Mona Lisa, an
Allegory of Seeing / © 1974-2003 by
Franz Gnaedinger,
MONA LISA, an Allegory of
Seeing
Noi conosciamo
chiaramente chella vista e delle veloci operationi chessia, ed in un punto vede
infinite forme: niente di meno non comprende se non una cosa per volta. Poniamo
chaso che tu lettore guarderai questa carta scritta, e subito giudicherai questa
esser piena di uarie lettere, ma non conoscierai in questo tempo che lettere
sono, ne che volino dire, onde ti bisogna fare apparola apparola verso per
verso a voler notizia d’esse lettere. (Leonardo da Vinci, B.N. 2038.
28a) Dicho
chellochio portando consecho infinite linie le quali sono appichate overo unite
con la sopravenienti chessi partano dalle chose vedute, e sola la linia di mezo
d’essa sensuale e quella che cogniosce e giudicha i chorpe colori, tutte
l’altre sono false e bugiarde (W
19148b)
L’occhio a una sola linia centrale, e tutte le chose che vengono
all’ochio per essa liniasono bene vedute. Dintorno a essa linia sono infinite
altre linie aderenti a essa centrale, le quale son di tanto minore valitudine
quanto esse son di magore remotinone dalla centrale (W 19010b) L’occhio a in se una sola linia
posta in mezo a infinite altre linie aderenti a quella la quale e detta
centrale e tutto le spetie delli obietti che venghono all’occhio per essa linia
sono perfectamente vedute sella troppa lungha disstantia non le impedisce.
Dintorno a essa linia ne sono infiniti aderenti a quella le quali son di tanta
magore o minor valitudine quanto sono vicine o remote a tal centrale (D 10b) La linia media / centrale /
maestra / principale / maestra delle altre linie / abraccia con vera cognitione
le chose grandi da lontano come le pichole da presso / si dirizza sempre a
tutti quelli obietti di che sa avere certa e vera notizia / L’occhio fa una
linia maestra / capace di comprendere i termini / L’ochio manda moltitudine di
linie che circundano questa principale di meza / linie di debole comprensione,
meno potente die conoscere il vero / onde le chose, delle quali i termini sono
giudicati di esse linie, son confuse (B.N.
2058. 23b, D 8b) //
Muovesi lamato per per la cosamata come il senso per il sensibbile e
consecho s’uniscie effassi una cosa medesima.
// l’anima, figliola della
natura // essai chelluomo emodello dello mondo // La
natura e piena d’infinite ragione che furono mai in esperienza // Le
spetie del nostro emisperio enitrino epasino con tutti li corpi cielesti per il
punto naturale nel quale s’infondano e vniscano nella penetratione e
interseghatione luna dellaltra come laltra delluna ... la spetie della luna
alloriente elle spetie del sole allocidente in tal punto naturale sono unite
... chi crederebbe chesi brevissimo spatio fussi capacie delle spetie di tutto
luniverso o magnia actione qualle ingiegnio potra penetrare tale natura qual
linghua fia quella chesplicare possa tal maraviglia cierto nessuna // Inefetto
l’omo non si uaria dalli animali senon nell’accidentale chol quale si dimostra
essere cosa diuina perche doue la natura finissce il produrre le sue spetie,
lomo quivi comincia colle cose naturali affare collaiutorio dessa natura infinite
spetie le quali nonessendo necessarie achiben si correggie come fan li animali
none disspositio cercarne (Windsor
19030 verso) // Qui
Adam, Eva di là – Oh human misery; of how many things you make yourself the
slave for money // Se tu sprezzarai la pittura, la quale è sola
imitatrice di tutte l’opere evidenti di natura, per certo tu sprezzarai una
sottile inventione, la quale con filosofica e sottile speculatione considera
tutte le qualità delle forme: mare, siti, piante, animali, herbe, fiori, le
quali sono cinte d’ombra e lume. E veramente questa èscientia e legittima
figlia di natura // Non mi legga chi non è mathematicho // e
se tu dicessi la musica essere composta di proporzion, o io con questa medesima seguito la pittura
‘Seeing’ may appear to be the simplest of acts:
we merely open our eyes and perceive the world around us. However, it is
actually a wonderfully complex physiological and psychological process. Let me
explain.
