Art Compare and Contrast Essay

Leonardo’sVal di ChianaMap in theMona Lisa Donato Pezzutto London / ON / Canada Abstract Leonardo arranged the landscape in theMona Lisato hold two disjoined halves of one image. That image can be reassembled by juxtaposing two copies of the painting side by side. The newly reconstituted landscape corresponds to an actual place, as depicted in Leonardo’sVal di Chianamap. In this article, the identity of the sitter and opinions relevant to the background landscape are considered, Leonardo’s developments in the depiction of depth outlined, and his technique of topographic perspective introduced. Analysis of these observations, along with Leonardo’s investigations in perception, perspective, monocular and binocular vision, and cartography, lead to understanding of his technique.

Speculation as to Leonardo’s motivation include a pun onLa Giocondaand his attempt at stereoscopy.

Keywords:Leonardo da Vinci,Mona Lisalandscape,La Gioconda,Val di Chianamap, perception, topographic perspective, cartography, visual pun, binocular vision, stereoscopy Re´ sume´ Le´ onard de Vinci a fait le paysage du portrait deMona Lisade manie` re a` ce qu’il repre´ sente deux moitie´ s disjointes d’une image. Cette image peut eˆ tre re´ unie par juxtaposition de deux copies de l’œuvre mises coˆ te a` coˆ te. Le nouveau paysage reconstitue´ correspond a` un lieu re´ el, repre´ sente´ dans la carteVal di Chianapar Le´ onard. Dans l’article, on parle de l’identite´ deMona Lisaet des diverses opinions concernant le paysage, on e´ tudie l’e´ volution de la repre´ sentation de la profondeur par Le´ onard et on examine sa technique de perspective topographique. Une analyse de ces observations, ainsi que des e´ tudes mene´ es par Le´ onard sur la perception, la perspective, la vision monoculaire et binoculaire, et la carto- graphie permettent de mieux comprendre sa technique. Parmi les hypothe` ses e´ mises sur les motivations de Le´ onard, on inclut un jeu de mots visuel surLa Joconde(La Gioconda) et sa tentative de ste´ re´ oscopie.

Mots cle´ s:Le´ onard de Vinci, paysage du portrait deMona Lisa,La Joconde, carteVal di Chiana, perception, perspective topographique, cartographie, jeu de mots visuel, vision binoculaire, ste´ re´ oscopie All our knowledge has its origins in our perceptions.

—Leonardo da Vinci Introduction Leonardo da Vinci’sMona Lisais traditionally viewed as mysterious (see Figure 1). The enigmatic smile is em- blematic of the notion that she and Leonardo are hiding secrets from the viewer. Efforts at solving this mystery or puzzle have largely focused on the sitter, but perspective, as displayed in this work, will be shown to provide the answer to this puzzle.

Much of the effort aimed at solving the puzzle has focused on the identity of the sitter, who is generally accepted to have been Madonna Lisa Gherardini, wife of a Florentine merchant, Francesco del Giocondo – henceMona Lisaor La Gioconda(Greenstein 2004, 17–38). Many alternative candidates have been, and are still being, proposed (Zapperi 2010, 40), including the suggestion that the painting is a self-portrait of Leonardo as a woman (Schwartz, 1988, 40–48). The traditional view,as above, (Vasari 2008 [1550],294) is well supported by the work of Frank Zo¨ llner (1993, 115–38) and bolstered with recently discovered contemporaneous documentation dated October 1503. A handwritten note by Agostino Vespucci, an acquaintance of Leonardo, stated that he was working on three paint- ings, including a portrait of Lisa del Giocondo (Dorfman 2008, 39).

In his thorough review of the evidence that Lisa Gherardini is or is not the subject of the painting, Jack Greenstein (2004, 32) questions whether or not the identity of the sitter matters, as I will show below. The termgioconda can be translated from Italian as ‘‘playful or jocular.’’ Thus we can rephrase Greenstein’s conclusion as follows:

whetherLa Giocondais or is not Mona Lisa, she remains agioconda. So the exercise of identifying the sitter leads back to the conclusion that the painting is agioconda–a jocular prank or puzzle.

Cartographica 46:3, 2011, pp. 149–159 doi:10.3138/carto.46.3.149 149 The mystery has also been approached from the perspec- tive of the landscape as allegory. This approach has been thoroughly discussed by Webster Smith (1985, 183–99), who summarizes the view that theMona Lisalandscape re ects the analogy that Leonardo drew, guratively and literally, between the body of humans and the Earth as a body. Smith quotes opinions such as that of Kenneth D.

Keele: ‘‘Mona Lisarepresents Leonardo’s concept of the formulation of the earth and the analogy so vital to him of the macrocosm of the world and the microcosm of man’’ (Smith 1985, 183) and of Martin Kemp on the landscape as ‘‘a meditation on the human and terrestrial bodies’’ (Smith 1985, 184). This exploration of the land- scape as metaphor does not help to solve the puzzle but does add to the painting’s mystique. Smith does con- tribute some key observations, however:

The surfaces of the upland lakes, both to the right and to the left, appear slanted or curved rather than horizontal, as though to indicate the curvature of the earth or, rather, ‘‘the sphere of water,’’ and thus that the landscape represents not amere view but the globe, ‘‘the body of the earth’’ itself. It does appear that Leonardo introduced this effect of curvature on the basis of a concept rather than empirical observation (how comparable expanses of actual water would really look in the distance as seen from Mona Lisa’s balcony) . . .

Two sheets of water, one to the upper right, not far below the eye level of the ﬁgure, and the other, merely glimpsed, on the same level to the left, might be understood as parts of one enormous lake, and, seen together, these two indications of water describe a curvature, a bowed effect, across the panel.

