In this insightful work, Martin H. Krieger shows what physicists are really doing when they employ mathematical models as research tools. He argues that the technical details of these complex calculations serve not only as a means to an end, but also reveal key aspects of the physical properties they model.

Krieger's lucid discussions will help readers to appreciate the larger physical issues behind the mathematical detail of modern physics and gain deeper insights into how theoretical physicists work. Constitutions of Matter is a rare, behind-the-scenes glimpse into the world of modern physics.

"[Krieger] provides students of physics and applied mathematics with a view of the physical forest behind the mathematical trees, historians and philosophers of science with insights into how theoretical physicists go about their work, and technically advanced general readers with a glimpse into the discipline."—Scitech Book News

Marginalism and Discontinuity is an account of the culture of models employed in the natural and social sciences, showing how such models are instruments for getting hold of the world, tools for the crafts of knowing and deciding. Like other tools, these models are interpretable cultural objects, objects that embody traditional themes of smoothness and discontinuity, exchange and incommensurability, parts and wholes. Martin Krieger interprets the calculus and neoclassical economics, for example, as tools for adding up a smoothed world, a world of marginal changes identified by those tools. In contrast, other models suggest that economies might be sticky and ratchety or perverted and fetishistic. There are as well models that posit discontinuity or discreteness. In every city, for example, some location has been marked as distinctive and optimal; around this created differentiation, a city center and a city periphery eventually develop. Sometimes more than one model is applicable—the possibility of doom may be seen both as the consequence of a series of mundane events and as a transcendent moment. We might model big decisions or entrepreneurial endeavors as sums of several marginal decisions, or as sudden, marked transitions, changes of state like freezing or religious conversion. Once we take models and theory as tools, we find that analogy is destiny. Our experiences make sense because of the analogies or tools used to interpret them, and our intellectual disciplines are justified and made meaningful through the employment of characteristic toolkits—a physicist's toolkit, for example, is equipped with a certain set of mathematical and rhetorical models. Marginalism and Discontinuity offers a provocative and wide-ranging consideration of the technologies by which we attempt to apprehend the world. It will appeal to social and natural scientists, mathematicians and philosophers, and thoughtful educators, policymakers, and planners.