1) We see what we look at, and we see what we
know
When we open our eyes we see a multitude of
varied and shifting colors. Using our minds we turn them into objects: one of
the reds I see becomes my pullover, another my blanket, and yet another a ring
binder. I can only see the spines of the books on my shelf, but – as I know my
books well - I have a visual image of their respective covers. You may see only
your sleeping wife’s cheek and her hair on the pillow, and yet you see the
whole person so familiar to you. If a tourist asks me the way to the Chagall
windows in the Zurich Fraumünster, I virtually see the alleys and streets
threading between the mass of houses; the church I know from all sides and at
every hour of the day; the small chapel; its tall windows; and the colors in
Chagall’s beautifully stained glass. Even if a house is hidden behind foliage,
with only a few stones and bricks visible, we nevertheless perceive a hole
structure and not a ruin. .When I turn my head I see a moving kaleidoscope of
colors, and yet all the objects in my room, the walls included, stay firm, for
I know that they remain still while I move my eyes. I see only one side of the
objects in front of me, and yet I see whole objects, for I know them from all
sides. What I see and what I know and what I believe come together in my visual
perception.
Ask
someone to draw a can, and he will most probably render the lid as a kind of
circle rather than an ellipse, for he knows intellectually that the round piece
of sheet metal is formed in a circle. Beginners in artistic drawing have to
forget much of what they know in favor of what they actually see. They learn to
see anew: they discover the wonderful, stimulating garden of opposing and
blending colors, lights and shadows which are the common objects of our daily
life as they appear to our eyes. Once I read about a blind man who underwent a
successful operation on his eyes. Afterwards, could he see immediately? No: the
man was lost in a sea of colors, lights and shadows, and it took months for him
to move securely in this disturbing world. As children we learn how to see, how
to use our senses, bodies and limbs; we experience our surroundings and
gradually acquire a reliable knowledge of the world. It is this knowledge,
combined with an inborn, which allows us to perceive the world ‘simply’ by
opening our eyes.
2a) We dispose of a ‘drop’ of concentrated and
moveable attention in a wide field of stationary attention; 2b) We perceive the
thing to which we apply our moveable attention, while everything else remains
in a more subconscious background; 2c) the more moveable attention an object
attracts, the larger this object appears, and when two objects of different
sizes attract an equal amount of the moveable attention, they seem to have the
same size
Look at the moon rising above the horizon: its
beautiful, round, orange form attracts all of our moveable attention and thus
appears much larger than in a photograph. However, when the moon is seen high
on the sky we have to raise our heads to see it, and are no longer secured by
the firm objects along the horizon. We see a small disk of light swimming in an
ocean of dark air, we may feel slightly dizzy, and are therefore no longer able
to concentrate wholly on the moon – this, in my opinion, is why we now perceive
its size as a camera might. Or you may observe a herd of grazing cows. Now and
then a cow jumps, and then something peculiar happens: that cow appears to be
much nearer than her companions, if only for a fraction of a second. The
jumping animal attracts all of our moveable attention at once, and therefore
appears much larger than the other cows, yet as we know that they are more or
less the same size, our minds turn large into near. Imagine a row of people
sitting at a table. Those nearby should appear large, those farther away small.
Yet we perceive all human faces to be about the same size, for each face
attracts roughly the same amount of moveable attention. Only a face very close
up appears very large (for example when kissing), and only people very far away
appear truly small (or tiny when seen from a tower, or wandering along a hill).
Thus the drawings of children and so-called naïve artists often demonstrate a
peculiar perspective that may be called a perspective of attention.
The
moveable drop of high attention may focus on a visual contrast, a sound, a
touch, or another stimulus provided by one of our senses (there is no
outer-sensual perception, but we may have more senses than we know). It may
move from one contrast to another; it may zoom in on a tiny spot of the highest
concentration; it may expand to a larger field of weaker attention. It may even
be absorbed by the field of stationary attention – and immediately spring to
life again, for example if, while reading or daydreaming, we suddenly hear a
door slam.
