  Dynamical similarities are non-standard symmetries found in a wide range of
physical systems that identify solutions related by a change of scale. In this
paper we will show through a series of examples how this symmetry extends to
the space of couplings, as measured through observations of a system. This can
be exploited to focus on observations that can be used distinguish between
different theories, and identify those which give rise to identical physical
evolutions. These can be reduced into a description which makes no reference to
scale. The resultant systems can be derived from Herglotz's principle and
generally exhibit friction. Here we will demonstrate this through three example
systems: The Kepler problem, the N-body system and
Friedmann-Lema\^itre-Robertson-Walker cosmology.
