It is basic to construct funcion orthogonal to others , thought as vectors with

Infinite coordinates

So you get fourierr and many other systems. Tbe special functions.

Talcott Parsons and Robert K. Merton, both key figures in sociological functionalism, offered distinct approaches to understanding how social structures contribute to societal stability. Parsons adopted a grand, abstract, and system-oriented model. His structural functionalism focused on the idea that every part of society functions to maintain social equilibrium, emphasizing four functional imperatives (AGIL: Adaptation, Goal attainment, Integration, Latency) that systems must meet. He viewed social institutions as inherently positive and self-correcting, with little room for dysfunction or conflict. In contrast, Merton offered a more critical and flexible perspective. He introduced the concepts of manifest and latent functions, allowing for unintended consequences of social actions, and acknowledged dysfunctions—where some institutions could harm society. Unlike Parsons’ universalism, Merton emphasized middle-range theories, preferring empirical analysis over abstract system-building. He accepted that structures may not always serve society harmoniously, making his approach more nuanced and adaptable to real-world complexity. In essence, while Parsons built a macro-level ideal model, Merton refined it with empirical depth and critical realism.

Talcott Parsons and Robert Merton, two key theorists in sociology, both contributed to functional analysis but took notably different approaches. Parsons developed a grand theory of structural functionalism, aiming to explain all aspects of social systems through a universal framework. His AGIL schema—Adaptation, Goal attainment, Integration, and Latency—emphasized how all parts of society serve to maintain stability and equilibrium. He saw society as a cohesive system where each structure has a clear, positive function, and he largely ignored dysfunction or conflict. In contrast, Merton offered a middle-range theory approach, focusing on more specific social phenomena rather than attempting to explain society as a whole. He introduced key concepts like manifest and latent functions to highlight both intended and unintended consequences of social behavior. Importantly, Merton acknowledged that not all structures are beneficial, introducing the idea of dysfunctions and questioning the assumption of universal social harmony. While Parsons leaned toward abstract system-building, Merton’s approach was more empirical, flexible, and realistic in analyzing the complexities of modern society.