DHQ: Digital Humanities Quarterly
2019
Volume 13 Number 3
Volume 13 Number 3
Dendrography and Art History: a computer-assisted analysis of Cézanne’s Bathers.
Abstract
Using DIAS and DENDRON, computer applications designed for the study of infectious fungi and cancer cells, we forge a connection in color, composition, and theme between Paolo Veronese’s Les Noces de Cana and Paul Cézanne’s Baigneuse debout, s’essuyant les cheveux. From this connection, we bring to light a “hidden” compositional structure, heretofore unidentified, in Cézanne’s Bathers as a series. Using computer-assisted systems such as DIAS and DENDRON allowed us to detect relatedness in these paintings not necessarily visible to the human eye. With DIAS and DENDRON, we generated dendrograms that clustered paintings related in brightness, saturation, complexity, and color. After studying color, we applied DIAS to the study of Cézanne’s composition. Because Cézanne expressed Neoplatonic ideals regarding paintings in his conversations and letters, we programmed DIAS to compute axial lines and “golden sections” according to the dimensions of the square or rectangular painting under scrutiny. Using DIAS we identified the golden rectangle for Veronese’s Les Noces de Cana, Cézanne’s Baigneuse debout, s’essuyant les cheveux and Ingres’ La Source (another likely model for Baigneuse debout, s’essuyant les cheveux). From the similarities and differences between the three paintings we identified, regarding their use of axial symmetry and the golden section, we have formulated a new approach to “seeing” Cézanne’s composition in his Bather series. Cézanne’s noumenal bodies, formerly perceived as “awkward” and composed with “baffling imbalance,” we can now see as “golden.”
Figure 1.
L. Paolo Veronese, Les Noces de Cana, 1563,
oil on canvas, 22 ft. x 3 in. x 32 ft. Louvre (before conservation) R. Paul
Cézanne, Baigneuse debout, s’essuyant les
cheveux, 1869-71, oil on canvas, 11 3/8 in. x 5 1/8 in. Private
Collection. A computer-assisted comparison using the newly developed
DIAS/DENDRON ART (DDA) software of fifty-five oil paintings by Paul Cézanne,
exhibited at the Galerie Vollard, Paris, in 1895, suggests that Cézanne’s
Baigneuse debout, s’essuyant les cheveux,
is highly related to Veronese’s Les Noces de
Cana, in color, saturation, brightness, and complexity (Figures
2-4). Further computer-assisted analysis using DDA suggests that Cézanne
drew from Veronese a “hidden” compositional structure to
organize his Bather paintingsIntroduction
Wölfflin V.2
Art history as an academic discipline is relatively new [Bod 2013, 311–325]. [1] Formally established in 1834 at the University
of Berlin with the appointment of Franz Kugler (1808-1858) as the first
professor of art history, Kugler and his successors Jacob Burkhardt
(1818-1897), and Heinrich Wölfflin (1864-1945) instituted methods for the
formal analysis of art and specified many categories used today for
classifying art [Bod 2013, 316]. [2] Wölfflin is noted for “using parallel projectors in the delivery of art history
lectures so that images could be compared.”
[3]
If art history is relatively new as an academic course of study in the west,
computer-assisted analysis of art is in its “infancy,”
with Wölfflin, aided by slide projectors, as the first scholar to
demonstrate the utility of technology in the field. [4] As the editors of
Digital Art History note in their 2015
inaugural issue, Wölfflin’s mode of comparison “changed
the method of art history for good:”
“His scientific achievements were a game changer in
perceiving, analyzing, and presenting works of art in the scientific
world and beyond”
[Klinke 2015, 7].
To say that comparisons have produced the categories that structure art
history as we know it today is not overstating the case. In “Collections and/of Data: Art History and the Art Museum in
the DH Mode,” Matthew Battles and Michael Maizels stress the
centrality of the comparative slide lecture in the discipline. They write:
“The slide lecture maintains a powerful grip on the
collective art-historical imagination; it is the format through which
art historical [sic] training begins, and it is by far the most popular
means by which the discipline spreads its views and virtues to the mass
of uninitiated undergraduates.”
[5] Lev Manovich,
in the first issue of DAH concurs: “to explore is to compare. And to compare, we first need to
see”
[Manovich 2015, 33]. While computer-assisted text
analysis has a robust history since the 1950’s, the Proceedings of Computer Vision and Image Analysis of Art in
2008, 2010 and 2011 are the only journals devoted to exploring
computer-assisted methods for art analysis prior to DAH in 2015. In the 2008 Proceedings, editors David Stork and Jim Coddington propose
that computers “can reveal the fallibility in our
perception and teach all of us to see with a more informed eye and
mind”
[Stork 2008]. [6] Computer-assisted methods of analysis can “question the categories we already have, generate new
ones, or create cultural maps that relate cultural artifacts in original
ways”
[Stork 2008, 24]. Since 2008, computer scientists in
collaboration with museum curators have applied computational methods to art
for conservation, reconstruction, and restoration. X-ray imaging, infrared
reflectography, UV-induced fluorescent imaging, and photo-induced
luminescence photography can reveal the under-layers of paintings, identify
the properties of pigments and binders, authenticate artworks, detect
forgeries, and gauge optimal designs for museum and digital displays.
Computer algorithms are used to measure and count brushstrokes, sort and
classify artworks by style, identify the salient features of an artist’s
style, and produce three-dimensional models that illustrate an artist’s
working methods.
Even though digital tools make art available for viewing, pedagogy, and
research like never before, [7]
the use of data-enabled science, or algorithms, to interpret digitized art
and compare painting styles continues to provoke skepticism among humanists.
[8] As Stephen Ramsay observes in
“Humane Computing”: “They
fear an epistemology that does not merely value empirical data, but
which (in its extreme philosophical forms) considers empirical data to
be the only valid form of evidence”
[Ramsay 2016]. We believe that the visualizations produced by
computer applications do not replace direct experience of the artifact.
Correlations do not necessarily indicate causality or an ultimate
relationship in every instance. While a computer may place together certain
artists with similar styles in a cluster, this does not always imply that
there is a historical relationship between them, as their styles may have
simply undergone convergent evolution. The computer’s lack of historical and
artistic context means that the process always has a requirement of human
interpretation.
We propose here computer-assisted techniques for comparing color, saturation,
brightness and complexity between digitized paintings that updates
Wölfflin’s method. No studies of digitized art to date use dendrography, a
well-established method in computational biology since 1990. DIAS [Soll 1995, 43–104], an image analysis program, and
DENDRON [Soll 2000, 332–370], a method for generating
trees reflecting relatedness, are patented, tried-and-true software
programs. Over 400 citations in peer-reviewed literature for the basic
methods paper describing DENDRON support efficacy [Soll 1995].
