  A central physical question is the extent to which infrared (IR) observations
are sufficient to reconstruct a candidate ultraviolet (UV) completion. We
recast this question as a problem of communication, with messages encoded in
field configurations of the UV being transmitted to the IR degrees of freedom
via a noisy channel specified by renormalization group (RG) flow, with noise
generated by coarse graining / decimation. We present an explicit formulation
of these considerations in terms of lattice field theory, where we show that
the "misanthropic entropy" -- the mutual information obtained from decimating
neighbors -- encodes the extent to which information is lost in marginalizing
over / tracing out UV degrees of freedom. Our considerations apply both to
statistical field theories as well as density matrix renormalization of quantum
systems, where in the quantum case, the statistical field theory analysis
amounts to a leading order approximation. As a concrete example, we focus on
the case of the 2D Ising model, where we show that the misanthropic entropy
detects the onset of the phase transition at the Ising model critical point.
