Information closure is the degree to which a System’s own states suffice to predict its next states, so that knowing the state of its Environment adds nothing further. Formally, a process is informationally closed to the degree that the mutual information between its next state and the current state of its environment, conditional on its own current state, vanishes.
There are two ways to achieve closure:
- Trivial closure – the system is simply decoupled from its environment; nothing outside influences it, so there is nothing to predict. Rocks approximate this.
- Non-trivial closure – the system remains richly coupled to its environment but has internalised the environmental regularities that matter for its persistence: its self-model already carries the information the environment would otherwise contribute. The environment still drives the system, but through the system’s model of it.
Non-trivial information closure is what makes something an agent rather than a mere pattern: Every system is a model of its environment, but an agent maintains that model actively, from within, at the degree of closure its persistence requires – just enough model to persist, no more. The Markov Blanket is the surface across which closure is maintained; Free Energy Minimisation is the process by which it is maintained.
Two consequences:
- Closure cannot be imposed from outside. A model installed by an external designer is, informationally, part of the designer’s closure, not the system’s; a system is closed only over regularities it has internalised through its own dynamics. This is why collective agents – movements, organisations, networks – must construct their self-model from within, since an attractor maintained from within cannot be installed from without.
- Closure is a Scale-free Abstraction: cells, organisms and Social Systems all maintain it, and a higher-level system’s closure is not decomposable into that of its components – which is what gives higher levels genuine causal traction (cf. Causal Emergence).
References
- Bertschinger, Olbrich, Ay & Jost (2006), “Information and closure in systems theory”
- Chang et al. (2020), “Information closure theory of consciousness”
- Krakauer, Bertschinger, Olbrich, Flack & Ay (2020), “The information theory of individuality”