Dendrography pre-dates the bourgeoning field of artificial intelligence and
machine learning. The efficacy of the very latest computer cognition systems
based in machine learning is viewed at this time as inconclusive. As Science Daily (1/7/19) reports in “Can artificial intelligence tell a teapot from a golf
ball? Severe limitations of ‘deep learning’ machines” — even
the latest programs cannot accurately identify shape when a pattern
associated with another shape is grafted onto it. Machine learning systems
“are easily fooled.”
[9] Dendrography is a traditional computer-assisted
method of comparing images and patterns. To that end, we believe that the
computer applications DIAS and DENDRON, having been validated in many
fields, may reliably “extend the senses,”
[10] of the art historian. The
visualizations they produce suggest similarities between paintings easily
missed by human beings whose capacity to compare is limited by conceptual
and subjective bias, lack of access to a work, or any number of reasons that
make creating interesting comparisons challenging.
Dendrography has enormously productive applications for the comparison of
formal and iconographic elements in paintings. Since formal analysis is
often viewed as outdated in today’s art history, its potential as a subject
for computational analysis has been overlooked (except for the few
curatorial forays in this direction). As such, our approach not only
attempts to see the value of the computational method, but also what DENDRON
and DIAS may do to open up in surprising new ways what has been considered a
finished part of the field. This may be the first study in digital art
history that uses dendrography to cluster similar paintings and that employs
computer programs to calculate golden rectangles in paintings for
comparative purposes. The ever-growing raft of digitized paintings online,
and the continual improvement of digital photography, calls for
computer-assisted methods as long as these programs are reliable, the
questions posed are appropriate for computer-assisted investigation, and the
final interpretations are considered just that, namely interpretations.
Using the newly customized DIAS/DENDRON (DDA) programs (Appendix I), we investigate in Part I a
persistent connection between Les Noces de Cana
by Veronese and Cézanne’s first female bather La
Baigneuse debout, s’essuyant les cheveux. Les Noces de Cana is enormous in scale, more than twenty-two
feet by thirty-two feet in height and length, while the baigneuse is tiny, only eleven inches in height and five inches
in width. Les Noces de Cana’s subject matter is
biblical, Christ transforming water into wine at the marriage feast, while
Cézanne’s work is prosaic, a woman drying her hair after a bath. A
traditional art historian, guided by genre expectations, might conclude that
scale and theme obviate potential connections between the works, but using
DDA, which normalizes scale, we can grasp surprising connections. Now, using
DDA analysis, we can see how Cézanne capitalizes on Veronese’s color scheme
in his first female baigneuse. We may also use
DDA to suggest new approaches to old problems. For example, Cézanne painted
over eighty bathers in his lifetime, but these paintings continue to mystify
scholars. To date, they are mostly interpreted in psychanalytic terms as
representing Cézanne’s repressed sexuality and/or aggression.[11] When we saw that Cézanne’s baigneuse might be intimately connected to Les Noces de Cana, we then employed DDA to explore
potential similarities in composition. In Part 2, using DDA analysis, we
discovered that the composition of Les Noces de
Cana is based on axial symmetry and the golden ratio (phi). When
we apply DDA to identify axial symmetry and the golden ratio to Baigneuse debout, s’essuyant les cheveux and the
rest of Cézanne’s bathers, we find that Cézanne imitates the composition of
Les Noces de Cana in virtually every bather
painting. Based on axial symmetry and the golden section, then, we have
formulated a computer-assisted approach to “seeing”
Cézanne’s composition in his Bather series. Cézanne’s bathers, formerly
perceived as “awkward” and composed with “baffling imbalance,” can now be viewed as “golden”
[Danchev 2013, 11]. With DDA, we find that Cézanne is
more likely guided by mathematics in designing his bather paintings, rather
than by unconscious drives or motives.
This approach is an intervention in the newly established trend within the
digital humanities of the “micro-digital
humanities.”[12] We are
not, as Michael Greenhalgh imagines of digital art historians, “throw[ing]
data” at the computer while hoping that somehow “the computer will make sense of them”
[Greenhalgh]. We are not sifting “the
great unknown”
[Cohen 2009] for connections between texts or visual images,
instead, we are comparing smaller curated datasets in order to measure
influence between a master and student, a source and a re-imagining.[13] In this case, we are
comparing fifty-five curated digital facsimiles of Cézanne’s oil paintings
exhibited in Ambroise Vollard’s 1895 Salon to Veronese’s Le Noces de Cana, a source Cézanne
identified as influential to him as an artist.
Standing before Les Noces de Cana, Cézanne is
reported to have said regarding its color:
Art Historian Susan Sidlauskas describes Cézanne’s experience of the Veronese painting as like “a mystic’s fusion with the deity” [Sidlauskus 2004, 12]. Cézanne thought of Veronese’s colors as “great noumenal entities, living ideas, creatures of pure reason…with whom we might correspond” [Doran 2001, 124]. By “great machine,” we take Cézanne to mean that Veronese’s work delivers to the aspiring painter figure studies, compositions, color combinations and more, structures that an artist can imitate.That is what a painting should give us, a harmonious warmth, an abyss in which the eye can sink, a silent germination. A state of grace in colors…To love a painting, first you have to drink it in this way, in long drafts, lose consciousness; descend with the painter into the dark, complicated roots of objects come up again with colors, bloom with them in the sun. You have to know how to see, to feel, especially in front of a great machine such as the one Veronese built [Doran 2001, 133].
Quality of digital reproductions
As Philip Ball observes in Bright Earth, “all reproductions are approximations”
[Ball 2001, 271].[14] And in regards to Les Noces
de Cana and Cézanne’s bathers, we must ask of any facsimile
whether it is “well or badly reproduced”
[Latour 2011, 278]. Digital reproductions must be as
close to the original as possible. Bruno Latour and Adam Lowe discuss at
length Les Noces de Cana’s complex
“trajectory” as an image. What Cézanne saw between
1861, his first trip to Paris, until his death in 1906 is not the Les Noces de Cana that we see now in the Louvre,
as conservationist efforts have modified the painting. Currently Les Noces de Cana exists in its
“original” (though repainted) version at the Louvre,
and it exists in a fully “restored” version, based on
digitization, housed in its “original” context, in a
Benedictine refectory in Venice. The Louvre Les Noces
de Cana is considerably darker than the Benedictine digital
facsimile. The coat of the server depicted in the foreground of the Louvre
Les Noces de Cana was originally red but
was changed to green in 1989. Thus, no version today is exactly what Cézanne
saw. For our purposes here, we use a digitized image of the pre-1989 Les Noces de Cana, with the tabard in his
“original” red coat. This, perhaps begrimed with more
dust, is the closest “approximation” to what Cézanne
would have seen. However, we demonstrate that DDA grouped Baigneuse debout, s’essuyant les cheveux in the
same cluster with both renditions of Le Noces de
Cana in dendrograms (Appendix
II).
