DOCSLIB.ORG

Mathematics and the Roots of Postmodern Thought This Page Intentionally Left Blank Mathematics and the Roots of Postmodern Thought

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Mathematics and the Roots of Postmodern Thought This Page Intentionally Left Blank Mathematics and the Roots of Postmodern Thought Mathematics and the Roots of Postmodern Thought This page intentionally left blank Mathematics and the Roots of Postmodern Thought Vladimir Tasic OXFORD UNIVERSITY PRESS 2001 OXTORD UNIVERSITY PRESS Oxford New York Athens Auckland Bangkok Bogota Buenos Aires Cape Town Chennai Dar es Salaam Delhi Florence Hong Kong Istanbul Karachi Kolkata Kuala Lumpur Madrid Melbourne Mexico City Mumbai Nairobi Paris Sao Paulo Shanghai Singapore Taipei Tokyo Toronto Warsaw and associated companies in Berlin Ibadan Copyright © 2001 by Oxford University Press, Inc. Published by Oxford University Press, Inc. 198 Madison Avenue. New York, New York 10016 Oxford is a registered trademark of Oxford University Press All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior permission of Oxford University Press. Library of Congress Cataloging-in-Publication Data Tasic, Vladimir, 1965- Mathematics and the roots of postmodern thought / Vladimir Tasic. p. cm. Includes bibliographical references and index. ISBN 0-19-513967-4 1. Mathematics—Philosophy. 2. Postmodernism. I. Title. QA8.4.T35 2001 510M—dc21 2001021846 987654321 Printed in the United States of America on acid-free paper For Maja This page intentionally left blank ACKNOWLEDGMENTS As much as I would like to share the responsibility for my oversimplifications, misreadings or misinterpretations with all the people and texts that have in- fluenced my thinking, I must bear that burden alone. For valuable discussions and critiques, I am indebted to Hart Caplan, Gre- gory Chaitin, Sinisa Crvenkovic, Guillermo Martinez, Lianne McTavish, Maja Padrov, Shauna Pomerantz, Goran Stanivukovic, Marija and Milos Tasic, Jon Thompson, and Steven Turner. I also thank a number of anonymous re- viewers at Oxford University Press, and acknowledge the patient guidance of executive editor Kirk Jensen. Their thoughtful and critical comments led me to rethink the text many times over, and helped me improve it considerably. Last, but certainly not least, I express my deepest love and gratitude to Maja, to whom I am fortunate to be married. This page intentionally left blank CONTENTS 1. Introduction, 3 2. Around the Cartesian Circuit, 7 2.1. Imagination, 7 2.2. Intuition, 10 2.3. Counting to One, 14 3. Space Oddity and Linguistic Turn, 20 4. Wound of Language, 32 4.1. Being and Time Continuum, 36 4.2. Language and Will, 45 5. Beyond the Code, 50 5.1. Medium of Free Becoming, 53 5.2. Nonpresence of Identity, 58 6. The Expired Subject, 67 6.1. Empire of Signs, 67 6.2. Mechanical Bride, 77 7. The Vanishing Author, 84 8. Say Hello to the Structure Bubble, 100 8.1. Algebra of Language, 101 8.2. Functionalism Chic, 114 9. Don't Think, Look, 119 9.1. Interpolating the Self, 123 9.2. Language Games, 127 9.3. Thermostats "H" Us, 132 10. Postmodern Enigmas, 138 10.1. Unspeakable Differance, 139 10.2. Dysfunctionalism Chic, 154 Notes, 159 Select Bibliography, 177 Index, 183 x Contents Mathematics and the Roots of Postmodern Thought This page intentionally left blank 1 INTRODUCTION To know the world, one must construct it. —Cesare Pavese he antagonism between two vaguely conceived entities, collo- T,quially labeled "science" and "postmodernism," seems to have become part of public life. In the past few years, pages filled with entertain- ing invective have sprung up both on the Internet and in print, attracting the attention of such mainstream media as The New York Times, The Guardian, and Liberation. These exchanges come under the heading "science wars." This passionate debate—which revolves around the problem of how sci- ence in general and mathematics in particular are read or misread—raises a number of social, historical, and even political questions. I am primarily in- terested in the following one: Why would various postmodern intellectuals bother invoking mathematics in their theories at all? It could, of course, be a matter of "fashion," as is sometimes claimed. But let us imagine, if only as a counterfactual, that these theorists are try- ing to convey something that may not be entirely disconnected from mathe- matics and its history. Can one divine what that is, and how would one go about it? Whatever it is, it seems unlikely that it would reveal its secret if we restrict ourselves to considering the quasi-mathematical content of assorted post- modern texts. This was fairly clearly demonstrated in Alan Sokal and Jean Bricmont's Fashionable Nonsense: Postmodern Intellectuals' Abuse of Science (1998). On the other hand, it could perhaps be recovered by tracing the con- nections between mathematics and continental philosophy, by searching for 3 historical ties that go deeper than today's tedious incantations of chaos, fractals, and fuzziness.1 Perhaps. But there is a small obstacle standing in the way of realizing this idea: No one knows what