Additional, concentric curves are suggested by the tongues of shoreline on the lower lake to the left and the streaks of light on its surface. ‘‘The globe of our world,’’ Leonardo says in MS A (fol. 58v) ‘‘. . . is composed of water and earth, having the shape of a sphere,’’ although it is not perfectly round ‘‘excep- ting in the places where the sea is, or marshes or other still waters.’’ In the Codex Hammer (fol. 34v) he speciﬁes that the surface of any large and still body of water is everywhere equidistant from the center of the earth, even ‘‘lakes placed at the tops of high mountains’’ and ‘‘those that give rise to great rivers.’’ His diagrams of the world, in MS A and the Codex Arundel and also MS L, show schematically something like the Mona Lisa landscape as though in the full round: the entire globe, ‘‘composed of water and earth,’’ the water surfaces all spherical, the earth here protruding above, there submerged beneath, the watery sphere. (Smith 1985, 190) The passage above reiterates the idea that Leonardo’s cosmological view is demonstrated in the painting, but it also illustrates the vast scale and depth portrayed in the landscape. The scale is ‘‘global’’; the distances portrayed require including the curvature of the Earth. This high- lights the unusual perspective demonstrated by Leonardo. Reconstituted Landscape At rst glance, the painting seems to be a simple portrait of a lady at a balcony; we see the subject sitting in a loggia with a view behind her (see Figure 1). But as we study the work, it becomes obvious that its perspective is most unusual. The sitter is shown as viewed from eye level; she is gazing directly at the viewer. The perspective of the landscape, however, is that of an aerial view; the vantage point is at, or above, the highest peaks, looking out onto a vast territory. The enormous depth of this territory con- tinues to a vaguely de ned horizon – so distant that, as noted above, the curvature of the Earth is appreciable. A large section of the cosmos is revealed. Furthermore, we see that the horizon on one side does not match the hori- zon on the other side. To reconcile this mismatch we can consider two copies of the paintings viewed in tandem with a slight gap between them (see Figures 3a and 3b below.) The juxtaposed images allow the waters, referred to above as ‘‘two sheets of water, one to the upper right, not far below the eye level of the gure, and the other, Figure 1.Leonardo da Vinci,Mona Lisa / La Gioconda (1503), oil on poplar panel, 79.4 53.4 cm. Muse´ edu Louvre, Paris. Photo credit: Re´ union des Muse´ es Nationaux / Art Resource, New York.

Donato Pezzutto 150 Cartographica 46:3, 2011, pp. 149–159 doi:10.3138/carto.46.3.149 merely glimpsed, on the same level to the left, [to] be understood as parts of one enormous lake’’ (Smith 1985, 190). With the surface of this reconstituted lake aligned, we can see that the horizon is thereby aligned, as is the edge of the balcony. The painting has deliberately been created in such a way that the view of the balcony and the landscape on one edge continues on the other (Bair, 2007, 173–77).

Compared to the old landscape, with its ambiguous sense of the ow of its waterways and roadways, or waterways that resemble roadways, the new landscape shows a logical depiction of terrain. The newly reconciled landscape shows a distant mountain lake and a closer lake, which ows into a meandering stream that joins a wider stream.

That wider stream is crossed by a bridge that leads to a road, which proceeds over a plain to a gap in a ridge of hills. The old landscape remains confusing; the new land- scape could resemble an actual place.

Drs Carlo Starnazzi and Carlo Pedretti have identi ed features in theMona Lisalandscape as matching those in Leonardo’sVal di Chianamap. The bridge, behind the subject’s left shoulder in the painting, matches the medieval Ponte Buriano, and the lake behind her right shoulder matches Lake Chiana (Owen 2003). But that is not how they should appear relative to each other. The reconstituted landscape would place these features, and others, in their proper relative positions. This new land- scape does, in fact, resemble an actual place: it is an aerial view of the Tuscan Val di Chiana region, seen from above Castiglion Fibocchi in the Pratomagno hills, looking in a south-south-easterly direction toward Castiglione del Lago on Lake Trasimeno. A review of the reconstituted landscape allows us to match the painting to the area, and that area is depicted in Leonardo’s Val di Chiana map. Hypothesis These observations yield the key hypothesis of this article:

that Leonardo incorporated the Val di Chiana, as depicted in his map, in theMona Lisalandscape. To arrive at this hypothesis, it was necessary to reconstitute that landscape, as described above. To further develop the hypothesis, the Val di Chianamap will be examined and a point-to-point correspondence of the map to the landscape will be re- viewed. Aspects of Leonardo’s landscapes will be com- pared to his maps. The analogous techniques he used in creating landscapes and maps resulted in landscapes and maps that share similar characteristics. Further support for the hypothesis and implications of accepting it follow. Observations TheVal di Chianamap (see Figure 2) is a topographic map, created by Leonardo, that shows the Chiana owing from right to left into the Arno. At the top right is LakeTrasimeno with Castiglione del Lago, then Perugia beyond them. Siena is at bottom centre, and Arezzo at top left. The Ponte Buriano can be seen as it crosses the Arno upriver from the con uence with the Chiana. This map corre- sponds well with present-day maps, but with some distor- tions, especially with the course of the Tiber River. The most obvious difference from then to now would be the Chiana itself. Leonardo’s map features what was then a wide dove-shaped lake, which has now been reduced to a narrow drainage canal. A road, corresponding to a spur of the Roman Via Cassia, is shown in part as it runs from the Arezzo plain through a gap in the ridge of hills, then along the base of the foothills below Cortina to Lake Trasimeno.

We can take Leonardo’sVal di Chianamap and consider a line from the Castiglione del Lago to Castiglion Fibocchi (just off the left-hand edge of the map). Let us call this line theligna castigliona. If we then rotate the map counter-clockwise until theligna castiglionais vertical, the line now corresponds to the seam in the reconstituted Mona Lisalandscape. The reconstituted landscape shows obvious correspondence with the repositioned map (see Figure 3c).

