The Poetics of Perspective 9781501723896

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THE POETICS OF PERSPECTIVE

JAMES ELKINS

THE POETICS OF PERSPECTIVE

CORNELL UNIVERSITY PRESS

ITHACA AND LONDON

Copyright © 1994 by Cornell University All rights reserved. Except for brief quotations in a review, this book, or parts thereof, must not be reproduced in any form without permission in writing from the publisher. For information, address Cornell University Press, Sage House, 512 East State Street, Ithaca, New York 14850. First published 1994 by Cornell University Press. First printing, Cornell Paperbacks, 1996.

Library of Congress Cataloging-in-Publication Data Elkins, James, 1955The poetics of perspective I James Elkins. p. em. Includes bibliographical references and index. ISBN o-8014-2796-7 (cloth).-ISBN o-8014-8379-4 (paper) 1. Perspective. 2. Space perception. 3· Aesthetics. I. Title. NC750.E44 1944 701'.82-dc20 94-16310

§ The paper in this book meets the minimum requirements of the American National Standard for Information SciencesPermanence of Paper for Printed Library Materials, ANSI

z39-48-1984. Paperback printing 10 9 8 7 6 5 4 3 2

CONTENTS

List of Plates Preface 1

I Into the Maelstrom of Metaphor

2

I Argus/Polyphemus

3 I The Harmonious, the Compatible, the Equivalent

vii

xi 1

45 81

4 I Demonstration, Play, Arcanum

117

5 I Curved Foundations

181

6 I The Fossilization of Perspective

217

Envoi Appendix Mathematics and Perspective References Index

262 2 73 2 79

317

PLATES

1 A modern perspective schema, from Spanton 1893 2 "How to Make Landscapes through a Window," from Johann II von Pfalz-Simmeren [1531] 1970 3 Bartolomeo Romano's Military Proteus, from Romano 1595 4 Masaccio, Trinity, 1428(?). San Lorenzo, Florence 5 Uccello, Deluge, c. 1445-47. Santa Maria Novella, Chiostro Verde, Florence 6 Bronzino, Christ in Limbo, 1555, detail. Museo di Santa Croce, Florence. (Bottom) Detail of line engraving 7 Wentzel Jamnitzer 1568, geometric solids 8 Hans Lencker, "Radio Iatino," from Lencker c. 16oo 9 The problem of peripheral distortion, adapted from Piero della Francesca [c. 1482]1942 and Field 1986 10 Four projects for a marble relief of the Annunciation in the Cathedral of Milan, from Martino Bassi 1572 11 Barbaro's first perspective method, after Barbaro 1568 12 Barbaro's third perspective method, after Barbaro 1568 13 The circumscribed-rectangle method reconstructed from Alberti's Elementi di pittura, from Gambuti 1972 14 Durer's mistaken circumscribed-rectangle method, after an illustration in Durer [1525]1977 15 One of Giovanni Battista Benedetti's two circumscribed-rectangle methods, from Benedetti 1585 16 Hans Lencker's circumscribed-rectangle method, from Lencker 1571 17 Guidobaldo del Monte's second circumscribed-rectangle method, from Guidobaldo del Monte 16oo

10 51 52 54 57 59 6o 66 70 74 92 93 97 98 99 100 100

viii I

PLATES

18 Pomponius Gauricus's circumscribed-rectangle construction ([1504]1969). Pelerin's initial diagrams showing the distance point ([1505]1962) 19 Piero della Francesca's proof of perspective and three parts of it, after Piero della Francesca, De prospectiva pingendi 20 Federico Commandino's method for putting an arbitrary plane into perspective, from Commandino 1558 21 Figures used in Giovanni Battista Benedetti's proof of perspective, from Benedetti 1585 22 Guidobaldo del Monte's proof of the punctum concursus, from Guidobaldo del Monte 16oo 23 Fernando Gallego, Nativity and Adoration of the Shepherds, late fifteenth century. Retablo, San Lorenzo, Toro 24 Ercole de' Roberti, Pala portuense, 1481, detail of Madonna's throne. Milan, Brera 25 Vincenzo Catena, Saint Jerome in His Study, c. 1510. National Gallery, London 26 Intarsia panel depicting a lute, c. 1475. Studiolo, Palazzo Ducale, Urbino 27 Lorenzo da Lendinara or Pierantonio da Modena, intarsia panel, c. 1475. Cathedral sacristy, Padua 28 Anonymous artist, Madonna and Child with Saints, late fifteenth century 29 Copy of Michelangelo's David, late nineteenth century. Piazza della Signoria, Florence 30 Vincenzo Foppa, Crucifixion, 1456. Accademia Carrara, Bergamo 31 Bernardo de Prevedari after Bramante, Interior of a Ruined Church, 1481, detail. British Museum 32 Girolamo Marchesi da Codignola, Adoration of the Magi. Sixteenth century. Cassa di Risparmio, Cesena

103 105 109 111 113 122 125 126 130 132 136 141 148 151 152

33 Pontormo, Visitation, 1528. Pieve, Carmignano 34 Pontormo, Visitation, schematics

155 156

35 Serlio, scena tragica, from Serlio 1545 36 Writing table, German, sixteenth century 37 Meister mit der Hausmarke, Kabinettschrank "WrangelSchrank." Augsburg, 1566. Inside of right-hand door 38 "Perspective garden," from Lorenz Stoer 1567 39 Cesare Reverdino, Geometry, c. 1530 40 Monogrammist F. B., Melancolia, 1561

157 161 162 164 168 169

PLATES

41 Hans Holbein, Fat;ade Design for the Haus "zum Tanz," formerly in Basel 42 Tintoretto, Removal of the Body of Saint Mark, with reconstruction of original lines, c. 1562. Accademia, Venice 43 Leonardo Parasole [Norsini], Miracle of the Blind Man, c. 16oo 44 Stereographic projection, plan, and elevation of a cube, from E. Keller 1926 45 Linear perspective projection of a pillar motif and Hauck's projection of the pillar motif, from Graf 1940 46 Andrea Castagno, The I.nst Supper and The Crucifixion, c. 1445-50. Santa Apollonia, Florence 47 Donatello, Feast of Herod, 1423-27. Baptistery, Siena 48 Wilhelm Otto Fiedler, paraboloid of revolution in perspective, from Fiedler 1871 49 Piero della Francesca, Flagellation of Christ, c. 1463-64. Palazzo, Urbino 50 Ernest Irving Freese, a visual-ray method, detail of final construction, from Freese 1930 51 Giorgione, Caste/franco Altarpiece (Madonna Enthroned with Saints Liberale and Francis), c. 1505. Chiesa Parrochal, Castelfranco 52 Jan van Eyck, Lucca Madonna, c. 1435-40. Reconstruction by the author 53 Vincenzo Foppa, Crucifixion. Bergamo. Reconstruction of the fictive space, from Wittgens 1944 54 "Chiasmatic" perspectival diagrams 55 Intarsia view of churches, detail of a trunk, 1580. Augsburg 56 Dan Pedoe's application of rabatment and the Desargues theorem to Piero della Francesca's projection of a pentagon

I ix

172 175 178 207 208 221 223 225 228 229 235 238 241 249 271 275

PREFACE

My principal concern in this book is the way we talk about pictures, and specifically those with a high complement of geometric forms. Renaissance writers and artists imagined perspective quite differently than we do, and "unchangeable" concepts such as the definition of perspective and the idea of pictures being "in perspective" have changed a great deal since the fifteenth century. I maintain, for example, that Renaissance authors and artists thought there were many compatible perspectives, so that their writing and painting evince a "pluralist" approach in strict contrast to the monolithic mathematical perspective we imagine today. Theirs was more a collection of rational methods than a "rationalization of sight," more a way of drawing objects than of setting them in an abstract "pictorial space." But the most important of these changes is the gradual recession of perspective as a mute method, a practical subset of geometry, and the growth of perspective as a metaphor, a powerful concept for ordering our perception and accounting for our subjectivity. It seems to me that this is the change that underwrites many more specific accounts (for instance, the idea of perspective as a "symbolic form") and that the preeminence of metaphor bears a reciprocal relation to the interest in technique. In thinking about metaphor, we have largely forgotten perspective as a practice-and that forgetting is not without consequence for our understanding of both Renaissance and modern paintings or for the way we put the concept of perspective to work in philosophy and literary studies. One of the reasons such a change has been possible is the multiple nature of perspective itself: as a subject, perspective is not fully at home in any one discipline, as its classification in contemporary li-

