Table Of ContentF{ans Belting
Florence and Baghdad
Renaissance Art and -4.rab Science
Tlanslated by Deborah Lucas Schneider
The Belknap Press of Harvard University Press
Cambridge, Massachusetts, and London, England
LOII
Contents
Irrtroclttction: Describing a Culture : ßlicþwechsel
(Sh.ifting Focus / Exchanging Glances)
r. Perspective as a Question of Images
Paths between East and \Øest
'ffha¡ Is a Symbolic Form? r3
Arab Mathematics and \Øestern Art . . z6
Geon'retry and Decorative Art: The Arabesque . . . . . 15
The Globalization of Perspective . +L
Copyright @ zorl by the President and Fellows of Harvard College ßlickuechsel: Orhan Parnuk and Perspective as a "Betrayal" 48
All rights reserved
Printcd in the United Statcs of America
z. The Tarningof the Eye:
This book n as originallv publishe d in Ge rr.nan as \-lorenz und Iiagdad: Eine uestöstliche Geschtchte des Cricicism of Seeing in Islam
ßlicks, copyright @ Verlag C. H' Beck oHG, Munich zoo8'
The translatior1 of this rvork was funde d by Geiste swissenschaften Inrernational-Translation Funding Religion ancl the Prohibition of Lnages 5t
for Humanities anci Social Sciences from German¡ a joint initiative of the Fritz Thysser.r Foundation, Images as a Becrayal of the Living Creation 6z
the German Fe de ral Foreign Of6ce, the collecting society VG W'ORT, and the Börsenve rein cles The l(oran as Scripture and Script 67
Deutschen Buchhandels (Gerrnan Publishers and Booksellers Association).
Under che Gaze ofAllah: Pictures as Narrative 78
Library of Congress Cataloging-in-Publication Data Blicletuechsel: Pictures rvith a Living Gaze . 84
Belting, Hans.
IFlorenz und Baghdad. English]
Florence and Baghdad Renaissance art and -A.rab science / Hans Belting; translated by 3. Alhazen's Measurernent of Light
'
Debor:rh Lucas Schneidcr.-rst English language ed' and the Arab Invention of the Camera Obscura
cm.
P.
Originally publishecl' Florenz unVde Brlaagg dCa.d H : .e iBnee crkv cosHtöGst,l iczhoeo 8G.eschichte des Blicks. Munchen : Alhazent Book of Optics, the Perspectiu/t . 9o
Includes bibliographical references and index' Distance from Ancient Visual Culture 99
ISBN 978-o-674 -o5co +- 4 (alk. paper) Pathu'ays of Light and Properties of Objects roz
4r.. POeprisicpse-Icstliavme-iHc isctoouryn. trzi.e Asr-tH, iRsetonaryis.s aI.n Tceit-lIsela. mIIi.c Tinitlfelu 'e Rnecneaiss's a3n. cAee satrht eatincds ,A Craobmicp asrccietivnecc.. Mathernarics and Geometry in Islamic Art . . III
NC748.845r3 zorl Blicleuechsel: Kepler Rediscovers the Camera Obscura TL+
7ot' .82o9-dczz
zottoo3896
4. Perception as I(nowledge:
A Theory ofVision Becomes a Theory of Pictures
Scholasticism ancl the Conflict over Perception and Epistemology. IL9
Before Perspective: The Gaze in Giotto'.s Painting f)5 Florence and Baghdad
Pelaca¡ri's Invention of Mathernatical Space r+6
Gl-riberti's Commentari¿s and Pierot Mathematical Art ' . r50
Blickwechsel: All-razen or Euclid? The Option for Vitruvius r5g
Brunellescl'ri Measures the Gaze:
5.
Mathematicai Perspective ancl Theater
Two Inventors iu Florence t6+
Physical Space: The Architecture of the Gaze. 171
"Prospects" on the Stage . I85
Panorarnas in Urbino rg8
Blickwechsel: The Geometry of theMuq/ffnas Lo4.