A review of the reconstituted landscape allows us to match the painting to the map. It may also provide insight into how the master created the work. As we follow the seam joining the two halves (theligna castigliona) from bottom to top, we nd that the landmarks correspond to the following sequence: fFrom a point above Castiglion Fibocchi we see a slope of the Pratomagno (lower left), followed by fthe con uence of the Arno with Ponte Buriano (left) and the Chiana River (right), separated by the high ground between them, then fa road meandering past Arezzo (behind the subject) to a gap in a ridge of hills (left), then fa ridge of hills (right) with the wide Chiana beyond them. Siena would be to the right (behind the sub- ject), then fthe hills around Cortona leading up to Lake Trasi- meno, with the spit of land holding Castiglione del Lago (just to the left), and, nally, fthe distant mountains to the horizon.

These features are linked together by a road. We can see its path from the Ponte Buriano, veering through the plain toward Arezzo, then through the gap in the ridge of hills, where it would merge with theligna castigliona. This route corresponds to that of the Via Setteponti – a section of the Via Cassia, mentioned above, that joined Etruscan territory to Rome through the Val di Chiana. Via Sette- ponti still runs through the Pratomagno, Castiglion Fibocchi, and Ponte Buriano to Arezzo (Repetti 1833, 375, 607, 723). There it is called the Via Cassia and pro- Leonardo’s Val di Chiana Map in theMona Lisa Cartographica 46:3, 2011, pp. 149–159 doi:10.3138/carto.46.3.149 151 ceeds past Cortona through the Val di Chiana – a route Leonardo would have used (see Figure 4).

These observations allow us to compare Leonardo’s tech- nique of creating depth in a landscape with his method of creating a topographic map. As described in hisNotebooks (Leonardo 2005, 95), features closest to the viewer are treated with full colour and lighting. Beyond that, the bands of terrain are treated with increasingly muted colour and diffused lighting, until nally the most distant lakes and mountains are depicted in a colour-drained haze. The same is true in theMona Lisa. In reviewing the work, we can start at the bottom, with proximal features such as the Pratomagno slope. This is treated with the same full colour and light as the subject; in fact, the shoulder of the hill resembles the shoulder of the sitter.

The band of features including the con uence of the Arno and the Chiana with the bridge and high ground gets less colour and light. Likewise the bands of ridges, then Lake Chiana, then the Cortona hills, are sequentially less saturated in colour and light. Finally, distant Lake Trasimeno and its surrounding mountains are washed of colour and light. Bruno Mottin, inMona Lisa: Inside the Painting, states that ‘‘this skilful use of aerial perspective,in which the depth of eld is rendered by a gradation of colors, prevents us from noticing that the landscape in theMona Lisadoes not obey the rules of traditional per- spective, but is rendered in a manner suggesting a relief map’’ (Mottin 2006, 66).

A topographic map is similarly assembled as bands of terrain sequenced one behind the other. The effect is like reading the tabs of a le cabinet. Thus Leonardo could recall a series of observations to create aerial maps or to create landscapes. TheMona Lisalandscape is not simply a bird’s-eye view from one vantage point, however. There is no one point from which an observer can view the slope of Pratomagno, the Ponte Buriano, and the sur- face of the distant, elevated Lake Trasimeno. (Castiglion Fibocchi and Castiglione del Lago are 50 km apart; see Michelin map 563.) The landscape should correspond to a bird’s-eye view along theligna castigliona, from a point above Castiglion Fibocchi over the Arno, up the Chiana valley, to Castiglione del Lago on Lake Trasimeno. If we try to re-create this using a program such as Google Earth 3D, we see slight discrepancies. First, it must be remem- bered that the now drained Chiana plain was once marsh- land. Second, the program tends to atten height and Figure 2.Leonardo da Vinci,Val di Chiana(RL12278) 1502–3, 33.8 48.8 cm, pen and ink, watercolour, bodycolour, and chalk on paper; The Royal Collection, Windsor. Photo credit: Scala / Art Resource, NY.

Donato Pezzutto 152 Cartographica 46:3, 2011, pp. 149–159 doi:10.3138/carto.46.3.149 slope, while Leonardo takes licence to enhance the hills and mountains. In particular, the high ground separating the rivers at their con uence seems too high for a vantage point on or above the Pratomagno hills; it is depicted as it would appear to an observer at a lower elevation, closer to the banks, but from that vantage point an observer would be too low to see the surface of Lake Trasimeno. So a static view does not t well.

If, instead, we take a virtual y-over, staying on the same heading as theligna castigliona(as above), we will observe the sequence of vistas used to create the map. From aboveCastiglion Fibocchi we see the slope of Pratomagno; we then descend, ying toward the rivers, and the vista of the con uence with Ponte Buriano will appear. Likewise, as we continue on the same heading but at a higher eleva- tion, the vista will match the distal sections of the land- scape on to Castiglione del Lago. In this manner we can appreciate the process that Leonardo used to compile these remembered vistas and reproduce them so faith- fully. This treatment, which can be called ‘‘topographic perspective,’’ uses the cartographic techniques of map- making to depict depth in landscapes.

Figure 3.The images in (a) and (b) show the reconstituted landscape of theMona Lisa. Compare the features along the seam of the juxtaposed halves with those along the line on theVal di Chianamap in (c). This demonstrates the painting as a puzzle and reveals its solution. Leonardo’s Val di Chiana Map in theMona Lisa Cartographica 46:3, 2011, pp. 149–159 doi:10.3138/carto.46.3.149 153 Results I have demonstrated above the rst objectives of this article, namely that 1. TheMona Lisacontains, as background, a land- scape image divided in two parts.

2. The two parts can be reconciled into one image by aligning the two lateral edges, as outlined above.

3. The reconstituted image depicts an actual place, namely the Val di Chiana as mapped by Leonardo.

4. That image consists of a sequence of vistas assem- bled in the form of a topographic map. Discussion Support for these observations would include compari- sons of the reconstituted image to photographic images obtained during an actual y-over of the Val di Chiana.

