  Defining the entropy of classical particles raises a number of paradoxes and
ambiguities, some of which have been known for over a century. Several, such as
Gibbs' paradox, involve the fact that classical particles are distinguishable,
and in textbooks these are often `resolved' by appeal to the quantum-mechanical
indistinguishability of atoms or molecules of the same type. However, questions
then remain of how to correctly define the entropy of large poly-atomic
particles such as colloids in suspension, of which no two are exactly alike. By
performing experiments on such colloids, one can establish that certain
definitions of the classical entropy fit the data, while others in the
literature do not. Specifically, the experimental facts point firmly to an
`informatic' interpretation that dates back to Gibbs: entropy is determined by
the number of microstates that we as observers choose to treat as equivalent
when we identify a macrostate. This approach, unlike some others, can account
for the existence of colloidal crystals, and for the observed abundances of
colloidal clusters of different shapes. We also address some lesser-known
paradoxes whereby the physics of colloidal assemblies, which ought to be purely
classical, seems to involve quantum mechanics directly. The experimental
symptoms of such involvement are predicted to be `isotope effects' in which
colloids with different inertial masses, but otherwise identical sizes and
properties, show different aggregation statistics. These paradoxes are caused
by focussing one's attention on some classical degrees while neglecting others;
when all are treated equally, all isotope effects are found to vanish.