6. The Subject in the Picture:
Perspective as a Syrnbolic Form
Stealing an Emblem: The Ëye as Representative of the Gaze LII
Niclrolas of Cusa and the Sovereignty of God's Gaze . . ' . LLI
The Subject as New Narcissus
The Horizon and che View through a \Øindow Lï8
Blickwechsel: The Mashrabilta as a Symbolic Form . L5L
Cor-rclusion:
Comparing the Gaze in Different Cultures
Afterworcl L67
Notes. L7)
L-rclex . . . L95
Introduction
Drs c RrB IN c e Cur,ru r.Ei B LI c KWE c rr s EL (SnrrrIN c
Focus / Exc¡IeNGING GraNcrs)
I.
This book and its topic grew out of research on the history of seeing that \Mas
originally lirnited to \(/estern culture. The name "Florence" in the title stands for
rhe Renaissance, since perspective-probably'Sl'estern culture's most important
pictorial idea-was invented there. The name "Baghdad" refers symbolically to
Arab science, which had a profound impact on the Renaissance. In our context
this means the historical Baghdad, the city that as the seat of the Abbasid caliphs
long functioned as the center of the Arab world. The tide of a recent book by
George Saliba, professor of Islamic science at Columbia Universit¡ sums up
my topic perfectly: Islaznic Science and tbe Maleing of tbe European Renaissance.l
Since this title expresses a hypothesis that runs counter to the generâl understand-
ing of the Renaissance, readers are entitled to demand evidence. The same applies
to the argument developed in what follows, that perspective art is based on a rhe-
ory of Arab origin, a mathematical theory having to do with visual rays and the
geometry of light.
One will search in vain for this argument in the scholarly research on perspec,
tive, but it makes sense to inquire about the history of a term rhar means some-
thing different in the history of science than it does in the history of art, The
word "perspe ctive" Qterspectiua in Latin) was commonly used in the Middle Ages
by scientists before it was introduced in the field of art during the Renaissance.
Then it denoted a visual theory that was Arab in origin; only late¡ during the
sixteenth century, did writers begin using it as a synonym for the term "opticsj'
which occurs in scientific texts of classical anriquiry. Nowadays it survives as a
technicai term solely in art histor¡ where perspecrive refers to the first theory to
INrRoouc'rrow
I
iÈ
calculate in-rages âs rhe projecrions of a viewer. The earlier meaning has fallen into o' a hisrorical encounter with Arab culture that has hacl a lasting ef-
c-*o.n,c err¡:àrc
disuse except among historians of science. The mere fact thac the two fields share ctllttlre olrthe Wesr'
'- nrrrhe
a ternì would not lnean much, however, if there were no inner connection be- ilr,, effècc appe arecl rvith a time lag that requires a word of explanation. In the
tween the dreory of percepcion and the theory of art. The creators of perspeccive 6.ld of .rr hisrory it is custouary nowadays to elnphasize cþe close parallels be-
in art asserted that they were using percePtiolÌ as the standard for their works, but lrl.,"i. a¡cl rnedieval European art, for example in the area of manuscript
,ru..n
they based this claim on a definition of percepcion that they had not invented bur rny own study addresses a different question. The rationalisrn
illr.in",ior-,,
themselves. In fact they had found it in the legacy of an Arab mathematician that in the era when Arab science reached its peak could not bear fruit in
Jo,otn^",
had reached the \Øest. Lorenzo Ghiberti, one of the leading artists of Florence itt lüesr until the moclern period, since it was based on scientific experinrents
rhe
the early Renaissance, still used rhe term "perspective" in a double sense; in his liberate cl frorn every kind of theological baggage. During the epoch that we in the
Cornrnentarir-s he quoted long passages from the Italian translation of an Arabic ,üest call rhe Middle Ages, the subjects of rnathematics and âstrolÌomy were poP-
treatise that set forth a scientific theory ofvision. ular i¡r the Arab worid, which had not yet come under the kind of dogrnacic con-
Perspective will nor be treated as a subject belonging solely to the domain of strainrs so prevalent later. In Andalusia the coexistence or cohabitation of three
arr, even though it has been an important topic of discussion in'Western art. The cu¡ur€s c{uring the Middle Ages provided the irnpetus for cranslations of many
true significance of the term becomes evident only when it is viewed in the larger Arabic rexrs, includingAlhazent treatise on optics to which Chapter 3 is devoted.
