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One of the many questions surrounding Leonardo’s Mona Lisa concerns the landscape visible in the portrait’s background: Does it depict an imagination of Leonardo’s mind, a real world landscape or the motif of a plane canvas that hung in Leonardo’s studio, behind the sitter? By analyzing divergences between the Mona Lisa and her Prado double that was painted in parallel but from an- other perspective the authors found mathematical evidence for the motif-canvas hypothesis: The landscape in the Prado version is 10% increased but otherwise nearly identical with the Louvre one, which indicates both painters used the same plane motif-canvas as reference.
Claus-Christian Carbon, experimental
psychologist at the Department of
General Psychology and Methodology,
University of Bamberg, D-96047
Bamberg, Germany
E-mail: <ccc@experimental->.
Vera M. Hesslinger, experimental
psychologist at the Department of
Psychology, Johannes Gutenberg
University Mainz, Germany &
Department of General Psychology and
Methodology, University of Bamberg,
Germany; E-mail:
Submitted: <leave for Editor to date>
Abstract 100 words
One of the many questions surrounding Leonardo’s
Mona Lisa concerns the landscape visible in the
portrait’s background: Does it depict an imagination
of Leonardo’s mind, a real world landscape or the
motif of a plane canvas that hung in Leonardo’s
studio, behind the sitter? By analyzing divergences
between the Mona Lisa and her Prado double that
was painted in parallel but from another perspective
we found mathematical evidence for the motif-
canvas hypothesis: The landscape in the Prado
version is 10% increased but otherwise nearly
identical with the Louvre one, which indicates both
painters used the same plane motif-canvas as refer-
When the conservators of the Museo
Nacional Del Prado in Madrid were
asked by the Louvre to lend them their
copy of “La Gioconda” to be presented
in a special exhibition in 2012, they
started to inspect the painting closely.
Though the Prado’s Gioconda and the
Louvre’s original Mona Lisa both depict
a similar looking young lady in about the
same pose, their resemblance was rather
limited at first sight, particularly because
of the dense black background of the
Prado version. So it must have been kind
of an “Aesthetic Aha!” [1] when the first
infrared examination revealed a land-
scape hidden beneath the black color.
In the course of the subsequent resto-
ration, the black overpainting was re-
moved and it became visible that the
landscapes in the Prado’s Gioconda and
the Louvre’s Mona Lisa do very much
look alike (see Fig. 1). Using infrared
and x-rays, the Prado’s conservators
further analyzed and compared the por-
traits. They found that both share several
corrections also in the tracing and lower
paint layers why it is now assumed that
the paintings were executed simultane-
ously in Leonardo’s studio [2].
On the perspective
The high visual similarity of the Prado
and the Louvre versions could addition-
ally be confirmed by means of bi-
dimensional regression analysis. Apply-
ing this method to compare the coordi-
nates of corresponding landmarks in the
two paintings (e.g., the tip of Mona Li-
sa’s nose), Carbon showed that the
landmark configurations of the face are-
as do match to a degree of above 99.8%
Still, there is a small systematic differ-
ence: The sitter is depicted from slightly
different perspectives. As we revealed
recently [4], this difference does not only
allow for reconstructing the positions of
Leonardo and the second artist relative to
each other and the sitter, respectively. It
also causes grounds for the hypothesis
that the two versions together represent a
stereo pair as the identified horizontal
disparity between the two depictions of
the sitter (about 69 mm) quite well re-
flects the perspectival difference result-
ing from human interocular distance. In
fact, it is statistically not different
(p=.13, n.s.) from the mean interocular
distance of (Italian) Caucasians being
approximately 64 mm [5]. Whether this
was or was not intended by Leonardo is
debatable indeed. Nevertheless, the Pra-
do version and the Louvre version, gen-
erated in Leonardo’s studio about 330
years before Wheatstone invented the
stereoscope [6], can be combined to an
image of Mona Lisa that has obvious
stereoscopic qualities.
On the background
The background is one of the much dis-
cussed aspects of Leonardo’s Mona Lisa.
The issue is whether it depicts just some-
thing Leonardo had imagined or rather
something real, be it a real-world land-
scape (e.g., the Val di Chiana [7]) or
simply the motif of a plane canvas that
hung in Leonardo’s studio behind the
sitter. (The same question can also be
asked with regards to the loggia, includ-
ing balustrade and the columns to the
right and left of the portrayed lady.)