xii /

PREFACE

braries reveals. At the University of Michigan at Ann Arbor, to take one example, perspective is dispersed among the mathematics library, the fine arts library, the architecture library, the engineering library, and both general libraries; and within a given library, it is to be found on various floors and under various headings: in one place for photogrammetry, in another for aerial surveying, another for philosophy, and so forth. This disarray is not merely a superficial trait but mirrors the conceptual scattering of the field as a whole. Perspective has no canonical site, no single definition or description that can provide an adequate or standard account of what it is. Writing on perspective is currently done in a variety of more-or-less distinct fields, including experimental and cognitive psychology, linguistics, literary criticism, analytic and existential philosophy, phenomenology, semiotics, psychoanalysis, metaphorology, and various strains of art history, mathematics, engineering, and pedagogy. Some mathematicians write without thinking of history, and some literary critics, historians, and philosophers write without interest in mathematics. Even within art history there are several ways of addressing perspective which draw on distinct bibliographies. The larger subject of this book, then, is the question of what it means to write "between" disciplines and to engage a subject that is traditionally not fully present. It is-to say the least of it-a little strange that a concept so central to the Western imagination should be treated in this way. There may not be a perspective from which we can apprehend the entirety of the subject "perspective" -and in fact, I contend that it does not make sense to try to attain such a positionbut it seems important that we not assume there are no significant consequences when a philosophic exposition of a picture bypasses a mathematical exposition or vice versa. I mean the word poetics in my title to refer to the partly rational, partly poetic nature of perspective and to indicate my intention, within the bounds of a book designed for a general audience, not to favor history or philosophy over geometry, but to explore both the possibilities of speaking in a more inclusive fashion and the consequences of speaking in a more limited way. Such, in brief, is the subject of this book. Chapter 1, "Into the Maelstrom of Metaphor," is an attempt to survey the components of our modern concept of perspective, including the various ways in which it has become a metaphor for vision, for pluralism, for states of mind, and for epochs of art. My purpose is to gain a sense of what the

PREFACE

/

xiii

word perspective means now, not merely in its narrow, "proper" definition but in relation to other aspects of contemporary thought. Chapters 2 through 6 trace the prehistory of that meaning from its beginnings in Renaissance thought. Chapter 2, "Argus/Polyphemus," concerns the degree to which perspective was conceived as a unitary phenomenon. In particular I believe that the Renaissance sense of perspective was less unified than ours and that there was no clear understanding of perspective's origins. Renaissance authors refer to "perspectives" rather than "perspective," and there could be various incommensurate perspectives within a single picture. The concepts explored in Chapter 3, "The Harmonious, the Compatible, the Equivalent," bear on Renaissance proofs of perspective. Renaissance texts evince a general sense that perspective methods are harmonious but relatively less interest in whether or not they are compatible or mathematically equivalent. Those differences are telling, inasmuch as the modern concept of perspective requires that its methods be compatible with some ultimate standard that owes strict allegiance to mathematics and optics. In Chapter 3 perspective practice is imagined less as an import from geometry into painting than as a kind of picture making, akin to painting, which involves the viewer and the viewed in an especially radical dynamic. In the fourth chapter I explore the practice of Renaissance perspective, which was wide ranging and capable of a variety of expressive forms. I consider three in particular: the "demonstrations of skill" typical of the quattrocento, the sense of play that marks the High Renaissance and earlier sixteenth century, and the arcana that accompany the recession of perspective into the hands of mathematicians at the end of the Renaissance. The fifth chapter, "Curved Foundations," considers the ways modern writers have sought to ground or prove perspective or to place it definitively among various disciplines. That line of inquiry leads into the question of "curvilinear perspectives," which have intermittently been proposed as improvements on linear perspective, and the problem becomes a matter of explaining why an unlikely mix of art history, physiological optics, art practice, and art history constitutes our best attempt at understanding perspective. By "The Fossilization of Perspective," which is the title of the final chapter, I mean the gradual impoverishment of perspective practice which has accompanied the rise of metaphorical meanings. For the most part, modern writers do not use the panoply of Renaissance and baroque methods. Instead,

xiv /

PREFACE

they employ simplified, holistic techniques, typically involving the tracing of pictures that exhibit perspective and the drawing of simple schematics. That practice is employed by art historians, phenomenologists, Lacanian psychoanalysts, and contemporary perspectival painters. Our perspective is ossified, and Chapter 6 is an attempt to understand our praxis both as a kind of perspective and as an expression of our interests. Though perspective's efflorescence into metaphor and its retreat from nonverbal practice are cardinal facts in its conceptual history, we must not be content with describing its relation to philosophy, its nature as a technique, or its origin and meanings in history. The conceptual field of perspective is a chronic fragmentation, and it has led to the adoption of certain conventional ways of speaking. Some problems have recurred in much the same forms since the Renaissance. They continue to impel our writing, so that in any given case we are likely to be writing on topics that were discussed centuries before. In the Envoi I consider how this condition and the reasons for it are promising topics for further writing. I conclude with a thought about how the thesis and the exposition of this book find their places in the history and economy of perspective. Since I first sketched this book in 1982, many people have had a hand in it. First acknowledgments are due to E. E. Rosenthal, whose patience was invaluable in shaping it from a collection of random forays into something usable. Many scholars have answered questions and helped with difficult points. Among them are Phillip Jones, who gave advice several times on matters pertaining to the history of perspective; Kim Veltman, who offered friendly encouragement and a number of obscure sources; and Charles Cohen of the University of Chicago, who provided references on quattrocento painting and fa~ade painting. In addition, I am happy to thank Barbara Stafford, for many interdisciplinary ideas; John White of the University of London, for reading a draft of the section on curvilinear perspective; Morris Kline, the historian of mathematics; Dan Pedoe, for responding to questions about the historical relevance of the Desargues theorem; Erhard Scholz of the Gesamthochschule Wuppertal; Kirsti Andersen of the Institute for the History of Science in Ny Munkegade, Denmark; Boris Rosenfeld of the Institute for History of Science and Technology in Moscow, for a letter summarizing Soviet research;

PREFACE / XV

H. S. M. Coxeter of the University of Toronto, for references on matters of projective geometry; Stephen Stigler, for help with a statistical analysis; Nelson Goodman, for responding to a criticism of his criticism of perspective; David Lindberg of the University of Wisconsin, who helped with a reading of Witelo; Kate Desulis and Peggy Kidwell, for assistance with an odd "perspectival instrument"; Hans WufSing of Karl Marx University, Leipzig; Ian Mueller, for helping reconstruct part of Piero della Francesca's proof of perspective; John Ward, for a vigilant reading of material on Jan Van Eyck; Martin Jay, for several crucial references I had overlooked; Mina Gregori, for quick identification of a painting I had thought was obscure; and E. H. Gombrich, for references to current research. An anonymous reviewer contributed, in a single line, a structural key that changed the book from an unwieldy collection of chapters into a coherent narrative. Something with not much resemblance to this book was once projected as a book to be written with Joel Snyder, and I thank him for patient readings of some especially intractable early essays. It is not irrelevant to my theme that the more technical analysesones that would not be pleasant reading for those outside the specialties of Renaissance perspective-have been restricted to the references and Appendix. In these pages I wrestle several times with this unavoidable casting of techne as "support" for literary narrative and the apparent absurdity of using literary narrative to "support" techne. Earlier (and more technical) versions of parts of Chapters 2, 3, 4, 5, and 6 originally appeared as essays in the Art Bulletin 69 (1987): 2203o and 73 (1991): 53-62 (reprinted by permission of the College Art Association, Inc.), Oud Holland 102 (1988): 257-76, Art History 14.2 (1991): 143-74, the Journal of the Warburg and Courtauld Institutes 51 (1988); 190-96, the Journal of the History of Ideas 53.2 (1992): 209-30, and Storia dell'arte 67 (1989): 257-62. Material on the baroque, which I have neglected here in order to make what I think are more essential points, has appeared in the Zeitschrift fiir Kunstgeschichte. All photos, diagrams, and modifications of plates are my own unless otherwise credited. }AMES ELKINS