3a) We see sharply by focusing our eyes on a
given object; 3b) we see clearly by looking straight at a given object
Many years ago I made a series of drawings by
means of an unusual procedure. I fixed my eyes on a delicate but strong, small
but clear point of contrast in my visual field and tried to depict and the
surrounding objects as unclearly as my eyes rendered them. What happened? As
long as my moveable attention was busy exploring the point of contrast
everything was fine. But after the spot had received lengthy and careful
examination, my moveable attention, restless, fanned out in all directions and
tried to tug my focus towards another promising point near the first. I refused
to give in, and kept my look steadily on the same tiny spot. My moveable attention
made another urgent plea to move on, which I ignored – so it freed itself from
my focus and explored my visual field on its own! At this juncture something
odd began to happen. The objects around me began to lose their shapes; a dark
portion of one object joined the dark portion of another; shapes began joining
and melting; and instead of the common objects I perceived a peculiar world of
shadows and lights that had a strange life of their own. But when I could
retain my focus no longer and finally released it, it joined my moveable
attention, and all the objects were restored at once to their proper states and
looked firm and steady as never before! Thus: as long as we move our eyes we
revive and update our transient knowledge of the many casual details of our
respective surroundings; yet if we fix on a single point in the visual field
over a long period this transient knowledge fades away and we begin to see what
we see with our eyes alone, without the help of our minds.
4) Thanks to the wonderfully complex
organization of our visual system we see a complete and ever-renewed picture of
the world we live in: an image we construct from a few impressions and which we
influence by our feelings, needs and desires
When we are in love, the world seems bright and
shining; fresh, as if wet; or in warm, soft pastel shades. But when we suffer
through love the same world may appear gray and closed. We notice what
corresponds to our being and mood, and as we fabricate our image of the world
from a few impressions we color it according to our needs, wishes and feelings.
With great difficulty I managed to keep my
focus on a single point of contrast for up to twenty minutes. It was hard work!
You will realize this if you try it for yourself. It was even harder to draw
the unclarity that I perceived peripherally, for my hand, incorporating
subconscious knowledge, freely produced all kinds of forms and shapes. One
afternoon a model was invited to our drawing class. She stood naked in front of
us, and I carried out one of my experiments: I looked straight into her eyes
and drew her body as unclearly as it appeared to me. She noticed my strange
behavior and smiled charmingly. It was my best drawing ever (unfortunately,
someone else ‘stole’ it from me). In those weeks I had a casual look at a
reproduction of the Mona Lisa – and was immediately fascinated by her smile: I
looked into her eyes, steadily and firmly as I had during my experiments, and
there was a real smile! Then I looked at her lips, and the smile disappeared. I
looked into her eyes again, more systematically. When I looked into her left
(the eye in the center of her head), the smile returned: a kind smile, a loving
smile, full of warmth and understanding. I repeated my experiments over several
weeks, and I saw many other smiles, which seemed to depend upon my own:
sometimes critical, at times closing and withdrawing; at others kind and
embracing
When
I looked into her eye, the shadows of the lips and those of her rounded cheeks
blended until I could no longer really discern the corners of her mouth; yet as
I knew that the corners were there I placed them somewhere in the field of
blending shadows, and as these places lie to the sides of the actual corners of
her mouth and slightly above them, her lips seemed to extend toward the sides,
while the ‘stroke’ of her mouth turned into a bow, and so she seemed to smile.
Yet when I looked at her lips in order to catch her smile it was gone. For I
could see her lips clearly again and discern the corners of her mouth from the
shadows on her cheeks. A surprisingly moveable smile, capable not only of
moving its appearance but also of altering its expression! The smile appeared
especially beautiful when I smiled myself. Try this: look slightly from below
at a reproduction of the Mona Lisa’s face in its original size, relax your
lips, keeping them free of any emotion, and then draw in the corners of your
mouth. As easily as you are smiling now, the shadows on the woman’s face will
blend, and your smile will reinforce hers to bring forth her most beautiful and
loving.