In order to obtain further insights con-
cerning the background, we utilized the
above mentioned logic of analysis [3, 4]:
We defined so-called landmark points,
that is unique pictorial properties (such
as a specific tear-off edge of a mountain)
to be found in the background of both
versions. Fig. 2 displays the linear trajec-
tories between corresponding landmarks
in the Louvre version (start) and the Pra-
do version. Black arrows indicate trajec-
tories for the landscape; light blue
arrows indicate trajectories for the log-
Mere visual inspection of the trajecto-
ries reveals already that there is a con-
stant pattern of expansion, except for a
slight deviation concerning the upper left
part of the mountainside. Most im-
portantly, the expansion is not stronger
for parts that seem to be nearer (e.g., the
loggia should be the nearest while those
bizarrely shaped higher mountains in the
upper part of the painting should be the
farthest). Following Gibson’s ecological
Fig.1. La Gioconda/Mona Lisa: The Prado (left panel) and the Louvre (right panel)
this paper is "in press" (Leonardo)
approach to visual perception [8] such
a constant pattern of expansion is in-
compatible with the actual depth provid-
ed by a real landscape.
Using bi-dimensional regression anal-
ysis, we revealed constant scaling factors
that were around 10 % (Euclidean geom-
etry approach; 10.4 % for the landscape
and 10.2 % for the loggia; ps < .0001).
This means that the backgrounds of the
Prado and the Louvre versions are statis-
tically not different with regards to
shape, yet the background of the Prado
version is zoomed in by a constant factor
of 10 % as compared to the background
of the Louvre version. (The zooming can
be well observed in a movie to be re-
trieved elsewhere [4] showing the
morphing transition between both ver-
sions. Interestingly, an inconsistency can
be detected here as the foreground figure
itself is not zoomed at allthis might
reflect the process of painting the two
portraits: while the same cartoon might
have been used to transfer the outlines of
the figures onto the panels, the outlines
of the backgrounds were probably creat-
ed using a different technique.)
In sum, our analysis of the trajectories
revealed that Mona Lisa’s background
was not created after a real world land-
scape actually present during painting.
This is indicated by the constant pattern
of expansion to be found in the trajecto-
ries which does not fit the pattern that
would arise from actually present depth
information in a real-world setting. Most
probably, the background was produced
by reference to a plane landscape motif
painted on canvas. Such a canvas may
have hung behind the sitter in Leonar-
do’s studio serving as scenery. Further,
we showed that the background of the
Prado version is zoomed in as compared
to the background of the Louvre version.
This means that the artist working on the
Prado version must have stood closer to
the motif-canvas than did Leonardo.
With the given data we can, however,
not decide whether the landscape depict-
ed on the motif canvas itself was of im-
aginary or real quality, but as several
journeys to Northern Italy in the recent
years have revealed, such landscapes do
not seem to be too far away from what
we can observe in parts of Tuscany or
Lombardy. We will keep our eyes open
to find the area finally.
Concluding remarks
The present paper paradigmatically
shows how methods from mathematics
and natural sciences can enrich aesthetic
and art (history) research. Integrating
these multiple disciplines into a compre-
hensive framework provides a fascinat-
ing and promising approach for future
aesthetics research. Such a joint “new
science of aesthetics” will give the op-
portunity to recapitulate unsolved ques-
tions and opens new perspectives on
issues awaiting investigation.
References and Notes
1. Muth, C. and C.C. Carbon, The Aesthetic Aha: On
the pleasure of having insights into Gestalt. Acta
Psychologica, 2013. 144(1): p. 25-30.
2. Prado Museum (2012) Study of the Prado Museum's
copy of La Gioconda.
3. Carbon, C.C., BiDimRegression: Bidimensional
regression modeling using R. Journal of Statistical
Software, Code Snippets, 2013. 52(1): p. 1-11.
4. Carbon, C.C. and V.M. Hesslinger, Da Vinci’s
Mona Lisa entering the next dimension. Perception,
2013. 42(8): p. 887-893.
5. Farkas, L.G., M.J. Katic, and C.R. Forrest,
International anthropometric study of facial
morphology in various ethnic groups/races. J ournal
of Craniofacial Surgery, 2005. 16(4): p. 615-646.
6. Wade, N.J., On the late invention of the
stereoscope. Perception, 1987. 16(6): p. 785-818.
7. Pezzutto, D., Leonardo’s Val di Chiana map in the
Mona Lisa. Cartographica, 2011. 46(3): p. 149-159.
8. Gibson, J.J., The ecological approach to visual
perception. 1979, Boston, MA: Houghton Mifflin.
Aesthetic Aha: The effect that patterns in which
we detect objects or Gestalts are particularly
aesthetically pleasing [1].
Ecological approach (to visual perception): The
psychologist J.J. Gibson [see 7] favored direct
perception and direct realism instead of the in-
formation processing view of cognition.
Stereoscopy: A technique for creating the illu-
sion of visual depth in a plane image by means
of binocular vision [see 6].
Trajectory: A path through space [see 4].
Fig.2. The perspectival change between the backgrounds of the Louvre and the Pra-
do versions is indicated by arrows showing the linear trajectories between corre-
sponding landmark points, with the Louvre coordinates taken as starting points. The
contrast and color spectrum have been modified in order to enhance visibility of the
this paper is "in press" (Leonardo)
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Study of the Prado Museum's copy of La Gioconda
  • Prado Museum
Prado Museum (2012) Study of the Prado Museum's copy of La Gioconda.