Chicago, Illinois

THE POETICS OF PERSPECTIVE

CHAPTER 1

/

INTO THE MAELSTROM OF METAPHOR

For those whose interest in painting takes them in other directions, studies of perspective can be tough going. Perspective is the most geometric of the theories applied to paintings, and it has never been at home with the more freely rhetorical and literary strains in art history. Expositions of the perspective of paintings tend to be dry or to have an uneasy mix of historical and mathematical insights. These difficulties are due in part to the nature of the subject. The mathematics of perspective is not complicated, but its lexicon is, and reading can be slowed by shifting and unfamiliar terminology as well as by the usual geometric obstacles. 1 No authoritative account can shirk these problems entirely, and they can be compounded by the dissonant effect that perspective studies have when they are put side by side with explanations of narrative, style, or social meanings. In such cases perspective seems an interloper, an "intrusion" of mathematics into an ostensibly more expressive and varied discourse. Perspective analyses are intricate in a different way than iconologic or other interpretive narratives: the former are monothematic and often ahistorical, while the latter can be both meticulous and varied. It may be, as Wesley Trim pi has said, that "geometric" and "literary" discourses spring from fundamentally different roots and that their ways of organizing experience are irremediably at odds.2 1. The necessary background to analyze perspective problems within art history can be reliably obtained from Rehbock 1957, 1978 (excluding pictorial analyses); Adhemar 1836, 1843-49, 1846, 1861; La Gournerie 1860-64, 1884; Ware c. 1882; Spanton 1893, 1895; and Bartel 1934. Fielder 1871; Wiener 1884; Schmid 1922-23; and Scheffers 1920 are more technical expositions. The best single overall work, in my opinion, is Scheffers 1920. 2. Trimpi 1983 is a superlative study of these two modes of experience.

2

f

THE POETICS OF PERSPECTIVE

In a more specific way, there has always been something a bit philistine about the perspective lines that art historians add to paintings. Ruled lines and painted curves make a strong contrast, and the difference between a harsh, strictly drawn grid and an artist's superior sensibility can be jarring. Worse, perspective analyses may succeed only in adding a structure the eye cannot perceive or positing a mathematical procedure that seems remote from what we take the artist to have been doing. (Sometimes the analyses themselves form beautiful configurations, but that beauty is seldom unambiguously related to the painting underneath.) Drawn perspectives are, after all, a kind of picture and not a kind of speech, and it is difficult to put even the clearest and strongest perspective line into words. A line that possesses instant force and persuasiveness may require a paragraph of patient and measured prose. In the end, the project of connecting familiar paintings to rigid geometric patterns can be less than convincing. Perspective is a cold, mathematical endeavour, and it often risks seeming a little irrelevant in the face of a painting's richer meaning and warmth. Cold, dissonant, uneasy, remote, harsh, and philistine-perspective creates interesting effects when it is brought near the other meanings of pictures, and the resulting texts can be more absorbing for those "faults" than for their ostensive content. As a consequence of these obstacles, perspective has a peripheral role in art history: it is both widely known and little studied, indispensable in principle and awkward in practice. Its ambiguous marginality is linked to an essential trait of the modern concept: perspective is no longer the "sweet" and "beautiful" thing it once was, and it is not charged with the religious and social meanings it had for the early Renaissance. For us-meaning for those of us who study itperspective is a subject without much significance outside Renaissance paintings. 3 Contemporary art has largely abandoned it, or more precisely, the founding of modernism was bound up with a rejection of perspective, a rejection that has itself been abandoned in postmodern developments. This double isolation is both inbuilt and curious, since it may be argued that perspective itself helped give postRenaissance art the impetus to continual innovation which was a fundamental condition for modernism. In mathematics, too, perspective has lost the Ptolemaic position it 3· For the pedagogic consequences, see Harris 1955; Beal 1965; and Prentiss 1972.

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3

once had, and has become a subset of a relatively neglected branch of geometry (Table 1). 4 Even though the most sophisticated perspective methods date from the middle of the nineteenth century, virtually no new mathematical research is being done.s In historical scholarship, but not in mathematical history, perspective is said to be tied to certain mathematical developments such as the Desargues theorem; but that connection is virtually nonexistent, and mathematics and perspective have developed in parallel, mutually isolated streams since the mid-sixteenth century. (I argue this point in the Appendix.) Within linear perspective, methods developed in the Renaissance and those of importance to painting and drawing account for only a small fraction of the total number of theorems. In consequence, perspective as a whole has become a backwater, no longer central to our painting or to our imagination. The invention that-to quote a formulation whose only fault is its generality-"introduced subjective thought into painting" and was "the heart of a vast intellectual and moral project" -has now become an antiquarian or scholastic concern, something for the perilously dry "history of ideas." 6 A kind of sea change has overcome the subject: instead of the bewitching "secret" that lured Durer across the Alps, it has become a commonplace, ubiquitous and routine. Daniel Libeskind puts it in theatrical terms when he says that perspective has "all the force of a fool who remains on the stage at the end of the play in order to tell a tale 'full of sound and fury, signifying nothing.' "7 I make this acknowledgment at the outset, as a kind of extended 4· Table 1 makes use of several approximations. Of the three kinds of homologies, relief perspective is included on the chart only for convenience. Technically, it belongs in an entirely different classification, since it is the only transformation listed that does not take three-dimensional space onto planes or surfaces. It is, properly speaking, a general case of which linear perspective is the special case. Among the large literature on such topics the following are particularly helpful: Krylov, Lobandievsky, and Men 1968; Fiedler 1871, 1882; Bogolyubov and Voinov 1973; Nystrom 1945, 1-8; and French 1918. For the use of "perspective grids," see Fischer 1891; Boys 1942; and Clutterbuck 1966. For methods without vanishing points, see Borissavlievitch 1957, 1958. For analytic methods, see Doppler 1840; Mossbruger 1848; Grunert 1859; Kahrer 186o; Roever 1938; and Capelle (1969]. For scale methods using proportional division, see Crowther 1937. For examples of pseudoperspectives, which have been excluded from my discussion, see Forseth 1984; and Watson 1955. 5· The most interesting relatively recent work is Tammi 1964, 1965. See also Niklova 1980. For an example of the sophistication of perspective methods, see Fiedler 1871. One might propose an alternative mathematical history of perspective: instead of locating its essential moments with Guidobaldo and Brook Taylor, such a history could follow its increasing analytic power up to a "Renaissance" in works such as Fiedler's. 6. Bonnefoy 1988, 18, 19. 7· Libeskind 1984, 107.

4 f

THE POETICS OF PERSPECTIVE

TABLE 1

Perspective in relation to other projections and to branches of mathematics

symmetries-Euclidean

axial point

homothetic transformations

non-Euclidean

Mathematics

analysis

differential

number theory

analytic

geometry--

projective ..

set theory

descriptive

algebra

topology

orthographic--affine transformations

parallel projections--

graph theory oblique projective collineations: homologies----------projective collineations: nonaffine transformations

elations

projective collineations: correlations

azimuthal stereographic Hauck's

curvilinear perspectives-

hyperbolic cylindrical---Deininger's

epigraph, because it has far-reaching consequences for our understanding of the subject. The possibilities of speaking about perspective in the language of loss and mourning are typically modern. As we survey the modern concept in more detail, it is helpful to bear in mind two aspects of this intellectual melancholy: on the one hand, it

INTO THE MAELSTROM OF METAPHOR

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5

two and three view oblique view multiplanar-

rotations sectional views developments plans parallel (orthographic)-

uniplanar--

angular (oblique)

sections

elevations

axonometric-------

isometric

1.

methods using only visual rays

dimetric

2.

methods using only the principal point

trimetric

3· methods using distance points

cavalier

cabinet 4· methods using marginal or lateral vanishing points linear perspective------------stereoscopic perspective relief (accelerated) perspective

5· methods using accidental vanishing points 6. methods using vanishing lines 7. free three-point perspective 8. fractional points, scales, and measuring points 9· proportional methods

vertical--horizontal

projected

10.

analytic methods

developed (panoramic perspective)

11.

mechanical methods

offers us ways to construct a history of the subject by contrasting something receding or dying to something under construction; on the other, it provides a working contrast between the fundamental, generative idea of perspective, which has woven itself into so much of modern epistemology, and the essentially technical and narrow aes-

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THE POETICS OF PERSPECTIVE

thetic norms that govern the ways it is exposited. Within the conceptual field of this book, those contrasts are irreducible, even though it does not always make sense to express them in the language of pathos. They provide the impetus and the sense for the account I want to make.