When
I was carrying out these experiments I had the impression that the Mona Lisa’s
changing smile was kind of an answer to me, her viewer. Why? As we don’t really
see her lips we project our feelings onto those vague shadows. My happy
surprise evoked a loving, understanding smile. Other feelings evoked different
expressions that in some way reflected my state of mind.
I
read what several authors had written on the Mona Lisa’s smile, and developed
the impression that a description of the smile could be a description of its
author. Leonardo had, after all, said that a picture must be like a mirror. His
painting of the Mona Lisa was an accurate portrait of a Florentine beauty, and
is, moreover, a mental mirror of the viewer’s nature and feelings.
When
we gaze into a normal looking glass we see our own faces; yet when we look into
the very special ‘mirror’ offered to us by a great artist – such as the Mona
Lisa by Leonardo da Vinci – we see our feelings appear on the face of a
stranger, such that we do not recognize them as our own; rather, we have the impression
that she can read our minds and souls, and that she, in order to understand us
better, adopts our feelings for a while and radiates them in her smile. We are
surprised, feel recognized, and in reaction to this new feeling her smile once
again changes, into the smile of someone we believe able to read our very
souls.
I was convinced that Leonardo da Vinci had
carried out similar experiments to my own, and was of course pleased to find
evidence of it. Over the years I have found seven passages in his surviving
written works that mention rays of vision and say that only the central rays
are strong and true, while those surrounding weak (debole) and deceitful (bugiarde).
Studying the Mona Lisa painting, I could see how the soft shadows of the cheeks
lead our focus and moveable attention to the left eye, and how the shadow of
that eye leads them right inside it, a clear and delicate point of contrast
pleasing to our moveable attention. And why does the Mona Lisa have no
eyebrows? This may have been the current fashion, but it may also have been one
that pleased Leonardo, as lack of eyebrows lays more emphasis on the eyes.
Leonardo made very sure, in all ways, that we would look into the eyes of the
Mona Lisa, and doing so be rewarded by a loving smile.
When the eye of a woman is given so much
importance, it must have special significance. What if the Mona Lisa is not
only a lively and accurate portrait of a Florentine beauty, but also an
allegorical embodiment of seeing? This woman is looking at us, and we are
looking at her. She is looking and being looked at, thus seeing both in the
active and passive form. We see with our eyes, and for this we need light. Her
eyes occupy the center of the upper part of the painting, while the brightest
part of the painting area, namely the shine on her breast, lies just above the
very center of the painting. The dark green-brown hem of her garment may bee
seen as the horizon, while the bright shining spot may represent the rising
sun, and the lines of the veil thrown over her left shoulder would symbolize
the trajectories of the sun traveling over the sky. We see the Mona Lisa
sitting in a dark room, close to the bright opening of a small balcony. If the
lateral columns were still there, we would have the strong impression that it
were a window. We stay inside the dark chamber, looking out: the chamber may
well symbolize the chamber of the eye. If so, the opening of the balcony would
represent kind of a pupil (square instead of round). The windows are to the
house what the eyes are to the body. Inside the virtual eye, the Mona Lisa
would occupy the so-called natural point hailed by Leonardo: namely that
wonderful interface of the eye where all rays of light received from seen
objects meet and join at one single point. The woman is turning towards us from
the picture plane. Her legs are parallel to the balcony, but the upper part of
her body is rotating in our direction, her face first: but her eyes have
already reached us, and gaze straight out of the picture at the viewer, joining
the plane of vision with the direction of view. Her upper part body forms a
kind of circle, and her head forms a second, smaller one around her left eye in
the center of the upper part of the painting.
