Download or read book Ad Infinitum The Ghost in Turing s Machine written by Brian Rotman and published by Stanford University Press. This book was released on 1993 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: This ambitious work puts forward a new account of mathematics-as-language that challenges the coherence of the accepted idea of infinity and suggests a startlingly new conception of counting. The author questions the familiar, classical, interpretation of whole numbers held by mathematicians and scientists, and replaces it with an original and radical alternative--what the author calls non-Euclidean arithmetic. The author's entry point is an attack on the notion of the mathematical infinite in both its potential and actual forms, an attack organized around his claim that any interpretation of "endless" or "unlimited" iteration is ineradicably theological. Going further than critique of the overt metaphysics enshrined in the prevailing Platonist description of mathematics, he uncovers a covert theism, an appeal to a disembodied ghost, deep inside the mathematical community's understanding of counting.
Download or read book Ad Infinitum The Ghost in Turing s Machine written by Brian Rotman and published by . This book was released on 2022 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: This ambitious work puts forward a new account of mathematics-as-language that challenges the coherence of the accepted idea of infinity and suggests a startlingly new conception of counting. The author questions the familiar, classical, interpretation of whole numbers held by mathematicians and scientists, and replaces it with an original and radical alternative--what the author calls non-Euclidean arithmetic. The author's entry point is an attack on the notion of the mathematical infinite in both its potential and actual forms, an attack organized around his claim that any interpretation of "endless" or "unlimited" iteration is ineradicably theological. Going further than critique of the overt metaphysics enshrined in the prevailing Platonist description of mathematics, he uncovers a covert theism, an appeal to a disembodied ghost, deep inside the mathematical community's understanding of counting.
Download or read book What Painting Is written by James Elkins and published by Routledge. This book was released on 2019-12-24 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this classic text, James Elkins communicates the experience of painting beyond the traditional vocabulary of art history. Alchemy provides a strange language to explore what it is a painter really does in the studio—the smells, the mess, the struggle to control the uncontrollable, the special knowledge only painters hold of how colors will mix, and how they will look. Written from the perspective of a painter-turned-art historian, this anniversary edition includes a new introduction and preface by Elkins in which he further reflects on the experience of painting and its role in the study of art today.
Download or read book Quantum Anthropologies written by Vicki Kirby and published by Duke University Press. This book was released on 2013-07-22 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt: In Quantum Anthropologies, the renowned feminist theorist Vicki Kirby contends that some of the most provocative aspects of deconstruction have yet to be explored. Deconstruction’s implications have been curtailed by the assumption that issues of textuality and representation are specific to the domain of culture. Revisiting Derrida’s claim that there is “no outside of text,” Kirby argues that theories of cultural construction developed since the linguistic turn have inadvertently reproduced the very binaries they intended to question, such as those between nature and culture, matter and ideation, and fact and value. Through new readings of Derrida, Husserl, Saussure, Butler, Irigaray, and Merleau-Ponty, Kirby exposes the limitations of theories that regard culture as a second-order system that cannot access—much less be—nature, body, and materiality. She suggests ways of reconceiving language and culture to enable a more materially implicated outcome, one that keeps alive the more counterintuitive and challenging aspects of poststructural criticism. By demonstrating how fields, including cybernetics, biology, forensics, mathematics, and physics, can be conceptualized in deconstructive terms, Kirby fundamentally rethinks deconstruction and its relevance to nature, embodiment, materialism, and science.
Download or read book Ethics and Mathematics Education written by Paul Ernest and published by Springer Nature. This book was released on 2024 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edited volume is an inquiry into the ethics of mathematics education, and to a lesser extent, the ethics of mathematics. The imposition of mathematics for all raises questions of ethics. What are the ethics of teaching school mathematics? What are the costs as well as the benefits? What are the ethical issues raised by the official aims of mathematics teaching, the planned curriculum, the pedagogies employed in school and college mathematics and the assessment systems? These questions are addressed in the book as well as what systems of ethics we might use. The volume ventures into a burgeoning new field. It offers a unique set of investigations, both theoretical and in terms of practices. It announces the ethics of mathematics education as a new subfield of research and includes valuable contributions from many of the best-known researchers in mathematics education; additionally, it is a valuable resource for students, teachers and researchers in the field. This is an enduring and classic source book in the field. From the wisdom of leading scholars to the little heard voices of students, this collection offers the reader many striking new insights into the ethics of mathematics and education.
Download or read book Social Constructivism as a Philosophy of Mathematics written by Paul Ernest and published by SUNY Press. This book was released on 1998-01-01 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: Extends the ideas of social constructivism to the philosophy of mathematics, developing a powerful critique of traditional absolutist conceptions of mathematics, and proposing a reconceptualization of the philosophy of mathematics.
Download or read book Connectionism and the Philosophy of Psychology written by Terry Horgan and published by MIT Press. This book was released on 1996 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this volume, the authors present their view of cognition. They propose that unlike the classical paradigm that takes the mind to be a computer, the mind is best understood as a dynamical system realized in a neural network.
