study a two-parameter family of generalized angularities, which
includes familiar infrared and collinear (IRC) safe observables like thrust and
broadening, as well as IRC unsafe variants like $p_T^D$ and hadron
multiplicity. At leading-logarithmic (LL) order, the bulk of these variables
exhibit Casimir scaling, such that their truth overlap is a universal function
of the color factor ratio $C_A/C_F$. Only at next-to-leading-logarithmic (NLL)
order can one see a difference in quark/gluon performance. For the IRC safe
angularities, we show that the quark/gluon performance can be improved by
combining angularities with complementary angular exponents. Interestingly, LL
order, NLL order, Pythia 8, and Herwig++ all exhibit similar correlations
between observables, but there are significant differences in the predicted
quark/gluon discrimination power. For the IRC unsafe angularities, we show that
the mutual information can be calculated analytically with the help of a
nonperturbative "weighted-energy function", providing evidence for the
complementarity of safe and unsafe observables for quark/gluon discrimination.
