The value of information in multi-scale feedback systems

Complex adaptive systems (CAS) can be described as system of information flows that dynamically interact across scales to adapt and survive. CAS often consist of many components that work toward a shared goal and interact across different informational scales through feedback loops, leading to their adaptation. In this context, understanding how information is transmitted among system components and across scales becomes crucial for understanding the behavior of CAS. Shannon entropy, a measure of syntactic information, is often used to quantify the size and rarity of messages transmitted between objects and observers, but it does not measure the value that information has for each observer. For this, semantic and pragmatic information have been conceptualized as describing the influence on an observer’s knowledge and actions. Building on this distinction, we describe the architecture of multi-scale information flows in CAS through the concept of multi-scale feedback systems and propose a series of syntactic, semantic, and pragmatic information measures to quantify the value of information flows for adaptation. While the measurement of values is necessarily context-dependent, we provide general guidelines on how to calculate semantic and pragmatic measures and concrete examples of their calculation through four case studies: a robotic collective model, a collective decision-making model, a task distribution model, and a hierarchical oscillator model. Our results contribute to an informational theory of complexity that aims to better understand the role played by information in the behavior of multi-scale feedback systems.