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“‘111”’ ”11111”

THE ‘DELVEDERE’BY ESCHER: LE ‘6ELVEDERE’D’ESCHER: A MODEST HYPOTHESIS UNE MODESTE HYPOTHESE

Michele Emmer DABAC Universita della Tuscia 01 100 Viterbo, ITALIA

French translation: Traduction franpise Jean-Luc Raymond

1. HISTORY

In 1961 Escher edited a book entirely dedicated to his graphic work. He himself wrote the introduction and a small description for all the reproductions of the volume. A revised and expanded version of the book was published in 1967 [I] .

He made a classification of his works by subject. The last section is entitled ‘Impossible buildings’ [I p.161. He wrote for the lithograph ‘Belvedere’ (Figure 1):

“In the lower left foreground there lies a piece of paper on which the edges of a cube are drawn. Two small circles mark the places where edges cross each other. Which edge comes at the front and which at the back? In a three-dimensional world simultaneous front and back is an impossibility and so cannot be illustrated. Yet it is quite possible to draw an object which displays a different reality when looked at from above and from below. The lad sitting on the bench has got just such a cube-like absurdity in his hands. He gazes thoughtfully at this incomprehensible object and seems oblivious to the fact that the belvedere behind him has been built in the same im-

1. HISTOIRE

En 1961, Escher publia un livre entikrement dedi4 a son oeuvre gra- phique. 11 ecrivit lui-meme I’introduction et une c a r t e description pour chacune des reproductions apparaissant d a m le volume. On publiait en 1967 [ I ] une version revisee et augmentee de ce livre. 11 faisait une classification par sujet de ses oeuvres. La derniere sec- tion est intitulee ((lmmeubles impossibles~~. II ecrivait a propos de la lithographie ((Belvedere>, (figure 1) :

(( Au premier plan inferieurgauche, on trouve une feuille de papier sur laquelle on a dessine les argtes d’un cube. Deux petits cercles indi- quent /‘emplacement des points d’intersection des argtes. Quelle est I’arbte quipasse a I’avant et quelle est celle quipasse a l’arriere? Dans un monde tridimensionnel, la simultaneite de I’avant et de I’arrigre est une impossibilite et ne peut donc &re illustree. D’autre pan‘, il est tout a fait possible de dessiner un objet qui represente une realite diffe- rente selon qu’il est observe du dessus ou du dessous. Le garcon assis sur le banc a justement une telle absurdite e n forme de cube dans ses mains. I1 regarde pensivement cet objet incmprehensible et semble inconscient du fait que le belvedere qui se trouve derriere

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FIGURE 1

'Belvedere' Lit hog raph of M C Escher 462 x 295 c m (1 958)

((Belvedere)) Lithogra- phie de M C Escher. 462x295cm (1958)

possible style. On the floor of the lower platform, that is to say in- doors, stands a ladder which two people are busy climbing. But as soon as they arrive a floor higher they are back in the open air and have to re-enter the building. Is it any wonder that nobody in this company can be bothered about the fate of the prisoner in the dun- geon who sticks his head through the bars and bemoans his fate?"

It is well-known that the first 'impossible building' was designed by Escher completely independently from the 'impossible objects' cre- ated by L.S. and R. Penrose [2] in 1956, the so-called 'impossible triangle' and the 'impossible staircases'. This independence was made clear by Roger Penrose himself in the movie "M.C. Escher: Geometries and impossible worlds". realized in 1984 [3]. Part of the explanation of Penrose in the film was published elsewhere [4], [5, p.801. In his paper for the Proceedings of the congress M.C. Escher: ArtandScience [6, p.1501 Pen rose wrote: "In the meantime, and quite independently, Escher had produced his lithograph 'Belve- dere' which illustrates a very similar kind of impossibility."

There is no doubt that one of the explicit inspiration for the litho- graph was the 'Necker's cube' (Figure 2) (see [7]).