Choosing Cézanne’s paintings for computer-assisted analysis is also
complicated. Cézanne left many works unfinished, therefore, we selected for
this study paintings exhibited during his lifetime. The paintings exhibited
in the 1895 Vollard exhibition is an exemplary dataset for computation, as
it was Cézanne’s first one-man show, with examples of paintings from every
stage of his development. Most important, we can presume Ambroise Vollard,
Cézanne’s friend and patron exhibited the works as
“finished” with the artist’s support. For information
about Cézanne’s paintings, and for digital facsimiles, we relied on John
Rewald’s printed Catalogue Raisonné and Walter
Feichenfeldt, Jayne Warman and David Nash’s The
Paintings of Paul Cézanne: an Online Catalogue Raisonné
[Rewald 1996]. Supplemental
Table I lists all paintings used for this study and their digital
and material provenance. All digital images are in the public domain for
research and educational use. When there were multiple versions of digitized
images on the web with different levels of brightness, saturation, and
coloring, we consulted the online Catalogue
Raisonné, for the best match, or the websites of the museums
that housed the work. In many cases, we checked digital facsimiles against
original paintings on site in New York, Philadelphia, Chicago, and Detroit,
not only for accuracy in color, brightness, and saturation, but also for
correct margin between figure and frame for our geometric partitioning.
Generating dendrograms
The software program we have developed to compare digitized paintings is a
composite of two patented programs DIAS (US patent #5,655,028 1997) and
DENDRON (US patent #5,400,249 1995). The customized program DDA, allows the
user to store and sort digitized images of pictures in a data file, measure
parameters for comparison and then generate dendrograms, visual phylogenies
of relatedness based on one or any combination of parameters. Both DIAS and
DENDRON began development in the late 1980’s. DIAS was developed to analyze
cell morphology, shape, cell movement and the dynamics of populations of
cells, and has recently been used to study tumorigenesis in 2D and 3D.
Dendron was developed to analyze and compare DNA fingerprints of infectious
organisms and has been used to follow the progression of diseases in human
populations. In “The Ins and Outs of DNA Fingerprinting
the Infectious Fungi,” DENDRON is described in terms that we
apply here for the comparison of paintings between the same or different
painters. The combined programs, including the parameters we have measured
and compared, and the generation of dendrograms, are described in Appendix I
in more detail, with relevant references. In brief, images of a collection
of pictures were scanned into a DDA data file. The DIAS portion of the
program then automatically computed nine parameters, which included
brightness, saturation, complexity, redness, orangeness, yellowness,
greenness, blueness and purpleness. These parameters are described in
Appendix I. To assess a similarity coefficient between two pictures for any
one of these parameters or amongst any combination of these parameters, each
parameter is assessed in a range of 0.00 to 1.00, 0.00 representing no
relatedness and 0.01 to 1.00 representing progressively increasing values.
The similarity coefficient (SAB) for one or any
combination of parameters is then computed between all pairs of paintings in
a collection, generating a matrix of SAB’s as
demonstrated in Appendix I, Table A. Based on the matrix of SAB’s, a dendrogram (i.e., a phylogenetic tree of
relatedness) is then generated by the unweighted pairgroup method based upon
the arithmetic averages (UPGMA), originally used by Rohlf [Rohlf 1963], discussed in detail by Sneath and Sokal [Sneath and Sokal 1973] and developed for DENDRON by Schmid et al. [Schmid 1990]. The accuracy of the program was validated by
Pujol et al [Lockhart et. al. 1997], with more than 410 citations in
the literature reported by Google Scholar just for the methods paper “The Ins and Outs of Fingerprinting for Infectious
Fungi”
[Soll 2000]. In the generated dendrogram (e.g., in Figures 2
and 3), the nodes (i.e., vertical connections) approximate the hierarchy of
similarity. An arbitrary threshold is drawn as a black vertical line through
the dendrogram simply is a tool for visualizing the refutation of similarity
or clades, related groups and clusters of paintings.
Analysis of relatedness using dendrography
Using DDA, we compared Cézanne’s fifty-five oil paintings presented at the
Galerie Vollard in 1895 and Veronese’s Les Noces de
Cana. The SAB’s for all DIAS
parameters were used in generating the dendrogram in Figure 2. The
dendrogram generated in this case could be separated into seven clades, a
through f, using an SAB threshold of 0.83. Both
Veronese’s Les Noces de Cana, Baigneuse debout, s’essuyant les cheveux and six
additional Cézanne paintings were included in clade f (Figure 2).
Interestingly, of the three paintings painted in the 1860s by Cézanne after
first viewing Les Noces de Cana, two of them,
Baigneuse debout, s’essuyant les cheveux
(1869) and L’orgie de Nabuchodonosor (1967),
resided in clade f, and were highly related. Since it was obvious that the
one color assessed by DIAS in the unrestored Les Noces
de Cana that appeared disproportionally faded was “green”, (and since the painting lacks the heavy
green coat of the tabard as in post-1989 retouched versions), we generated a
dendrogram in which the composite SAB was computed
for all parameters but green (see table in the right lower corner of Figure
3). Using a high threshold, 14 clades were distinguished (Figure 3). One
clade, b, clustered six pictures, which included Baigneuse debout, s’essuyant les cheveux and Les Noces de Cana in a subclade with a node of
0.92 and a subcluster of four paintings, three of which (Les Begonias, La
Baignade, Nature Morte) also
resided in the clade b, containing Les Noces de
Cana and Baigneuse debout, s’essuyant les
cheveux, using all parameters in Figure 2. Since a digital
version of the restored Les Noces de Cana is
widely accessable on the web, we generated a dendrogram using the complete
collection of parameters and obtained similar clustering of the restored
facsimile of Les Noces de Cana and Cézanne’s
Baigneuse debout, s’essuyant les cheveux
(Appendix II). Again, Cézanne’s L’Orgie de Nabuchodonosor clustered with
Veronese’s Les Noces de Cana and Cézanne’s
Baigneuse debout, s’essuyant les cheveux.
The two Cézanne paintings were painted in 1867 and 1869, respectively, so
both reflect early works potentially highly related to Le Noce de Cana. We also analyzed the restored Les Noces de Cana facsimile and the Cézanne
collection using all parameters but green, and found that the restored
facsimile was in a cluster containing Cézanne’s Baigneuse debout, s’essuyant les cheveux and the other
clustered paintings (Appendix II). We
generated a dendrogram of the Cézanne collection that included, both the
unrestored and restored Les Noces de Cana. The
Baigneuse debout, s’essuyant les cheveux
and both unrestored and restored Les Noces de
Cana paintings clustered, and the cluster contained the same
additional paintings in the clusters of the dendrograms generated with
either the unrestored Les Noces de Cana alone
or the restored Les Noces de Cana (Appendix II, Figure A, B, C, D). In support of
the similarity assessed by DDA in the collection in Figure 2, we generated a
dendrogram that included Veronese’s Les Noces de
Cana, Cézanne’s Baigneuse debout,
s’essuyant les cheveux, and 19 paintings by other artists
including Delacroix, Rubens and Tintoretto, all of which were shown in the
Louvre between 1861 and 1906 (Appendix III,
Figure A). The Les Noces de Cana and Baigneuse debout, s’essuyant les cheveux paintings
grouped into a primary cluster, indicated by thick red lines, again
indicating not only the similarity between Veronese’s Les Noce de Cana and Cézanne’s Baigneuse paintings, but also the accuracy of the DDA
programs.