THE SEARCH FOR THE ORIGIN OF PERSPECTIVE

In a way, the modern concept of perspective is schizophrenic, because it has two incompatible aspects. On the one hand, perspective is thought to be a rather formal, rigorously defined branch of mathematics-or, to be precise, an offshoot of Euclidean and Cartesian geometry. This first perspective is, in the strict sense, meaningless; that is, it "means" only equations, points, lines, angles, and various geometric operations. In accord with our rather repressive conception of this first perspective, we require it to have certain clear relations with a particular place and time where it is said to have first appeared. This "meaningless" perspective is the perspective that we trace from Brunelleschi's experiments through the latest software. The second perspective, on the other hand, has long escaped these shackles. It means a great deal, from subjectivity to eternity, and it is to be found virtually everywhere, from philosophy texts to political speeches. A principal restriction on this second perspective, which I call metaphorical perspective, is that it not appear next to an equation or in a complicated graphic. It is "our" perspective, the one we think about, and the one that describes how we view the world and constitute ourselves as viewing subjects. I give this simplified description in order to dramatize the most general form of our modern understanding of perspective. To explore these versions, and to see the connections between them, it is clearest to begin with the more restrictive perspective, and in particular with its historical beginnings. Most of what we know of perspective we know about its origins. There has been considerable scholarship on the perspective practices of the early figures, including Brunelleschi, Alberti, Donatello, Ghiberti, and Masaccio, and less work on later artists just as involved in perspective such as Carpaccio, Botticelli, Peruzzi, Salviati and Pontormo. By the same token we know much about the first six extant

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7

perspective treatises, and less about the forty-odd others written before 1601. Beyond the Renaissance, there are some seven thousand treatises and essays, virtually a terra incognita to mathematical and art historical scholarship. s For the most part our interest has been centered on the moment when perspective first appeared. A triad of events rules our understanding of those first years: Brunelleschi's experiments, the inception of perspective (shortly before 1413); Masaccio's Trinity, the first surviving perspective picture (1427-1428); and Alberti's book on painting, the first written record (1435). In the last twenty-five years many problems generated by this triad have been solved. Thanks largely to Martin Kemp, we can now say with as much precision as is possible what Brunelleschi did when he stood in the entrance of the Duomo and drew the first perspective picture. 9 Masaccio's Trinity is not as perfectly understood, but the salient points are clear. 10 Little has been added to our knowledge of Alberti's so-called costruzione legittima, the first surviving written technique, in the quarter century since Cecil Grayson untangled it.l 1 In general, the earliest appearances of perspective are as closely circumscribed as the surviving documents permit, and current studies, despite some claims to radical revision, tend to raise minor points or study less influential sources. There is a sense that these three early events are really one large event, and when some authors maintain that Uccello's or Ghiberti's methods were not in accord with linear perspective, they mean that 8. Veltman 1993. There have been some excellent surveys of particular subjects, such as Sjostrom 1978; and M. Kemp 1984a. The emphasis within histories of perspective may be judged in texts such as Zeuthen 1903, 173-92. A good general text is Wunderlich 1911; see further Amodeo 1933. 9· On the specifics of Brunelleschi's achievement, the most reliable source remains M. Kemp 1978 and 1990, 12ff.; see also White 1987, 280. The wide range of alternative interpretations may be sampled in Panofsky 1924-25; Argan 1946, 104; Antal 1948; Gioseffi 1957, Bo-81, and 1956-58, 484; Boskovits 1962; Kitao 1962; Hartt 1964; Parronchi 1964a, 11431; Francastel1965; Baron 1966; Krautheimer 1970, 1:240; Beltrame 1973, 194; Edgerton 1975; Gablik 1976; Gombrich 1976, 93-110, 143-52; Kubovy 1986, 37; Dubery and Willats 1983, 5657; Damisch 1987, passim; and Tsuji 1990. 10. See Elkins 1991b for literature and partial analysis. A text not discussed there is Cristiani-Testi 198411. Two principal topics remain to be investigated: the sources of the method and Alberti's knowledge of his own construction. See Grayson 1964, 1972; Spencer 1966; the review of Spencer by Giles Robertson (1957). The further literature includes Simonelli 1971, 75-102; Edgerton 1966; Parronchi 1964; J. Green and P. S. Green 1987; Veltman 1986a, 389-90; Aiken 1986, 96-155; Klein 1961, 216 and 226; Ivins [1938] 1973; Ackerman 1978, 4-6; Wolff 1936; Doesschate 1964, chap. 22, pp. 123-29; Brion-Guerry 1962, 36-3T and Staigmiiller 1891.

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THE POETICS OF PERSPECTIVE

the artists intentionally turned away from the canonical methods defined by that triad.l 2 Perspective proper, including its many methods and sometimes eccentric disciples, is thought to be a single thing, discovered in one form by Brunelleschi and elaborated upon by later workers. Behind this notion is the idea that perspective began in one place, Florence, and more or less at one time (c. 1413-1435). 13 This sense of a unified origin is one of several unities that play parts in the modern concept of perspective. I suggest not that it is mistaken or that perspective has miscellaneous or exotic origins but rather that this unified origin was not perceived as such in the Renaissance and that Renaissance artists and writers saw many techniques where we see a single discovery.

THE NEED FOR MATHEMATICAL INTEGRITY

An example of the sense of unity that we see in the Renaissance is provided by vanishing points. The concept of a vanishing point was exposited only in 16oo, at the very end of the period I am considering, and so we need to think ourselves back to a time when perspective did not necessarily include vanishing points, when, for example, the precipitous zooming and rushing that we associate with perspective was present in a different sense (it may be necessary to reconsider texts such as Norman Bryson's Vision and Painting which see the "first geological age of perspective" as "the epoch of the vanishing point"). 14 There is ample material to help us describe the change, but we tend to be less careful than we might be, and references to vanishing points can creep unnoticed into our assumptions and descriptions. Much the same may be said about horizon lines, planes of projection, centers of projection, and other terms that now seem to constitute the indispensable elements of perspective. Perspective is accorded a kind of special status in this regard: since it is "at bottom" a mathematical endeavor, it is thought not to change 12. For example, Parronchi 1979. 13. The limiting dates are those of Alberti's De pictura and the recently discovered mention of panels by Brunelleschi in a text from 1413. See Tanturli 1980. The early dating has been favorably received by Martin Kemp (1978) and Jane Aiken (1986, 138 n. 3). A very early date was also proposed in the nineteenth century, long before the documentary support had been unearthed; see Semper 1875, 139, quoted in Wieleitner 1920, 254 n. 18. 14. Bryson 1983, 107, repeated in Rotman 1987, 14 and 32.

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as completely as other aspects of painting. In some sense it has no history at all, only a "mathematical core" that can be discovered or rediscovered or invented but never altered. This is a subtle point. To a certain extent it is true, but the danger is that what is anachronistic in our understanding of perspective may make perspective itself seem timeless, and historical change may be telescoped more than is historically justifiable.IS The best way to define this danger more clearly is to consider how modern scholarship depicts perspective's relation to mathematics. An interesting sign of the presence in our scholarship of an informal definition of "meaningless" perspective unrelated to the passage of time is a particular kind of perspective picture that I will call a perspective schema.l6 Such pictures often represent an observer facing a wall or a window laced with geometric lines (Plate 1). Normally these schemata are placed at the beginning of essays, monographs, and artists' and architects' manuals, where they are meant to stand for all the essential elements of perspective without illustrating any particular method. In this example there are eleven elements, including the viewer's eye and the picture she holds.1 7 Such schemata imply that perspective can be epitomized in this way and that the bulk of the treatises can be given over to applications and particular problems. They are often accompanied by explanations introducing the ostensibly indispensable elements one by one. Although few texts aimed at art historians or artists attempt to find the minimum number of such elements, each schema is made possible by the assumption that such a set exists. This notion prompts us to search for the mathematical core of perspective in texts and pictures. We need not have investigated this assumption or even thought about it for our texts to reflect it: there would be no sense in concentrating on fifteenth-century Florence and studying the "origin," "invention," "discovery," or "rediscovery" of perspective if there were no single entity named "perspective." Un15. For examples of varieties of axiomatic thinking, see Alexandroff and Chintschin 1969; Pohlke 1859, 109; Emch 1918; Amaral 1976; Bartschi 1976; and Wyllie 1903. 16. Modern schemata are quite varied and could be made the subject of a separate study. Examples include Poudra 1864a, pl. 1, fig. 2; Doesschate 1964, 24, fig. 6; and Carter 1967, 842 fig. 42. 17. The eleven elements are the four labeled ones; the perspective representation labeled a; projectors (dotted lines leading down from the perspective representation); the viewer's eye (the center of projection); the visual rays leading to it; the picture she holds; and the plan of the visual rays that converges to the standpoint (or "station point") on the ground under her eye.