Download or read book Logic and Computational Complexity written by Daniel Leivant and published by Springer Science & Business Media. This book was released on 1995-08-02 with total page 534 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains revised versions of papers invited for presentation at the International Workshop on Logic and Computational Complexity, LCC '94, held in Indianapolis, IN in October 1994. The synergy between logic and computational complexity has gained importance and vigor in recent years, cutting across many areas. The 25 revised full papers in this book contributed by internationally outstanding researchers document the state-of-the-art in this interdisciplinary field of growing interest; they are presented in sections on foundational issues, applicative and proof-theoretic complexity, complexity of proofs, computational complexity of functionals, complexity and model theory, and finite model theory.
Download or read book Reassembling the Social written by Bruno Latour and published by Oxford University Press. This book was released on 2005-07-28 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: French sociologist Bruno Latour has previously written about the relationship between people, science and technology. In this book he sets out his own ideas about 'actor network theory' and its relevance to management and organisation theory.
Download or read book New Directions in the Philosophy of Mathematics written by Thomas Tymoczko and published by Princeton University Press. This book was released on 1998-02 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: The traditional debate among philosophers of mathematics is whether there is an external mathematical reality, something out there to be discovered, or whether mathematics is the product of the human mind. This provocative book, now available in a revised and expanded paperback edition, goes beyond foundationalist questions to offer what has been called a "postmodern" assessment of the philosophy of mathematics--one that addresses issues of theoretical importance in terms of mathematical experience. By bringing together essays of leading philosophers, mathematicians, logicians, and computer scientists, Thomas Tymoczko reveals an evolving effort to account for the nature of mathematics in relation to other human activities. These accounts include such topics as the history of mathematics as a field of study, predictions about how computers will influence the future organization of mathematics, and what processes a proof undergoes before it reaches publishable form. This expanded edition now contains essays by Penelope Maddy, Michael D. Resnik, and William P. Thurston that address the nature of mathematical proofs. The editor has provided a new afterword and a supplemental bibliography of recent work.
Download or read book Culturally Responsive Mathematics Education written by Brian Greer and published by Routledge. This book was released on 2009-05-20 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: At a time of rapid demographic change and amidst the many educational challenges facing the US, this critical new collection presents mathematics education from a culturally responsive perspective. It tackles the most crucial issues of teaching mathematics to an ethnically diverse school population, including the political dimension of mathematics education within the context of governmental efforts to improve achievement in school mathematics. Culturally Responsive Mathematics Education moves beyond a point of view that is internal to mathematics education as a discipline, and instead offers a broad perspective of mathematics as a significant, liberating intellectual force in our society. The editors of this volume bring together contributions from many of the leading teachers, teacher educators, researchers, scholars, and activists who have been working to reorient mathematics education in ways that reflect mathematics education as accomplished, first and foremost, through human interactions.
Download or read book Worlds of ScienceCraft written by Sal Restivo and published by Routledge. This book was released on 2016-02-11 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: A response to complex problems spanning disciplinary boundaries, Worlds of ScienceCraft offers bold new ways of conceptualizing ideas of science, sociology, and philosophy. Beginning with the historical foundations of civilization and progress, assumptions about the categories we use to talk about minds, identities, and bodies are challenged through case studies from mathematics, social cognition, and medical ethics. Offering innovative approaches to these issues, such as an integrated social brain-mind-body model and a critique of divisions between the natural and technological, this book provides novel conceptions of self, society and an emerging ’cyborg’ generation. From the micro level of brains and expanding all the way out to biopolitical civics, disciplinary boundaries are made permeable, emphasizing the increased need for interdisciplinary scholarship. By rejecting outdated and restrictive categories and classifications, new horizons in studies of science, technology, and medicine can be explored through the incorporation of feminist, international, and postmodern perspectives. A truly interdisciplinary examination of science and technology as cultural phenomena, Worlds of ScienceCraft will appeal to scholars and students of science and technology studies, as well as philosophers, historians, and sociologists of science, technology, and medicine.