conrexr in which it originaced. Perspective reveals its cultural dimension wherr yer the explosively controversial implications of such texts, not all of which were
it is understood in terms of pictures. Even within the domain of art, perspective based on Greek originals by any means, remainecl hidden for a long time; some
does not stand alone but is closely linked to the modern conception of the por- did nor become evident until the Renaissance, in the work of Copernicus, for ex-
trair. From the very beginnings ofsecular theater, it also played a striking role as ample, or, in the case of the camera obscura, in the work of Kepler and Descartes.
an element of stage sem. The norion of a "window" in the artistic and philosophi- The conrroversial implications of Arab visual theory also came to light oniy
cal sense cannor be separated from the window as a model of perception. Along with the passage of time; this is the subject of Chapter 4. The debates over knowl-
r,vith the discovery of the horizon, a tÌew conception of space also belongs to the edge ,rr-rd perception in rvhich scholastic theologians and men of science partici-
context from which perspective emerged. The panorarna is not complete, how- pated represent one instance of controversy; another is the introduction of the
ever, without mention of the modern subject or subjective consciousness that Po- concept of mathematical space by Biagio Pelacani, who made innovative use of
sitions itself before a perspective image in the most literal sense-and by standing his source, Alhazen. Yet it is not until the essentially nonpictorial Arab theory of
in such a location, discovers itself. The âctivity in which viewers engage there is vision was transformed into a pictorial theory along'$l'estern lines that we arrive
one of gazing This introduces a facror that played no role in the earlier visual at the central concern of this study, which is to look at two different cultures with
theory on which perspective in art is based, and the scholarly literature on per- the issue of pictures as our theme. These two cultures differ markedly both in
spective still lacks a general investigation ofthe topic. their practice with respect to pictures and in the way the member societies prac-
If perspective as Filippo Brunelleschi invented it and Leon Battista Alberti de- tice looking and seeing. This is obvious in the artistic use of pelspective, for noc
fined ic in the early fiÍteenth century had been or remained a problem solely for only does no equivalenr ro perspecrive exisr in rhe Middle East, bur the exisrence
artists, the topic could be handled within the confines of a single culture-as hap- ofsuch an equivalent would be impossible, as will become apparenr. The concep-
pens for the most part in any case. As a question of pictures, however, it brings tion of pictures is entirely different rhere, and for a long tirne pictures rhat repro-
another culture into play and raises the new questions discussed in this book. The ducecl reality one-ro-one, as ir were, were banned. For rhe momenr it may suftce
phrase "two cultures" refers noc just to the naturâl sciences and the humanities, to note drat while Arab visual theory gave a predominant role to ilght, which ls
the subject of so much discussion these clays, even though there will have to be essentially aniconic, it relegated picrures to the realm of the mind exclusively.
some mention of the relationship of science to philosophy and art, and thus even- From this it follows that mental images could not be turned into somethingphys-
tually to the society in which scientific work is undertaken. Rather, I mean to ical, could nor be copied or reproduced in corporeal form.
L INllRoouc:lroN IN:tnoouc:rtoN )
lVhen I delivered a lecture series on the cultural history of seeing at the Col- beco¡re rnore striking when they are seen next to each other than when
ecrerisrics
lège de France in the spring of zoo7, it stood to reason that the topic ofperspec- .".f, t, viewed separately and elucidated solely on its own terms, âs is still nor-
dve would crop up, since at bottom it is nothing other than a cultural technique ,Jfy ,f.,. case for \Øestern culture. \Øith my chosen topic, such a shifr of focus
that has altered the visual culture of the modern period pervasively and to lasting ;;";r, an obvious advantage because it makes unnecessary the constant use of
effect. The quantum leap consisted in the way PersPective introduced the gaze Jord, ,u.l-, as "influence" and "differences." The text is designed so that each
into the picture and thus, at the same time, the human subject doing the gazing. c:hapter is devored to one culture and ends with a Bhckwechsel to the other, thus
For precisely this reason Renaissance art was understood as a professional disci- orouiding a natural break; the discussion changes direction without the need for
pline based on a theory that had to be mastered. Artists saw themselves as Practic- 'a cation each time'
speci6. ¡ustifi
'My
ing an applied science that had adopted a mathematical theory of visual Percep- int..,rion was to place both cultures side by side and on the same level, so
