Applications of Physics and Mathematics to Social Science

2010

Mathematical models are a well established tool in most natural sciences. Although models have been neglected by the philosophy of science for a long time, their epistemological status as a link between theory and reality is now fairly well understood. However, regarding the epistemological status of mathematical models in the social sciences, there still exists a considerable unclarity. In my paper I argue that this results from specific challenges that mathematical models and especially computer simulations face in the social sciences. The most important difference between the social sciences and the natural sciences with respect to modeling is that in the social sciences powerful and well confirmed background theories (like Newtonian mechanics, quantum mechanics or the theory of relativity in physics) do not exist. Therefore, an epistemology of models that is formed on the role model of physics may not be appropriate for the social sciences. I discuss the challenges that modeling faces in the social sciences and point out their epistemological consequences. The most important consequences are that greater emphasis must be placed on empirical validation than on theoretical validation and that the relevance of purely theoretical simulations is strongly limited.

In context of my studies to date, and in particular my newfound understanding of the common good, I have experienced a surprising insight. I can best describe the occurrence as a spontaneous emergence, in my mind, of a conception of sociophysical phenomena. I was not yet aware of sociophysics and thought that I had coined the term to help define a path of study. Simply, I wanted a word to help me focus more closely upon the physical phenomena that emerge from social interactions. Searching for the literature of sociophysics, I was initially surprised to find a sparse population of recent mathematical probabilistic treatments and models, stemming form quantum physics early in the twentieth century, game theory in the mid-twentieth century, and analyses of computer modeling of adaptive networks early in our twenty-first century. My search soon led me near to the origin of the sociophysical concept – an absolute origin escapes me, though sociophysics seems closely tied to Aristotelian animism. Nevertheless, I now realize that sociophysics has presented itself in a variety of apparitions to many a kindred spirit. If it is a science, then it is the strangest, vaguest, and widest of them – indeed, it has been called “the science that comes after all the others” – and fascinatingly, the men who have studied it knowingly, were and for the greatest part still are outcast by orthodoxy. I certainly am no stranger to their ranks, perhaps that is part of the reason why I feel a sense of familiarity and belonging among the concepts exposed in the current exploration of ‘the last science’.

Methodological Investigations in Agent-Based Modelling, 2018

The examination of the use of 'artificial worlds' in the previous chapter seemed to produce some rather damning concerns for those involved in agent-based simulation. While such models can provide a nicely compartmentalised and distilled view of a vastly more complicated real-world system, such a model can create tremendous difficulty when the researcher must begin to analyse the resultant data. In the context of our overall discussion, however, the examples and analysis presented so far have focused largely on models based upon or inspired by biology. Agent-based modelling is far from confined to this singular area of study, so this chapter will introduce a major theme of this text: the uses and limitations of agentbased models in the social sciences. As agent-based modelling spreads through various disciplines, there are certain applications which seem particularly promising due to an attendant lack of empirical data underwriting those disciplines. Social science seems an especially relevant example of this situation; by its very nature, the study of social systems makes data-gathering a difficult proposition. In such an instance, can agent-based models provide a means for developing social theories despite the lack of empirical data to validate the models themselves? This chapter will examine this question in detail, first by describing the current

ugb.ro

Research today becomes impossible without a special way of thinking and modelling the reality as an object with more and more dimensions. From the great diversity of sciences, the importance of the concepts of models in mathematics and economics has been emphasised by the complexity of contemporary scientific research, which has made them evolve, in an interdisciplinary manner, along at least five directions: the econometrical models, the econophysics models, the sociophysics models, the quantum economics models, and the science of complexity models. The new way of thinking the continuity of the natural processes using models from physics, apparently forgotten in point of the importance of its proximity to the nature and reality, seems to be decisively prevalent in the new scientific researches forming new many domains of activity, belonging to the vast field of the quantifications of progress in social economic reality. The physics models used in econophysics or sociophysics do not analyze only economic or social processes and phenomena, but rather their continuity in evolution or involution. The authors of the present paper propose a different approach to the modelling process, a new systemic approach which involves new attitudes, ranging from acknowledging the differences between mental or intellectual models of econometrics and experimental models of physics, to repositioning the educational system, as well as scientific research. Finally, the paper illustrates, through the new paradigm of an apparent conflict between the two species of models, an old dispute between mental and experimental attitude in scientific research and academic education.

An obituary for the founder of 'Sociodynamics' the study of social change by using mathematical models.

Discrete Dynamics in Nature and Society, 2000

Weidlich "Quantitative models never comprise the full richness of qualitatively different properties in a social system. On the contrary: Only models which are parsimoniously designed with respect to the number of variables and trendparameters are sufficiently transparent to yield possible insights into the structure and dynamics of a social system". These words of Wolfgang Weidlich underline one of the basic ideas behind the development of the framework of Sociodynamics.

Big data

In the early 19th century, Adolphe Quetelet, the Belgian pioneer of empirical social research, investigated what he called the “homme moyen”. This “average man”, or so Quetelet presumed, is the gravitational center of society. Measuring individual and collective, social and physical attributes allowed one to trace the dynamics of society. Quetelet stressed (1842: vii) that “I confine myself to the citation of facts, such as society presents to our view.” Quetelet was the first social researcher to accumulate and analyze large stocks of empirical data. He may therefore be described as the originator but largely forgotten predecessor of today’s “data scientists”. Our presentation today edges out similarities between the pioneer of what he himself called “Social Physics”, and today’s re-incarnation of very similar ideas. We will try to demonstrate the likeness of these approaches to the social world and uncover some of the fundamental, and in our opinion, flawed premises of both endeavors. Let us start with looking briefly at Adolphe Quetelet’s work.

2022

Models of Society and Complex Systems introduces readers to a variety of different mathematical tools used for modelling human behaviour and interactions, and the complex social dynamics that drive institutions, conflict, and coordination. What laws govern human affairs? How can we make sense of the complexity of societies and how do individual actions, characteristics, and beliefs interact? Social systems follow regularities which allow us to answer these questions using different mathematical approaches. This book emphasises both theory and application. It systematically introduces mathematical approaches, such as evolutionary and spatial game theory, social network analysis, agent-based modelling, and chaos theory. It provides readers with the necessary theoretical background of each toolset as well as the underlying intuition, while each chapter includes exercises and applications to real-world phenomena. By looking behind the surface of various social occurrences, the reader uncovers the reasons why social systems exhibit both cultural universals and at the same time a diversity of practices and norms to a degree that even surpasses biological variety, or why some riots turn into revolutions while others do not even make it into the news. This book is written for any scholar in the social sciences interested in studying and understanding human behaviour, social dynamics, and the complex systems of society. It does not expect readers to have a particular background apart from some elementary knowledge and affinity for mathematics.

Mathematical Models and Methods in Applied Sciences, 2009

This special issue is the third of a sequel devoted to the development of mathematical tools for the modeling, qualitative analysis and simulations of complex systems in life and human sciences. Namely of systems of many living individuals interacting in a nonlinear manner.