The original map and painting, along with early copies of theMona Lisa, including un-cropped versions, should be reviewed in consideration of the above. Further support would be the nding of any study sketches of the com- ponent vistas. Some support does exist in Leonardo’s works in which the landscape is treated using topographic perspective. Examples of such works, including the Annunciation, theMadonna of the Yarnwinder, and the Virgin and Child with St Anne and Lamb, are discussed inthe Appendix. The discussion that follows also bolsters the hypothesis.

Descriptions of Leonardo’s maps could well apply to his landscapes after 1500. Eugen Oberhummer, describing Leonardo’sMap of Tuscany, reveals that the mountains, mostly crowned by towns, are drawn in perspec- tive, with the light falling from the left (south). Rivers are indicated by double lines, towns and villages by vignettes. The second [Val di Chiana] map is similarly executed and embraces eastern Tuscany between Arezzo, Siena, and Perugia. The scale is about the same, but the orientation is to the east, and the light falls from the right (south). Besides the blue expanse of Lake Trasimeno with its three rather exaggerated islands, we notice in the Valle di Chiana a large and long sheet of water, no longer existing, which drains both to the Arno and the Tiber. (Oberhummer 1909, 546) Both Leonardo’s maps and his landscapes feature topogra- phy drawn in perspective, with the vertical heights ‘‘exag- gerated.’’ Vegetation and human-made features – trees, towns, bridges – are rare; when they do appear, they may be indicated as vignettes. Maps, by their nature as projec- tions of the Earth’s curved surface onto a plane, amend the laws of linear perspective. Distortions are required; straight lines become curved, and areas are expanded or contracted; the vertical axis may be attened or enhanced.

The scale, or point of view, of any vignette may not match its surroundings. The same is true of Leonardo’s land- scapes.

Oberhummer also offers his opinion on landscapes by Leonardo that display the map characteristics described above, some of which are also referred to in the Appendix:

His studies of Alpine scenery were not conﬁned to the western Alps, as is shown by his geographical observations in the Adige basin and the artistic reproduction of mountain forms evidently taken from the Dolomites, and partly, perhaps, from the Karst. His preference for steep and rugged rocks and grottoes is seen in his treatment of the background of several of his most famous pictures. Among these are one of his greatest masterpieces, the portrait ofMona Lisain the Louvre, and also theMadonna of the Rocks(‘‘La Vierge aux Rochers’’), which exists in two versions, one in the Louvre, the other in the National Gallery in London, of which the relationship has not been deﬁnitely explained; theMadonna [and Child]with St. Anna[and Lamb] and [Madonna]with the scales(‘‘La Vierge aux Balances’’) [now titledMadonna of the Yarnwinder]. (Oberhummer 1909, 560–61) Implications These observations should rekindle the ongoing debate as to the nature of Leonardo’s landscapes – whether they are reproductions of a speci c place or a synthesis of various elements (Kemp 2004, 219). In the case of theMona Lisa, along with the examples in the Appendix, it has been Figure 4.Schematic drawing outlining the features that correspond between the reconstituted landscape and the repositioned map: (1) Pratomagno, (2) Arno, (3) river conﬂuence, (4) Chiana stream, (5) Ponte Buriano, (6) ridge of hills, (7) Via Setteponti, (8) road in gap of ridge, (9) hills near Siena, (10) Chiana Lake, (11) Cortona hills, (12) Trasimeno Lake, (13) Castiglione del Lago, (14) island in Trasimeno, (14) mountains beyond lake Donato Pezzutto 154 Cartographica 46:3, 2011, pp. 149–159 doi:10.3138/carto.46.3.149 demonstrated that the landscape is actually the synthesis of a series of vistas of a speci c place. This can be restated using Leonardo’s terminology. The landscape is not simply a work offantasia(imagination); rather, Leonardo usedintelletto(the faculties of intellect) to survey and memorize an area, then recall and assemble a sequence of vistas. Hisintelletto, combined withfantasia, would transform each vista from the observed vantage point to an aerial view by imagining a ight over that area. perspective These ndings – the reconstituted landscape matching a speci c location documented as a map by Leonardo – provide a unique opportunity to study his innovative approach to perspective.

By the time Leonardo was studying in the school of Verrocchio, linear perspective had been codi ed by Filippo Brunelleschi and Leon Battista Alberti inDe picture (1435), available in Italian asDella pittura(1436) (Wright 1984, 52–71). Leonardo demonstrated his mastery of this perspective in the Cartesian grid-like study and nal work with theAdoration of the Magi(1481; Pedretti 2000, 34), which remained un nished. HisNotebooksrefer to linear perspective as ‘‘nothing else than the seeing of an object behind a sheet of glass, smooth and quite transparent, on the surface of which all the things may be marked that are behind this glass’’ (Leonardo 2005, 92). The use of the phrase ‘‘nothing else’’ makes this statement seem dismis- sive, but Leonardo may have been implying that there is more to the creation of depth than linear perspective alone.

Leonardo proceeded to consider the effect that the air between object and viewer would have on the depiction of depth. What he termed ‘‘atmospheric perspective’’ is masterfully demonstrated in theMadonna of the Rocks (1483; Pedretti 2000, 36). Yet he reached beyond atmo- spherics in considering the limitless portrayal of depth available in cartography – that is, topographic perspective – for use in painting. As I have noted, cartography allows, even demands, the manipulation of linear perspective.

With topographic perspective, a series of vistas are treated to atmospheric perspective and sequenced, as I have demonstrated, with diminished colour and light. Instead of linear perspective’s vanishing point on a distinct hori- zon, Leonardo’s landscapes recede to a suggested in nity.

