Information Systems in Management Science---Geometry of Information Systems. Part I

This column advocates an unbounded and irrational faith in mathematical models. I believe, as stated repeatedly in these columns, that mathematical discourse is the way to combat semantic pollution, obtain understanding, and create insight to managerial situations. I also advance the proposition that the fields of mathematics traditionally used by management scientists are inadequate to deal with management information systems. Restricting the concept of the mathematical model to systems of equations or relations, as in mathematical programming or calculus, leads to failure. For example, I introduced the concept of function spaces to deal with certain aspects of information systems. Now I call attention to another field of mathematics which appears to be particularly suitable for dealing with management information systems.A system is, roughly speaking, an organized collection of men, machines and methods required to accomplish a set of specific functions and goals. Whatever definition of an MIS you accept, there is an immediate implication of structure, relations and hierarchy. Herbert Simon advanced the concept that systems are complex not because of the complexity of the elements constituting the system, but because of complex environmental relations. I want to show now that the relationships between the agents of a system can best be described by geometry, or more specifically by a branch of mathematics called topology. But first let us take a little historical journey on the application of geometry to management science.