- FIGURE 2

The Necker s cube (1832)

~.

u

lui a ete construit dans le m i m e style impossible. Sur le sol de la plate-forme inferieure, c'est-a-dire a I'interieur, se tient une echelle sur laquelle deuxpersonnes sont en train de monter. Mais aussitdt qu'ils arrivent a I'etage du dessus, ils se retrouvent a I'exterieur et ont a rein- tegrer I'immeuble. N'est-il pas extraordinaire que personne en cette assemblee ne s'inquiete du destin du prisonnier du donjon quipasse la t i te entre les barreaux et pleure sur son sort? )) [ 1 , p.161

I1 est bien connu que ce premier 'immeuble impossible' a ete conqu par Escher de faGon completement independante des 'objets impos- sibles' Crees par L.S. et R. Penrose [2] en 1956, le soi-disant 'trian- gle impossible' et les 'escaliers impossibles'. Roger Penrose Iui- m&me mettait en evidence cette independance dans le film (( M.C. Escher: Geometries and impossible worlds,), realise en 1984 [3]. Des extraits de I'explication de Penrose emise dans le film ont ete publies ailleurs [4], [5, p.801. Dans son article pour les Comptes rendus du congres M.C. Escher: Art and Sclence [6, p.1501, Penrose ecrivait ~ ((Pendant ce temps, et de fa$on tout 4 fait independante, Escher avait produit sa lithographie 'Belvedere ' qui illustrait une im- possibilite d'un type vraiment similaire. )'

II n'y a aucun doute que, pour la lithographie, I'une des sources d'inspiration explicite fut le 'cube de Necker' (figure 2) (voir [7]).

En reponse a un article de Marianne Teuber [a]. George Escher, le fils de Maurits Cornelis, ecrivait:

(( Sur un point important, je suis en accord avec Mme Teuber: le ce- Iebre vase de Rubin, les escaliers de Schroeder et le cube de Necker ont presque certainement fourni le germe de /'inspiration de M. C. Escher pour ses travaux sur la subdivision reguliere du plan et pour plusieurs estampes. Ces concepts visuels fascinants ont passe entre ses mains, non pas par les publications psychologiques, pour les- quelles il n 'a jamais demontre d'intergt, mais. de facon plus vraisem- blable, a travers les chroniques d'enigmes et de casse-tite de perio- diques plus prosai'ques dont j'ai un vague souvenir. )) [9]

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FIGURE 3 Engraving on wood by M.C. Escher: ‘%.Peter seen from the Gianicolo”, 241 x321 cm (1934).

Gravure sur bois de M.C. Escher: <<Saint-Pierre vu du Gianicolo 241 x321 cm (1934).

Answering to an article by Marianne Teuber [8], George Escher, son of Maurits Cornelis, wrote [9]:

“On one important point I do agree with Mrs. Teuber: Rubin’s well known vase, Schroeder’s stairs and Necker’s cube did almost cer- tainly provide the seed of inspiration for M.C. Escher’s work on the regular subdivision of the plane and for many prints. There fascinat- ing visual concepts come into his hands, however, not through psy- chological publications, in which he never showed interests but more likely through the puzzle department of more prosaic periodicals of which I have a vague recollection. ”

For the possible influences of the theories on visual perception on Escher’s works see [lo], [ I l l and [12].

A propos des influences possibles des theories de la perception vi- suelle sur les travaux d’Escher, on peut consulter [lo], [I I] et [12].

Versluis [13, p.3781 a propose une hypothese differente pour la creation de ‘Belvedere’ : <c Ilmesemble quela descriptionlaplussim- ple et la plus juste de ce qu’Eschera probablement fait n’impliquepas du tout la tripoutre (le triangle impossible), et seulement un peu Necker. >)

Dans ce court article, je voudrais proposer une hypothese plus “pro- saique)), plus evidente meme: durant son sejour a Rome, Escher ((avu)) un immeuble ((impossible))!

