Encounters With Infinity

The original title of this manuscript was Pages - A Voyage to Infinity. It's kinda like Walt Whitman's Leaves of Grass; a collection of poems with an underlying mystical theme. My dissertation is a kaleidoscope puzzle of images and thoughts and concepts and ideas taken from mysticism, science, logic, and mathematics. The end result, as the puzzle pieces are linked together, is a new portrait of Number. The reader is challenged to solve a conceptual picture puzzle using the chaotic scattering of puzzle pieces set forth in the thesis. Some of the pieces challenge established ideas. Some of the pieces are decoys leading to dead ends. Some are background. Others are transition pieces. And, there are pieces that give the reader glimpses of me, the writ er of this thesis. So, exact ly what is infinit y? As the pieces of the puzzle are put together a new concept of infinity emerges, a concept that may be of interest to the mystics, the philosopher, the quantum physicist, and mathematicians who are open to a new window through which to view reality.

Infinity is an intriguing topic, with connections to religion, philosophy, metaphysics, logic, and physics as well as mathematics. Its history goes back to ancient times, with especially important contributions from Euclid, Aristotle, Eudoxus, and Archimedes. The infinitely large (infinite) isintimately related to the infinitely small (infinitesimal). Cosmologists consider sweeping questions about whether space and time are infinite. Philosophers and mathematicians ranging from Zeno to Russell have posed numerous paradoxes about infinity and infinitesimals. Many vital areas ofmathematics rest upon some version of infinity. The most obvious, and the first context in which major new techniques depended on formulating infinite processes, is calculus. But there are many others, for example Fourier analysis and fractals.In this Very Short Introduction, Ian Stewart discusses infinity in mathematics while also drawing in the various other aspects of infinity and explaining some of the major problems and insights arising from this concept. He argues that working with infinity is not just an abstract, intellectualexercise but that it is instead a concept with important practical everyday applications, and considers how mathematicians use infinity and infinitesimals to answer questions or supply techniques that do not appear to involve the infinite.ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, andenthusiasm to make interesting and challenging topics highly readable.

A guide to the spiritual meaning and magic of the infinity symbol and how to activate its positive powers • Explains how the infinity symbol is the antidote to a negative, imbalanced world and how it can help reconnect the two halves of the brain and achieve balance and harmony in yourself, your relationships, and the wider world • Offers simple and practical exercises that harness the power of the infinity symbol for balance and harmony, including simple visualizations, physical exercises, and directed drawing of the symbol • Explores the many appearances of this universal symbol in history, mythology, different cultures, and the natural world Through the ages, the infinity symbol, a sideways figure eight, has represented eternal development and balance. Also known as the lemniscate, this powerful symbol stands for equilibrium, harmony, and the interconnectedness of all things. Although magical knowledge of symbols has often been kept secret throughout history, today the power of this symbol is available to all. In this accessible, hands-on guide, Barbara Heider-Rauter explores the spiritual world of the infinity symbol in a personal and practical way, allowing each of us to benefit from its positive influence for balance and harmony in ourselves, our relationships, and the wider world. She begins with a short exercise to attune readers to the energy field of the lemniscate. She explains how the infinity symbol offers the perfect response to a system that encourages separation and a world in which the negation of our feelings is often the source of illness and pain. She details simple exercises to reconnect the two halves of the brain, the analytical and the emotional, resulting in harmony and healing. She teaches how to use simple visualisation, physical exercises, and directed drawing of the symbol to achieve practical results in our daily lives. Beautifully illustrated in full color, the book also offers a wealth of information on the appearance of the infinity symbol through the ages in all its forms and contexts, from history and mythology to our own tiny body cells and the natural world. This book urges the reader to establish wholeness, to balance the scales of duality and find harmony. With the power of the lemniscate at hand, decisions will be made with greater ease and relationships filled with harmony and a lighter heart.