Download or read book Mathematics Science and Postclassical Theory written by Barbara Herrnstein Smith and published by Duke University Press. This book was released on 1997-03-04 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics, Science, and Postclassical Theory is a unique collection of essays dealing with the intersections between science and mathematics and the radical reconceptions of knowledge, language, proof, truth, and reality currently emerging from poststructuralist literary theory, constructivist history and sociology of science, and related work in contemporary philosophy. Featuring a distinguished group of international contributors, this volume engages themes and issues central to current theoretical debates in virtually all disciplines: agency, causality, determinacy, representation, and the social dynamics of knowledge. In a substantive introductory essay, the editors explain the notion of "postclassical theory" and discuss the significance of ideas such as emergence and undecidability in current work in and on science and mathematics. Other essays include a witty examination of the relations among mathematical thinking, writing, and the technologies of virtual reality; an essay that reconstructs the conceptual practices that led to a crucial mathematical discovery—or construction—in the 19th century; a discussion of the implications of Bohr’s complementarity principle for classical ideas of reality; an examination of scientific laboratories as "hybrid" communities of humans and nonhumans; an analysis of metaphors of control, purpose, and necessity in contemporary biology; an exploration of truth and lies, and the play of words and numbers in Shakespeare, Frege, Wittgenstein, and Beckett; and a final chapter on recent engagements, or nonengagements, between rationalist/realist philosophy of science and contemporary science studies. Contributors. Malcolm Ashmore, Michel Callon, Owen Flanagan, John Law, Susan Oyama, Andrew Pickering, Arkady Plotnitsky, Brian Rotman, Barbara Herrnstein Smith, John Vignaux Smyth, E. Roy Weintraub
Download or read book Environmental Apocalypse in Science and Art written by Sergio Fava and published by Routledge. This book was released on 2013-01-04 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: At a time when it is clear that climate change adaptation and mitigation are failing, this book examines how our assumptions about (valid and usable) knowledge are preventing effective climate action. Through a cross-disciplinary, empirically-based analysis of climate science and policy, the book situates the failures of climate policy in the cultural history of prediction and its interfaces with policy. Fava calls into question the current interfaces between scientific research and climate policy by tracing multiple connections between modelling, epistemology, politics, food security, religion, art, and the apocalyptic. Demonstrating how the current domination of climate policy by models and scenarios is part of the problem, the book examines how artistic practices are a critical location to ask questions differently, rethink environmental futures, and activate social change. The analysis starts with another moment of climatic change in recent western history: the overlap of the Little Ice Age and the "scientific revolution," during which intense climatic, scientific and political change were contemporary with mathematical calculation of the apocalypse. Dealing with the need for complex answers to complex and urgent questions, this is essential reading for those interested in climate action, interdisciplinary research and methodological innovation. The empirical analyses amount to a methodological experiment, across history of science, theology, art theory and history, architecture, future studies, climatology, computer modelling, and agricultural policy. This book is a major contribution to understanding how we are precluding effective climate action, and designing futures that resemble our worst nightmares.
Download or read book Mathematicians as Enquirers written by Leone L. Burton and published by Springer Science & Business Media. This book was released on 2004-04-30 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is amazing that the usual reply to being introduced to a mathematician is a stumbling apology about how bad someone is at mathematics, no matter how good they may be in reality. The problem is that we have come to view mathematics as an arcane branch of knowledge that only a few can aspire to understand or grasp. The sense of separation between those who have the knowledge and those who do not, is present even amongst academics where many of the same skills and research practices exist - intuition, the use of symbolic structures and the use of intuition and insight. The more worrying aspect of this separation is the ever declining numbers of students choosing mathematics as part of their curriculum beyond the stage when it is mandatory. Even worse, it would seem that the mathematics community has created a discriminatory environment that deters many students from continuing beyond secondary and tertiary education. Exit interviews with graduates show a stark rejection of their previously chosen subject. What about mathematicians themselves - how do they see themselves? Do male and female mathematicians come to know their mathematics in different ways, do they tackle different problems with varying results for their status in the research community? Does the pervasive labelling that mathematics is a male domain arise because of a lack of role models for women or through its highly competitive, hierarchical nature? Are the negative labels often associated with mathematics, i. e.
Download or read book Complementarity written by Arkady Plotnitsky and published by Duke University Press. This book was released on 1994 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many commentators have remarked in passing on the resonance between deconstructionist theory and certain ideas of quantum physics. In this book, Arkady Plotnitsky rigorously elaborates the similarities and differences between the two by focusing on the work of Niels Bohr and Jacques Derrida. In detailed considerations of Bohr's notion of complementarity and his debates with Einstein, and in analysis of Derrida's work via Georges Bataille's concept of general economy, Plotnitsky demonstrates the value of exploring these theories in relation to each other. Bohr's term complementarity describes a situation, unavoidable in quantum physics, in which two theories thought to be mutually exclusive are required to explain a single phenomenon. Light, for example, can only be explained as both wave and particle, but no synthesis of the two is possible. This theoretical transformation is then examined in relation to the ways that Derrida sets his work against or outside of Hegel, also resisting a similar kind of synthesis and enacting a transformation of its own. Though concerned primarily with Bohr and Derrida, Plotnitsky also considers a wide range of anti-epistemological endeavors including the work of Nietzsche, Bataille, and the mathematician Kurt Gödel. Under the rubric of complementarity he develops a theoretical framework that raises new possiblilities for students and scholars of literary theory, philosophy, and philosophy of science.
Download or read book Mathematics and the Aesthetic written by Nathalie Sinclair and published by Springer Science & Business Media. This book was released on 2007-12-28 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of essays explores the ancient affinity between the mathematical and the aesthetic, focusing on fundamental connections between these two modes of reasoning and communicating. From historical, philosophical and psychological perspectives, with particular attention to certain mathematical areas such as geometry and analysis, the authors examine ways in which the aesthetic is ever-present in mathematical thinking and contributes to the growth and value of mathematical knowledge.