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PICTURE

1 A modern perspective schema. From Spanton 1893, 9 fig. 15

like medieval and Renaissance pseudoperspectives-such as herringbone, polyfocal, inverted, and axial "perspectives"-the authentic methods could be brought into accord with each other and with a single, simplest version: or so our account might run. We tend to speak of the "basic geometric logic" underlying different methods and sometimes go as far as to say that all Renaissance methods are equivalent. 1 b When transcribing Renaissance perspective proofs, we follow the standard practice of historians of mathematics and assume that Renaissance ways of reasoning can be "cleaned up," translated into modern terms, without harm to their essential sense. Modern geometric notation, reasoning, and theorems are ubiquitous in historical scholarship of mathematics, even in periodicals such as Historia mathematica. While it is not always harmful to translate Renaissance mathematical reasoning into modern terms, and while there is not always something to be gained by being alert to the specific forms of Renaissance argument, I suggest that the Renaissance concept of perspective is best appreciated by following Renaissance proofs as closely as possible. A kind of "close reading," on the model of the close reading that is applied to poetry, is a necessity when the subject involves expressive content and not just the history of mathematics. 18. For the "basic geometric logic," see Edgerton 1966, 374; and for claims of equivalence, see Parronchi 1964b, 35-40; and Brownson 1981, 165-94.

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The idea of automatic translation makes it clear we mean to require that versions of the true perspective are compatible with one another and that the vehicle of that compatibility is mathematical analysis. If perspective methods are unified in this sense, then it should be possible to show how they proceed from other mathematical propositions: that is, it should be possible to prove perspective rigorously and properly. The proof may depend on geometry, or it may depend mostly on optics; either way, it would consist of a connection between perspective and a certain set of mathematical laws. It may seem that the idea of proving perspective in a historical or philosophic essay is inappropriate, and it is true that there is usually no need to speculate on such matters; but as we will see, a proof was attempted in a seminal twentieth-century essay on perspective, Erwin Panofsky's "Die Perspektive als 'Symbolische Form.'" For Panofsky, the necessity of trying was the logical consequence of pursuing the questions of cultural relativism and pictorial realism; and as a parallel, the necessity of our studying his proof follows from the importance his ideas have been accorded. Proof is the invisible accompaniment, the shadow, in texts that emphasize perspective's novelty as an epistemological paradigm, because epistemology inevitably leads back to questions of origin and proof.I9 Although we don't think of it every time we write about naturalism in visual art, perspective is there at the foundations of our concept. It is the firmest link between paintings and the measurable word known to physics, and therefore, even if that link is not usually invoked in any great detail, perspective plays a central role in art historical writing that involves versions of naturalism. 20 Whether or not perspective can be proved and whether it can be proved in the way Panofsky thought it could are questions that affect our sense of pictures and the world; and conversely, contemporary writing that eschews the concept of proof is likely to be burdened by especially troubled notions of representation, naturalism, realism, and mimesis. In this way perspective is of ultimate but not direct interest to any writer concerned with pictures, and the self-contradictions and incoherences I point out in this book have inescapable consequences for the project of art history in general. When the concept of perspective is unexamined, it can become corrupt in ways that we may not ex19. It does so, for example, in Damisch 1989, pt. 2, pp. 65-154. For "naturalism" and "realism," see Summers 1987, 3-9, esp. 5 n. 4·

20.

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pect, and that corruption settles at the heart of our accounts of pictures, shaping the coherence our "wider" arguments can possess. The ways that perspective is avoided in art historical narratives and the rhetorical and epistemological consequences of its partial eclipse could well form the subject of a separate book. What I am concerned with here is the opposite end of the problem, specifically, the question of what happens when a writer such as Panofsky sets out to found "wider" arguments by proving perspective directly. That question, it seems to me, is logically prior to a study of how we lean on concepts of representation and naturalism which in turn lean on perspective. It may appear odd at first glance that perspective has not been justified, once and for all, to everyone's satisfaction. Several proofs were offered in the Renaissance and more difficult and oblique proofs and counterproofs continue to be offered today. There are interesting parallels. In both periods, the proof of perspective is generally deferred: authors refer to predecessors' work or to Euclid or mathematics in general. In both periods, optics and mathematics are unevenly mixed in the proofs, and no one is quite sure how to handle them together. The choice between optics and mathematics-it continues to appear as a choice, even when the two are said to be strongly related-is never quite made. And in both periods, the texts that attempt proofs are thought to be obscure or "useless," to quote one Renaissance author, but at the same time essential to the integrity and prestige of the discipline.

SPACE, SEEN THROUGH A WINDOW

Another part of the relation between the modern concept of "meaningless" perspective and mathematics is the notion that the way perspective generates pictures is analogous to the act of tracing a scene on a pane of glass. The metonymic substitution of tracing for the rules of perspective and the metaphoric replacement of the plane of projection with a window .are as close as we normally come to an informal definition of perspective or a guide to everyday analyses of perspective paintings.21 21. Among many examples, see Galassi 1981, 16.

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Again it is Panofsky who has expressed this strategy most eloquently. His essay opens with a brief discussion of this window figure, as I will call it, and then in a footnote he offers this elaborate formal definition:22 For us, perspective in the strict sense is the capacity so to represent several objects in one area of space that the appearance of a material surface is entirely displaced by the appearance of a transparent plane, beyond which we believe we see an imaginary space, occupied by whole objects in apparent succession and cut but not delimited by the borders of the picture. 23 The definition links perspective with the window figure in such a way that the two might easily be conflated: the window figure stands both for an emblematic technique and for perspective itself. And in arelated way, the passage assumes that perspective properly orders pictures as wholes and "not just isolated objects," as Panofsky says elsewhere.24 Thus, Panofsky provides us with another unity demanded by modern scholarship, that of pictorial space. (We have now seen three ways that perspective is imagined as a unity: in its management of pictorial space, in its single origin, and in its unchangeable mathematical core. Together they show how strongly we have welded perspective into a single subject. In Chapters 2 and 3 I search for these three unities in the Renaissance texts.) It is worth looking a little more closely at the use of "space" in this passage. In Panofsky's definition, perspective is imagined as an a priori organizing principle that is applied to an "area of space." Panofsky speaks of objects "in" a certain space, depicted "with" that space, and says perspective gives us "whole" objects in a "succession." Here objects are nothing more than necessary examples, things that occur not merely in space but because of it: they are knowable because they exist in space. There are deliberate echoes of Kant here, but the salient point is not so much that genealogy as the propaedeutic status it confers on perspective itself. Linear perspective in Panofsky's sense is a preliminary step, a thing that has to be done to produce pictures, rather than an ancillary or logically posterior ac22. Panofsky 1966, 4, uses the term "window simile." Since it is more than a simile and since "trope" is too literary sounding, I have opted for "figure." 23. Panofsky 1924-25, 292 n. 5· My translation. 24· Ibid., 258.

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complishment. Space is primary, and the objects in it are ontologically secondary. "Perspective space" and informal or ungeometric synonyms such as "fictive space" and "pictorial space" are encountered so frequently that they have come to seem quite natural. In H. H. Amason's History of Modern Art, pictorial space is identified as "the first matter to be considered" when introducing the art that came before modern painting. Pictorial space, in turn, is chiefly perspective space, which "governed European art for ... four hundred years." 25 Decio Gioseffi's article on perspective in the Encyclopedia of World Art opens in a similar fashion: PERSPECTIVE. The study of the techniques of representing the optical configuration of space .... Artists and theorists, especially from the Renaissance onward, have sought theoretical and practical solutions to the problem of conveying spatial relations through lines and volumes.z6

These are not incorrect formulations, but the phrase "perspective space" is a Janus figure, half Renaissance and half modern. The Renaissance artists had no conceptual equivalent for our term space, and when they juxtaposed prospettiva and spazio (or perspectiva and spatium), they usually had something decidedly scholastic or humanistic in mind.27 The Renaissance painters made perspective pictures without the benefit of a concept of space, and much of what I have to say in this book is connected to that absence. The window figure and associated space-oriented definition of perspective have foundational importance. Panofsky's definition is more carefully articulated than the working version most of us use when imagining or teaching perspective, but its finesse is not out of line with the concept as it is implied in the literature. Even in a loose account, an accurate perspective drawing is imagined to be like a window on the world, since its lines "could have been" traced on a windowpane (a difficult idea to make sense of, not least because paintings depict imaginary objects). The connections between our notions of pictorial realism and our ideas of unified pictorial space run 25. Amason 1986, 13. 26. Gioseffi 1969, 11:183 col. a. 27. See, for example, the treatise by Pomponius Gauricus [1504] 1969.