Luba Freedman (1997) notes that Leonardo’s innovation of the ‘‘blurred’’ horizon was used to create the effect that, as Leonardo wrote, ‘‘one should lose oneself in look- ing’’ at theMona Lisa. motivation Any attempt to answer the question of how Leonardo came to hide a map in a landscape should start with a re- view of what is known. The means has been demonstrated by exploring his technique. The opportunity was present,as the map was likely in his workshop when he worked on the painting. Before starting theMona Lisa(1503), Leonardo had travelled through and extensively studied the Arno and Chiana valleys; he was employed as a military engineer by Cesare Borgia, notorious son of Pope Alexander VI, during Borgia’s campaign through Romagna, including the Val di Chiana. Leonardo was also involved with Niccolo` Machiavelli in a failed scheme to divert the Arno away from Pisa during the latter’s hostilities with Florence (Masters 1998, 88). Leonardo created maps of the region, including theVal di Chiana map (ca. 1502–3).

To understandwhyLeonardo came to create theMona Lisaas he did, we must look beyond his well-known pursuits in the arts and his inquiries in the sciences to consider his jocular nature. There is less scholarly material on this aspect of Leonardo’s life, but there is evidence of his fondness for puzzles and puns (Feinberg 2004, 38– 41), rebuses (Marinoni 1954, 186), and transformations (Capra 2007, 267–70). A most satisfying explanation for Leonardo’s motive in creating theMona Lisainvolves his taste for trickery. Leonardo is known to have been involved in entertainment and spectacles; for example, he apparently used the intestines of a bullock, hidden in one corner and in ated (by means of a bellows hidden in one corner) to ll a room, to crowd people into another corner (Vasari 2008, 296). Vasari also offers another anec- dote that shows the extent to which Leonardo would go just to play a practical joke. A buckler, or round shield, was left to be painted; Leonardo turned it into a monster from which issued venom and smoke, and presented it in such a way as to startle his father (Vasari 2008, 287–9).

Leonardo used perspective to create an illusion with the Mona Lisa. The viewer is certainly manipulated by the master, who fools us into the sense of depth created by the atmospherics of the landscape. Viewers accept the effect even though the rules of logic are stretched to a surrealistic breaking point; the horizons to left and right do not match, the waterways ow in a nonsensical manner, and the perspective of the background is different from that of the subject. Mona Lisa’s loggia would seem to be situated on an impossibly high tower. The sense of dis- tance is expanded beyond linear perspective. Although logically there is so much wrong with the work, emo- tionally the viewer seems compelled by it. visual pun Leonardo, as a jester performing this trick of illusion, would have been rewarded by observing the reaction it created in the viewer. The piece is relatively small (ca.

79 53 cm), and therefore portable. It was a commis- sioned portrait, but it was kept by the artist, frequently displayed to visitors, and remained with him throughout his travels, even to the court of the French king, Francis I. It has remained in France, now displayed in the Louvre museum in Paris (McMullen 1975). As discussed, whether Leonardo’s Val di Chiana Map in theMona Lisa Cartographica 46:3, 2011, pp. 149–159 doi:10.3138/carto.46.3.149 155 La Giocondais or is not Mona Lisa, she remains agioconda.

More to the point is who she is not. She is not a religious gure, nor is she a powerful and dangerous man; she is someone whom it would be safe to depict in a prank. In retrospect, a prank seems conceivable in a work that con- tains such a glaring error as a mismatched horizon and a clue in the bridge featured in the scene. The Ponte Buriano would be recognized by anyone familiar with the area. Another clue may be in the placement of the sitter’s hands and the crossed arms, meant to point out a criss- crossed background (and, some would add, a cross-dressed subject). Leonardo would have found it amusing to see who might recognize the deception.

Accepting the painting as a prank or puzzle places the Mona Lisaalongside Leonardo’s other portraits of women, which generally follow a motif or theme. His ‘‘Madonna’’ paintings follow conventional religious icon- ography, with Mary looking on the Christ Child in a scene foreshadowing the Passion. In theVirgin and Child with St Anne and Lamb, the sacri cial lamb seems the obvious reference (Pedretti 2000, 38); the winder, held as an upright cross in theMadonna of the Yarnwinder, recalls the Cruci xion (38). His non-religious female portraits, likewise, include visual emblems as clues to their identi- ties. ThePortrait of a Woman(Ginevra De’Benci) features a juniper bush behind the subject, juniper (gineproin Italian) being a pun onGinevra(Pedretti 2000, 38). In Portrait of a Lady with an Ermine, the subject fondling the pet is Cecilia Gallerani, mistress of Ludovico Sforza; Sforza apparently commissioned the work, and the ermine was a reference to him (Shell and Sironi 1992, 47–66).

Such references seem conspicuously lacking in theMona Lisa, until we consider the split landscape. It would be in keeping with Leonardo’s typical practice that theMona Lisawould also follow a theme:La Gioconda, the play- ful lady, features a prank or puzzle, namely a landscape hidden and nally revealed. stereoscopy For a genius such as Leonardo, play was a legitimate pur- suit and an opportunity for investigation and inspiration.

An example is Leonardo’s approach to the geometric games inDe Ludo geometrico; his obsessiveludo(game) of sectioning the circle by lunes can be seen as a proto- calculus (Capra 2007, 270–74). This form of amusement- as-muse also characterized his exploration of optical illusions – basically experiments in which visual variables are controlled to investigate perception. We have discussed Leonardo’s dissatisfaction with the Albertian approach to perspective, which is essentially monocular; his investiga- tion of binocular aspects of perspective is seen in the Mona Lisa. What has been described as a playful approach in the painting proved a legitimate opportunity for inves- tigating perception: ‘‘Leonardo correctly observed that because the eyes normally receive different views of a 3-Dscene, it is impossible, even in principle, to convey a full sense of 3-D on a 2-D canvas . . . He puzzled over how we can see a single world of solid objects given the dif- ferent eye views (now known as Leonardo’s paradox)’’ (Ramachandran and Rogers-Ramachandran 2009, 12).

