The Mathematical Imagination The Mathematical Imagination On the Origins and Promise of Critical Theory Matthew Handelman fordham university press new york 2019 This book is freely available in an open access edition thanks to TOME (Toward an Open Monograph Ecosystem)—a collabora­ tion of the Association of American Universities, the Association of University Presses, and the Association of Research Libraries— and the generous support of Michigan State University. Learn more at the TOME website, available at: openmonographs.org. This work is licensed under a Creative Commons Attribution­ NonCommercial­NoDerivatives 4.0 International License. Through the generous funding of Michigan State University, this publication is available on an open access basis from the publisher’s website. Fordham University Press gratefully acknowledges financial assistance and support provided for the publication of this book by Michigan State University. 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Printed in the United States of Amer i ca 21 ​20 ​19 5 ​4 ​3 ​2 ​1 First edition contents Introduction: The Prob lem of Mathe matics in Critical Theory 1 1. The Trou ble with Logical Positivism: Max Horkheimer, Theodor W. Adorno, and the Origins of Critical Theory 25 2. The Philosophy of Mathe matics: Privation and Repre sen ta tion in Gershom Scholem’s Negative Aesthetics 65 3. Infinitesimal Calculus: Subjectivity, Motion, and Franz Rosenzweig’s Messianism 104 4. Geometry: Projection and Space in Siegfried Kracauer’s Aesthetics of Theory 145 Conclusion: Who’s Afraid of Mathe matics? Critical Theory in the Digital Age 187 Acknowl edgments 201 Notes 205 Bibliography 245 Index 269 v The Mathematical Imagination introduction The Prob lem of Mathe matics in Critical Theory Humanists are learning mathe matics— again.1 Amidst a renewed sense of crisis in literary, cultural, and language studies, many humanists have turned to mathematics and digital technologies based on mathematical pro cesses in hopes of modernizing and reinvigorating humanistic inquiry. Literary, cultural studies, and media studies scholars as well as historians are using algorithms to read novels, making digital maps to plot the geographies of films, using online tools to annotate and publish texts collaboratively, and applying other computational technologies to explore historical and liter- ary rec ords. According to proponents of such new methods, the so- called digital humanities promise to bring the analytic power of computation to bear on the study of culture and the arts, lending the humanities a more public face and, thus, renewed relevance in the early twenty- firstcentury. Of course, not every one shares the digital humanists’ enthusiasm and op- timism. One recent op-ed in The Atlantic alleges that the digital turn in the 1 2 Introduction humanities simply reacts to economic worries about funding increases in and administrative emphasis on STEM fields (science, technology, engineering, and mathe matics).2 The proposed digital rejuvenation of the humanities threatens to forfeit precisely what the critical study of art, lit er a ture, and history offer our advanced scientific society: access to concepts such as under- standing and empathy that, by their very nature, resist quantification. In- deed, other critics of the digital humanities worry that, beyond not bringing anything essentially new to humanistic inquiry, the climate around the digital, in fact, eschews the rigorous historical research and critical discourse central to the humanities.3 If the digital humanities embrace the tech in- dustry, do the humanities not also acquiesce to the merger of technology and industry, whose mechanisms of manipulation and control critical the- ory seeks to expose and oppose? What often goes unacknowledged in these con temporary debates is the long history of similar disagreements over epistemology that date back to the very inception of critical theory. As Max Horkheimer (1895–1973) and Theodor W. Adorno (1903–1969) first conceived of it in the 1930s, critical theory steadfastly opposed the mathematization and quantification of thought. For them, the equation of mathematics with thinking, embraced by their intellectual rivals, the logical positivists, provided the epistemological con- ditions leading reason back into the barbarism and vio lence that culmi- nated in World War II and the Holocaust. However, the fact that Horkheimer and Adorno interwove mathe matics with the dialectics and downfall of enlightenment obscures how mathematics provided some of their intellectual forerunners and friends— Gershom Scholem (1897–1982), Franz Rosenzweig (1886–1929), and Siegfried Kracauer (1889–1966)— with concepts, meta phors, and tools that helped negotiate the crises of moder- nity. Although Scholem, Rosenzweig, and Kracauer are not often counted as critical theorists, we can find in their work the potential for theory that is at once mathematical and critical.4 In par tic u lar, their theories of aesthet- ics, messianism, and cultural critique borrow ideas from mathematical logic, infinitesimal calculus, and geometry to theorize art and culture in ways that strive to reveal and, potentially, counter the contradictions of mod- ern society. By revisiting and rethinking the origins of critical theory, this book seeks to recapture the potential contribution that mathe matics holds Introduction 3 for the critical proj ect. To understand the influence of mathematics on Scho- lem, Rosenzweig, and Kracauer is to uncover a more capacious vision of critical theory, one with tools that can help us confront and intervene in our digital and increasingly mathematical pres ent. The Eclipse of Mathe matics in Critical Theory In 1935, Edmund Husserl saw the world of reason that he had helped con- struct crumbling before him. A founder of the philosophical school of phe- nomenology earlier in the century, Husserl held a series of lectures that year in Prague recounting how, over time, the positivistic special sciences had eliminated all the genuine prob lems of reason— the question of rational knowledge, the ethics of truly good action, and the notion of values as val- ues of reason. At some point, Eu ro pe ans had traded a mode of thinking genu- inely concerned with reason, ethics, and values— the basic questions of humanity and their meaning in life— for the facts of science and the formulae of mathe matics. First published in Belgrade as “Die Krisis der europäischen Wissenschaften und die transzendentale Phänomenologie” (“The Crisis of the Eu ro pean Sciences and Transcendental Phenomenology,” 1936), these lectures took on a very dif fer ent tone than Husserl’s other introductions to phenomenology, not least because they could not be delivered or published in Nazi Germany (Husserl was of Jewish descent).5 Instead of the “Age of Enlightenment” producing the great phi los o phers to whom Husserl had turned in Cartesian Meditations (1931), it now appeared as if the advent of the mathematical natu ral sciences in the Enlightenment had been the pro- genitor of a radical turn away from reason in philosophy, manifest in a new type of thought that threatened to “succumb to skepticism, irrationalism, and mysticism.” 6 For Husserl, stripped of his German citizenship and re- moved from the roster at the University of Freiburg, the ramifications of the situation were undeniable. This was not merely a crisis in the natu ral sciences or philosophy but a fundamental prob lem with knowledge and rea- son as such, as implied by the broader German term Wissenschaft (literally, body or collection of knowledge). And yet Husserl thought crisis could still be avoided and Eu rope could still be saved, but only if, as he put it in the 4 Introduction preface to the 1936 publication, the heirs of the Enlightenment embraced “the unavoidable necessity of a transcendental- phenomenological re- orientation of philosophy.”7 Husserl died in April 1938; a year later, Germany invaded Prague on its way to total war. Eu rope and its sciences had, of course, been in crisis for de cades. A “cri- sis of language” (Sprachkrise) had plagued the intellectual life of fin- de- siècle Vienna, inspiring the work of poets such as Hugo von Hofmannsthal, cul- tural critics such as Fritz Mauthner, and phi los o phers such as Ludwig Witt- genstein. For these thinkers, language no longer offered a reliable means of capturing and communicating experience and thought, the more problem- atic aspects of which Wittgenstein famously recommended that we pass over in silence.8 In 1922, the idea that history called into question the state, mor- als, and religion, instead of providing their justification,