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Novalis and Mathematics COLLEGE of ARTS and SCIENCES Imunci Germanic and Slavic Languages and Literatures Novalis and Mathematics COLLEGE OF ARTS AND SCIENCES ImUNCI Germanic and Slavic Languages and Literatures From 1949 to 2004, UNC Press and the UNC Department of Germanic & Slavic Languages and Literatures published the UNC Studies in the Germanic Languages and Literatures series. Monographs, anthologies, and critical editions in the series covered an array of topics including medieval and modern literature, theater, linguistics, philology, onomastics, and the history of ideas. Through the generous support of the National Endowment for the Humanities and the Andrew W. Mellon Foundation, books in the series have been reissued in new paperback and open access digital editions. For a complete list of books visit www.uncpress.org. Novalis and Mathematics A Study of Friedrich von Hardenberg’s Fragments on Mathematics and its Relation to Magic, Music, Religion, Philosophy, Language, and Literature martin dyck UNC Studies in the Germanic Languages and Literatures Number 27 Copyright © 1960 This work is licensed under a Creative Commons cc by-nc-nd license. To view a copy of the license, visit http://creativecommons. org/licenses. Suggested citation: Dyck, Martin. Novalis and Mathematics: A Study of Friedrich von Hardenberg’s Fragments on Mathematics and its Relation to Magic, Music, Religion, Philosophy, Language, and Literature. Chap- el Hill: University of North Carolina Press, 1960. doi: https://doi. org/10.5149/9781469657455_Dyck Library of Congress Cataloging-in-Publication Data Names: Dyck, Martin. Title: Novalis and mathematics : A study of Friedrich von Hardenberg’s fragments on mathematics and its relation to magic, music, religion, philosophy, language, and literature / by Martin Dyck. Other titles: University of North Carolina Studies in the Germanic Languages and Literatures ; no. 27. Description: Chapel Hill : University of North Carolina Press, [1960] Series: University of North Carolina Studies in the Germanic Languages and Literatures. | Includes bibliographical references. Identifiers: lccn 60062924 | isbn 978-1-4696-5744-8 (pbk: alk. paper) | isbn 978-1-4696-5745-5 (ebook) Subjects: Novalis, 1772-1801. | Mathematics — History. Classification: lcc pd25 .n6 no. 27 | dcc 510/ .9 PREFACE The present study grew out of my dual interest in literature and mathematics. Though literature, mainly German, is my principal field of endeavor, I have, as an adventure in thought, and in search for basic methods and principles, successfully completed a dozen advanced courses in mathematics within the Canadian honors program. Although interest in Novalis' fragments, and in other early Romantic fragments, is growing steadily, Novalis' fragments on mathematics have, apart from Kate Hamburger's basic study, been treated in the most sciolistic manner, for two obvious reasons. First, many mathematicians who are not also historians of mathematics, limit their attention to contributions advancing the formal science of mathematics. Novalis made no such contribution. Second, many literary critics and scholars are either not qualified to deal with the subject, or are prejudiced against mathematics, which they vaguely associate with computation and technology. While mathematics is indeed highly applicable in these fields, most pure mathematicians regard this useful aspect of mathematics as an incidental and accidental feature that does not concern them, just as the literary writer would view the use of his medium of expression in, say, advertising. Mathematics, on the proper level, is a magnificent web of thought expressed in a subtle net of symbols, affording, if one is willing and able to master it, aesthetic experiences of the same order as those afforded by music and poetry, opening to the imagination vistas as bold and colorful and exciting as in the most Kafkaesque work of literature. Many prominent literary figures have been aware of the aesthetic and thought-challenging qualities of mathe­ matics. Novalis was one of them. He devoted himself intensively to this science throughout his brief adult life. Yet critical opinion on the exact relationship of Novalis to mathematics, as much as there is of it, has fluctuated from one extreme to the other, from de­ scribing Novalis' fragments on mathematics as manifestations of a morbid mind to detecting in them an adumbration of the theory of relativity. This state of opinion, though steadily moving toward mature evaluation, demands an elucidation of the relationship of Novalis to mathematics. That is the purpose of the present study. The first version of this study was presented in 1956 to the Graduate School of Arts and Sciences of the University of Cincinnati as a doctoral dissertation under the title "The Relation of Novalis to