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deep. The window figure is central to our imagining: it has "conquer[ed] the world," in one historian's words. 28 In later chapters I will have occasion to reassess this view, and I will suggest that the Renaissance had things the other way around in regard to space and that artists and writers thought first of objects and second of what we call perspective space or fictive space. In a phrase, the Renaissance notion is "object oriented" and the modern concept "space oriented."

FROM METHOD TO METAPHOR

The purpose of Panofsky's essay, which I consider in Chapter 5, is roughly to claim that versions of perspective are expressive of the cultures that invented them. This is the most volatile and poorly defined component of the modern concept of perspective. We know that perspective cannot be conventional in the strong sense-that is, logically independent of scientific experiment-because we can measure its products against other ways of recording the world (such as maps). But it can be conventional in many weaker senses, depending on which parts of it are taken to be fundamental. If something in linear perspective is a convention, an expression of our postRenaissance culture, then its "discovery" (or perhaps "invention") in the fifteenth century may have been only loosely or fortuitously related to the facts of vision. Since Panofsky's essay, art historians have tended to accept the idea of a relativized or conventional perspective without subscribing to Panofsky's specific interpretive program or his supporting argument. The idea that perspective is culturally relative has been equated with the idea that perspective can express cultural ideas, and perspective has been put to various uses as social or intellectual signifier.29 Meanwhile the question in philosophy and visual theory has drifted from Panofsky's equation of perspectives and cultures and has landed on the more abstract idea of conventionality itself. It has seemed to recent authors that if perspective could be proved to be conventional in some strong sense, then consequences like Panofsky's could follow. As we will see, few authors attempt such arguments, and I think it is 28. Gombrich 1988, 8. 29. Among many sources, Quintavalle 1967 and Bryson 1983 are instructive examples.

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widely assumed that perspective's ties to something that might, without further cultural qualification, be called vision or perception-not to mention its possible connections to mathematics or the quantifiable dimensions of the world-are so problematic that it is not unreasonable to speak about perspective as if it were, for practical purposes, entirely conventional. It seems to me the motivation behind that kind of writing is not only the traditional uninterest historians have felt in matters of ahistorical "truth" but also the postmodern desire to be freed of the obligation to speak of experimentation, logic, and science in the "naked" terms in which they appear in scientific discourse. We are uncertain about the harsh language of science, or we find it crude or distasteful. The fact that perspective does not easily allow arguments to drift from their moorings in ideas such as experiment, science, and logic creates difficulties for all the discourses involved. But for the moment I want to swerve away from these debates and try to say something about their root cause: and here my interest turns from the elements of the modern concept to the history behind it. We can consider the art historical, historiographic, and philosophic debates about different perspectives, conventionality, and symbolic forms together as a single development, one that depends on a very basic, even elemental occurrence: the possibility of considering perspective itself as a metaphor. This possibility is different from conceiving a pictorial analogy such as the window figure, and it is different from assigning particular meanings to parts of perspective pictures. In the Renaissance as in modernism, the vanishing point might mean heaven or death, and perspective might be employed for any number of expressive ends. There is a large, miscellaneous literature on the expressive aspects of perspective pictures, which I consider when I look at practice in Chapter 4· What I have mind mind here is the more general possibility that the entirety of perspective, perspective itself, might be a metaphor for something. In this sense the metaphorology of perspective is not a Renaissance phenomenon. Panofsky and the writers who followed have seen perspective as a metaphorical object, whether it expresses a culture (whether it is, as Panofsky said, a symbolic form) or stands for some unnamed convention (Nelson Goodman considers it a "language of art," a particular system of symbols). One historian, concluding a wide-ranging study of perspective's history, mathematics, and experimental foundations, defines perspective as "one of many

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languages" artists can use to express emotions. 30 In recent writing, the field of metaphor has opened still further. For one art historian, perspective has moved from a method of representing the world to a way of "envisioning" it; and for another, perspective is merely "a way of thinking about observation. "3 1 Perspective in contexts like these is no longer a strategy for making pictures, an artist's or mathematician's tool. It is a sign signifying a mental state, a culture, or an expressive language. Perspective has become a metaphor. It is a metaphor in precisely the same sense as it was for Panofsky, different though the predicates may be. There is, incidentally to my present purpose, a countermovement intended to show that perspective is "just" a technique. E. H. Gombrich, whose work heads this loosely associated "movement," has said many times that perspective is based on simple facts of vision and is "merely" a discovery, not a symbol of some "new philosophy" or weltanschauung.32 "Can it not be argued," he wrote, in one of his clearest formulations of this idea, "that perspective is precisely what it claims to be, a method of representing a building or any scene as it would be seen from a particular vantage point?" 33 His struggle against Germanic historical concepts such as the weltanschauung has been well publicized, but it is also helpful to think of Gombrich's position here as exemplary of an even larger category (and an even more powerful argument): those who deny perspective's metaphoricity. A weltanschauung is only one thing perspective can symbolize. Gombrich's position is slightly muddied by his allowance for conventions, but in the main he would deny that perspective is properly or usefully or meaningfully a symbol for something larger than itsel£.34 The conviction that perspective is merely a technique is also strong in some French scholarship that is otherwise quite different from Gombrich's empiricism. Thus authors such as Fernande de Saint-Martin understand perspective as a semiotic system or a "code" or "web" of lines, and Hubert Damisch argues that perspective is a way of "thinking in painting, in forms and through means proper to 30. Doesschate 1964, 159· 31. Battisti 1960, 96; P. Descargues 1977, 9· 32. Gombrich 1960, 250, 257. For a sensible review of a related position, see Edgerton 1991, 4-10. 33· Gombrich 1967, 8o. 34· For assessments of Gombrich's position, seeM. Kemp, 1984b; Carrier 1980; and Hester 1976.

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it" and that it cannot be reduced to a question of vision, epistemology, or language.3s These French and Anglo-American approaches occupy separate poles in the current discourse on perspective, but in the widest possible reading they are united by their common distaste for metaphoricity and cultural connections of all sorts. The point I mean to make here is that this modern understanding of perspective as a metaphor is not an outcome of Panofsky's claim but a fundamental condition for it: Panofsky would not have been able to argue that perspective is bound to individual cultures unless he had been able to conceive of perspective as something expressive of culture in general. This metaphorical perspective is a precondition for even imagining that it is possible to displace perspective from its apparent timelessness. Metaphor itself is the ruling concept here, as alien as that statement may sound to art historians used to thinking of perspective as a historical datum or a method; and our native idea of the half culturally determined, half mathematically certain painter's perspective comes from the metaphorization of perspective. How did the metaphorical concept arise? What led from the dry, late-medieval geometric treatises to meditations such as Panofsky's? Like any historical claim, this one has its exceptions, and they reach all the way back to Aristotle, who used a perspectival ronstruction as a metaphor for memory.36 In the Renaissance, the poetic imagination found many uses for perspective-much as today's theorists plumb perspective for seductive metaphors-but in the treatises perspective continued to be expounded as if it had no determinate meanings.37 The modern concept of perspective, I suggest, is properly an Enlightenment invention, and since my interest here is firmly dichotomous -the Renaissance and its modern interpreters-an outline will have to take the place of the much-needed history of the development of our sense of perspective.38 One enabling concept behind the metaphorization of perspective is 35· See, for example, Damisch 1994, 45, 446-47; Chaste! 1965, 1980; Saint-Martin 1990, 109-44. A review of Damisch 1989 by Yve-Alain Bois (1990) stresses the nationalist allegiances of the concept that perspective is "merely" a technique (France, Italy) and that it is derived from optics ("Anglo-Saxon"). 36. Aristotle, On Memory 452b15, and Sorabji 1982, 57-58, 108-110. 37- For metaphors of perspective in Shakespeare and other Renaissance writers, see Guillen 1971. A further evaluation of Guillen's work would have to take into account which of those metaphors are common to medieval optics and the traditional discourse of deception, truth, and falsehood. For metaphors of perspective in Castiglione's Book of the Courtier, see Patrizi 1984. 38. See Damisch 1987, 53-63, for another account of point of view.