rion. The previous history of this theory appears all the more contradictory when rhar neither rvould be overvalued or undervalued. This is the only way to limit or
one reestablishes the scientific context in which it originated. For how could it conrain dre inevitable Eurocentrism that long characterized rùØestern views of
happen that an Arab visual theory based on geometrical abstraction could be re- other cultures. I must leave it to the reader to decide whether my attempt has
conceived in the \Øest so as to reverse its meaning completely and transform it been successful. The fact that it was by necessity a difficult undertaking could not
into a theory for making pictures ? How could it have come about that the same be an excuse for giving up before I had even started, nor could the question ofex-
theory now made the human gaze the pivotal point of all perception and enabled perrise be allowed to stand in the way, a question that plays a certain role in aca-
artists to reproduce this gaze in paintings or, in the vocabulary of modern pho- demia. There was a way out: I could have chosen to speak in terms of "influences,"
tograph¡ "analog images"? The formulation of this question determined the path as I do, in fact, in certain passages. But this familiar term encourages a tendency
that the present study would follow, but also made it inevitable that I would have ro use rwo different yardsticks and to reinforce a colonial point of view, conced-
to cross the boundaries of my own area of specialization in order to relate two ing a non-European culture's influence in one area but still relegating it to a lower
culrures. Viewing\Øestern pictorial culture through the lens of a different culture level of importance overall. The shift of focus I have undertaken has no such in-
remains a daring undertaking, but it may result in seeing both in a better light. renrion behind it; rather, it strives to describe both cultures berter, and it also
My sole aim in taking up this twofold topic and discussing Renaissance and Arab avoids the awkward questions ofwho influenced whom and whether one culture
cultures in one and the same context has been to achieve such a Blickutechsel, a was more open to outside influences than the other. Finally, a focus that places
word that can mean both a "shift of focus" and an "exchange of glances'" But what two cultures side by side offers access to the topic to two different groups of read-
does that really mean? ers, namely to'S7'esterners interested in the subject of linear perspecrive, who will
come across information about Arab culture here, and to readers in the Middle
East who want to become more familiar with lØestern perspective-based arr, irs
cultural profile and irs foundations.
u. Such a shift of focus makes somerhing else evidenr as well: rhe rwo cukures
that concern us here have a long shared history of encounters in which they in-
spired or challenged each other. For this reason it is worthwhile taking a look at
Usually an exchange of glances takes place between two people or two sPeakers them i'the context of Medirerranean histor¡ and easilypossible to dispense with
in a discussion. And in the course of history Arab and \Øestern culture have also all the controversy rhat dominates the media today. Even in the area of religion,
"exchanged glances," if such a broad metaphor is permissible, although these ex- common ground exists under the heading "monotheism." One need only men-
changes have been very different at different times and not always peaceful in na- tion the word 'Andalusia" to evoke a rime in which Muslim, Jewish, and Chris-
ture. However, I would like to speak not about an exchange of glances between tian cultures coexisred peacefully and fruitfully. Yet an overly simplistic accenr on
two cultures but about a shift of focus from one culture to the other. Their char- the positive raises its own dangers, namely a truncared. and-rherefore false-
Iw:rRoouc:lloN INrnoouc:rloN
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view of history. For exarnple, the clicl-ré that Europeans owe their knor'vledge of self ancl enrer i¡ro rhe kincl of clialogue ir-r which facts and knowleclge carry rnore
classical Greek literature to rranslacions from the Arabic cloes not do justice to dre *at*n, rhtrll tncre avowals ofgood intentions'
actual historical role played by Arab culture. The example of Ibn al-Haytham, or fhe pl-,iloropheL Régis Debray recently categorized dialogues becween cul-
Alhazen, to whom Chapter 3 is devoted, reveals a very different story. The correc- rures as ".o,rr.,rlpotary myth'"r While science and tecfi¡ology provide the foun-
tions he made to ancient optics were revolutionar¡ offering yet rnore proof that J"rior., f^o ,. ,r sharecl world, he sees culture as "a natural place of confrontation,
the contribution of classical Arab culcure cannot be reduced to one of mere trans- ,in.. i, is w6ere iclentity is forged, and that in turn Prestunes a urinilnutn of dis-
lation. ,.nr.', H. cites Claude Lévi-Strauss, observing that "civilization contains within
In a recent study George Saliba founcl new proof that even Copernicus hacl imelf rhe coexisrence of extremely diverse cultures and lives precisely from this