Figure 2.
1895 Galerie Vollard paintings and Les Noces de
Cana. The dendrogram sorted 56 digitized oil paintings (55
by Cézanne, 1 by Veronese) into clades based on relatedness defined by
six parameters. The vertical black line represents an arbitrary
threshold (.83) to define moderately related clusters of paintings based
on all parameters maximized. These major clades are noted (a through f)
by shorter and thinner vertical bars to the right of the dendrogram.
Paul Cézanne’s Baigneuse debout, s’essuyant les
cheveux and Paolo Veronese’s Les Noces
de Cana are connected at .83.In our first experiment (Figure 2), we found potential correlation between
the Les Noces de Cana and the Baigneuse, along with other paintings. In our
second experiment (Figure 3), we found that when we control for green,
Les Noces de Cana and the Baigneuse correlate more closely at .9.
Figure 3.
1895 Galerie Vollard paintings and the unrestored Les Noces de Cana, controlled for green.In Figure 3, Les Noces de Cana and Baigneuse debout, s’essuyant les cheveux cluster
with three other paintings: Les Bégonias,
La Baignade, Pommes et
Linge, and Nature Morte at .9 with
Le Noces de Cana and Baigneuse debout, s’essuyant les cheveux further discriminating
as similar at .91.
Part 2. Hidden Patterns
Just like Veronese’s Les Noces de Cana, Paul
Cézanne’s paintings continue to inspire wonder in his admirers. His
contemporaries, Renoir and Matisse, spoke of his deployment of color and
composition in godlike terms, while scholars today “struggle to
know” his secret. Cézanne’s last words in 1904 to the young
painter Emile Bernard heighten the sense of mystery and unknowability that
surround the painter’s process. Richard Shiff’s 2004 Introduction to
Conversations with Cézanne illustrates this mystery:
“He takes his secret to the grave,” remarked Bernard to his wife, upon receiving word of Cézanne’s death: “he wrote that he wanted to tell me everything, and I don’t know what he meant by that.” Regretting his failure to visit Aix in 1906 as planned, Bernard knew that Cézanne, only a month before, had suggested that both men would better “explain themselves” whenever they finally met again in person. Even more poignantly, Bernard could recall the cryptic promise Cézanne included in a letter of the previous year: “I owe you the truth in painting [en peinture], and I will tell it to you” [Doran 2001, xxxiv].
Shiff concludes, “Like Bernard-like Cézanne himself-we
struggle to know” (my italics). We propose Cézanne worked from a
plan, and that his comments to Bernard indicate guardedness about sharing
his process. As he advised the fellow painter Maurice Denis: “You have to have a method. My father [said], ‘People
have to play games.’ That’s what I search for in
painting...theories, sensations and theories...I wanted to copy nature
but I never could do it”
[Doran 2001, 93–94]. In this second part of our analysis
we identified parameters for DDA which we believed would allow us to begin
to assess similarities based on composition. We tested whether Les Noces de Cana and Baigneuse debout, s’essuyant les cheveux shared potential
compositional similarities, and we sought parameters related to composition
that could be quantified. Because of Cézanne’s frequent references to “harmony” in his conversations and letters, and his
documented love for classical Greek and Roman culture, we turned to
Classical conceptions of harmony, based on numbers and geometry, for
parameters that we could quantify.
In this section, we compare only the relationship between axial lines and
golden rectangles as determined by the picture’s frame in Les Noces de Cana and Baigneuse debout, s’essuyant les cheveux. We decided to
automate identification of the center and central axis of a painting,
because of their technical importance to an artist, and because of their
semantic weight. For Rudolf Arnheim, the dead center of a painting is not
dead but “alive with tension”
[Arnheim 1974, 11, 16]. The vertical and horizontal
bisecting lines emanating from the center establish a “solid spatial trellis in the brain.” An artist must master the
axis first, according to Arnheim, as it “remains the
base of reference that alone make obliqueness possible. Obliqueness is
always perceived as a deviation [from the axis] hence its strongly
dynamic character.” Computer-assisted methods for identifying
centers and axial lines are helpful as these can be mis-apprehended by a
viewer. For example, upon first glance, many people see Christ as the center
of Les Noces de Cana, as opposed to the men
carving meat on the balustrade above him. Once we used DDA to identify the
center and the horizontal and vertical bisecting lines of Les Noces de Cana, we chose to automate the
identification of golden sections in a painting as determined by the square
picture plane. In Appendix IV, we present the steps in the DDA program
employed to automatically identify a number of geometric landmarks including
what we have defined as the “golden window,” in a
painting. This involves identifying the “golden
rectangle” and the axial lines bisecting both vertically and
horizontally the picture plane.
Many scholars have attempted to find hidden patterns in art works based on
numbers. Most recently, Robert Bork’s studies of golden sections in medieval
cathedral ground plans show that for centuries, artists and architects have
used the mysterious divine proportion or golden ratio (1.618...) in their
designs [Bork 2012]. For Arnheim, the golden ratio is
satisfying “because of its combination of unity and
dynamic variety, whole and parts are nicely adjusted in strength so that
the whole prevails without being threatened by a split, but at the same
time, the parts retain some self-sufficiency”
[Arnheim 1974]. Veronese and Cézanne would have been familiar
with Luca Pacioli’s handbook for artists, De Divina
Proportione, published in 1509. Seventy-one chapters are
dedicated to demonstrating the “golden” section, a mathematical
proportion based on an equation that produces “phi” or the never-ending
value of 1.618... in artworks [Pacioli 2014]. Cézanne’s
contemporary Symbolists, Odilon Redon and Paul Serusier, considered Platonic
geometry, holy, or mystical, because it appeared in nature as repeated
numbers and patterns. Cézanne and Veronese absorbed the concept of divine
proportion in their training, and when they had the problem of creating a
two-dimensional structure that expressed “witnessing the
holy,” they found a rule or “game” in
the golden section that suited their purposes. Using DDA, as a tool to
section a painting geometrically, we show that the golden section may have a
formal and thematic purpose for Veronese in Les Noces
de Cana (Figure 4) and that
Cézanne might have elaborated on this compositional structure in his Bather
paintings.
While we could have discovered this hidden composition by applying a ruler
and compass to reproductions from books, the advantage of DDA in studying
composition is the mechanization of the geometer’s tools, and the quantity
of digital reproductions we can quickly, and more precisely, “rule”
than with human hands. It also allows for the quantification of parameters
from the digitized image for further comparison using DDA software. DDA
determines and saves golden ratio rectangles from any point on a painting,
drawing up to nine symmetrical vertical or horizontal staves across a
painting, and imposing and saving geometrical shapes on digital paintings.
