Reviewed by
Stefano Balietti
ETH Zürich, Department of Humanities and Social Sciences
The book is a comprehensive review of the mathematical models of science from its origins. It looks at "[models that aim to] replicate and predict the structure and dynamics of science". The book opens a privileged window over the epistemic diversity of mathematical models of science and closes a long standing, and burdensome gap in the literature on quantitative science studies. The work provides conceptual order in a field that is scattered, highly interdisciplinary, and whose approaches form, as the authors put it, "more an ephemeral than a persistent thread in scientometrics".
The review is organized by methodological approaches rather than by research topics. Statistical models, deterministic and stochastical models, agent-based models, evolutionary game theory models, and recent contributions from network science on citation and co-authorships analysis are covered. On the other hand, the book offers more than a traditional outlook on the field. Indeed, the first part of the book (Foundations) provides a thorough introduction to modelling that helps the reader to familiarize with the science-modelling terminology. A short glossary is also supplied. Chapter 2 (Mathematical Approaches to Modeling Science from an Algorithmic-Historiography Perspective) quantitatively retraces the diffusion trajectories of three seminal contributions in the citation network of a selected number of publications in the field of informetrics. This analysis highlights how ideas spread among papers over time and confirms the general impression of the presence of different "schools" that share common roots without communicating so much. Even though the approach used is not new, its application inside a review book is certainly original and may be considered the real novelty of the book. Overall, this first part effectively acts as the glue that binds the following chapters together. Moreover, the reader is visually aided in this introduction by a large number of charts and network diagrams that complement the study.
The central chapters follow a uniform structure: first, a brief introduction to the methodology is given, usually supplemented by historical remarks, and the specific aim of the chapter is clearly stated; then relevant models are discussed, generally sorted by the level of complexity and sophistication. Furthermore, each chapter has "checkpoints", i.e., a box or a table presenting either a list of relevant questions together with short answers or a summary of the key-points discussed. This particular structure makes the book especially suited for graduate students and scholars new to the field (or to the particular methodology). At the same time, experts will surely appreciate the richness and depth of the cited literature, for the first time so well organized into a single book.
It is worth noting that the relative independence of the approaches in scientometrics is reflected in the book's structure. Indeed, the authors freely presented each chapter with their own language and style, so offering a cross section of various epistemic cultures. If this can make the reading more lively and interesting, a certain overlap is inevitable between certain chapters. On the other hand, "fast" or "selective" readers will be able to jump from one chapter to another, without losing their orientation.
Once said about positive aspects of the book, some criticism could be raised for what the book left out. For example, the link between models of science and science policy decisions is touched too briefly in the final chapter (Science Policy and the Challenges for Modeling Science). However, it seems to me more problematic the lack of a chapter dedicated to introducing the reader to the main philosophical issues connected to science modelling. Although someone could consider this not so essential for a book focused on mathematical modelling of science, my opinion is that discussing philosophy of science issues is crucial for any mathematical model of science, especially if it deals with social dynamics.
Overall, the editors embarked upon a difficult task: pulling together the scattered and multidisciplinary literature on quantitative models of science into a single review book. The result is certainly a very valuable contribution. Moreover, it is also very timely, given the revived interest in quantitative models of science, as shown by the special issue of JASSS on Simulating the Social Processes of Science (see Edmonds et al 2011). Are we on the verge of a new wave of mathematical models of science?