The "Belvvedere" by Escher: a Modest Hypothesis

5 “‘111”’ ”11111” THE ‘DELVEDERE’BY ESCHER: LE ‘6ELVEDERE’D’ESCHER: A MODEST HYPOTHESIS UNE MODESTE HYPOTHESE Michele Emme DABAC Uni e si a della Tuscia 01 100 Vi e bo, ITALIA F ench ansla ion: T aduc ion anpise Jean-Luc Raymond 1. HISTORY In 1961 Esche edi ed a book en i ely dedica ed o his g aphic wo k. He himsel w o e he in oduc ion and a small desc ip ion o all he ep oduc ions o he olume. A e ised and expanded e sion o he book was published in 1967 [I]. He made a classi ica ion o his wo ks by subjec . The las sec ion is en i led ‘Impossible buildings’ [I p.161. He w o e o he li hog aph ‘Bel ede e’ (Figu e 1): “In he lowe le o eg ound he e lies a piece o pape on which he edges o a cube a e d awn. Two small ci cles ma k he places whe e edges c oss each o he . Which edge comes a he on and which a he back? In a h ee-dimensional wo ld simul aneous on and back is an impossibili y and so canno be illus a ed. Ye i is qui e possible o d aw an objec which displays a di e en eali y when looked a om abo e and om below. The lad si ing on he bench has go jus such a cube-like absu di y in his hands. He gazes hough ully a his incomp ehensible objec and seems obli ious o he ac ha he bel ede e behind him has been buil in he same im- 1. HISTOIRE En 1961, Esche publia un li e en ik emen dedi4 a son oeu e g a- phique. 11 ec i i lui-meme I’in oduc ion e une ca e desc ip ion pou chacune des ep oduc ions appa aissan dam le olume. On publiai en 1967 [I] une e sion e isee e augmen ee de ce li e. 11 aisai une classi ica ion pa suje de ses oeu es. La de nie e sec- ion es in i ulee ((lmmeubles impossibles~~. II ec i ai a p opos de la li hog aphie ((Bel ede e>, ( igu e 1) : (( Au p emie plan in e ieu gauche, on ou e une euille de papie su laquelle on a dessine les a g es d’un cube. Deux pe i s ce cles indi- quen /‘emplacemen des poin s d’in e sec ion des a g es. Quelle es I’a b e quipasse a I’a an e quelle es celle quipasse a l’a ie e? Dans un monde idimensionnel, la simul anei e de I’a an e de I’a ig e es une impossibili e e ne peu donc & e illus ee. D’au e pan‘, il es ou a ai possible de dessine un obje qui ep esen e une eali e di e- en e selon qu’il es obse e du dessus ou du dessous. Le ga con assis su le banc a jus emen une elle absu di e en o me de cube dans ses mains. I1 ega de pensi emen ce obje incmp ehensible e semble inconscien du ai que le bel ede e qui se ou e de ie e 6 FIGURE 1 'Bel ede e' Li hog aph o M C Esche 462 x 295 cm (1 958) ((Bel ede e)) Li hog a- phie de M C Esche . 462x295cm (1958) possible s yle. On he loo o he lowe pla o m, ha is o say in- doo s, s ands a ladde which wo people a e busy climbing. Bu as soon as hey a i e a loo highe hey a e back in he open ai and ha e o e-en e he building. Is i any wonde ha nobody in his company can be bo he ed abou he a e o he p isone in he dun- geon who s icks his head h ough he ba s and bemoans his a e?" I is well-known ha he i s 'impossible building' was designed by Esche comple ely independen ly om he 'impossible objec s' c e- a ed by L.S. and R. Pen ose [2] in 1956, he so-called 'impossible iangle' and he 'impossible s ai cases'. This independence was made clea by Roge Pen ose himsel in he mo ie "M.C. Esche : Geome ies and impossible wo lds". ealized in 1984 [3]. Pa o he explana ion o Pen ose in he ilm was published elsewhe e [4], [5, p.801. In his pape o he P oceedings o he cong ess M.C. Esche : A andScience [6, p.1501 Pen ose w o e: "In he mean ime, and qui e independen ly, Esche had p oduced his li hog aph 'Bel e- de e' which illus a es a e y simila kind o impossibili y." The e is no doub ha one o he