Mathematics." Since then I have learned a great deal more about the subject, especially from research conducted in the M.I.T. and Harvard Libraries during 1956-1958. Hand in hand with this study, a cognate monograph entitled "Goethes geistige Welt im Lichte der Mathematik" is nearing completion. Essential results of the latter were published in two American journals: "Goethe's Views on Pure Mathematics," Germanic Review, XXXI (1956), pp. 49-69, and "Goethe's Thought in the Light of His Pronouncements on Applied and Misapplied Mathematics," Publications of the Modern Language Association of America, LXXIII (1958), pp. 505-515. On the basis of these endeavors the dissertation was re-written. I wish to express my gratitude to Professors Edwin H. Zeydel, Gottfried F. Merkel, and K. W. Maurer for continuous support, criticism, and help; to Privatdozent Dr. Alexander Peyerimhoff (Giessen), Visiting Professor of Mathematics at the University of Cincinnati, for reading the manuscript from the mathematical point of view and providing it with better formulations and various emendations; to Professor Dr. Joseph Ehrenfried Hofmann (Tii­ bingen), noted historian of mathematics, who examined difficult fragments on mathematics by Novalis, identified them in historical contexts and offered invaluable bibliographical references; to my mathematics teachers at the University of Manitoba, in particular Professors J. W. Lawson and N. S. Mendelsohn, who graciously tolerated my "bigamous" association with literature and mathe­ matics; to members of the mathematics staff at the University of Cincinnati an.d M.I.T.; to my graduate student, Mr. Emery E. George, whose critical reading of the final version of the manuscript resulted in several improvements; to my colleagues, Professors Henry W. Nordmeyer and Walter A. Reichart, to Mr. F. D. Wieck, Director of the University of Michigan Press, and to Professor Frederic E. Coenen, for their kind advice and help in the publication of the book. I also wish to acknowledge my debt of gratitude to the Libraries of the Universities of Manitoba, Cincinnati, Harvard, and of Michigan; of the Massachusetts Institute of Technology; to the Cincinnati and New York Public Libraries; and to the Library of Congress. Finally, I wish to thank Dean Ralph A. Sawyer and the Executive Board of the Horace H. Rackham School of Graduate Studies of the University of Michigan for a subsidy from the Publication Fund of the School, which made publication of this book possible. May 1, 1959. MARTIN DYCK Department of Germanic Languages and Literatures University of Michigan, Ann Arbor die, Marieche, mine lewe fru. Published with aid from the Publication Fund of the Horace H. Rackham School of Graduate Studies of the University of Michigan TABLE OF CONTENTS PREFACE 1 DEDICATION 3 CHAPTER I - INTRODUCTION 10 1. The Problem 12 2. The Sources . 13 3. Critical Discussion of Previous Studies on the Subject 15 CHAPTER II - THE IMPACT OF MATHEMATICS ON NOV ALIS 20 1. Some Aspects of the History of Mathematics in the Eighteenth Century 20 2. Novalis' Study of Mathematics and His Acquaintance with Mathematicians . 25 3. Philosophical Sources for N ovalis' Fragments on Mathe- matics 37 4. Mathematical Sources for Novalis' Fragments on Mathe- matics 46 CHAPTER III - NOVALIS' FRAGMENTS ON MATHEMATICS, PART ONE . 52 MATHEMATICS DISCUSSED PHILOSOPHICALLY 52 1. Basic Concepts . 52 2. Geometry 58 3. Arithmetic and Algebra 61 4. Analysis . 68 CHAPTER IV - NOVALIS' FRAGMENTS ON MATHEMATICS, PART TWO . 75 MATHEMATICAL CONCEPTS PROJECTED INTO FIELDS OF KNOWLEDGE OTHER THAN THE PHYSICAL SCIENCES 75 1. Mathematics as the Ideal Science and the Basis for a Universal Encyclopedia of Knowledge 75 2. Mathematics and Philosophy . 77 3. Mathematics and Magic 79 4. Mathematics and Religion 80 5. Mathematics and Language 81 6. Mathematics and Literature 83 7. Mathematics and Music 89 SUMMARY AND CONCLUSIONS 93 BIBLIOGRAPHY 95 INDEX • 104 CHAPTER I INTRODUCTION Novalis, a man of the most indisput­ able talent, poetical and philosophi­ cal; whose opinions, extraordinary, nay altogether wild and baseless as they may often appear, are not without a strict coherence in his own mind, and will lead any other mind, that examines them faithfully, into endless considerations; opening the strangest enquiries, new truths, or new possi­ bilities of truth, a whole unexpected world of thought, where, whether for belief or denial, the deepest questions await us (Critical and Misc. Essays, London, 1847, p. 5). THOMAS CARLYLE, 1827 1. THE PROBLEM When Novalis, the German Romantic poet and philosopher, whose real name was Georg Friedrich Philipp von Hardenberg, died in 1801, not quite twenty-nine years old, there was left among his papers a large number of notes on philosophy, literature, religion, medicine, mathematics, engineering,
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