Exploring the Disproportion Between Scientific Productivity and Knowledge Amount

The pursuit of knowledge is the permanent goal of human beings. Scientific literature, as the major medium that carries knowledge between scientists, exhibits explosive growth during the last century. Despite the frequent use of many tangible measures, such as citation, impact factor and g-index, to quantify the influence of papers from different perspectives based on scientific productivity, it has not yet been well understood how the relationship between scientific productivity and knowledge amount turns out to be, i.e., how the knowledge value of papers and knowledge amount vary with development of the discipline. This raises the question of whether high scientific productivity equals large knowledge amount. Here, building on rich literature on academic conferences and journals, we collect 185 million articles covering 19 disciplines published during 1970 to 2020, and establish citation network research area to represent the knowledge flow from the authors of the article being cited to the authors of the articles that cite it under each specific area. As a result, the structure formed during the evolution of each scientific area can implicitly tells how the knowledge flows between nodes and how it behaves as the number of literature (productivity) increases. By leveraging Structural entropy in structured high-dimensional space and Shannon entropy in unstructured probability space, we propose the Quantitative Index of Knowledge (KQI), which is taken as the subtraction between the two types of entropy, to reflect the extent of disorder difference (knowledge amount) caused by structure (order). With the aid of KQI, we find that, although the published literature shows an explosive growth, the amount of knowledge (KQI) contained in it obviously slows down, and there is a threshold after which the growth of knowledge accelerates...