explici inspi a ion o he li ho- g aph was he 'Necke 's cube' (Figu e 2) (see [7]). - FIGURE 2 The Necke s cube (1832) ~. u lui a e e cons ui dans le mime s yle impossible. Su le sol de la pla e- o me in e ieu e, c'es -a-di e a I'in e ieu , se ien une echelle su laquelle deuxpe sonnes son en ain de mon e . Mais aussi d qu'ils a i en a I'e age du dessus, ils se e ou en a I'ex e ieu e on a ein- eg e I'immeuble. N'es -il pas ex ao dinai e que pe sonne en ce e assemblee ne s'inquie e du des in du p isonnie du donjon quipasse la i e en e les ba eaux e pleu e su son so ? )) [ 1 , p.161 I1 es bien connu que ce p emie 'immeuble impossible' a e e conqu pa Esche de aGon comple emen independan e des 'obje s impos- sibles' C ees pa L.S. e R. Pen ose [2] en 1956, le soi-disan ' ian- gle impossible' e les 'escalie s impossibles'. Roge Pen ose Iui- m&me me ai en e idence ce e independance dans le ilm (( M.C. Esche : Geome ies and impossible wo lds,), ealise en 1984 [3]. Des ex ai s de I'explica ion de Pen ose emise dans le ilm on e e publies ailleu s [4], [5, p.801. Dans son a icle pou les Comp es endus du cong es M.C. Esche : A and Sclence [6, p.1501, Pen ose ec i ai ~ ((Pendan ce emps, e de a$on ou 4 ai independan e, Esche a ai p odui sa li hog aphie 'Bel ede e ' qui illus ai une im- possibili e d'un ype aimen similai e. )' II n'y a aucun dou e que, pou la li hog aphie, I'une des sou ces d'inspi a ion explici e u le 'cube de Necke ' ( igu e 2) ( oi [7]). En eponse a un a icle de Ma ianne Teube [a]. Geo ge Esche , le ils de Mau i s Co nelis, ec i ai : (( Su un poin impo an , je suis en acco d a ec Mme Teube : le ce- Ieb e ase de Rubin, les escalie s de Sch oede e le cube de Necke on p esque ce ainemen ou ni le ge me de /'inspi a ion de M. C. Esche pou ses a aux su la subdi ision egulie e du plan e pou plusieu s es ampes. Ces concep s isuels ascinan s on passe en e ses mains, non pas pa les publica ions psychologiques, pou les- quelles il n 'a jamais demon e d'in e g , mais. de acon plus aisem- blable, a a e s les ch oniques d'enigmes e de casse- i e de pe io- diques plus p osai'ques don j'ai un ague sou eni . )) [9] 7 FIGURE 3 Eng a ing on wood by M.C. Esche : ‘%.Pe e seen om he Gianicolo”, 241 x321 cm (1934). G a u e su bois de M.C. Esche : <<Sain -Pie e u du Gianicolo 241 x321 cm (1934). Answe ing o an a icle by Ma ianne Teube [8], Geo ge Esche , son o Mau i s Co nelis, w o e [9]: “On one impo an poin I do ag ee wi h M s. Teube : Rubin’s well known ase, Sch oede ’s s ai s and Necke ’s cube did almos ce - ainly p o ide he seed o inspi a ion o M.C. Esche ’s wo k on he egula subdi ision o he plane and o many p in s. The e ascina - ing isual concep s come in o his hands, howe e , no h ough psy- chological publica ions, in which he ne e showed in e es s bu mo e likely h ough he puzzle depa men o mo e p osaic pe iodicals o which I ha e a ague ecollec ion. ” Fo he possible in luences o he heo ies on isual pe cep ion on Esche ’s wo ks see [lo], [Ill and [12]. A p opos des in luences possibles des heo ies de la pe cep ion i- suelle su les a aux d’Esche , on peu consul e [lo], [I I] e [12]. Ve sluis [13, p.3781 a p opose une hypo hese di e en e pou la c ea ion de ‘Bel ede e’ : <c Ilmesemble quela desc ip ionlaplussim- ple e la plus jus e de ce qu’Esche a p obablemen ai n’impliquepas du ou la ipou e (le iangle impossible), e seulemen un peu Necke . >) Dans ce cou a icle, je oud ais p opose une hypo hese plus “p o- saique)), plus e iden e meme: du an son sejou a Rome, Esche ((a u)) un immeuble ((impossible))! 