sorne familiarity with Arabic texts. The work of astronomers and philosophers coexiste¡ce." Debray considers it more necessary than ever today to open doors
like al-Kindi gave Arab science standing and authority in the lØest, as did the and tear ciou,n walls built of prejudice. Nevertheless, having the greatesc possible
mathematicians who took up and discussed the 'Arabic" numerals tl-rat had origi- amounr i¡ co¡rmon should not become the issue, because only diversitv can save
nated in Flindu culrure.' In this cotÌtext optical theory ('ilnt al-ruanazir)-the us from rn isturclerstandings'
science of "what appeârs" as distinguished from what is-was of the greatesr sig- My choice of topic will also be misunderstood. For rnany people in dre \Øest,
nificance.s It is represented by such famous figures as al-Fãrãbi (died ca. 95o), but an incre asir.rgly clefensive attitude goes l-rand in hand with their fear of Iosing cheir
it was Alhazen's chief work-known by the title of the Latin translacion, Perspec- own culrurâl identity (sometimes rnistakenly believed to be universal) and be-
tiua-thathad the greatest resonance in the West, as Friedrich fusner's ry72 edr' coming contaminated by other cultures. On the opposite side, people feel threat-
tion of the work proves. Alhazen, the inventor of the camera obscura, is co¡rsid- ened by a comparison of cultures because chey are afraid of losing in the compari-
ered ro have pioneered the modern scientific method in his research, but his son. They may also object to their culture or science being labeled as "Islamic";
psychology ancl aeschetics reflecr the rvorlclview of his tirne ancl culture. afrer all, the \Øest does not refer to its own culture and science as "Christian." Ancl
nowadays merely addressing the topic of pictures can quickly elicit charges of Eu-
rocenrrisur, even if for Islarnic cultures every efforc is rnade to differentiate be-
tween epochs and geographical regions. A suspicion arises that Europeans want
III to deny the Midclle Easc its right to images, a right to which every culture is enti-
ded. To this one can reply that it is possible to define visual culture in terms other
than the pictorial art that is taken as the standard in rhe \Øest. The present study
Islam has become a hot topic in today's intense debates, but its very topicalicy car- pursues this aim by seeking to find out what occupies the place of such art in Mid-
ries the risk of distorting or even falsifying history. Many atternpts to debate in a dle Eastern culture and how calligraphy and geometry have established an aes-
politically correcr mannef, to insist that onet own views are right or one's oppo- thetic stanclard l¡asecl on marhematical models. In this conrexr the question can-
nents' views are wrong, fail because they do not create the necessary space for not be, "Vhy did linear perspecrive not exist in other cultures ?" Racher we musr
other positions and impede a deeper view into our shared pasr, In "deep time"- ask about the parricular conditions under which it originated in the \Øest.
the geological rnetaphor used by siegfried Zielinski in his archeology of the me- Distinctions of the kind made in this study neverrheless always presume rhar a
dia-divlding lines and commonalities that are forgotten or ignored in current larger whole exisrs in which they have their place. One can speak of differences
debates become visible. In a climate of mutual suspicion it is often very difficult to only where there is also common ground. This requires an undersranding of cul-
make one's voice heard at all, yet it is pointless to join in the chorus of those who ture that is based on a premise not of inevitable conflict (as proposed by Sarnuel
simply call for solidarity with the Islamic world and have turned the phrase "alli- Huntington) but of shiÍiing and flexible boundaries, rhe course ofwhich becomes
ance of cultures" in¡o a superñcial slogan. \Øe must go a steP further if we are to visible through the study of cultural history. ilija Tiojanow and Ranjit Hoskote's
identify the necessary distinctions that every culture needs in order to express it- recent book Karnpfabsage ("Renouncing Battle") offers a passionare argumenr
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6 IN:lRooucrroN 7
againsr Huntingtont position.5 In it they reject confrontation and profess their Nor'r¿r' Bryson preparecl the way for dris shift in accent more than fifty years
belief in a shared history in which Europe was perÍnanently stamped by Arab cul- .'^-','^. rìDÞeârârÌce of Panofsky's essay.T Bryson distinguishes between two eras
ture and irs ties to India. Only as a result of modern colonialisrn, it seems, clicl the :ä;...åe in rvhich the kind of look directecl at a work of art underwent a
rigid ideological barriers arise that divicle the world today' ;:;rr'The Rer-raissance favored the procracted and quiet gaze, which is con-
::;.i ro a' observeL's bod¡ while in the seventeenth century its place was taken
*, .1. ,.Oi.l a'd fleeting glance, The emphasis on a brief glance tended to efface
l. Or.r*.. of rn actual physicai body performing the act of viewing. When a
IV tor.r all connection to a real observer, the"gaze" represented by a picture
"ì*..
