  We suggest a quantitative and objective notion of emergence. Our proposal
uses algorithmic information theory as a basis for an objective framework in
which a bit string encodes observational data. A plurality of drops in the
Kolmogorov structure function of such a string is seen as the hallmark of
emergence. Our definition offers some theoretical results, in addition to
extending the notions of coarse-graining and boundary conditions. Finally, we
confront our proposal with applications to dynamical systems and
thermodynamics.