postmodernism is supposed to be. Attempts to make sense of this elusive concept threaten to outnumber attempts to square the circle. The confusion seems to have reached a peak when the sociologist of science Bruno Latour, who is sometimes categorized as a "postmodernist," published We Have Never Been Modern.2 The term "post- modernism" has become a signifier burdened with so many signifieds that it may well be sinking toward insignificance. (At the least, it appears that its meaning is undecidable.) It therefore seems best not to rush to judgments and definitions. Rather, I would like to look into the possibility of reconstructing some aspects of postmodern thought, especially its theoretical aspects known as "post- structuralism" and "deconstruction," from a mathematical point of view. (I will use "postmodernism" as a convenient umbrella term and provide neces- sary differentiations on a case-by-case basis.) Mathematics has always been an important testing ground. It is not un- reasonable to say, paraphrasing a famous postmodern proverb, that few things can escape the mathematical "text." Mathematics has been part of the Western tradition, inseparable from its culture and its philosophy. Among other things, it has been a source of metaphors. Plato's Republic, for instance, advises philosophers that they should study mathematics in order to rise above the world of change and grasp "true being." The modern era owes a good deal to this old tenet of Plato's. In the six- teenth century, Galileo said that the Book of Nature is written in the lan- guage of mathematics. Dutch philosopher Benedict Spinoza authored Ethics, Demonstrated in Geometrical Order (1677), whose title, while not self- explanatory, seems telling nevertheless. It has been claimed that the entire project of the Enlightenment had as its goal achieving the clarity of mathe- matics everywhere by employing the method known as "analytic thinking," whose origins are traceable to mathematics. Even Martin Heidegger, a phi- losopher known for his sharp critiques of science, endeavored to explain "in what sense the foundation of modern thought and knowledge is essentially mathematical."3 It would be possible to skip a few details at this point and tell a wonder- fully uplifting story of unstoppable mathematical progress and cultural im- pact of mathematical ideas—the story of how mathematicians started tack- ling difficult problems regarding formal reasoning, infinity, sets, logic, and abstract structures; how a number of influential twentieth-century thinkers (e.g., Edmund Husserl, Ludwig Wittgenstein, and Bertrand Russell) were dili- gent students of mathematics; how mathematics contributed to the con- ceptualization of computability, intelligence, information, randomness, in- 4 Mathematics and the Roots of Postmodern Thought completeness, chaos, and even the conceptualization of the structure of language itself. I intend to tell parts of that narrative in due course. Its im- portance is impossible to disregard even if it has been told many times. But mathematics is as much a science as it is an art. It is a peculiar hybrid that—as Byron wrote, not of mathematics but of humanity in general—is "half dust, half deity, alike unfit to sink or soar."4 Mathematics is practiced by people who are influenced by philosophy and cultural circumstances, by science and poetry, by politics, style, and other passions, by all the traditions to which they belong. Hence, mathematical "accidental tourists" occasionally happen upon places that do not come highly recommended in rationalist guides. These excursions cannot be ignored here, since my project is to reconstruct certain "antirationalist" exercises of contemporary continental philosophy from a mathematical viewpoint. I would therefore like to consider, among other things, an important part of Western heritage that did not rely on mathematically inspired methods, but that nevertheless informed the views of several influential mathematicians at the turn of the twentieth century. I have in mind nineteenth-century romanticism. Its philosophical contri- butions were, for the most part, separate from mathematics and were opposed to the ideal of formal reasoning that mathematics represented. Romanticist rebellion, sometimes called "the counter-enlightenment," is known for its cri- tiques of science and reason. Romanticist "linguistic turn," with its empha- sis on the importance of language and culture, art and myth, on the indis- pensability of imagination and inexhaustibility of the flux of lived experience by means of formal reasoning, played a significant role in placing language and its limits on the philosophical agenda. In this sense, we might regard the early 1800s as the time when the seeds of the conflict that we now call science wars were planted. Yet the story of science wars seems to be more complex. It is more than a mere episode in a two-centuries-old dispute. It appears, for example, that parts of postmodern theory—despite some superficial similarities with romantic anti-rationalism— find themselves applauding the ultimate in all reductionist projects: artifi- cial intelligence.