This volume contains essays that examine infinity in early modern philosophy. The essays not only consider the ways that key figures viewed the concept. They also detail how these different beliefs about infinity influenced major philosophical systems throughout the era. These domains include mathematics, metaphysics, epistemology, ethics, science, and theology. Coverage begins with an introduction that outlines the overall importance of infinity to early modern philosophy. It then moves from a general background of infinity (before early modern thought) up through Kant. Readers will learn about the place of infinity in the writings of key early modern thinkers. The contributors profile the work of Descartes, Spinoza, Leibniz, and Kant. Debates over infinity significantly influenced philosophical discussion regarding the human condition and the extent and limits of human knowledge. Questions about the infinity of space, for instance, helped lead to the introduction of a heliocentric solar system as well as the discovery of calculus. This volume offers readers an insightful look into all this and more. It provides a broad perspective that will help advance the present state of knowledge on this important but often overlooked topic.

In contemporary psychoanalysis, a key concept and aim of clinical practice is to distinguish the boundaries of any mental state. Without this boundary-setting, the patient has nothing but the 'formless infinite' of primitive mental states. Formless Infinity: Clinical Explorations of Matte Blanco and Bion draws on the work of these two authors to explore how analysts can work with patients to reveal, understand and ultimately contain their primitive mental states. Riccardo Lombardi discusses the core concepts of the unconscious, the role of the body in analysis, time and death. He displays the clinical implications of Matte Blanco’s theoretical extension of Freud’s theory of the unconscious, presenting numerous clinical examples of working with psychosis and other severe pathologies. Formless Infinity, a stimulating teaching text for students, trainers and seasoned mental health practitioners, is essential reading for psychoanalysts and psychoanalytic psychotherapists. It is particularly recommended to analysts interested in widening the scope of the analytic practice by exploring the functioning of the deep unconscious, primitive mental states, psychosomatic pathologies and psychotic conditions.

This study traces the connection of infinity and Levinasian ethics in 21st-century fiction. It tackles the paradox of how infinity can be (re-)presented in the finite space between the covers of a book and finds an answer that combines conceptual metaphor theory with concepts from classical narratology and beyond, such as mise en abyme, textual circularity, intertextuality or omniscient narration. It argues that texts with such structures may be conceptualised as infinite via Lakoff and Núñez’s Basic Metaphor of Infinity. The catachrestic transfer of infinity from structure to text means that the texts themselves are understood to be infinite. Taking its cue from the central role of the infinite in Emmanuel Levinas’s ethics, the function of such ‘fictions of infinity’ turns out to be ethical: infinite textuality disrupts reading patterns and calls into question the reader’s spontaneity to interpret. This hypothesis is put to the test in detailed readings of four 21st-century novels, David Mitchell’s Cloud Atlas, Jeanette Winterson’s The Stone Gods, Ian McEwan’s Saturday and John Banville’s The Infinities. This book thus combines ethical criticism with structural aesthetics to uncover ethical potential in fiction.

STEM of Desire: Queer Theories and Science Education locates, creates, and investigates intersections of science, technology, engineering, and mathematics (STEM) education and queer theorizing. Manifold desires—personal, political, cultural—produce and animate STEM education. Queer theories instigate and explore (im)possibilities for knowing and being through desires normal and strange. The provocative original manuscripts in this collection draw on queer theories and allied perspectives to trace entanglements of STEM education, sex, sexuality, gender, and desire and to advance constructive critique, creative world-making, and (com)passionate advocacy. Not just another call for inclusion, this volume turns to what and how STEM education and diverse, desiring subjects might be(come) in relation to each other and the world. STEM of Desire is the first book-length project on queering STEM education. Eighteen chapters and two poems by 27 contributors consider STEM education in schools and universities, museums and other informal learning environments, and everyday life. Subject areas include physical and life sciences, engineering, mathematics, nursing and medicine, environmental education, early childhood education, teacher education, and education standards. These queering orientations to theory, research, and practice will interest STEM teacher educators, teachers and professors, undergraduate and graduate students, scholars, policy makers, and academic libraries. Contributors are: Jesse Bazzul, Charlotte Boulay, Francis S. Broadway, Erin A. Cech, Steve Fifield, blake m. r. flessas, Andrew Gilbert, Helene Götschel, Emily M. Gray, Kristin L. Gunckel, Joe E. Heimlich, Tommye Hutson, Kathryn L. Kirchgasler, Michelle L. Knaier, Sheri Leafgren, Will Letts, Anna MacDermut, Michael J. Reiss, Donna M. Riley, Cecilia Rodéhn, Scott Sander, Nicholas Santavicca, James Sheldon, Amy E. Slaton, Stephen Witzig, Timothy D. Zimmerman, and Adrian Zongrone.