This book deals with a topic that has been largely neglected by philosophers of science to date: the ability to refer and analyze in tandem. On the basis of a set of philosophical case studies involving both problems in number theory and issues concerning time and cosmology from the era of Galileo, Newton and Leibniz up through the present day, the author argues that scientific knowledge is a combination of accurate reference and analytical interpretation. In order to think well, we must be able to refer successfully, so that we can show publicly and clearly what we are talking about. And we must be able to analyze well, that is, to discover productive and explanatory conditions of intelligibility for the things we are thinking about. The book's central claim is that the kinds of representations that make successful reference possible and those that make successful analysis possible are not the same, so that significant scientific and mathematical work typically proceeds by means of a heterogeneous discourse that juxtaposes and often superimposes a variety of kinds of representation, including formal and natural languages as well as more iconic modes. It demonstrates the virtues and necessity of heterogeneity in historically central reasoning, thus filling an important gap in the literature and fostering a new, timely discussion on the epistemology of science and mathematics.

This volume explores the interaction of poetry and mathematics by looking at analogies that link them. The form that distinguishes poetry from prose has mathematical structure (lifting language above the flow of time), as do the thoughtful ways in which poets bring the infinite into relation with the finite. The history of mathematics exhibits a dramatic narrative inspired by a kind of troping, as metaphor opens, metonymy and synecdoche elaborate, and irony closes off or shifts the growth of mathematical knowledge. The first part of the book is autobiographical, following the author through her discovery of these analogies, revealed by music, architecture, science fiction, philosophy, and the study of mathematics and poetry. The second part focuses on geometry, the circle and square, launching us from Shakespeare to Housman, from Euclid to Leibniz. The third part explores the study of dynamics, inertial motion and transcendental functions, from Descartes to Newton, and in 20th c. poetry. The final part contemplates infinity, as it emerges in modern set theory and topology, and in contemporary poems, including narrative poems about modern cosmology.

This book deals with a topic that has been largely neglected by philosophers of science to date: the ability to refer and analyze in tandem. On the basis of a set of philosophical case studies involving both problems in number theory and issues concerning time and cosmology from the era of Galileo, Newton and Leibniz up through the present day, the author argues that scientific knowledge is a combination of accurate reference and analytical interpretation. In order to think well, we must be able to refer successfully, so that we can show publicly and clearly what we are talking about. And we must be able to analyze well, that is, to discover productive and explanatory conditions of intelligibility for the things we are thinking about. The book's central claim is that the kinds of representations that make successful reference possible and those that make successful analysis possible are not the same, so that significant scientific and mathematical work typically proceeds by means of a heterogeneous discourse that juxtaposes and often superimposes a variety of kinds of representation, including formal and natural languages as well as more iconic modes. It demonstrates the virtues and necessity of heterogeneity in historically central reasoning, thus filling an important gap in the literature and fostering a new, timely discussion on the epistemology of science and mathematics.