Load more

Recommended publications
  • Beyond the Hoax: Science, Philosophy and Culture Kindle
    BEYOND THE HOAX: SCIENCE, PHILOSOPHY AND CULTURE PDF, EPUB, EBOOK Alan Sokal | 488 pages | 19 Mar 2010 | Oxford University Press | 9780199561834 | English | Oxford, United Kingdom Beyond the Hoax: Science, Philosophy and Culture PDF Book Jul 02, Ugh rated it liked it. Views Read Edit View history. He works in statistical mechanics and combinatorics. Friend Reviews. Read an excerpt of this book! This may have been his thinking, but I thought it came off as arrogant. Javascript is not enabled in your browser. Everyone in the US - even the Amish - makes at least some use of the fruits of science. Sokal is one of the most powerful voices in the continuing debate about the status of evidence-based knowledge. Religion, politics and survival It may be a particularly shitty butterfly, but that doesn't mean it's at all interesting to break. I found Sokal's critiq The only aspect of the Sokal Hoax I was aware of before I read this book was that the hoax article Sokal wrote about physics was submitted to a publication that did not subject articles to peer review. To ask other readers questions about Beyond the Hoax , please sign up. His critique would also gain more credibility from encompassing his own community: the failure of scientific institutions to address the abuse of statistical methods or promote systematic reviews is no less of a threat to progress than the ramblings of postmodernists or fundamentalists. However, he is a de The first couple of chapters the ones describing the hoax were pretty good, but after that it veers off into armchair philosophizing about the philosophy of science; it's not that I didn't agree with him on most points, but if I'm going to spend time reading about the philosophy of science, I'm going to read what a specialist says about it.
    [Show full text]
  • An Artistic and Mathematical Look at the Work of Maurits Cornelis Escher
    University of Northern Iowa UNI ScholarWorks Honors Program Theses Honors Program 2016 Tessellations: An artistic and mathematical look at the work of Maurits Cornelis Escher Emily E. Bachmeier University of Northern Iowa Let us know how access to this document benefits ouy Copyright ©2016 Emily E. Bachmeier Follow this and additional works at: https://scholarworks.uni.edu/hpt Part of the Harmonic Analysis and Representation Commons Recommended Citation Bachmeier, Emily E., "Tessellations: An artistic and mathematical look at the work of Maurits Cornelis Escher" (2016). Honors Program Theses. 204. https://scholarworks.uni.edu/hpt/204 This Open Access Honors Program Thesis is brought to you for free and open access by the Honors Program at UNI ScholarWorks. It has been accepted for inclusion in Honors Program Theses by an authorized administrator of UNI ScholarWorks. For more information, please contact [email protected]. Running head: TESSELLATIONS: THE WORK OF MAURITS CORNELIS ESCHER TESSELLATIONS: AN ARTISTIC AND MATHEMATICAL LOOK AT THE WORK OF MAURITS CORNELIS ESCHER A Thesis Submitted in Partial Fulfillment of the Requirements for the Designation University Honors Emily E. Bachmeier University of Northern Iowa May 2016 TESSELLATIONS : THE WORK OF MAURITS CORNELIS ESCHER This Study by: Emily Bachmeier Entitled: Tessellations: An Artistic and Mathematical Look at the Work of Maurits Cornelis Escher has been approved as meeting the thesis or project requirements for the Designation University Honors. ___________ ______________________________________________________________ Date Dr. Catherine Miller, Honors Thesis Advisor, Math Department ___________ ______________________________________________________________ Date Dr. Jessica Moon, Director, University Honors Program TESSELLATIONS : THE WORK OF MAURITS CORNELIS ESCHER 1 Introduction I first became interested in tessellations when my fifth grade mathematics teacher placed multiple shapes that would tessellate at the front of the room and we were allowed to pick one to use to create a tessellation.