Since these parameters are associated with Neoplatonic ideals and classical
harmony, we feel these might have bearing on Cézanne’s painterly concerns in
his Bathers series. Baigneuse debout, s’essuyant les cheveux achieves its
uniqueness not only from a masterful deployment of color modelled on
Veronese’s Les Noces de Cana, but also from its
invisible scaffolding, based on Platonic geometry. We believe that Cézanne
hides this “game” in plain sight.
Cézanne left eighty Bather paintings in various
states of completion after his death in 1906 at the age of 68. He repeats
this, heretofore unidentified, compositional structure throughout his Bather
series. Since Cézanne appears to have modeled his first female bather on
Les Noces de Cana, as our dendrograms
imply, it is likely that Cézanne is linking Les Noces
de Cana and Baigneuse debout, s’essuyant
les cheveux semantically. The subject of Les Noces de Cana is a wedding feast at Canaan where Christ
performs the miracle of turning water into wine, a potent metaphor for the
artist translating raw materials into representations. Christ transmutes
water, something common, into something holy, strange, and magical;
likewise, Cézanne divinizes his bathers; he makes them noumenal, by way of
his predecessor Veronese — through color harmonies and divine geometry.
Cézanne viewed geometry as a divine architecture, and he understood the
center of a bounded four-sided square to be its axial eye. The center of a
painting represents the “truth” or the “eye of god”
[Hendrix 2004]. In its aggressively axial construction Figure 4, Veronese appears to take account of
the square frame, its center, the golden rectangle, and the golden window in
organizing his composition for thematic effect (Appendix IV). The sacrificial meat above Christ’s head is at the
exact center of Les Noces de Cana. Like a
blade, the vertical and horizontal axes divide the meat. The axis signifies
that the focus of the painting is sacrifice, and its cognates, Christ,
directly below the sacrificial meat, and the dog at the bottom of the
painting. The vertical axis bisecting the painting runs directly through
Christ’s right eye and the left eye of the dog. As a dog signifies loyalty
in medieval/renaissance Christian iconography, the implied vertical line
uniting sacrifice/Christ’s eye/loyalty appears to emphasize Veronese’s aim
of producing a sensually enlightening painting. To make the painting’s
purpose legible, he provides a strong horizontal balcony across the middle
of the painting above Christ’s head. The top of the balcony passes through
the exact center of the painting.
Figure 4.
Les Noces de Cana (restored
version). Golden rectangle, golden window, horizontal and vertical
bisecting lines.In Les Noces de Cana
Figure 4, just as axial intersection
emphasizes theme, so too does the golden section. The golden section
intersects Christ’s eyes, and the eyes or mouths of the witnesses flanking
Christ. The “golden window” we have identified frames a
quarter of Christ’s face, partial faces of three witnesses to his left
(specifically through the mouth and eyes). Then, above and behind them,
three convex columns supporting the balustrade where butchers are preparing
sacrificial meat. Technically, the benefit of a “golden
window” for Veronese is that it allows him to represent depth
by mediating the distance between flat wall and blue sky with a band of
recessing modulations. In the golden window of Figure 4, we glimpse the
tablecloth behind the columns of the balustrade above Christ’s head, as well
as the robes of the butcher, and a building in the distance. In Figure 4,
the golden window underscores theme and creates a sense of depth or of
“descended” figures within the composition of the
painting. As Christ has “descended” from his godlike
nature to be among humans, the golden ratio becomes the line along which
Veronese arranges Christ and his witnesses at the feast. In Figure 5, we see
the lowering effect afforded by the golden window. Through the golden
window, we see Cézanne’s central bather (whose right knee and shoulder are
aligned with the vertical axis of the picture frame), descending into a pool
of water. We can now say that, in addition to discovering surprising
connections in color, saturation, complexity and brightness in paintings,
there are landmarks in paintings that DDA automatically computes. These are
the center of the painting, the horizontal and vertical bisecting lines
(axis), the golden rectangle, the golden strips (the space between the
vertical and horizontal bisecting lines and the golden sections of the upper
right and lower left sides of the picture plane), and the golden window
(located at the right base of the golden rectangle).
Figure 5.
Golden Window: Cézanne signaling its
“lowering” effect. Paul Cézanne, Baigneurs, 1890, 15 3/8 x 20 7/8in. In
addition to being the source as life and the means of ritual
purification, water has literary associations with the bucolic poetry of
Theocritus and Virgil.Like Leonardo da Vinci, Cézanne thought paintings were superior to poems
because they inspired reverence in viewers [Kemp 1989, 28]. As he expressed to Leo Larguier, “Art is a religion.
Its goal is the elevation of thought”
[Doran 2001, 17]. He wanted to create in paintings a
“harmony parallel to nature,” a noumenon, in
that the painting would be a thing in itself (with a life of its own) whose
purpose was to “enlighten”
[Doran 2001, 39]. Cézanne stated his commitment to the
“law of harmony,” numerical patterns he saw
in nature, throughout his letters and conversations. He stated: “To read nature is to see it beneath the veil of
interpretation as colored patches succeeding one another according to a
law of harmony. The major hues are thus analyzed through
modulations”” [Doran 2001, 38].
By harmony, Cézanne means harmonia in a Platonic sense of “fitting together:” not only the ideal forms and
proportional arrangements of forms based on number found in nature, but also
as “the reconciliation of opposites by a third element,
bringing them all into a new unity”
[Schneider 1994, 236]. Cézanne synthesized contrasts: he
“modulated” color as a way of building form.
He saw the task of reconciling opposites as a magician’s task. He stated:
“Painting is not beautiful if the surface plane
remains flat. Objects must turn, grow distant, live. That is the magic
of our art”
[Doran 2001, 66]. To restate, in the golden section,
Cézanne finds a way to represent infinity in his paintings, which for him,
like the Symbolists, was the essence of nature. In the synthesis of
opposites, whether in color contrasts, spatial “near and
far,” or “up and down,” Cézanne
creates a “harmonious” painting.
Cézanne and Ingres
Certainly, Les Noces de Cana is not the sole
model for Baigneuse debout, s’essuyant les
cheveux. Relevant to our purposes here, a study of Cézanne’s
Bathers, as a series, from their origin and into their development,
Cézanne’s ambivalence toward French Neo-Classicism, and its
arch-representative Dominique Ingres is well-documented. Cézanne would have
seen La Source at the Louvre (Figure 6).[15]
La Source, begun by Ingres in 1820, and
completed in 1856, when Ingres was 76-years-old, was infamous to
impressionist painters as its graceful lines and classicism represented the
highest standard in Fine Art at the time. Cézanne did not care for the
painting. He called it “system and false spirit”
[Doran 2001, 132]. Applying axial lines and golden
windows to La Source and Baigneuse debout, s’essuyant les cheveux, we can now see
Cézanne copying and departing from his model in surprising ways.