To the left and right of the woman mountains,
lakes and river valleys can be seen. They form an almost prehistoric landscape
which, in its dreamlike breadth, may symbolize nature itself. It has well been
noted that in the painting we are looking down upon the left lake, but are on
the same level as the right one. You will recall the two perspectives that we
found in the Last Supper. Here we have another pair of perspectives, and they
communicate to us the same thing: that we can never really understand the world
and life by looking at it from just one point of view. Leonardo himself
concurred with the antique understanding of the living being as a tiny cosmos.
The Mona Lisa, by representing the natural point in the eye, may refer to the
ancient belief of microcosm within macrocosm (this belief may appear strange
belief, but the modern theory of fractal geometry teaches us that the same
forms may appear on the highest and deepest level of structures). In the
picture we have nature; a living being; and ‘artificial’ objects: a veil, a
dress, a stool, a balcony, a house, roads, a bridge. The woman is depicted in
obvious balance with the nature surrounding her, while the artificial objects
occupy a modest place and accompany and suit her; they also form a kind of
artificial pupil (window) in an artificial body (house). All of this may be a
symbol of art as the harmony of the artificial world with life and nature. And
yet the house lifts the Mona Lisa high above nature: it hovers above the
landscape in the background, much as would a balloon. This may symbolize that
our artificial trappings lift us higher than the lives and necessities of
common animals. In a mysterious and frequently mistranslated passage, Leonardo
wrote that humans are distinguished from the animals by our use of tools. In
one of his drawings he depicted objects falling to Earth. Above he wrote: Adam here, Eve there; and below: Oh human misery; of how many things you make
yourself the slave for money. In other passages of his writings he praised
the human eye. It would not be too difficult to find a quote for every element
of my above interpretation.
May I also mention that Leonardo’s writings are
full of geometrical sketches? He considered his art to be a science, and said
that no science can do without mathematics. Furthermore he praised proportions,
and compared his way of putting together a picture with that of composing a
piece of music: e se ti dicessi la musica
essere composta di proporzione, o io con questa medesima seguito la pittura –
and if you say that music consists of proportions, I as a painter also use that
means (namely proportions).
Take me, thus, take a look at the underlying
geometry of the Mona Lisa painting. If the columns on the sides of the balcony
were still there, the inside format would be 4:3, a much-used proportion during
the Italian Renaissance. The unit is given by the breadth of the woman’s head
on the height of the small fold in her hair veil (nearly on the level of her
eyes). Move one unit to the left and one to the right of her head and you
obtain the original width, while the height measures 4 units. The left line of
the balcony sill divides the height 4 units in the ratio 2:3 (or into 1.6 and
2.4 units). Draw two arcs of the radius 4 units around the lower corners of the
inside format. Now draw a circle, whose radius should measure 1,5 units, around
the center of the inside format. It will seize the edge of Mona Lisa’s hair.
Draw another pair of arcs with a radius 4 units around the upper corners of the
inside format. The four arcs will touch the circle in four points: the very
points where the two diagonals of the inside format 4:3 cross the circle. These
four points are very important in the geometry of this composition. Their horizontal
distances measure 1.8 units, their vertical distances 2.4 units, and their
oblique distances 3 units. Now imagine circles around all four points. Their
radii shall measure 0.1 / 0.2 / 0.3 / 0.4 / 0.5 / 0.6 / 0.7 / 0.8 / 0.9 / 1 /
1.1 / 1.2 / 1.3 / 1.4 / 1.5 / 1.6 / 1.7 / 1.8 / 1.9 / 2 / 2.1 / 2.2 / 2.3 / 2.4
… units. Apply the circles as very fine and precise grooves on a transparency
and place this over a reproduction. If seen from below and from the sides the
circles joining into S-lines. Two vertical lines follow the cheeks of the
woman, cross on her breast and follow the upper arms, while a horizontal S-line
explains the shifting of the landscape. It is all as if the figure of the woman
were created by the circles; as if Leonardo, who had carefully studied all
motions of the water, had anticipated the wave-nature of light and matter!
