More really is different

Abstract

In 1972, P. W. Anderson suggested that 'More is Different', meaning that complex physical systems may exhibit behavior that cannot be understood only in terms of the laws governing their microscopic constituents. We strengthen this claim by proving that many macroscopic observable properties of a simple class of physical systems (the infinite periodic Ising lattice) cannot in general be derived from a microscopic description. This provides evidence that emergent behavior occurs in such systems, and indicates that even if a 'theory of everything' governing all microscopic interactions were discovered, the understanding of macroscopic order is likely to require additional insights.

Phase-response curves and synchronized neural networks

“…It is also becoming clear that some framework needs to be developed to study neurophysiology at a network level, as theoreticians have proved that for even simple networks for which both the elements and their connections are completely defined, there are some emergent properties that cannot be inferred (i.e. the problem of predicting emergent properties from a purely reductive perspective is undecidable) (Anderson 1972;Gu et al 2009). …”

Neuronal network analyses: premises, promises and uncertainties

“…But even where data are available, the complexity of detailed models can make them as difficult to understand as the actual system (e.g. Greenberg & Manor 2005), and even relatively simple questions in artificial neural nets are practically non-solvable (NP-complete; Gu et al 2009). Models are thus inevitably simplified and cannot be reified in assumptions that they reflect actual systems.…”

Thermodynamics of emergence: Langton's ant meets Boltzmann

“…Then it would provably be undecidable whether a given initial state will result in emergent behavior. This shows in addition to the above mentioned Loschmidt configurations that the concept of emergence is related to undecidable properties of system states (see also [49]). …”