Research

This article introduces a novel mathematical model to quantify the Skill-Challenge Balance, essential for achieving a Flow state, through the lens of information theory. It contrasts with existing models this approach addresses the balance between an individual's perceived capabilities (prior knowledge) and task challenges (knowledge to be discovered), offering a refined method for identifying Flow states.

The model uses mutual information (I(X;Y)) and conditional missing information (H(Y|X)) to define the balance essential for flow. The balance function, governed by the Knowledge Discovery Efficiency (KEDE), quantifies the alignment between a person's capabilities and task complexity. An optimal KEDE value of 1/2 suggests a perfect balance, indicative of flow, while values deviating from this point suggest tendencies towards anxiety or boredom.

This model not only enriches our theoretical understanding of Flow but also holds practical implications for enhancing workplace productivity and well-being. It paves the way for future research and practical applications, encouraging the development of strategies and tools to help individuals and organizations better achieve and sustain flow states. Ultimately, this work contributes to a deeper appreciation of the psychological and informational dynamics at play in achieving optimal experiences in professional settings.

We show how to operationalize the Multi-Scale Law of Requisite Variety as a multi-scale knowledge-matching problem by defining a scale-dependent “knowledge gap” H(X|Y)n and its corresponding Knowledge-Discovery Efficiency (KEDE) profile. KEDE provides an operational way to quantify how efficiently a system converts prior knowledge into effective responses, both globally and across scales, making it possible to diagnose where regulation fails, where knowledge is missing, and why success at one scale cannot compensate for failure at another.

We address Real-world applications of Ashby's Law by adopting Ashby's strict black-box perspective: only external behaviour is observable. First we define the multi-staged selection process of narrowing down and selecting the appropriate response from the set of alternative responses as the Knowledge Discovery Process. We then label H(X|Y) as the knowledge to be discovered, which is the gap in internal variety that had to be compensated by selection. This quantifies how much disorder the regulator still permits and, conversely, how close the system comes to meeting Ashby's requisite-variety condition. In information-theoretic terms, perfect regulation requires H(X|Y) = 0. Then we quantify the knowledge to be discovered H(X|Y) based on the observable outcomes E. Building on this result, we generalize Knowledge-Discovery Efficiency (KEDE) - scalar metric that quantifies how efficiently a system closes the gap between the variety demanded by its environment and the variety embodied in its prior knowledge. KEDE operationalises requisite variety when internal mechanisms remain opaque, offering a diagnostic tool for evaluating whether biological, artificial, or organisational systems absorb environmental complexity at a rate sufficient for effective regulation. Finally we present applications of KEDE in diverse domains, including typing the longest English word, measuring software development, testing intelligence, basketball game, assembling furniture, and speed of light in medium.

We discuss problem for the quantification of the productivity of knowledge workers. We introduce a measure of this productivity called KEDE (Knowl-edgE Discovery Efficiency). The main application of KEDE can be for performance improvement. Then KEDE is extended to account for errors in knowledge discov-ery and for the lost time in a working day. Characteristic features of KEDE are discussed.