    [Show full text]
  • Jean Baudrillard
    The Mirror of Production by Jean Baudrillard Translated with "Introduction" by Mark Poster TELOS PRESS • ST'. LOUIS Published originally as Le Miroir de la Production. English translation copyright © 1975 by Telos Press. All rights reserved. ISBN : 0- 914386-06-9 Library of Congress : 74- 82994 Manufactured in the United States of America. TABLE OF CONTENTS Translator's Introduction 1 Preface 17 Chapter I: The' Concept of Labor 21 . Critique of Use Value and Labor Power 22 The Concrete Aspect of Labor : The "Dialectic" of Qu ality and Qu antity 25 Man's Double "Generic" Face 30 Ethic of Labor ; Esthetic of Play 33 Marx and the Hieroglyph of Value 41 Epistemology I : In the Shadow of Marxist Concepts 47 The Critique of Political Economy Is Basically Completed 50 Chapter II: Marxist Anthropology 53 and the Domination of Nature The Moral Philosophy of the Enlightenment 56 Lycurgus and Castration 60 Judaeo-Christian Anti-Physis 63 Epistemology II : Structural Limits of the Marxist Critique 65 Chapter III: Historical Materialism 69 and Primitive Societies Structural Causality and the Primitives 70 Surplus and Anti-Production 74 Magic and Labor 81 Epistemology III: Materialism and Ethnocentrism 84 Chapter IV: On the Archaic and Feudal Mode 93 The Slave 93 The Artisan 96 Epistemology IV : Marxism and Miscomprehension 106 Chapter V: Marxism and the System of Political Economy Ill A Euclidean Geometry of His tory? Ill The Third Phase of Political Economy 119 Contradiction and Subversion : The Displacement of the Political 129 The Economic as Ideology and Simulation Model 14 7 Marxist Theory and the Workers' Movement: The Concept of Class 15 2 Revolution as Finality : History in Suspense 160 The Radicality of Utopia 163 TRANS LA TOR'S INTRODUCTION For some time now many of us have harbored the knowledge or at least the Euspicion that Marxism is an inadequate perspective for the critical analysis of advanced society.
    [Show full text]
  • Qualitative Freedom
    Claus Dierksmeier Qualitative Freedom - Autonomy in Cosmopolitan Responsibility Translated by Richard Fincham Qualitative Freedom - Autonomy in Cosmopolitan Responsibility Claus Dierksmeier Qualitative Freedom - Autonomy in Cosmopolitan Responsibility Claus Dierksmeier Institute of Political Science University of Tübingen Tübingen, Baden-Württemberg, Germany Translated by Richard Fincham American University in Cairo New Cairo, Egypt Published in German by Published by Transcript Qualitative Freiheit – Selbstbestimmung in weltbürgerlicher Verantwortung, 2016. ISBN 978-3-030-04722-1 ISBN 978-3-030-04723-8 (eBook) https://doi.org/10.1007/978-3-030-04723-8 Library of Congress Control Number: 2018964905 © The Editor(s) (if applicable) and The Author(s) 2019. This book is an open access publication. Open Access This book is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence and indicate if changes were made. The images or other third party material in this book are included in the book’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the book’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.