2. HYPOlHhE II est bien connu qu’Escher a passe plusieurs annees en Italie. II habita Rome de 1923 a 1935. Son fils George, qu i naquit a Rome en 1926, a decrit la permanence de la famille Escher a Rome dans le catalogue de I’exposition de 1985 [14], [15]. O n trouvera dans [16] une biographie fidele de la periode italienne. L a famille Escher habitait a Rome dans un petit appartement au h aut de la Monte Verde (montagne verte), I’un des ‘quartieri’ de la ville ; I’adresse etait 100 Via (rue) Alessandro Poerio. Cette rue n’est pas tres eloignee de I’une des plus celebres rues de Rome, la Passeggiata del Gianicolo (la promenade du Gianicolo). Le Gianicalo est I’une des nombreuses collines de laville et est vraiment pres du Vatican. Tous les visiteurs de Rome font I’ascension du Gianicolo pour voir toute la ville de I’autre cBte de la riviere Teber. Escher a realise quelques oeuvres en tirant son inspiration des monuments classiques de Rome. En 1934, il fit une gravure intitulee ((Saint-Pierre vu du Gianicolo)) (figure 3).

L’une des f a ~ o n s de se rendre de sa demeure au Vatican etait de descendre le Gianicolo par la Passeggiata (figure 4).

Dans les annees 1930-1931, on completait la construction, en bor- dure de la Passeggiata del Gianicolo, du College de St-Josaphat, un college ukrainien propriete de la cite du Vatican. L’irnmeuble fut ter-

a

FIGURE 4

Map of Rome (detail):

0 Apartment of Escher’s family, via A. Poerio.

0 College St. Josap hat and Passeggiata del Gianicolo.

(3 %Peter, Vatican.

Carte de Rome (dktail):

0 Appartement de la famille Escher, via A. Poerio.

0 College St-Josaphat et la Passeggiata del Gianicolo.

Vatican. 0 Place Saint-Pierre,

Versluis [13, p.3781 has proposed a different hypothesis for the creation of ‘Belvedere’: “It seems to me that the simplest and more accurate description of what Escher probably did involves the tribar (the impossible triangle) not at all and Necker only slightly.”

In this short note I would like to propose a more ‘prosaic’, even ob- vious hypothesis: Escher ‘saw’ during his staying in Rome an ‘im- possible’ building!

2. HYPOTHESlS

It is well known that Escher spent many years in Italy. He lived in Rome from 1923 till 1935. His son George, who was born in Rome in 1926, described the permanence of the Escher’s family in Rome in the catalogue of the exhibition in 1985 [14], [15]. An accurate bi- ography of the Italian period can be found in [16]. The Escher fam- ily lived in Rome in a small apartment up on the Monte Verde (Green Mountain), one of the ‘quartieri’ of the town: the address was Via (street) Alessandro Poerio 100. This street is not far away from one of the most famous street in Rome, the ‘Passeggiata del Gianicolo’ (the walk of the Gianicolo). The Gianicolo is one of the many hills of the town and it is quite close to the Vatican. All the people coming

mine en 1932, sous le pape Pie XI ; I’architecte etait Leone Castelli.

Dans les dernieres annees, j’ai ete amene a gravir la Passeggiata chaque jour pendant plusieurs mois, pour des raisons personnel- les. J’avais, quelquefois, une impression de deja vu. Et une fois, je realisai. Je regardais le ((Belvedere )) !

II est clair qu’il y a, en Italie, plusieurs loggias et belvederes, mais si vous visitez I’ltalie et que vous montez la Passeggiata, au detour d’un angle, vous aurez la m6me impression : il est ici, I’immeuble im- possible.

Escher est reconnu pour avoir utilise les m h e s images a des an- nees d’intervalle. On sait bien, par exemple, que le port de Malte a ete utilise pour diverses estampes realisees a des annees differen- tes. Ne peut-on pas supposer qu’il se souvint plusieurs annees apres de cette tour observee alors qu’il gravissait le Gianicolo? C’est peut- &re une hypothese ((impossible)) pour un immeuble ((impossible)).

Pour terminer, je tiens a remercier Marianne Teuber qui, apres avoir vu les photos du College a Rome, m’encouragea a ecrire cette note en guise de jeu, .11111.

