  This presentation explains why models with a dynamical symmetry often work
extraordinarily well even in the presence of large symmetry breaking
interactions. A model may be a caricature of a more realistic system with a
"quasi-dynamical" symmetry. The existence of quasi-dynamical symmetry in
physical systems and its significance for understanding collective dynamics in
complex nuclei is explained in terms of the precise mathematical concept of an
"embedded representation". Examples are given which exhibit quasi-dynamical
symmetry to a remarkably high degree. Understanding this unusual symmetry and
why it occurs, is important for recognizing why dynamical symmetries appear to
be much moreprevalent than they would otherwise have any right to be and for
interpreting the implications of a model's successes. We indicate when
quasi-dynamical symmetry is expected to apply and present a challenge as to how
best to make use of this potentially powerful algebraic structure.
