  Topological defects are typically quantified relative to ordered backgrounds.
The importance of these defects to the understanding of physical phenomena
including diverse equilibrium melting transitions from low temperature ordered
to higher temperatures disordered systems (and vice versa) can hardly be
overstated. Amorphous materials such as glasses seem to constitute a
fundamental challenge to this paradigm. A long held dogma is that transitions
into and out of an amorphous glassy state are distinctly different from typical
equilibrium phase transitions and must call for radically different concepts.
In this work, we critique this belief. We examine systems that may be viewed as
simultaneous distribution of different ordinary equilibrium structures. In
particular, we focus on the analogs of melting (or freezing) transitions in
such distributed systems. The theory that we arrive at yields dynamical,
structural, and thermodynamic behaviors of glasses and supercooled fluids that,
for the properties tested thus far, are in qualitative and quantitative
agreement with experiment. We arrive at a prediction for the viscosity and
dielectric relaxations that is universally satisfied for all experimentally
measured supercooled liquids and glasses over 15 decades.
