G
regory Bateson, in his book Mind and Nature, relates the story of teaching a group of psychiatry residents at a Veterans' Administration hospital. He started the course with an exam, telling his students that by the end of the course they would understand the questions. The exam asked for a brief definition of (1) sacrament and (2) entropy. I think of Bateson's exam when I deal with a rising tide of papers, books, and speeches dealing with complexity and management. I would like to set a qualifying exam for the authors of those works. Following Bateson's example, my first question would ask for a definition of entropy and an explanation of how we apply a concept from equilibrium thermodynamics to nonequilibrium systems. I would then ask for a definition of nonlinear systems, with an explanation of why nonlinear systems are so difficult to analyze. My third question would ask for a definition of deterministic chaos and how it differs from randomness. Then I would ask for the description of an emergent property and for a definition of selection algorithms. Finally I would ask for the computer modelling of a complex problem in management and a discussion of how the answers to all the other questions have a bearing on utilizing the model. Now you may think that this is a difficult qualifying examination. (Actually, there are a few former students out there who think that difficult qualifying exam questions is a character flaw of mine.) Others might feel that these questions are an attack on management science. Neither assumption gets to the root of the issue. I do feel that applications of complexity have potential in management, particularly in being able to model and understand better emergent properties and to guide emergence in favorable directions. The reason for the tough exam is that I believe we need common understandings in order to communicate with each other. Doubtless, each reader could set his own exam.
The most defined of all of the terms discussed above is entropy, starting with thermodynamics and integrals of dQ, the heat increment along reversible pathways. It is inextricably intertwined with the integrating factor 1/T, the reciprocal of the absolute temperature. The function S can be experimentally determined from values of the specific heat from absolute zero to the temperature of interest. Entropy can be defined in statistical mechanics in a precise way, but only for systems at equilibrium. Following Lars Onsager's work in the early 1930s, a near-to-equilibrium entropy was defined that became the basis of a discipline called nonequilibrium thermodynamics. Although only applicable in the very near-to-equilibrium range, there was and still is a tendency to apply the results to very far-from-equilibrium situations.
When information was defined in the post-World War II period, as a measure on