Nicholas Wade and others explain that ‘‘Leonardo . . .

struggled with the differences between the perception of a scene and a painting of it, which he reduced to the differences between binocular and monocular vision. He could not produce on canvas what, in the terminology of [Adelbert] Ames, was an equivalent con guration. This was provided 300 years after Leonardo by Wheatstone’s stereoscope’’ (Wade, Ono, and Lillakas 2001, 231). Kim Veltman (2007) writes, ‘‘After 1500, his major paintings can be seen as attempts to address one fundamental chal- lenge: how to create effects of three-dimensional relief under carefully controlled conditions. Speaking anachron- istically, he was trying to create auto-stereoscopic effects in paintings.’’ Leonardo’s investigations of binocular perception led him to attempt his own version of a stereogram in theMona Lisa. Early copies featuring two columns have been cited to support unsubstantiated reports that the work was originally larger, then cut down to its present size. Any cropping of aMona Lisathat originally included more of the two columns remains a contentious issue. In the opinion of Martin Kemp (2004, 219), no such painting existed; copyists included full columns as their own invention. E´ lisabeth Ravaud (2006, 32) relays evidence of trimming of the unpainted border, but not beyond the barbe(i.e., the crest of gesso and paint layer meeting a support frame). This seems conclusive with respect to the painting as it exists in its present frame, but still leaves open the possibility that a preliminary sketch or a mini- mally painted larger panel existed before the painting was cropped and framed, or that the remaining panel was previously kept in a frame that depicted these columns – either painted or in relief.

While the existence of such a purported painting, holding two columns, is debatable, attempting to re-create it does prove fruitful. Consider three copies of theMona Lisa arrayed in tandem, with two columns extrapolated into position. These would create a stereoscopic arrangement.

If theMona Lisawere to succeed as a stereogram, a column would have to be the central feature of the 3D effect, prominently situated on the balcony, before the distant landscape (see Figure 5.) Figure 5 shows a painterly display of the very example dis- cussed by Leonardo in hisNotebooksunder ‘‘Differences of perception by one eye and by both eyes,’’ where the column is the ‘‘object in relieft.’’ Let the object in relieftbe seen by both eyes; if you will look at the object with the right eyem, keeping the left eyen shut, the object will appear, or ﬁll up the space, ata; and if you shut the right eye and open the left, the object (will occupy the) spaceb; and if you open both eyes, the object Donato Pezzutto 156 Cartographica 46:3, 2011, pp. 149–159 doi:10.3138/carto.46.3.149 will no longer appear ataorb, but ate,r,f. Why will not a picture seen by both eyes produce the effect of relief, as [real] relief does when seen by both eyes; and why should a picture seen with one eye give the same effect of relief as real relief would under the same conditions of light and shade?

(Leonardo 1970, 29; see Figure 6) It is more likely, however, that this attempt at stereoscopy proved unsatisfactory, for several reasons, including the choice of foreground object, the scale of the painting, the position of the sitter, and the lack of suf cient image overlap. The column is an unfortunate choice because, being smooth and round, it lacks the characteristics that would make it appear distinct from the vantage point of one eye or the other. Compared to the smaller-scale images of stereograms in popular use, such as the Magic Eye, the larger-scale images of the painting would be more dif cult for the viewer to appreciate as stereoscopic without the use of special apparatus, such as the lenses or mirrors of a Wheatstone stereoscope. On a small scale, such that the image-overlap distance is less than the intra- ocular distance, it is easier for viewers to converge their gaze to fully appreciate the phenomenon. On the larger scale of the painted panel, the image-overlap distance is much larger than the intraocular distance, which means that it is more dif cult for viewers to diverge their gaze to appreciate the phenomenon. Placing the painting at a distance where convergence rather than divergence ofgaze could be used to appreciate the phenomenon would greatly diminish the 3D effect.

Another factor that diminishes the stereoscopic effect is the placement of the sitter, which hides the meeting-point of the disjointed landscape but distracts the viewer during eye convergence. Finally, the painting fails to provide more image overlap beyond the columns. If a painting or a preliminary work (as in Figure 5) did exist, an unsatis- factory result might have led Leonardo to crop out the repeated elements. Alternatively, damage similar to the ssure on the remaining panel (Menu and others 2006, 36) might have led to the loss of part of the original; cropping to create symmetry perhaps followed, giving us the painting we know today.

TheMona Lisacan be considered Leonardo’s failed or incomplete attempt at creating a stereoscopic effect. This idea should be viewed in the context of Vasari’s state- ments inLives of the Artists: It is clearly evident that because of Leonardo’s understanding of art, he began many projects but never ﬁnished any of them, feeling that his hand could not reach artistic perfection in the works he conceived, since he envisioned such subtle, marvellous, and difﬁcult problems that his hands, while extremely skilful, were incapable of ever realizing them.

(Vasari 2008, 286–87) Despite theMona Lisa’s appearance as a completed paint- ing, Vasari believed that ‘‘after toiling over it for four years, he [Leonardo] left it un nished’’ (Vasari 2008, 294). If theMona Lisais in fact an incomplete stereogram, Vasari would be correct in referring to it as un nished.

Leonardo might well have stumbled upon the stereoscopic phenomenon, as can happen to anyone staring at a repeated geometric pattern such as tilework. Just such a repeating pattern is actually featured in the stitching on the collar of Mona Lisa’s dress. The eye fatigue that results from depicting such demanding detail would inevitably lead to the cross-eyed view needed to appreciate this small-scale stereoscopic effect. Such incidental ndings could have inspired a larger-scale attempt at stereoscopy.

Another noteworthy feature, again relating to perspective, can be seen in what remains of the columns. The bases of the columns are another departure from linear perspec- tive. The convergence lines, imagined from the parallel edges of the column bases, do not recede to a single vanishing point on the horizon, as expected; instead, the lines of the left column base converge at the sitter’s right eye, while those of the right column base converge at the sitter’s left eye. This seems to signal Leonardo’s intent for viewers to do likewise – that is, to cross our eyes so that we see the left column and background with the right eye and the right column and background with the left eye.