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the trope point of view. Panofsky's dependence on point of view to argue about perspective is a paradox typical of this subject because point of view itself is perspectival: as we will see, it went from perspective practice into philosophy and was then applied back to perspective. Hence the very possibility of arguing that perspective is culturally relative came from a metaphor for perspective: that is, perspective may have provided the very means to argue about its nature. A second generator of the modern concept is the "space" that Panofsky made into a medium for perspective pictures. That space also has a long history and has become implicated in the ways we see and the things we look for in pictures. Like point of view, it was not known to the Renaissance.

POINTS OF VIEW

Panofsky's metaphorical use of perspective to denote the spiritual life of civilizations has usually been traced to Ernst Cassirer's philosophy of symbolic forms. Cassirer is the source he names and quotes, and his relation to Cassirer's concepts-including the possibility that Cassirer's "symbolic forms" cannot be used for arguments that involve historical change-has provided fertile ground for philosophic and historiographic critiques. 39 But for our purposes that etiology is too fine-grained: there is a much longer, more complicated and deeper history behind Panofsky's metaphorical perspectives than Cassirer's system of cultural symbols. It would be possible to begin that history a little outside of perspective, by exploring the connections between sight in general and the metaphors of knowledge, but for the moment I would like to resist assimilating perspective to vision in order to show how the problem can be posed as a story that begins in the Enlightenment. G. W. von Leibniz's metaphorical uses of perspective in the Monadology, the Theodicee, and other late works mark the formal introduction of specifically perspectival metaphors into philosophic discourse. The central text is chapter 57 of the Monadology, in which the imperfect points of view of the individual monads is compared to the perspective views of a town: 4 o 39· See Holly 1984, 130; Darnisch 1987, 24-36. 40. Further texts include the Discourse on Metaphysics 14 and Monadology, sec. 14.

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And as the same town, looked at from various sides, appears quite different and becomes as it were numerous in aspects [perspectivement]; even so, as a result of the infinite number of simple substances, it is as if there were so many different universes, which, nevertheless are nothing but aspects [perspectives] of a single universe, according to the special point of view of each Monad. 41 It has been pointed out that the perspectival metaphor in this passage is not meant to be interpreted exclusively in spatial terms, since neither the "confused" perceptions of the monads nor the "perfect" perception of God depends on their positions. 42 But however Leibniz meant to mix practice and trope, his usage had fundamental influence on the later conception of perspective. Hans-Georg Gadamer singles out Johann Martin Chladenius as the agent for the spread of Leibniz's "point of view." 43 Be that as it mayand it may not be-point of view became entangled in the larger history of the growing awareness of subjectivity, which first appeared in biblical exegesis and in the work of the philosophes and gradually blossomed into the particular kinds of historical relativism that gave rise to Panofsky's essay. To David Hume we owe the idea that we can read "in" the "emotional perspective" of a work of fiction and that works generate their own "points of view" for readers. 44 This concept is still being developed in modern linguistic studies that attempt to define narrative point of view, "foreground," and "background" in terms of grammar and syntax. 4 5 Friedrich Nietzsche is a turning point in this intermittently subterranean history. His rumination on perspectivism in section 636 of Der Wille zur Macht is part of his ongoing refutation of the scientific mentality, which he found both dull and dangerous, a premonition of a future of "bridge builders." The supposedly objective, unified world 41. Leibniz 1985, 248. The Monadology was not published in its original French until 1840; so the German (1720) and Latin (1721) translations are historically more important. 42. For Leibniz, to think of monads in physical space is "to use certain fictions of our minds when we desire to visualize conveniently what can only be understood" (Quoted in Mates 1986, 228). But see also Levin 1980. On Leibniz's perspectivism, see Graumann 1968, 33-35; and Guillen 1971, 314, 318. On the question of monadic points of view, see further Heintz 1973; Kaulbach 1972, 83-85; and Voise 1973, esp. 79-87. 43· Chladni [Chladenius]1742; Gadamer 1975, 160; Ermarth 1986, 208-21; and Jay 1993, 18. 44· This idea is argued in Hume 1965, 324. See further MacMillan 1987. 45· Banfield 1982; Kuno 1987; and Ehrlich 1990. Erich Auerbach (1953) discusses some of the same problems.

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posited by science, according to Nietzsche, is only a kind of collective agreement, something made by an aggregate of like-minded points of view. Each person "constructs" his own world. It is interesting, given the wide currency that perspectivism retains (if only in that favorite humanist title "Perspectives in ... ") that the term did not resonate for Nietzsche, and section 636 gives two alternatives: that perspectivism is a manifestation of the will to power and that it is "nothing more than a complex form of specificity." It is complex because the single, "specific" agents band together in their desire to remake the world in their own images, and the result is a partial consensus, an amelioration of Leibniz's atomistic perspectivism if not a step toward objectivity. The "specific bodies" make a war of interpretation against each other, "and end by ... conspiring together" -hence the "objective" world known to science. 46 Today the half-philosophic, half-artistic "point of view" is still prevalent in philosophy; we need only think of how Wittgenstein compares his thinking to partial views of a dark landscape and how Heidegger imagines his thinking as a walk along country paths, taking in views of distant hills.47 Perspectivism flourished in the same years that Panofsky wrote his essay, and varieties of it were present in the work of Jacob Burckhardt, Wilhelm Dilthey, and other writers who formed Panofsky's intellectual background and milieu. 48 Panofsky took the development full circle. What was for Leibniz a convenient image from the workshop practice of perspective had become a philosophic position in which perspective itself was no more than a slogan, a springboard for epistemological problems. When Panofsky writes about Greek perspective as if it were the expression of a subjective world and Renaissance perspective as if it were the record of an objective world, he is recalling the inherent paradox of philosophic perspectivism (that it cannot choose between the world as an objective whole and views as subjective fragments) and reapplying it to its original source, artistic perspective. It is that cycling involvement that should warn us that per46. Nietzsche, 1926, Der Wille zur Macht ... , sec. 636. See also Graumann 1960, 38-43. For Nietzsche and perspectivism, see Guillen 1971, 328. Nietzsche's early lecture notes on rhetoric are discussed in this light in Nietzsche 1989, xiv. 47· Wittgenstein 1984, 7, 50, 56, 66, and 8o; Heidegger 1966, 58. 48. Mannheim 1909; McGilvary 1933, 310; McGilvary 1956; and Chisholm 1950. Sometimes perspectivism takes an exclusively cultural form, as in Santucci 1967, 335a. See also Pollack 1912, for a wide-ranging, eccentric theory of perspective in ethics, government, and law.

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spective cannot even see itself: it is blind-that is, no perspective from which we can see perspective.

SPACES AND

RooMs

A second component of the modern concept of perspective and of Panofsky's definition is the idea that perspective pictures give us fictive space and that such space is a legitimate and root concern of art historical discussions. All Panofsky's descriptive terms for artistic spaces from ancient to Renaissance art are themselves modern: the "spiritual" space of the Odyssey Landscape, the "unifying fluid" of early Christian painting, the "suppressed space" in the Romanesque, the "individual spaces" of Gothic sculptures, and the "structural space" of the Renaissance. Anachronistic concepts of space are the rule in histories of pictorial space; and for that reason it may be argued that they work best when the subject is modern art. 49 The cardinal fact in the history of concepts of space is that the Renaissance could not inherit the modern concept of space from the ancients. It is well known that Euclid's Elements and even the Optics do not possess such a concept, and the work done by David Hilbert on a concept of "betweenness" was intended in part to remedy that deficiency and make Euclid logically acceptable.so Archimedes, Apollonius, and other ancient writers on mathematical topics also worked without specific attention to what surrounded and supported their geometric constructions. Panofsky has underscored Aristotle's concept of discontinuous, contingent space as an inhibiting factor in the development of the modern concept.s1 Although a number of terms for space circulated in the ancient world, including the Greek topos, none had the crucial component of all modern definitions, a sense of logical precedence over the objects themselves. 52 Our "spaces" are conditions for the existence and apprehension of objects; in modern terms, ancient and medieval "spaces," which the Renaissance inherited in part via medieval as49· Dunning 1991 has written a history of pictorial space that emphasizes Monet, Cezanne, and a number of abstract expressionists. 50. Hilbert 194451. Panofsky 1924-25, 271. A good summary of Panofsky's account here is in Edgerton 1975, 158-5952- Jammer 1964, 25; and Damisch 1987, 32-33.

