Quantifying Agency in time evolving complex systems.

Lead Research Organisation: Imperial College London
Department Name: Dept of Mathematics


This age of big data, where we are continuously monitoring the complex systems that drive our world, provides us with a unique opportunity to understand these systems as simple models that can be easily communicated to the general public. This effort of distilling the knowledge into simple stories can only come to fruition at a coarse-grained macro level which can be easily understood by people from all walks of life.

In recent years, it has been argued that this effective coarse-graining of the complex systems into interacting subsystems offers a deeper insight into the workings of complex systems than just making them more comprehensible. For example, it is now understood that there are functional and biological advantages like optimal self-prediction and control enabled by certain levels of hierarchy (Hoel and Levin, 2020).

Therefore, it can be argued that hierarchical complex systems self organizes into sub-systems that are known as "informational" individuals. These individuals possess characteristics like optimal self-prediction. Understanding the dynamics of the system at the scale of these individuals offers a natural way of coarse-graining the system, yet capturing the emergent phenomenon of interest.

In this proposal, we wish to explore the existence of these optimally self predicting clusters and their relevance in complex systems in two different settings,
1) In a mathematical model of ecological evolution, where agents co-evolve as individual species, as communities and as ecosystems. These emergent hierarchies in the system will enable us to probe is the self-organisation into these structures offers optimal prediction or control.
2) In a carefully designed experiment with two classical musicians improvising together, as they switch as leaders and followers, while their brain activity is simultaneously recorded using wireless EEG scanners. This experiment offers an opportunity to relate the observed optimally self-predicting structures in the data to the locus of agency in the complex system.

Therefore, in addition to developing methods to track informational individuals, we also aim to relate them to a measure of agency in complex systems.


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