2. HYPOlHhE II es bien connu qu’Esche a passe plusieu s annees en I alie. II habi a Rome de 1923 a 1935. Son ils Geo ge, qui naqui a Rome en 1926, a dec i la pe manence de la amille Esche a Rome dans le ca alogue de I’exposi ion de 1985 [14], [15]. On ou e a dans [16] une biog aphie idele de la pe iode i alienne. La amille Esche habi ai a Rome dans un pe i appa emen au h au de la Mon e Ve de (mon agne e e), I’un des ‘qua ie i’ de la ille ; I’ad esse e ai 100 Via ( ue) Alessand o Poe io. Ce e ue n’es pas es eloignee de I’une des plus celeb es ues de Rome, la Passeggia a del Gianicolo (la p omenade du Gianicolo). Le Gianicalo es I’une des nomb euses collines de la ille e es aimen p es du Va ican. Tous les isi eu s de Rome on I’ascension du Gianicolo pou oi ou e la ille de I’au e cB e de la i ie e Tebe . Esche a ealise quelques oeu es en i an son inspi a ion des monumen s classiques de Rome. En 1934, il i une g a u e in i ulee ((Sain -Pie e u du Gianicolo)) ( igu e 3). L’une des a~ons de se end e de sa demeu e au Va ican e ai de descend e le Gianicolo pa la Passeggia a ( igu e 4). Dans les annees 1930-1931, on comple ai la cons uc ion, en bo - du e de la Passeggia a del Gianicolo, du College de S -Josapha , un college uk ainien p op ie e de la ci e du Va ican. L’i nmeuble u e - a FIGURE 4 Map o Rome (de ail): 0 Apa men o Esche ’s amily, ia A. Poe io. 0 College S . Josap ha and Passeggia a del Gianicolo. (3 %Pe e , Va ican. Ca e de Rome (dk ail): 0 Appa emen de la amille Esche , ia A. Poe io. 0 College S -Josapha e la Passeggia a del Gianicolo. Va ican. 0 Place Sain -Pie e, Ve sluis [13, p.3781 has p oposed a di e en hypo hesis o he c ea ion o ‘Bel ede e’: “I seems o me ha he simples and mo e accu a e desc ip ion o wha Esche p obably did in ol es he iba ( he impossible iangle) no a all and Necke only sligh ly.” In his sho no e I would like o p opose a mo e ‘p osaic’, e en ob- ious hypo hesis: Esche ‘saw’ du ing his s aying in Rome an ‘im- possible’ building! 2. HYPOTHESlS I is well known ha Esche spen many yea s in I aly. He li ed in Rome om 1923 ill 1935. His son Geo ge, who was bo n in Rome in 1926, desc ibed he pe manence o he Esche ’s amily in Rome in he ca alogue o he exhibi ion in 1985 [14], [15]. An accu a e bi- og aphy o he I alian pe iod can be ound in [16]. The Esche am- ily li ed in Rome in a small apa men up on he Mon e Ve de (G een Moun ain), one o he ‘qua ie i’ o he own: he add ess was Via (s ee ) Alessand o Poe io 100. This s ee is no a away om one o he mos amous s ee in Rome, he ‘Passeggia a del Gianicolo’ ( he walk o he Gianicolo). The Gianicolo is one o he many hills o he own and i is qui e close o he Va ican. All he people coming mine en 1932, sous le pape Pie XI ; I’a chi ec e e ai Leone Cas elli. Dans les de nie es annees, j’ai e e amene a g a i la Passeggia a chaque jou pendan plusieu s mois, pou des aisons pe sonnel- les. J’a ais, quelque ois, une imp ession de deja u. E une ois, je ealisai. Je ega dais le ((Bel ede e )) ! II es clai qu’il y a, en I alie, plusieu s loggias e bel ede es, mais si ous isi ez I’l alie e que ous mon ez la Passeggia a, au de ou d’un angle, ous au ez la m6me imp ession : il es ici, I’immeuble im- possible. Esche es econnu pou a oi u ilise les mhes images a des an- nees d’in e alle. On sai bien, pa exemple, que le po de Mal e a e e u ilise pou di e ses es ampes ealisees a des annees di e en- es. Ne peu -on pas suppose qu’il se sou in plusieu s annees ap es de ce e ou obse ee alo s qu’il g a issai le Gianicolo? C’es peu - & e une hypo hese ((impossible)) pou un immeuble ((impossible)). Pou e mine , je iens a eme cie Ma ianne Teube qui, ap es a oi u les pho os du College a Rome, m’encou agea a ec i e ce e no e en guise de jeu, .11111. 