Cognitive Operator Theory: A Curvature Dependent Model of Organizational Cognition

This paper explains how an organization’s structure shapes its ability to think, learn, coordinate, and make decisions. Building on earlier work that showed how centralization can be measured as “curvature” in the organization’s communication network, the current paper develops a full computational model of how organizations process information. The model introduces three core mechanisms. The cognition operator describes how information is amplified or lost as it moves through the organization. The decision operator explains how groups convert information into stable choices. The cognitive load operator measures how muchstrain the organization experiences when processing information.Four findings matter directly for leaders. First, highly centralized structures dramatically reduce the organization’s ability to amplify and integrate information. Second, decentralized structures make decision making more stable and resilient. Third, the organization’s “cognitive capacity” its ability to handle complexity declines predictably as communication bottlenecks increase. Fourth, coordination capacity and cognitive capacity are two sides of the same coin: improving one automatically improves the other. The paper also provides a measurement framework that allows leaders to estimate these quantities directly from communication data (e.g., email or messaging logs). A simple four-node example shows how small structural differences can produce large differences in cognitive performance. Overall, the paper offers a unified, geometry-based explanation of how organizational design shapes thinking, decision making, and the ability to manage cognitive load.