  "Emergence", the phenomenon where a complex system displays properties,
behaviours, or dynamics not trivially reducible to its constituent elements, is
one of the defining properties of complex systems. Recently, there has been a
concerted effort to formally define emergence using the mathematical framework
of information theory, which proposes that emergence can be understood in terms
of how the states of wholes and parts collectively disclose information about
the system's collective future. In this paper, we show how a common,
foundational component of information-theoretic approaches to emergence implies
an inherent instability to emergent properties, which we call flickering
emergence. A system may on average display a meaningful emergent property (be
it an informative coarse-graining, or higher-order synergy), but for particular
configurations, that emergent property falls apart and becomes misinformative.
We show existence proofs that flickering emergence occurs in two different
frameworks (one based on coarse-graining and another based on multivariate
information decomposition) and argue that any approach based on temporal mutual
information will display it. Finally, we argue that flickering emergence should
not be a disqualifying property of any model of emergence, but that it should
be accounted for when attempting to theorize about how emergence relates to
practical models of the natural world.