Figure 6.
L. Dominque Ingres, La Source,
1820-1856, 5’4 x 2’7 in. R. Paul Cézanne, Baigneuse
debout, s’essuyant les cheveux, 1869-71, 11 3/8 x 5 1/8
in.As Michael Baxandall observes, “influence” works
in reverse [Baxandall 1985, 59]. Ingres’ La Source did not “influence”
Cézanne. Instead, Cézanne drew a pattern from Veronese and subjected another
model, Ingres’ La Source to the pattern, then
dilated upon the results to suit his aims, the “harmonizing” of the youthful nude body. First, we notice that
model and copy are mirror images. With arms raised, they form S shaped
figures in classical contrapposto. They are symmetrical only in that, when a
golden rectangle is formed over the rectangular plane of the canvasses, both
figures’ left breasts are framed by the middle vertical line and the golden
ratio vertical lines formed by the golden rectangle. The middle vertical
axis also runs through both figures’ left eyes. The golden window in Ingres’
work frames the girl’s left thigh. In Cézanne, the golden window alludes to
the girl’s thigh and hip by partially representing (yet with more convexity)
her right hip through tonal modulation. Pointedly, Cézanne uses the
subordinate horizontal line of the picture plane’s golden rectangle to
“lower” his figure. In La Source the axial eye (picture center) is the sex of the
young girl emptying the urn of water. The golden section runs across her
legs above her knees. Clearly, in La Source,
the picture center, as the “eye” of
“god,” is Ingres’ visual pun on the source, water,
and female genitalia. In Cézanne’s work, the exact center is the nude
female’s hip swiveled in classical contrapposto, perhaps indicating that his
“source” is “classical art,” while
her sex is aligned with the golden section, making it
“golden.” In Baigneuse debout,
s’essuyant les cheveux, by aligning the female sex with the
golden section, within a theme that involves washing the body, and in the
case of Baigneuse debout, s’essuyant les
cheveux, a woman drying her hair, Cézanne is “harmonizing”
the “studio” erotism of Ingres’ young nude — he is bringing
“the source” back to nature.[16] He
also “classicizes” the nude human form by posing his
bathers in natural settings, and by associating them with the idealized
friendships and homo-social eroticism of the Classical world. In his
earliest male bathers as well, Cézanne aligns sex with the golden section of
the left side of the frame (Figure 7).
Figure 7.
Early Male Bathers: Axiality and Golden Rectangles L. Paul
Cézanne, Baigneur aux bras écartés, 1876, 9
1⁄2 x 5 1⁄2 in. M. Paul Cézanne, Baigneur aux bras
écartés, 1876, 9 1⁄2 x 6 3/8 in. R. Paul Cézanne, Baigneur aux bras écartés, 1877-1878, 28 3⁄4 x
23 5/8 in. In Figure 7, as in female nudes, Cézanne encloses the left breast of an early
male bather (7.L.) in the golden rectangle and the vertical bisecting line
of the painting. In the middle painting (7.M.) he centers or aligns the left
male breast between the golden rectangle and the vertical bisecting line of
the painting. In the right painting (7.R), the bather’s left breast aligns
with the vertical bisecting line, while the bather’s left elbow aligns with
the golden rectangle. In all three works, the golden window captures thigh
and background. The navel aligns with the horizontal bisecting line and sex
aligns with phi (the bottom side of the golden rectangle determined by the
dimensions of the painting).
Golden Windows: Coming into Focus
Eighty Bather paintings exist in various states of completion out of
Cézanne’s extant oeuvre of 1300 oil paintings and watercolors [Feilenfeldt]. Of the 80 Bathers, 64 are available online
for download for research and educational purposes. Using DDA, we identified
the axis determined by the picture plane of each digital image, and
identified the golden window. In Supplemental Table 2, we provide a snapshot image of all 64
golden windows we collected. Here we present twenty of these images that
suggest the “lowering or descending effect”
afforded by the golden window. All feature a head, breast or rear end. Most
of the 64 paintings have a head, breast, thigh, or rear end framed by the
golden window, but some frame the brightest point in the painting, or a
faint structure in the far distance.
Figure 8.
Other “Noumenal” bodies. The golden
window frames the head, heart, thighs, hips and rear end of the
descending or descended body. Row 1: L-R: Trois
Baigneuses, 1876-1877, 9 1⁄2 x 12 1⁄2 in.,Trois Baigneuses, 1876-1877, 20 1⁄2 x 21 1⁄2
in, Trois Baigneuses, 1875, 12 x 13 in.,
Cinq Baigneurs, 1879-1880, 13 5/8 x 15
in., Cinq Baigneurs, 1880-1882, 23 5/8 x 28
3⁄4 in., Baigneurs et Baigneuses, 1880, 7
1⁄2 x 8 1⁄4 in. Row 2: L-R: Baigneuses devant une
tente, 1883-1885, 24 3⁄4 x 33 1/8 in., Baigneurs, 1890, 23 5/8 x 31 7/8 in., Baigneurs, 1890, 15 3/8 x 20 7/8 in., Baigneurs in Plein Air, 1890-1891, 21 1⁄4 x 25 5/8 in.,
Baigneurs, 1892, 8 5/8 x 13 in., Baigneurs et Baigneuses, 1890, 8 7/8 x 13
15/16 in., Groupe de Baigneuses, 1895, 18
1⁄2 x 30 1⁄4 in. Row 3: L-R: Baigneurs,
1890-1895, 7 1⁄2 x 10 1⁄4 in., Le Bain,
1892-1894, 10 1⁄4 x 15 3⁄4 in., Les Grandes
Baigneuses, 1894- 1905, 53 1⁄2 x 75 1⁄4 in., Les Grandes Baigneuses, 1896-1906, 52 3/8 x 81
1⁄2 in., Baigneurs, 1898-1900, 10 5/8 x 18
1⁄4 in., Baigneurs, 1900, 11 7/8 x 17 3/8
in. , Baigneurs, 1902-1904, 9 x 10 1⁄2
in.The Golden Strips
Adjacent to the “golden window” (Appendix
IV) are the “golden strips” which elaborate on
the point emphasized by the window. The “golden strip” in
a bather painting is between the axial and golden ratio horizontal lines or
vertical lines of the picture plane (Appendix
IV). The golden strips allow for an alternation of frontal and
rear nude forms with their sexes aligned with the golden section. As with
Veronese’s Les Noces de Cana, Cézanne aligns
the heads of the “descended” figures beneath the middle horizontal line
bisecting the picture. For Andre Lohte, Cézanne’s genius is in his
alternation of foreground and background figures. (What we call Cézanne’s
“game,” he calls Cézanne’s “ruse”). Lohte stated of Cézanne: “Genius consists in knowing how to compensate, through
constant repetition of each phenomenon, for every thrust into depth, by
an equal advance or return. Without this ruse the eye would immediately
find the horizon, the distance, without being excited by the successive
oppositions which retard its quest for space, and procure for it a
subtle pleasure”
[Loran 1943, 32]. We can now consider Veronese’s Les Noces de Cana a masterful example of this
phenomenon in fine art painting, a strategy in painting with an endless
“trajectory.”[17] In Figure 9, we present the horizontal golden strip of
Quatre Baigneuses (1888-1890) which shows
Cézanne’s “alternation of foreground and
background” described by Andre Lohte. In Figure 9, and in other
Bathers, Cézanne’s “successive oppositions” have
semantic meaning. For us, this signals Cézanne’s reconciliation of opposites
in his windows and strips. Thematically, Cézanne reconciles body and mind
into a third “noumenal” alliance. He aligns the
attentive and communicative heads, hearts, and sexes of his descended and/or
risen figures, along the golden section and the axial center of his Bather
paintings. In Supplemental Table 3,
we present the horizontal “golden strips” of the 64
bathers in this study.