9 FIGURE 5 The College o S Josapha up he Passaggia a del Gianicolo (Pho o by he au ho ) College S -Josapha u de la Passaggia a del Gianicolo (Pho og a- phie de l'au eu ) ~~ ~~ ~ FIGURE 6 M C Esche 'Bel ede e (de ail) De ail de la Ii hog a- phie <<Bel ede e)) de M C Esche ~~~ 10 o Rome make he walk up o he Gianicolo o see all he own on he o he side o he i e Tebe . Esche made ew wo ks aking in- spi a ion om he classic monumen s o Rome. In 1934 he made an eng a ing by he i le o 'S . Pe e seen om he Gianicolo' (Fig- u e 3). One way o go om his home o he Va ican is o go down he Gianicolo by he Passeggia a (Figu e 4). In he yea s 1930-31 along he Passeggia a del Gianicolo was com- ple ed he cons uc ion o he College o S .Josapha , an Uk ainian College, p ope y o he own o he Va ican. The building was in- ished in 1932, unde he Pope Pi0 XI; he enginee was Leone Cas elli. In he las yea s I was obliged o climb up he Passeggia a e e y day o many mon hs, jus o pe sonal easons. I had he imp ession, some imes, o ' emembe ' some hing amilia . And once I ealized. I was looking a he 'Bel ede e'! (Figu e 5, 6) I is clea ha he e a e so many Loggias and Bel ede es in I aly bu i you come o I aly and you climb up he Passeggia a, a e a co - ne , you will ha e he same imp ession: he e i is, he impossible building. Esche is amous o ha ing used he same images a a dis ance o many yea s. I is well-known he example o he po o Mal a used in a ious p in s in di e en yea s. Why no suppose ha he emem- be ed many yea s a e ha owe seen while he was walking up he Gianicolo? Pe haps an 'impossible' hypo hesis o an 'impossible' building. Finally I would like o hank Ma ianne Teube who, a e seeing he pho os o he College in Rome, encou aged me o w i e his li le game. .,Ill,. [l] M.C. Esche The G aphic Wo k. Macdonald & Co., London (1961) [2] L.S. Pen ose & R. Pen ose "lmposslble objec s: a special ype 01 isual illusion:' B i . J. Psych., 49 (1958), 31 [9] M. Emme "M.C. Esche : Geome les and Impo si- bie Wo lds:' Film, se ies 'A and Ma hema ics', 27 mi- nu es, colo , sound, FILM 7 P od., Rome (1 984). [I] M. Emme "Commen s on he no e by Jean C. Rush on he appeal 01 M.C. Esche pic u es:' Leona do, 13 (1980), 209-210. [5] 8. E ns "He bepoochelde oog: Onmopellike en mee zlnnipe llpu en!' Meulenho Nede land b , Ams e dam (1986). [6] R. Pen ose "Esche and he isual ep esen a ion o ma hema ical Ideas." In "M.C. Esche : A and Science", H.S.M. Coxe e , M. Emme , R. Pen ose, M. Teube (Eds.), No h-Holland, Am- s e dam (1986), 143-157. [7] M. Emme "Commen s on A.L. Loeb's co e- spondence wi h he p aphlc a is M.C. Esche :' Leona do, 17 (1984), 200-201. [8] M.Teube "Sou ce o ambigui y in he p in s o Mau i s C. Esche :' Scien i ic Ame ican, 231 (1974), 90-104. [O] G. Esche "Le e s:' Scien i ic Ame ican, 232 (1975). 8 [lo] M.L. Teube "Pe cep ual heo y and ambigui y In he wo k 01 M.C. Esche apalns he back- g ound o 20 h cen u y a ! In "M.C. Esche : A and Science", [ll] 8. E ns "Esche 's Imposslble igu e p lnk In a new con ex :' In "M.C. Esche : A and Science", 1121 R. G ego y "Puales 01 pic u es as un ouchable objec s:' In "M.C. Esche : A and Science", [13] E.B. Ve sluis "M.C. Esche 's 'Likely Impossibili ies' using he beau y o ma hema ics o c ea e he u h o a :' In "M.C. Esche : A and Science", 159-1 78. 125-134. 135-142. 375-382. [14] G. Esche "Roman memo ies:' in "Mau i s C. Esche ", ca alogue o he exhibi ion, M. Emme , C. an Vlande en (Eds.), ls i u o Olandese di Roma (1985), (151 G. Esche "M.C. Esche a wo k:' In "M.C. Esche : A and Science", 1-11. [16] F.H. Bool, J.R. Kins , J.L. Loche , F. Wie da, 6. E ns La ie e i'oeu e de M.C. Esche . ChCne, Pa is (1981). 12-17.