General Critical Properties of the Dynamics of Scientific Discovery

Scientific fields are difficult to define and compare, yet there is a general sense that they undergo similar stages of development. From this point of view it becomes important to determine if these superficial similarities can be translated into a general framework that would quantify the general advent and subsequent dynamics of scientific ideas. Such a framework would have important practical applications of allowing us to compare fields that superficially may appear different, in terms of their subject matter, research techniques, typical collaboration size, etc. Particularh' important in a field's history is the moment at which conceptual and technical unification allows widespread exchange of ideas and collaboration, at which point networks of collaboration show the analog of a percolation phenomenon, developing a giant connected component containing most authors. Here we investigate the generality of this topological transition in the collaboration structure of scientific fields as they grow and become denser. We develop a general theoretical framework in which each scientific field is an instantiation of the same large-scale topological critical phenomenon. We consider whether the evidence from a variety of specific fields is consistent with this picture, and estimate critical exponents associated with the transition. We then discuss the generality of the phenomenon and to what extent we may expect other scientific fields — including very large ones — to follow the same dynamics

General Critical Properties of the Dynamics of Scientific Discovery

Scientific fields are difficult to define and compare, yet there is a general sense that they undergo similar stages of development. From this point of view it becomes important to determine if these superficial similarities can be translated into a general framework that would quantify the general advent and subsequent dynamics of scientific ideas. Such a framework would have important practical applications of allowing us to compare fields that superficially may appear different, in terms of their subject matter, research techniques, typical collaboration size, etc. Particularh' important in a field's history is the moment at which conceptual and technical unification allows widespread exchange of ideas and collaboration, at which point networks of collaboration show the analog of a percolation phenomenon, developing a giant connected component containing most authors. Here we investigate the generality of this topological transition in the collaboration structure of scientific fields as they grow and become denser. We develop a general theoretical framework in which each scientific field is an instantiation of the same large-scale topological critical phenomenon. We consider whether the evidence from a variety of specific fields is consistent with this picture, and estimate critical exponents associated with the transition. We then discuss the generality of the phenomenon and to what extent we may expect other scientific fields — including very large ones — to follow the same dynamics

The Power of a Good Idea: Quantitative Modeling of the Spread of Ideas from Epidemiological Models

The population dynamics underlying the diffusion of ideas hold many qualitative similarities to those involved in the spread of infections. In spite of much suggestive evidence this analogy is hardly ever quantified in useful ways. The standard benefit of modeling epidemics is the ability to estimate quantitatively population average parameters, such as interpersonal contact rates, incubation times, duration of infectious periods, etc. In most cases such quantities generalize naturally to the spread of ideas and provide a simple means of quantifying sociological and behavioral patterns. Here we apply several paradigmatic models of epidemics to empirical data on the advent and spread of Feynman diagrams through the theoretical physics communities of the USA, Japan, and the USSR in the period immediately after World War II. This test case has the advantage of having been studied historically in great detail, which allows validation of our results. We estimate the effectiveness of adoption of the idea in the three communities and find values for parameters reflecting both intentional social organization and long lifetimes for the idea. These features are probably general characteristics of the spread of ideas, but not of common epidemics