Emergence and algorithmic information dynamics of systems and observers

Previous work has shown that perturbation analysis in software space can produce candidate computable generative models and uncover possible causal properties from the finite description of an object or system quantifying the algorithmic contribution of each of its elements relative to the whole. One of the challenges for defining emergence is that one observer's prior knowledge may cause a phenomenon to present itself to such observer as emergent while for another as reducible. When attempting to quantify emergence, we demonstrate that the methods of Algorithmic Information Dynamics can deal with the richness of such observer-object dependencies both in theory and practice. By formalising the act of observing as mutual algorithmic perturbation, the emergence of algorithmic information is rendered invariant, minimal, and robust in the face of information cost and distortion, while still observer-dependent. We demonstrate that the unbounded increase of emergent algorithmic information implies asymptotically observer-independent emergence, which eventually overcomes any formal theory that an observer might devise to finitely characterise a phenomenon. We discuss observer-dependent emergence and asymptotically observer-independent emergence solving some previous suggestions indicating a hard distinction between strong and weak emergence.