Another work that should be considered potentially auto- stereoscopic is Leonardo’sLast Supper. Matteo Bandello Figure 5.Mona Lisastereogram. Stare at the two white dots and cross your eyes until four dots appear, then reposition your eyes until the two central dots overlap.

Look down at the reconstituted column and landscape.

This illustrates the stereoscopic effect, easily shown on a small scale with a guide-frame that would be less satisfactorily seen on the larger scale of the actual painting. An original uncropped painting, or frame, may have included part of this image. Leonardo’s Val di Chiana Map in theMona Lisa Cartographica 46:3, 2011, pp. 149–159 doi:10.3138/carto.46.3.149 157 describes Leonardo as staring at his work: ‘‘He might labour on the piece all day without a break, then leave and not be seen for the rest of the week. He was observed on one occasion staring at the painting for several hours, then making one or two tiny brush strokes, then leaving’’ (Bandello 1554, 121). Leonardo could have been checking for stereoscopic opportunities; his composition, with the gures and food items arrayed in sequence along the horizontal line of the table, would be suitable for stereo- scopic effects (Ciuffreda and Engber 2002, 37–40). Un- fortunately the image quality of the painting may now be too deteriorated for us to see any intended auto-stereo- scopic effect. Conclusion Leonardo presents us with an enigma in theMona Lisa.

The two parts of the landscape, with their mismatched horizons and incongruous terrain, represent a puzzle to be solved. The gure,La Gioconda, hiding the unimagined con uence of this landscape, will be our playful guide in solving thisgiocondaor playful puzzle. She smiles know- ingly, looking directly at us and pointing to both edges of the panel. We follow as she indicates the hint of columns seen along those edges; we see that the bases of the columns have their lines of perspective converging not to one point but, instead, back to the eyes of Mona Lisa; the left lines converge on her right eye, the right lines on her left eye. We understand this as a direction to look back to the columns with our eyes converged. The two columns then resolve into a stereographic image of one column.

The resulting reconstituted landscape likewise is revealed – puzzle solved.

Thus we see that theMona Lisais an elaborate and sophisticated puzzle. Leonardo perpetrated this prank as a visual pun onLa Gioconda,the playful or jocular lady, and as an incomplete stereogram resulting from his investigations of binocular perception. TheMona Lisa landscape, as painted, is disjointed and unlikely, while the reconstituted landscape provides a plausible settingdisplayed as a topographic map. In fact, it matches an actual place, the Val di Chiana, as mapped by Leonardo.

This article presents ndings that should stimulate scholar- ship in the elds of art history and cartography. Art his- torians are challenged to reconsider the current interpre- tation of theMona Lisa, in particular, and of Leonardo’s landscapes, in general; cartographers are challenged to take the ndings of the painted landscapes’ matching spe- ci c locations and develop tests to measure the strength of this hypothesis. Author Information Donato Pezzutto is a graduate of the University of Western Ontario, School of Medicine, and practices family medicine in London, Ontario. His amateur pursuits include art his- tory and philosophy with an abiding interest in Leonardo and vintage maps. References Bair, D. 2007.Discovering Da Vinci’s Daughter. Raleigh, NC: Lulu Press.

Bandello, M. 1554.Novelle. Lucca: Edizioni Joker.

Capra, F. 2007.The Science of Leonardo: Inside the Mind of the Great Genius of the Renaissance. New York: Doubleday.

Ciuffreda, K.J., and K. Engber. 2002. ‘‘Is One Eye Better Than Two When Viewing Pictorial Art?’’Leonardo35 (1): 37–40.

doi:10.1162/002409402753689290.

Dorfman, J. 2008. ‘‘The ‘Mona Lisa’: Case Closed.’’Art and Anti- ques31 (3): 39–44.

Feinberg, L.J. 2004. ‘‘Visual Puns and Variable Perception:

Leonardo’sMadonna of the Yarnwinder.’’ Apollo 160: 38–41.

Freedman, L. 1997. ‘‘The ‘Blurred’ Horizon in Leonardo’s Paint- ings.’’Gazette des Beaux-Arts(ser. 6) 129: 181–94.

Greenstein, J.M. 2004. ‘‘Leonardo, Mona Lisa and La Gioconda:

Reviewing the Evidence.’’Artibus et Historiae25 (50): 17–38.

doi:10.2307/1483789.

Kemp, M. 2004.Leonardo. New York: Oxford University Press.

Leonardo da Vinci. 1970.The Notebooks of Leonardo Da Vinci, vol. 1, ed. and trans. J.P. Richter. New York: Dover Publications.

–––––. 2005.Leonardo’s Notebooks, ed. and trans. H.A. Suh. New York: Black Dog and Leventhal.

Marinoni, A. 1954. IRebus di Leonardo da Vinci, Raccolti e inter- preti. Firenze: L.S. Olschki.

Masters, R.D. 1998.Fortune Is a River: Leonardo da Vinci and Niccolo` Machiavelli’s Magniﬁcent Dream to Change the Course of Florentine History. New York: Free Press.

McMullen, R. 1975.Mona Lisa: The Picture and the Myth.

Boston: Houghton Mifﬂin.

Menu, M., J.P. Mohen, and B. Mottin, eds. 2006.Mona Lisa:

Inside the Painting. New York: Abrams. Figure 6.Differences of perception by one eye and by both eyes (image reversed to reverse mirror writing) Donato Pezzutto 158 Cartographica 46:3, 2011, pp. 149–159 doi:10.3138/carto.46.3.149 Michelin. N.d. Michelin map 563 regional, Tuscana, Umbria, San Marino, Marche, Lazio, Abruzzo.

Mottin, B. 2006. ‘‘Mona Lisa’s Wooden Support.’’ InMona Lisa:

Inside the Painting, ed. M. Menu, J.P. Mohen, and B. Mottin, 64–71. New York: Abrams.

Nicholl, C. 2004.Leonardo da Vinci: Flights of the Mind. New York: Penguin Group.