i..o*., a' absrracrion. This shift was a turning point for Perspeccive as a cul-
,urrl ,..lì,rique and also a turning point for its symbolism (Chapter 6). 'Vhereas
Mathernarical perspective has been a popular topic in art history ever since Erwin Bryson uses a comparison with East Asian art to describe the "deixis" of European
Panofsky published his study on it in ryz4.6The context in which it became the way it shows us the world-in this study I ttse a Blickwecbsel, a
a cultural rechnique of rhe modern period, however, has received scant atten- s^hrrif_t rohf ^foricsu,s to Arab arc to perform the same function'
don until now. Panofsky called perspective a "symbolic form," and the impression In the \Øestern use of persPective in art, according to Bryson, the picture is
arose rhar it was the only instance of such a form in the realm of art. To my knowl- Iinked ro an observer; the picture takes that persont gaze as a yardstick and turns
edge, until now no one has posed the fundamental questioll of whether other ir back on him or her. The (observing) subject takes up a position before the
"symbolic forms" exisr-least of all in other cultures-as I do in the Blickwecbsel painri¡g, ernbodying boch the painter and the viewer, so to speak, while the space
ar the end of each of the lasr two chapters. There I propose that the Tnuqarn/|' ih., rh. gaze normally traverses is contracted to a single geometrical point. Here,
u,ith its tlrree-climensional geometr¡ and the nt'ashrabiya, a forrn of windorv Brysor.r afgues, the viewer encounters the puncturn or point, a term introduced by
covered with latticework rhat screens out light, should be recognized as symbolic Rol¿ncl Barrhes. The gaze does not actually involve a singie point, howeve! since
forms in Arab arc. In \Øestern culcure, bodr the stage set (along$'ith the culturally it originates in a body with two eyes. For just this reason the Renaissance strove to
specific praccice of staging plays in the modern period) and the modern panel resolve rhe conflict between the abstract eye point and the real body by devising
fainting (particularly the genre of the portrait) could be considered symbolic rhe uanishing point, which stabilizes the gaze in the eye point. It is the vanishing
forms. Panel paintings wefe first introduced in other cultures in response to out- point thar represents the observer in the picture by assigning a symbolic location
side pressure under colonial rule. to him or her. In the vanishing point the visual rays come together ât the horizon,
Ernst Cassirer, who originated the term "syrnbolic form," defined it far more just as chey do on the other side, in front of the picture, in the eye point. In the
broadly, however, asserting that art in general was one such form, as were lau- geometry of perspective art this point lies just in front of the viewert eyes.