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tronomy, were special states of space (such as chaos) or else concepts intended to mean much more than space (such as the ordering principle of cosmos).53 From medieval astronomers and theologians, the preperspectival Renaissance had a concept of space which connoted vast extension, but it was still dependent on the existence of object.s. Panofsky believed that a "systematic," mathematical concept of space arose shortly before perspective, making perspective itself possible.s4 This is a problematic notion, both because the characterization of this new concept of space depends on paintings and not on texts and because the terms of his analysis ("systematic," "infinite, homogeneous, and isotropic," "mathematical space") are all modern and do not occur in mathematics until after the Renaissance. Yet in perspective, the mirror of a proposition is never far off, and here it may well be that the corpus of Renaissance perspective paintings in the fifteenth and sixteenth centuries had a decisive effect on the earliest formulations of the modern concept by Descartes: the same qualities Panofsky read into Renaissance perspectives could also have been read into them by Descartes. But as seductive a hermeneutic problem as this is, what concerns me here is the lack of the modern concept of space in the Renaissance, rather than readings that find it in Renaissance paintings in statu nascendi. The various spaces we see in perspective pictures-our "pictorial space," "fictive space," "rationalized space," "systematic space," "coherent" or "unified space," "corridor space," and the Italian "spettacolo of space" -began to crystallize after the Renaissance. 55 When Clement Greenberg writes about "flattened" space and artists such as Ad Reinhardt and Frank Stella talk about "squeezing" the space out of a painting like the juice from an orange or see Caravaggio as a master of "negative spaces," they participate in this same historical development. 56 Studies that concentrate on modernism, such as Jonathan Crary's Techniques of the Observer, tend to impute a "coherent," "classical" sense of "homogeneous, unified, and fully legible space" to pre53· For a quirky survey, see Bochner 1973. See further Klein 1961; and Brion-Guerry 1977, 73-

54· Panofsky (1924-25, 277) and Edgerton (1975), argue that a '"systematic space,' infinite, homogeneous, and isotropic," arose in the fifteenth century and "[made] possible the advent of linear perspective." (Edgerton [1975], 161.) 55· Henri Lefebvre (1991, 8) offers a Marxist explanation of this proliferation as a sign of the "endless divisions" of labor typical of our society. 56. Stella 1986.

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vious centuries, and that imputation remains as a grounding schema for modern interventions. 57 At times the abstract, objectless quality we require of our pictorial space is made explicit: in the semiotic analysis proposed by Fernande de Saint-Martin, "the notion of space ... must be thought of as anterior to any notion of the object."58 Jean Gebser's ambitious rewriting of Western thought turns on a triad of "megaperiods" that he calls "unperspectival," "perspectival," and "aperspectival."59 In Gebser's view Renaissance perspective operated primarily by "exteriorizing" our sense of space, and "aperspectival" modernism witnessed the complentary exteriorization of time. Gebser's interpretive strategies depend on the largely untenable early modernist idea that cubism gives us a succession of views through time, but what I want to emphasize is the central assumption that space is what was "exteriorized" in the Renaissance. Analogous observations may be made in architectural history and criticism, which depend heavily on the supporting role of this perspectival, antiperspectival, or preperspectival space. 60 In view of this diverse history, it is especially important not to lose sight of texts such as Alberto Perez-G6mez's Architecture and the Crisis of Modern Science, which stresses the baroque sense of a plenum of space, suffused with "the sensual qualities of materials"; but perhaps the best corrective is Peter Collins's observation: "It is a curious fact that until the eighteenth century no architectural treatise ever used the word" space. 61 Cartesian espace and Newtonian absolute space were not unopposed. Leibniz was a principal critic, 62 and Bishop Berkeley thought "absolute space" was a "phantom of the mechanic and Geometrical philosophers. "63 Nevertheless Descartes's and Newton's insistence on space as an independent "object" of contemplation provided the scientific foundation for Kant's a priori spatial intuition. For Kant the 57· Crary 1988, 33, and 1990, 3· 58. Saint-Martin 1990, xii. 59· Gebser 1985, 16 and passim. 6o. Among many examples, see Bek 1980, and compare Lefebvre's distinction between "representations of space" and "representational spaces" (1991, 38-39). 61. Perez-G6mez 1983, 175; Collins 1965, 285. "Space" is now also coupled with "perspective" in the treatises; see for instance Burnett 1966 and Butler 1923. 62. Leibniz held, and he argued with Isaac Newton, that the "absolute being" of space, conceived without the objects in it, is impossible since it violates the "axiom" of sufficient reason: God would have had no reason not to make east into west, and so forth. For Leibniz, "There is nothing but the distance between bodies." Quoted in Mates 1986, 233. 63. Berkeley 1744, sec. 271, p. 130; also cited in Popper 1965, 167.

INTO THE MAELSTROM OF METAPHOR

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a posteriori world of objects is firmly disconnected from the synthetic, a priori intuition of space itself: Space does not represent any property of things in themselves, nor does it represent them in their relation to one another. That is to say, space does not represent any determination that attaches to the objects themselves, and which remains even when abstraction has been made of all the subjective conditions of intuition. 64 Kant's "pure" space makes "the actual appearance of objects . possible" and is "the only explanation that makes intelligible the possibility of geometry. " 65 Later generations bridled at the idea, hinted at in the Prolegomena, that three mutually perpendicular axes define and delimit our intuition of space. Bertrand Russell's dissertation, An Essay on the Foundations of Geometry (1897), is an attempt to show that the only logically possible form of our intuition is projective geometry. His choice is dictated by the appearance of the single and double elliptic and hyperbolic non-Euclidean geometries of Nikolai Lobachevski, Janos B6lyai, Carl Friedrich Gauss, Bernhard Riemann, and Felix Klein, because projective geometry had been demonstrated to be a generalization of all of them. The history of "metageometry" is a history of "pure reason" mingled with questions of subjectivity: from John Locke's "subjective spaces" to Rudolf Carnap's "color spaces," the form of our spatial intuition has been open to philosophic, psychological, empirical, and geometric inquisition. By the fin-de-siecle, this problematic had found its way from philosophy into empirical psychology. The "psychophysiological" space of Cassirer, so crucial in Panofsy's account, comes from Ernst Mach. 66 Mach's Perception and Error (1906) distinguishes between "physiological space," which is the product of all our senses, and "metric space," which is known to science.67 The former is finite-the moon, it is said, never looks to be more than half a mile away6B_and the latter is infinite. The former is "anisotropic," 64. Kant 1965, 71. 65. Kant 1950, 31, and compare Hegel [1830]1970, sections 254-61, pp. 41-60. 66. Cassirer 1910, 105, and 1925, 2:83. 67. Veltman (1980, 571) notes that Mach was influenced by Franz Hillebrand, whose experiments in perception were also cited by Panofsky. 68. Minnaert 1954, 153-66; and see the literature cited in Kubovy 1986.

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and the latter "isotropic," meaning we cannot judge distances and directions, depth and width the way a ruler and compass can. Cassirer's version of Mach's space repeats the transformation that took Descartes's espace into Kant's Raum: that is, it rephilosophizes and unquantifies a theory born of mathematical and experimental facts. That particular characteristic, perhaps more than any specific quality of the psychophysiological space or its previous history, proved important in Panofsky's appropriation. Cassirer's space was the most personal, "intimate" model of subjective apprehension available when Panofsky wrote, and it seemed to be the proper antithesis to rigid perspectival geometry. The field has not ceased to develop. There have been theosophical readings of projective geometry and semiotic accounts of topology, both born of the sense that another kind of geometry might be chosen as a foundation for perception. 69 Theodor Wedepohl wrote an "aesthetics of perspective" that is remarkably close to a semiotics of perspective; he utilizes the three Euclidean axes, but notes that they are related to the human frame and hence may not apply to animals. 70 A synthesis by Gesenius Ten Doesschate distinguishes four "spaces," two measurable and two not. First of the measurable spaces is Euclidean space, the familiar "infinite, isotropic, three-dimensional, and homogeneous" space; and second is our local, unabstract version of Euclidean space, known variously as "physiological" or "psychophysiological" or "kinaesthetic" or "surveyor's space." The two opposing subjective spaces are "visual space," which is three-dimensional but not infinite, isotropic, or homogeneous; and our innate "imaginary space," by which a blind man can feel his way about. 71 There is even an art historical "perspective space," posited as a particular kind of space like cosmos, espace, or chaos, but it does not seem helpful to make a new category of space from a drawing method, unless it would also be useful to have a "descriptive geometry space" or an "oblique projection space."72 For our purposes these accounts may all 6