Oberhummer, E. 1909. ‘‘Leonardo Da Vinci and the Art of the Renaissance in Its Relations to Geography.’’Geographical Journal 33 (5): 540–69. doi:10.2307/1777084.

Owen, R. 2003. ‘‘Leonardo’s Maps Solve Mona Lisa Landscape Puzzle.’’Times[London], 21 June: 21.

Pedretti, C. 2000.Leonardo Da Vinci. Cobham, UK: TAJ Books.

Ramachandran, V.S., and D. Rogers-Ramachandran. 2009. ‘‘Seeing in Stereo: Illusions of Depth.’’Scientiﬁc American Mind,14 August: 12–14.

Ravaud, E. 2006. ‘‘Mona Lisa’s Wooden Support.’’ In Mona Lisa:

Inside the Painting,ed. M. Menu, J.P. Mohen, and B. Mottin, 32–37. New York: Abrams.

Repetti, E. 1833.Dizionario Geograﬁco Fisico Storico della Toscana, vol. 1. Firenze: Universita` degli Studi di Siena.

Schwartz, L. 1988. ‘‘The Mona Lisa Identiﬁcation.’’Visual Com- puter4: 40–48.

Shell, J., and G. Sironi. 1992. ‘‘Cecilia Gallerani: Leonardo’s Lady with an Ermine.’’Artibus et Historiae13 (25): 47–66.

doi:10.2307/1483456.

Smith, W. 1985. ‘‘Observations on the Mona Lisa Landscape.’’Art Bulletin67 (2): 183–99. doi:10.2307/3050907.

Veltman, K.H. 2007. ‘‘Leonardo da Vinci and Perspective.’’ Leonardo Studies, 1 December. Available at http://www.sumscorp.com/leonardo_studies/news_106.html Wade, N.J., H. Ono, and L. Lillakas. 2001. ‘‘Leonardo da Vinci’s Struggles with Representations of Reality.’’Leonardo34 (3):

231–35. doi:10.1162/002409401750286994.

Vasari, G. 2008.The Lives of the Artists[1550], trans. J.C.

Bondanella and P. Bondanella. Oxford: Oxford University Press.

Wright, D.R.E. 1984. ‘‘Alberti’sDe Pictura: Its Literary Structure and Purpose.’’Journal of the Warburg and Courtauld Institutes 47: 52–71. doi:10.2307/751438.

Zapperi, R. 2010. ‘‘Abchied von der Mona Lisa.’’Weltkunst80 (1):

40–45.

Zo¨ llner, F. 1993. ‘‘Leonardo’s Portrait of Mona Lisa del Giocondo.’’ Gazette des Beaux-Arts121: 115–38. Appendix Topographic perspective has been demonstrated here with theMona Lisaas a y-over view of the Val di Chiana.

Charles Nicholl, in his Leonardo biography (appropriately subtitledFlights of the Mind), seems to imply as much for the part of landscape visible under the wing in theAnnun- ciationwith a part of theMap of Tuscany(Nicholl 2004, 47–53). This is an early example of Leonardo’s use oftopographic perspective that corresponds to a particular place. The view is looking east from the mouth of the Arno River. At left, below the angel’s wings, are the Pisan hills, then thepalude(wetlands), with the gap between Montecatini to the north and the Monte Albano range, with the distinctive ‘‘mnemonic icon’’ peak of Monsu- mano, to the south. On the right is the view upriver, past a city that should be, but doesn’t quite resemble, Pisa, with high peaks on the south bank, to the distant and highest mountains on to the horizon. (This, incidentally, would place Leonardo’s hometown of Vinci hidden be- hind the angel’s head.) Some years after painting this work, Leonardo would produce theMap of Tuscany (c. 1503), outlining his plan to divert the Arno through Serravalle. Thus the painting came to feature the Arno with its actual course on the right and the proposed course on the left.

The landscape in theMadonna of the Yarnwindercorre- sponds to the Adda River. The view is looking north, up the Adda River from Vaprio with Trezzo sull’Adda, then steep banks upriver, then valley toward the Lecco arm of Lake Como, on the left side of the landscape. The high Alps along the horizon are seen at right. The area is fea- tured in Leonardo’sMap of the Adda at Trezzoand his drawing of theFerry Crossing at Vaprio. A problem arises because the Madonna and child are shown on high ground, with a bridge below them. The physical features t best with a view from the hills above Villa d’Adda, looking north, upriver, with a bridge at Brivio, but there is no record of such a bridge at that time. A possible solu- tion is that the bridge is at Trezzo, with the high ground near Vaprio (either imagined or the exaggerated slope of a steep and rocky riverbank), or that the initial vista is posi- tioned very far across the Po plain, in the Apennine range above Piacenza.

There are various candidate locations that may corre- spond with the landscape for theVirgin and Child with St Anne and Lamb. A good t is one based on theStorm over Valleydrawing and the Monte Rosa area discussed in Leonardo’sNotebooks. The view is looking north-west, from Mt Barone toward Mt Rosa (Dufour) across the Val di Sesia, with a valley to Rima San Giuseppe on the right and the main Sesia valley with Piode on the left.

All these landscapes, along with that in theMona Lisa, demonstrate topographic perspective. They include se- quences of mountainous terrain not appreciable from one vantage point but assembled as a series of y-over vistas, imagined above the highest peaks. It is with the human-made features (bridges and buildings), as scarce as they are, that Leonardo takes the most licence. These do represent some dif culty with matching. Allowing for Leonardo’s tendency to exaggerate the vertical height of hills and mountains, however, the natural features provide the best match for the landscapes to particular places. Leonardo’s Val di Chiana Map in theMona Lisa Cartographica 46:3, 2011, pp. 149–159 doi:10.3138/carto.46.3.149 159 Copyright of Cartographica is the property of University of Toronto Press and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission.

However, users may print, download, or email articles for individual use.