guage, myth, and science' It may be that art has been a symbolic forrn in every One of Brysont readers, the mathematician Brian Rotman, took up his argu-
..rlt.r.. and society, just as art was in the Renaissance precisely because of perspec- ments four years late¡ in ry87, and expanded them.t Rotman makes a surprising
tive, which distinguishes it from the earlier art of the Middle Äges. \üe can accePt suggestion, namely that the number zero should be seen as having a iink to the
Cassirert ideas if we understand persPective in art as a "cultural techniquei' since vanishing point and vice versa. He regards the introduction of zero to Ärabic nu-
the latter term incorporares cerrain aspects of the symbolic form, although it re- merals and the invencion of the vanishingpoinc as parallel occurrences. Zero and
fers more ro pracrice. The decisive question, though, is what such a "form" or the vanishing point both signify two different things. Just as zero is in one sense
"technique" expressed and in what way it was "symbolic." Panofsk¡ once again simply a number like all the others, so too the vanishing poinc is just one sign
following cassirer, decided that it was "spacei' although he left the definition among all the other signs in a painting (figures, objects, and so on). At the same
vague (see Chapter r). In the presenr study the idea of space as the central concePt time, hor,vever, this point represenrs a sign of a completely different kind; it is of a
is replaced by the idea of the gøze. different order, a sign that alters the meaning of all the other signs. Rotman calls
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INlnoouc:rtoN 9
8
ic a "meta-sign," because the presence of such a sign makes it possible to organize ttPt"lr"..:^.;1: ;1"..,; iAl'lh azetl, there was no conceptioll of a screen located between the
an inûnire number of pictures, just as infinitely many numbers can be derived rarher, light used countless poi'ts on the surfaces of objeccs
from zero.e The vanishing point is indispensable for pefspective art, no mattef wich che surface of the eye by means ofvisual rays. The imag-
;lto:Ï;.r.Jr1.,.,-,.,
what subject a given painting clepicts, despite the fact that-or because-it is an ;;; .;". rv6ose vertex lay in dre cen¡el of tire eye is not identical co the "visual
abstraction arnong real rnotifs. ,*..,¿" of perspecrive, which is bisected by the picture plane.'3 All-razen had no
Rotman uncovefs dre arnbivalence of the gaze that wanders between human '-Ti .fa va,ris¡ing point for his theor¡ which exists o'ly in the gaze, the act
body and picture when he describes the picture as the site of the gaze, even though ;;;.;,.,r. b*r nor in the world of objects. Nevertheless the geornetrical point
dre body cannor enrer rhe picrure itself. The vanishingpoint is "unoccupiable" by li."""lr"*lri.h dre world transforms itself into a picture became possible only
a person or indeed any physical object, but it gives a viewer "the possibility of ob- *i,ntí rn. fraureworl< of a system that could be calculated mathernatically'
jectifying himsell rhe means of perceiving himsell from the outside, as a unitary
seeing subject, since each image makes a deictic declaration; this is how I see . . .
from this parricular spot at this particular instant in tirne."lo According to Rot-
V
man, rhe indissoluble relationship between Presence and absence also applies to
zero, which can be considered a number only in the sense that it is a nonnumber.
Thus the viewer of a painting experiences hirnself precisely in the place where he
is not present because the picture leaves a space for him, a place that is at the same The rext of t6is book is structured as six chapters, each ofwhich ends with aBlicþ-
tir-ne empty- agap."Zero is written on rhe viewer's body, since onlywhere there wechseho the other of the two cultures. The first three chapters place the Arab
is nothing, but something could be, does he hirnself stand."rr Between the tenth aspect of che subject in the foreground. Chapter t introduces the topic by exam-
and the thirteenrh cenruries "che sign [o] stayed within the confines of Arab cul- inìng dr. spectrutÌ1 of possible meanings for the tefm "pefsPective" in art and sci-
ture, resisted by Christian Europe, and dismissed by those whose function it was .n... Ll-r.,-, offer a critical analysis of the term "symbolic form" and relate it to the
to handle numbers as an incomprehensible and unnecessary symbol," rvrites Rot- concepr of e "cul¡ural technique." In the encounter be cween East and \Øest, picto-
man. But in che fourteenth century, "wich the emergence of mercantile capitalism rial art-r.vhich was understood as the only "art" in the West-existed under dif-
in Northern ltaly, the handling of numbers passed . . . to merchants, ârrisan- ferent conclicions than applied arts and crafts, in which transfer between East and
scientists, architects . . . for whom arithmetic was an essential prerequisite for \Øesr occurred more easily. The final section takes up an idea of Orhan Pamuk's
uade and technology."t2 and examines Ottoman society and its interactions with \Øestern art of the mod-
The invention of perspective-which occurred in ltaly, the same place where ern periocl. Chapter z takes a stance on the question of pictures in Islar¡ic culture,
the number zero was introduced to the'West-belongs in the same environment. which is currendy a subject of controversy even among exPerts. In the last section
And so it makes sense to add a third element to Bryson and Rotmant arguments of Chaptel z, I contrast the dominance of the gaze in\Øestern art with the visual
and to include the Arab genealogy of the visual theory that was introduced in the taboos existir-rg in rhe religion of Islam. Chapter 3 offers a first attempt to incro-
\Øest at the same time as Arabic arithmetic. Rotman has already established this duce Alhazen's visual theory into the scholarly discussion of perspective art and
connection with regard to the vanishing point, but without including the transla- to shed light on the theoryt cuitural background. Here mathematics, \Mhich in
tion of Alhazen's theory from Arabic as part of the evidence. Adding it makes the the fomr of geornetry served as the great subject of Ar¿b art, occupies an essential
parallel he draws between zero and the vanishing point eyen more convincing, place. In the concluding section of Chapter 1, I distinguish between the dark
but its cultural and historical significance becomes âpparent onlywhen one makes room that Alhazen used to study the pathways of light and the camera obscura of
an essenrial distinction: Zero akeady existed in Arab mathematics, but the van- the seventeenth century; the latter caught the attention of the public as consum-
ishing point was first invented in Western art-because it makes sense only in a ers ofpictures, like audiences in modern cinemas.