Figure 9.
Golden Window, Golden Strip, and Complete Image. Quatre Baigneuses, 1888-1890, 28 3/8 x 36 1⁄4
in. In Quatre Baigneuses Cézanne alternates
frontal and rear nudity. He aligns the heads of “descended” bathers with the sex of “risen” bathers along the axial center and horizontal golden
section of the picture plane.Beyond the Church
Cézanne presents an affirmative and benedictory vision of youth and beauty in
his Bathers. In Les Grandes Baigneuses, a 1906
painting left incomplete when he died, the church in the distance shows that
his bathers exist in an intermediate space between the viewer outside the
picture plane and the church (Figure 10). The
bathers are in a space of their own, determined by the geometry that unites
them. When we apply the geometric analysis of DDA to the painting, we see
that the golden window frames a reality beyond the church. We feel this
illustrates Cézanne’s Neoplatonic leanings, and fuels his concept of art as
a religion. In his serial use of golden sections to structure his bather
series, we see an interest in the infinite, and an understanding of the
golden window as affording a glimpse of it.
Figure 10.
Imagining the infinite. In Les Grandes
Baigneuses (1906), we see in the golden strip, frontal and
rear nudity, descended heads (frontal, side and rear views), brightest
points, and far distance.Homage to the Classical World
Cézanne also uses sacred geometry to structure the imagined space of the
image. In Baigneurs en Plein Air (Figure 11), an unfinished painting from
1890-1891, the ground of the five figures forms a Pentagon, below the
horizontal line that bisects the painting.
Figure 11.
Baigneurs en Plein Air,
1890-1891. Five figures form a pentagon in the imagined space of the
painting.As stated in Appendix IV, DDA will discriminate a variety of geometric shapes
within a picture. The figure emerging in the golden window represents it
triangular point. This implied pentagonal shape illustrates Cézanne’s advice
to artists throughout his letters and conversations: “Interpret nature in terms of the cylinder, the sphere, the cone; put
everything in perspective, so that each side of an object, a plane,
recedes toward a central point”” [Doran 2001, 29]. In addition to an implied pentagon, these bathers form an
imaginary cone, a large triangle parallel to the surface plane whose tip
coincides with the middle vertical axis of the paintings. This triangle
provides vertical armature for the five bodies, linking them together in one
unit with the armpits aligned at the diagonal lines. This compositional
triangle both dynamically lifts the figures, and stabilizes the
composition.
Cézanne suggests with a few blue and red strokes the figure whose breast is
framed in the golden window of Figure 11. Cézanne repeated this particular
composition in his search for a realization commensurate with his ideal. We
can now think of a man lowering himself into a body of water as a
compositional “problem” Cézanne was trying to solve in
his Bather series. Painted in four-sided constructive strokes, and in
Veronesian, “noumenal” blue and red color patches that
resemble a harlequin’s costume, the figure is in motion, and not fully
formed. He is an intermediate being, not yet concretized, nor fully
translated between here and there within the noumenal square of the
painting. Cézanne is clearly attuned to magical conceptions of the number
four as representing the fourth element of earth in Platonic doctrine and
inherent in the squares of the harlequin’s costume. He was also aware of the
five-sided figure of the pentagon as representing the regenerative aspects
of creation. The Harlequin’s checkerboard costume has been described as
symbolizing “a chthonic force”
[Schneider 1994]. If so, this chthonic force’s heart is framed
in the golden window, a highly significant spot, charged with meaning, as we
now see in Cézanne’s Bathers, and particularly in this painting (Figure 11)
depicting five men in geometrical relationship to each other. In addition to
a sacred understanding of numbers and shapes, three (triangle: divinity),
four (square: earth) and five (pentagon: creation and regeneration), a means
to create a harmony “parallel” to nature, this
painting’s composition is Cézanne’s special homage to the pastoral poetry of
Theocritus and Virgil, the classical literature he loved. It is well- known
that Cézanne translated Theocritus and Virgil as a pastime in his youth [Doran 2001, 181]. The left side of Figure 11 appears to
represent the sympotic aspects of male fraternity with the seated figure
under the pine tree discoursing with the standing figure seen from behind.
The right side of the painting pays homage to the erotic aspects of
homo-sociality implied by Theocritus and developed in the bucolic poems of
Virgil. In the poems, herdsmen gather to sing songs about
“Daphnis,” a young man who drowns himself out of
erotic frustration, or his cognates in the classical tradition who die:
Hylas, Delphis, Adonis, and Narcissus, other beautiful boys, like the one in
Figure 11 “posing” in the foreground. Theocritus and
Virgil’s lost boys are the poets’ reflections on their own lost youth and/or
the loss of specific male friends, or lovers [Weinstein]. For
Cézanne, “Nature is not on the surface; it is in
depth,” hence, the man in the water (in the depths) crying on the
far right [Doran 2001]. Cézanne’s effort to divinize the nude
human body in company with other divinized bodies, whether
“co-ed” or segregated by sex, and in the many
paintings where difference in sex is not explicit, we see the artist’s
engagement with Neoplatonism, in that his goal is to create a harmoniously
simplified world with a playful, affirmative, benedictory vision of youthful
nudity.