    [Show full text]
  • The Creative Act in the Dialogue Between Art and Mathematics
    mathematics Article The Creative Act in the Dialogue between Art and Mathematics Andrés F. Arias-Alfonso 1,* and Camilo A. Franco 2,* 1 Facultad de Ciencias Sociales y Humanas, Universidad de Manizales, Manizales 170003, Colombia 2 Grupo de Investigación en Fenómenos de Superficie—Michael Polanyi, Departamento de Procesos y Energía, Facultad de Minas, Universidad Nacional de Colombia, Sede Medellín, Medellín 050034, Colombia * Correspondence: [email protected] (A.F.A.-A.); [email protected] (C.A.F.) Abstract: This study was developed during 2018 and 2019, with 10th- and 11th-grade students from the Jose Maria Obando High School (Fredonia, Antioquia, Colombia) as the target population. Here, the “art as a method” was proposed, in which, after a diagnostic, three moments were developed to establish a dialogue between art and mathematics. The moments include Moment 1: introduction to art and mathematics as ways of doing art, Moment 2: collective experimentation, and Moment 3: re-signification of education as a model of experience. The methodology was derived from different mathematical-based theories, such as pendulum motion, centrifugal force, solar energy, and Chladni plates, allowing for the exploration of possibilities to new paths of knowledge from proposing the creative act. Likewise, the possibility of generating a broad vision of reality arose from the creative act, where understanding was reached from logical-emotional perspectives beyond the rational vision of science and its descriptions. Keywords: art; art as method; creative act; mathematics 1. Introduction Citation: Arias-Alfonso, A.F.; Franco, C.A. The Creative Act in the Dialogue There has always been a conception in the collective imagination concerning the between Art and Mathematics.
    [Show full text]
  • Masses, Turbo-Capitalism and Power in Jean Baudrillard's Social
    International Journal of Theology, Philosophy and Science No. 3, Year 2/2018 MASSES, TURBO-CAPITALISM AND POWER IN JEAN BAUDRILLARD’S SOCIAL AND POLITICAL ONTOTHEOLOGY PhD. Prof. Spiros MAKRIS Assistant Professor in Political Theory University of Macedonia, Thessaloniki, GREECE Email: [email protected] ABSTRACT If postmodern Jean Baudrillard (1929-2007) could be defined as a theorist of power - to the extent that for some this is a contradiction by definition, although something very similar takes place in the case of Michel Foucault, he could be defined as a theorist of meta-power in the globalized era of turbo-capitalism. In his late texts (2005), which were published in 2010, the eminent French philosopher builds a provocative theory about power by using the classic concepts of domination and hegemony within the contemporary social, economic, political and ideological context of neoliberal globalization. In these papers, he analyzes in-depth the meta- power of hegemony in comparison with the power of domination. Actually, by signifying the critical passage of postwar capitalism from the phase of production to the phase of consumption, as Zygmunt Bauman does in his relevant work, Baudrillard formulates a meta-power theory as the equivalent of what he defines as turbo-capitalism. What is at stake is no longer the conventional issues of state sovereignty, Marx-inspired concept of alienation and Critical Theory-like negative dialectics but the crucial questions of hegemony, hostage and evilness. In short, Jean Baudrillard builds a new ontological and by extension disciplinary and theoretical field concerning global power, where the ‘Empire of Good’, or turbo-capitalism in his own terminology, is reborn in a totally catastrophic way (see simulation in the sense of a capitalist hypocrisy) either as an ‘Axis of Evil’ or as the ‘problem of terror’ (see simulacrum in the sense of a Lacanian stage of image within which turbo-capitalism represses, through a Freudian process of repelling, its unfamiliar self/i.e.