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FIGURE 5

The College of St Josaphat up the Passaggiata del Gianicolo (Photo by the author )

College St-Josaphat vu de la Passaggiata del Gianicolo (Photogra- phie de l'auteur )

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FIGURE 6

M C Escher 'Belvedere (detail)

Detail de la Iithogra- phie <<Belvedere)) de M C Escher

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to Rome make the walk up to the Gianicolo to see all the town on the other side of the river Teber. Escher made few works taking in- spiration from the classic monuments of Rome. In 1934 he made an engraving by the title of 'St. Peter seen from the Gianicolo' (Fig- ure 3).

One way to go from his home to the Vatican is to go down the Gianicolo by the Passeggiata (Figure 4).

In the years 1930-31 along the Passeggiata del Gianicolo was com- pleted the construction of the College of St.Josaphat, an Ukrainian College, property of the town of the Vatican. The building was fin- ished in 1932, under the Pope Pi0 XI; the engineer was Leone Castelli.

In the last years I was obliged to climb up the Passeggiata every day for many months, just for personal reasons. I had the impression, sometimes, to 'remember' something familiar. And once I realized.

I was looking at the 'Belvedere'! (Figure 5, 6)

It is clear that there are so many Loggias and Belvederes in Italy but if you come to Italy and you climb up the Passeggiata, after a cor- ner, you will have the same impression: here it is, the impossible building.

Escher is famous for having used the same images at a distance of many years. It is well-known the example of the port of Malta used in various prints in different years. Why not suppose that he remem- bered many years after that tower seen while he was walking up the Gianicolo? Perhaps an 'impossible' hypothesis for an 'impossible' building.

Finally I would like to thank Marianne Teuber who, after seeing the photos of the College in Rome, encouraged me to write this little game. .,Ill,.

[ l ] M.C. Escher The Graphic Work. Macdonald & Co., London (1961)

[2] L.S. Penrose & R. Penrose "lmposslble objects: a special type 01 visual illusion:' Brit. J. Psych., 49 (1958), 31

[9] M. Emmer "M.C. Escher: Geometrles and Imporsi- bie Worlds:' Film, series 'Art and Mathematics', 27 mi- nutes, color, sound, FILM 7 Prod., Rome (1 984).

[ I ] M. Emmer "Comments on the note by Jean C. Rush on the appeal 01 M.C. Escher pictures:' Leonardo, 13 (1980), 209-210.

[5] 8. Ernst "Het bepoochelde oog: Onmopellike en meerzlnnipe llpuren!' Meulenhoff Nederland bv, Amsterdam (1986).

[6] R. Penrose "Escher and the visual representation of mathematical Ideas." In "M.C. Escher: Art and Science", H.S.M. Coxeter, M. Emmer, R. Penrose, M. Teuber (Eds.), North-Holland, Am- sterdam (1986), 143-157.

[7] M. Emmer "Comments on A.L. Loeb's corre- spondence with the praphlc artist M.C. Escher:' Leonardo, 17 (1984), 200-201.

[8] M.Teuber "Source of ambiguity in the prints of Maurits C. Escher:' Scientific American, 231 (1974), 90-104.

[O] G. Escher "Letters:' Scientific American, 232 (1975). 8

[ l o ] M.L. Teuber "Perceptual theory and ambiguity In the work 01 M.C. Escher apalnst the back- ground of 20th century art! In "M.C. Escher: Art and Science",

[ l l ] 8. Ernst "Escher's Imposslble figure prlnk In a new context:' In "M.C. Escher: Art and Science",

1121 R. Gregory "Puales 01 pictures as untouchable objects:' In "M.C. Escher: Art and Science",

[13] E.B. Versluis "M.C. Escher's 'Likely Impossibilities' using the beauty of mathematics to create the truth of art:' In "M.C. Escher: Art and Science",

159-1 78.

125-134.

135-142.

375-382.

[14] G. Escher "Roman memories:' in "Maurits C. Escher", catalogue of the exhibition, M. Emmer, C. van Vlanderen (Eds.), lstituto Olandese di Roma (1985),

(151 G. Escher "M.C. Escher at work:' In "M.C. Escher: Art and Science", 1-11.

[16] F.H. Bool, J.R. Kinst, J.L. Locher, F. Wierda, 6. Ernst La vie et i'oeuvre de M.C. Escher. ChCne, Paris (1981).

12-17.