Moreover, four circles meet at the point where the parting in her hair begins:
a very close double point on the height 3.5 units (half a unit below the upper
edge of the inside format). The left radii measure 0.8 and 2.8 units, the right
ones 1.1 and 2.9 units, while the horizontal distance of the two very close
points measures 1.8 minus the square root of 0.55 minus the square root of 1.12
= 0.00007962… units. The numbers are based on the equations 55 = 8x8 – 3x3 =
28x28 – 27x27 and 112 = 11x11 – 3x3 = 29x29 – 27x27. The very small distance
marked by the double point may, once again, symbolize the two mental
perspectives of our human life: coming very close but never really meeting.
May I plead for the reconstruction of the
original inside format 4:3? One might simply add a pair of narrow panels and
color them according to the sky, the columns and the balcony. A new frame
should have a strength of one unit and measure 6 by 5 units (inside
measurements 4 by 3 units). Paintings by Leonardo, Raphael and others gain much
when displayed in their original formats. Leonardo’s Last Supper is a ruin of a
painting, in that it has lost much of its original color. However, its composition
has survived undamaged and still has a strong effect on its viewers.
Geometry: Non mi legga chi non è matematico / e se tu dicessi
la musica essere composta di proporzione, o io con questa medesima seguito la
pittura
For comparison: Isabella d’ Este,
reconstruction of the original format 4:3 (grid 8x6 small units); radius of the
circle of the head 1 small unit, radius of the circle of the upper part of the
body 2 small units, radius of the central circle around the first circles 3
small units, radius of the arc of the hair around the left upper corner of the
original format 4 small units
Villa Farnesina
PS. The explanation for the smile of the Mona
Lisa has been found by Marcel Duchamp (some 100 years ago), by me (1974), by
Dr. Margaret Livingstone, Harvard neurologist (2001); and presumably by several
others at various times. In an old movie the Toulouse-Lautrec character
declares that the charm of the Mona Lisa’s smile lies in her eyes ... Those
interested in Marcel Duchamp might have a look at his L.H.O.O.Q: the very fine endings of the moustache curl precisely
towards the Mona Lisa’s pupils. Pronounce the ominous letters L.H.O.O.Q in
English and you hear the word look.
Pronounce them in French and you hear the well-known iconoclasm elle a chaud au cul. Read the letters in
a spirited manner, namely by adding aire
(air), and you get elle a chaud
occulaire. In the elaborate artistic language of Marcel Duchamp, air
symbolizes the mind or spirit (ruach
in Hebrew, pneuma in Greek, spiritus in Latin) while warmth means
life in the sense of vivacity. Taken together we can read the five letters as
follows: Mona Lisa appears perfectly alive when you look into her eye ... The
wit of Marcel Duchamp’s famous joke is that while seemingly making fun of the
Mona Lisa he was actually proposing the first real interpretation of Leonardo’s
masterwork! You may also consider the enigmatic title of Marcel Duchamp’s Grand
Glass:
LA MARIEE MISE A NU PAR SES CELIBATAIRES,
MEME, MARCEL DUCHAMP
MON A
LIS A VUE PAR SES SPECTATEURS,
M’AIME, MARCEL DUCHAMP
‘Mona Lisa, looked at by so many people, loves
me, smile at me, Marcel Duchamp ...’
Readers of German may refer to my
online-essay DIE SYMBOLSPRACHEN VON MARCEL DUCHAMP UND PABLO PICASSO
Bibliography: I published my
interpretation of the Mona Lisa in various photocopied papers and books from
1974 on, for example: Mona Lisa ein
Gleichnis des Sehens, Zürich, 1989 (copies are kept in several Swiss
libraries); Amphitrite und Poseidon im
Salon der Villa Farnesina, oder “Alles ist gleich, alles ungleich” Zürich, 1974 - ?? (this project for an electronic book,. some 400 pages, also
contains a brief interpretation of the Mona Lisa, and won me a prize by the
university of Zurich, dies academicus
1994); Geometrische Bildanlagen in der
Griechischen Antike, im Mittelalter und in der italienischen Renaissance,
1979-2001 (again with a brief interpretation of the Mona Lisa and a
reconstruction of the painting’s original size)
Geometry in art (large files) gia.htm