    [Show full text]
  • Mathematics K Through 6
    Building fun and creativity into standards-based learning Mathematics K through 6 Ron De Long, M.Ed. Janet B. McCracken, M.Ed. Elizabeth Willett, M.Ed. © 2007 Crayola, LLC Easton, PA 18044-0431 Acknowledgements Table of Contents This guide and the entire Crayola® Dream-Makers® series would not be possible without the expertise and tireless efforts Crayola Dream-Makers: Catalyst for Creativity! ....... 4 of Ron De Long, Jan McCracken, and Elizabeth Willett. Your passion for children, the arts, and creativity are inspiring. Thank you. Special thanks also to Alison Panik for her content-area expertise, writing, research, and curriculum develop- Lessons ment of this guide. Garden of Colorful Counting ....................................... 6 Set representation Crayola also gratefully acknowledges the teachers and students who tested the lessons in this guide: In the Face of Symmetry .............................................. 10 Analysis of symmetry Barbi Bailey-Smith, Little River Elementary School, Durham, NC Gee’s-o-metric Wisdom ................................................ 14 Geometric modeling Rob Bartoch, Sandy Plains Elementary School, Baltimore, MD Patterns of Love Beads ................................................. 18 Algebraic patterns Susan Bivona, Mount Prospect Elementary School, Basking Ridge, NJ A Bountiful Table—Fair-Share Fractions ...................... 22 Fractions Jennifer Braun, Oak Street Elementary School, Basking Ridge, NJ Barbara Calvo, Ocean Township Elementary School, Oakhurst, NJ Whimsical Charting and
    [Show full text]
  • Jean Baudrillard's Encounter with Anthropology
    Journalism and Mass Communication, July 2016, Vol. 6, No. 7, 420-425 doi: 10.17265/2160-6579/2016.07.006 D DAVID PUBLISHING Jean Baudrillard’s Encounter With Anthropology: Toward A Radical Understanding of Marxism and Terrorism Gerry Coulter Bishop’s University, Sherbrooke, Canada Jean Baudrillard (1929-2007), a leading contemporary theorist from the 1970s to the present, was deeply influenced by anthropological thought. As an outcome of his prolonged encounter with anthropology he was able to devise a unique approach to the world. This approach enabled him to play a leading role in surpassing Marxist thought and in explaining contemporary terrorist attacks such as those of September 11, 2001 in the United States. Baudrillard, who is often correctly seen as making a contribution to contemporary anthropology, is also someone who is deeply indebted to anthropology. This aspect of Baudrillard is less well understood. Keywords: Baudrillard, anthropology, symbolic exchange, reversibility, terrorism, Marxism Introduction Jean Baudrillard is widely known to have developed a unique and radical approach to contemporary theory. For example, following the attacks on the United States of September 11, 2001, Baudrillard hypothesized that the attacks were one event in what he called the Fourth World War (the Cold War being the Third World War). According to his view, terrorism can be viewed as a symbolic exchange wherein a group of people long humiliated may return the humiliation by way of a terrorist attack. This view was not intended to support terror but rather, to offer a new way of understanding it beyond traditional journalism and foreign policy analysis.
    [Show full text]
  • Mathematical Concepts Within the Artwork of Lewitt and Escher
    A Thesis Presented to The Faculty of Alfred University More than Visual: Mathematical Concepts Within the Artwork of LeWitt and Escher by Kelsey Bennett In Partial Fulfillment of the requirements for the Alfred University Honors Program May 9, 2019 Under the Supervision of: Chair: Dr. Amanda Taylor Committee Members: Barbara Lattanzi John Hosford 1 Abstract The goal of this thesis is to demonstrate the relationship between mathematics and art. To do so, I have explored the work of two artists, M.C. Escher and Sol LeWitt. Though these artists approached the role of mathematics in their art in different ways, I have observed that each has employed mathematical concepts in order to create their rule-based artworks. The mathematical ideas which serve as the backbone of this thesis are illustrated by the artists' works and strengthen the bond be- tween the two subjects of art and math. My intention is to make these concepts accessible to all readers, regardless of their mathematical or artis- tic background, so that they may in turn gain a deeper understanding of the relationship between mathematics and art. To do so, we begin with a philosophical discussion of art and mathematics. Next, we will dissect and analyze various pieces of work by Sol LeWitt and M.C. Escher. As part of that process, we will also redesign or re-imagine some artistic pieces to further highlight mathematical concepts at play within the work of these artists. 1 Introduction What is art? The Merriam-Webster dictionary provides one definition of art as being \the conscious use of skill and creative imagination especially in the production of aesthetic object" ([1]).
    [Show full text]
  • Muse® Teacher Guide: January 2020
    Muse® Teacher Guide: September 2020 What Is Perfection? It may be a relief to discover that being “imperfect” has some advantages. This issue of MUSE explores how variation and diversity contribute to excellence. In a world where we are compelled to strive for excellence, the articles in this guide examine why the journey, rather than the destination, should be our primary focus. CONVERSATION QUESTION When can imperfection be extraordinary? TEACHING OBJECTIVES • Students will learn about the use of the golden In addition to supplemental materials ratio in art. • Students will learn why game developers avoid focused on core STEM skills, this perfection. flexible teaching tool offers • Students will learn how variations in biology can be the key to excellence. vocabulary-building activities, • Students will investigate number patterns utilizing questions for discussion, and cross- the Fibonacci sequence. • Students will compare and contrast the elements curricular activities. of a wide game with the elements of a deep game. • Students will examine the structure and function SELECTIONS of variations in the human body that contribute to • The Art of the Golden Ratio the extraordinary functioning. Expository Nonfiction, ~900L • Students will research examples of the golden • Good Gaming ratio in art history. Expository Nonfiction, ~1100L • Students will use mathematical concepts to express game preferences. • Perfectly Imperfect • Students will study additional examples of Expository Nonfiction, ~700L adaptation in the animal kingdom. U33T http://www.cricketmedia.com/classroom/Muse-magazine Muse® Teacher Guide: September 2020 The Art of the Golden Ratio ENGAGE pp. 20–22, Expository Nonfiction Conversation Question: When can imperfection be extraordinary? This article explores the use of mathematical concepts in art.
