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Previous work has shown that perturbation analysis in software space canproduce candidate computable generative models and uncover possible causalproperties from the finite description of an object or system quantifying thealgorithmic contribution of each of its elements relative to the whole. One ofthe challenges for defining emergence is that one observer's prior knowledgemay cause a phenomenon to present itself to such observer as emergent while foranother as reducible. By formalising the act of observing as mutualperturbations between dynamical systems, we demonstrate that emergence ofalgorithmic information do depend on the observer's formal knowledge, whilerobust to other subjective factors, particularly: the choice of the programminglanguage and the measurement method; errors or distortions during theinformation acquisition; and the informational cost of processing. This iscalled observer-dependent emergence (ODE). In addition, we demonstrate that theunbounded and fast increase of emergent algorithmic information impliesasymptotically observer-independent emergence (AOIE). Unlike ODE, AOIE is atype of emergence for which emergent phenomena will remain considered to beemergent for every formal theory that any observer might devise. We demonstratethe existence of an evolutionary model that displays the diachronic variant ofAOIE and a network model that displays the holistic variant of AOIE. Ourresults show that, restricted to the context of finite discrete deterministicdynamical systems, computable systems, and irreducible information contentmeasures, AOIE is the strongest form of emergence that formal theories canattain.

philosophical transactions - royal society. mathematical, physical and engineering sciences/philosophical transactions - royal society. mathematical, physical and engineering sciences

Emergence and algorithmic information dynamics of systems and observers