kind of picture rhar did not occur in Arab art. In the geometry of the visual field Chapter 4 opens tl-re investigation of perspective in the \Øest with a discussion
IO IN:rno tuc:rroN INrnooucl:IoN II
of the epochal change that occurred when an Arab visual theory was transfonned
into the new pictorial theory of the Renaissance. The invention of mathematical
space by the philosopher Biagio Pelacani of Parma played a key role il-r this transi-
tion. The final section here offers a reminder of how Euclid came to overshadoç Perspective âs a Question of Images
Alhazen in the cuitural memory of the Renaissance, as a way of stressing classical
anriquiry as the \Øesr's sole heritage. Chapter 5 takes the subjecc of perspective P¡:rgS BET\øEEN EAST AND \øEST
outside the confines of art history to describe the significant role it played in the
design of stage sers, for example, and the role of theater in \Øestern visual culture.
In each of the last two chapters the Bli.ckwech.r¿lserves to identify a symbolic forr¡
in Arab artl rhe geometric rnuql¿rnas in Chapter 5, and in Chapter 6, the window What Is a Symbolic Fonn?
lattice of rhe masbrabjyø. Chapter 6 expands che spectrum of areas in which per-
spective has made its effect felt by discussing the history of the self-aware "sub-
ject" as a philosophical concept. The symbolism of the gaze emerges from the use Neu e.testionç, It was Albrecht Dürer who first introduced perspective-or more
of the eye as an emblern and culminates in the figure of a new Narcissus who has or..iráy, rvhar is called "linear" or "mathematical perspective"-to the German
overcome the ancient fear of the gaze. oobli.. As the toots of the word suggest, perspectiYe created transparenc¡ mak-
ing it possibl e rc look througb pictures into the world they depicted. lØhen we
,pl"k of ..n,rai perspective we do not lnean to say that a picture has some partic-
uìarly irrrportânt cheme as its center, rather we mean only that its center is the
gaze of aviewer'. The measurement that was so important to Dürer, while it in-
volved the proportions of the human bod¡ was in the case of perspectiv e a mea'
,aïement of the gaze so thât it could be "constructed" or "reconstructed." Thus
artisrs who made use of perspective handed their new pictures over to the eyes of
the public by simulating their way of seeing. In Nuremberg this \Mas taken to be a
new fashion in ¿rt from Ital¡ and everyone took it to have been invented in Flor-
ence, even though Dürer had learned about it in Venice. Who could have fore-
seen rhar one day it would become the signum of what distinguishes pictures
made in the West from all others ? The fact that this is so means, however, that the
issue we are dealing with here is not a question specifc to art, even though it be-
came a subject of discussion in that field. Only when lve recognize that it is a
question of pictures does the cultural significance of the topic become aPparent,
for what cultures do with pictures and how they capture the world in them leads
straighr ro rhe cenrer of rheir way of thinking.
The pictorial invention rhat we call perspective was a revolution in the history
of seeing.r When perspecrive curned rhe gaze into the umpire of art, the world
became picture, as Heidegger would later observe. For the first time, paintings in
PersPective depicted the gaze that a spectator turned on the world, thereby trans-
forming the world inro auiew ofthe world. The term "analog imagei' to which we
IN:rnooucrroN \Øuer Is a SvNtsorlc FoRM? 13
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