    [Show full text]
  • Theory, Totality, Critique: the Limits of the Frankfurt School Critical Theory, Marxism and Modernity
    Studies in 20th Century Literature Volume 16 Issue 1 Special Issue on Contemporary Spanish Article 11 Poetry: 1939-1990 1-1-1992 Theory, Totality, Critique: The Limits of the Frankfurt School Critical Theory, Marxism and Modernity Philip Goldstein University of Delaware Follow this and additional works at: https://newprairiepress.org/sttcl Part of the German Literature Commons, and the Modern Literature Commons This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License. Recommended Citation Goldstein, Philip (1992) "Theory, Totality, Critique: The Limits of the Frankfurt School Critical Theory, Marxism and Modernity," Studies in 20th Century Literature: Vol. 16: Iss. 1, Article 11. https://doi.org/ 10.4148/2334-4415.1297 This Review Essay is brought to you for free and open access by New Prairie Press. It has been accepted for inclusion in Studies in 20th Century Literature by an authorized administrator of New Prairie Press. For more information, please contact [email protected]. Theory, Totality, Critique: The Limits of the Frankfurt School Critical Theory, Marxism and Modernity Abstract Theory, Totality, Critique: The Limits of the Frankfurt School Critical Theory, Marxism and Modernity by Douglas Kellner. Keywords Frankfurt School, WWII, Critical Theory Marxism and Modernity, Post-modernism, society, theory, socio- historical perspective, Marxism, Marxist rhetoric, communism, communistic parties, totalization, totalizing approach This review essay is available in Studies in 20th Century Literature: https://newprairiepress.org/sttcl/vol16/iss1/11 Goldstein: Theory, Totality, Critique: The Limits of the Frankfurt School Cr Review Essay Theory, Totality, Critique: The Limits of the Frankfurt School Philip Goldstein University of Delaware Douglas Kellner, Critical Theory, Marxism and Modernity.
    [Show full text]
  • BOOK S in Brief
    OPINION NATURE|Vol 464|15 April 2010 O To what extent UDI Creating wetlands around ST are we in control Manhattan could protect the AND of our actions? city from rising waters. L E/D Not as much as C we think, says neuroscientist OFFI H RC EA Eliezer Sternberg S in My Brain RE E R Made Me Do U CT E It (Prometheus Books, 2010). T Exploring thorny issues of moral HI responsibility in the light of recent ARC developments in neuroscience, Sternberg asks how the brain operates when we exercise our will, whether future criminals might be spotted from their brain chemistry and how consciousness might have evolved. Artificial reefs to buffer New York The Little Book Rising Currents: Projects for New York’s by the Brooklyn-based Bergen Street Knitters. of String Theory Waterfront A dredged-up oyster shell sits beside (Princeton Univ. Museum of Modern Art, New York Matthew Baird Architects’ model of ‘Working Press, 2010) Until 11 October 2010 Waterline’, a scheme for the low-lying lands by theoretical of Bayonne, New Jersey, and the Kill van Kull, physicist Steven the tidal strait that separates them from Staten Gubser puts Within the next 40 years, projected sea-level Island. The company proposes creating an arti- into words the rises of up to a third of a metre threaten coastal ficial reef and breakwater by sinking thousands abstract maths cities, including New York. By 2100, rising sea of 75-centimetre-high recycled-glass ‘jacks’ of some of the most challenging levels could inundate 21% of Lower Manhattan (shaped as in the game) into the sea bed.
    [Show full text]