Emerging properties of a systems are those properties we can't ascribe to any of the parts composing it, but instead arise from the way we compose them. In general systems theory, this usually manifests as a failure of naive compositionality of behaviour: to compute the behaviour of a system it is not enough to naively collate the behaviour of its parts. Instead, the pattern used to compose the system has to be taken into account to arrive at the true behaviour of the whole.
Using the framework of categorical systems theory we can characterize emergence very precisely as the failure of a certain lax naturality constraint to be invertible. The quest is thus to (1) develop tools to study these failure, inspired by cohomology theory and (2) develop tools to amend naive compositionality to take emergence into account.
Reading list
- Systems, Generativity and Interactional Effects by Elie Adam,
- Lax functors describe emergent effects by Jules Hedges,
- Fantastic sheaves and where to find them by myself,
- Structured Decompositions: Structural and Algorithmic Compositionality, by Benjamin Merlin Bumpus, Zoltan A. Kocsis, Jade Edenstar Master