Conclusion
In this paper, using the automated tools afforded by DDA, we have forged a
connection in color, composition, geometry, and theme between Les Noces de Cana and Baigneuse debout, s’essuyant les cheveux, and from this
connection, we have brought to light unifying characteristics in Cézanne’s
Bathers heretofore unidentified. We have identified the connection between
Les Noces de Cana and Baigneuse debout s’essuyant le cheveux by producing dendrograms
of Cézanne’s fifty- five 1895 Galerie Vollard Exhibition oil paintings
compared to Veronese’s Les Noces de Cana, a
painting we know Cézanne admired at the Louvre during his formative years as
a painter and throughout his life. Using computer-assisted methods we
generated dendrograms that clustered paintings related in color, saturation,
brightness and complexity. After studying these parameters, we applied the
geometric program of DDA to the study of Cézanne’s composition. Because
Cézanne expressed Neoplatonic ideals regarding paintings in his
conversations and letters, we programmed DDA to compute axial lines and
golden rectangles according to the dimensions of the square, rectangle, and
other geometric parameters to the painting under scrutiny. Using DDA we
identified the golden rectangle for Les Noces de
Cana, Baigneuse debout, s’essuyant les
cheveux and Ingres’ La Source
(another likely model for Baigneuse debout, s’essuyant
les cheveux). From the similarities and differences between the
three paintings identified, based on axial symmetry and the golden section,
we have formulated an approach to “seeing” Cézanne’s
composition in his Bather series. Cézanne’s noumenal bodies, formerly
perceived as “awkward” and composed with “baffling imbalance,” can now be viewed as “golden”
[Danchev 2013]. These are only the first parameters,
customized to the study of paintings that we have introduced to DDA. As we
continue to expand and use this computer program to compare influence
between painters, we will add new parameters such as measurements for
convexity, concavity, texture and composition, based on edge detection
technology in the original DIAS program. These tools will assist us in
investigating a variety of questions basic to art history.
Acknowledgments
This research began with an AAC&U TIDES (Teaching to Increase Diversity
and Equity in the Classroom) grant that supported applying technology to the
study of paintings from 2013-2017 at Lawrence Technological University. A
Howard Hughes Medical Institute’s Inclusive Excellence Initiative grant
(52008705) is sustaining LTU’s integration of computer-assisted analysis of
art, music, and literature into its undergraduate curricula until 2021. The
Developmental Studies Hybridoma Bank, an NIH National Resource, and the W.M.
Keck Dynamic Image Analysis Facility housed at the University of Iowa
provided the computational resources for this project. We thank LTU’s
Research Support Services for providing a Faculty Seed Grant for travel,
research assistants Liam Butler, Mary Cody, Irene Missler, and Neil
Fraylick. We thank Dean Hsiao-Ping Moore and Prof. Lior Shamir for guidance
and support, and LTU Provost Maria Vaz for approving a sabbatical leave
Spring 2018, to conduct this work at the W.M. Keck Dynamic Image Analysis
Facility at the University of Iowa.
Appendix I. Analyzing a collection of paintings using the customized DIAS/DENDRON-ART (DDA) program
The newly developed DIAS/DENDRON-ART (DDA) program integrates the 2D image
analysis program DIAS (Soll et al., US patent #5655028; Soll, D.R. 1995. The use
of computers in understanding how cell crawl. Int. Rev.
Cytol. 163: 43-104; Soll, D.R. and Wessels, D. (eds.) 1998. Motion
Analysis of Living Cells John Wiley, Ive., New York, 298 pages; Kuhl, S., Voss,
E., Scherer, A., Lusche, D.F., Wessels, D., Soll, D.R. 2016. 4D tumorigenesis
model for quantitation of coalescence, identification of unique cell behaviors
and testing anti-cancer drugs. Chemotaxis Methods in Molec.
Biol. 229-250), and the dendrography software program DENDRON.
Schmid, Jan, Edward Voss and David R. Soll. “Computer-Assisted Methods for Assessing Strain Relatedness in Candida
albicans by Fingerprinting with the Moderately Repetitive Sequence
Ca3.”
Journal of Clinical Microbiology. Vol 28.6 (June
1990). 1236-1243. Soll, D. R. “The ins and outs of DNA
fingerprinting the infectious Fungi.”
Clinical Microbiology Reviews. Vol.13.2 April 2000.
P.332-370. The programs originally written in C++ have been converted to JAVA
(Graphics Programming With Java, Second Edition. 2001. Steven’s Scott/Jones,
Inc.). Images of paintings are scanned into a DDA folder, with borders equal to
the inner edges of the frame and normalized for size. If a painting is faded,
hue will not be significantly affected since DDA employs HSB (hue, saturation,
brightness) color space (Oracle Java 7 documentation, online for “Class Color”), as opposed to RGB (red, green, blue).
DDA then automatically computes nine parameters that include brightness,
saturation, complexity, redness, orangeness, yellowness, greenness, blueness and
purpleness. Additional parameters based on DIAS edge detection programs are now
under development and will be incrementally added. The
“brightness” parameter is computed by converting the
pixels of the entire image to HSB. A value of 0% is black and 100% is white. The
average % for the entire picture is computed and the value converted to a range
of 0.00 to 1.00. The “saturation” parameter is treated in a
similar fashion. It represents the average richness of all colors assessed, is
computed from 0 to 100%, then normalized to a value in the range of 0.00 to
1.00. For the “complexity” parameter, the image is first
converted to grays with pixel intensities ranging from 0 to 255. The average
value is then normalized to 0.00 to 1.00. The final parameters are six hues. On
the color or “hue” wheel, they vary from 0 to 360°. The
number of pixels with redness at 0° ± 5°, orange at 20 ± 5°, yellowness at 60 ±
5°, greenness at 120 ± 5°, blueness at 240 ± 5° and purpleness at 270 ± 5°, are
computed and divided by the total number of pixels in the image. These
individual pixel proportions are then converted to 0.00 to 1.00. The values of
each parameter, all converted to a range of 0.00 to 1.00, were then used to
generate a similarity coefficient (SAB) between every
pair of paintings in a collection, using the following formula:
where ai and bi
are the values of a parameter I for paintings A and B respectively, and k is the
number of parameters. This formula was derived from that developed by Schmid,
J., Voss, E. and Soll, D.R. 1990. (J. Clin Microbiol. 28, 1236-1243) for banding
patterns of DNA fingerprints in which each band is a restrictive fragment length
polymorphism (RFLP) pattern representing a parameter (Soll et. al. 1997 US
Patent #5, 655, 028). An SAB of 0.00 represents
complete dissimilarity, an SAB of 1.00 identicalness,
and SABs of 0.01 to 0.99, increasing levels of
similarity. For this study the average of the parameters of paintings are used
to generate the SABs between all paintings in a
collection, which are logged into a matrix, as presented for 18 pictures in
Appendix I Table 1.
Figure 12.
The equation for the similarity coefficient.
Figure 13.
A matrix showing the SAB between all eighteen
paintings in the collection.The matrix is then used to generate a dendrogram using the unweighted pair group
method based on arithmetic averages (UPGMA), first employed by Rohlf ,1963
Classification of Aedes by numerical taxonomic
methods [Diptera, Culcidae]. (Ann. Entomal. Soc. Am. 56, 798-804) and discussed
in more detail for application by Snesth and Sokel (1973. Numerical Taxonomy
W.H. Freeman and Co., San Francisco, CA). In generating a dendrogram,
connections are identified in descending values. The matrix is first scanned for
the SAB with the highest value. The first two are
joined by a vertical node at that SAB. If two or more
pairs have the same highest SAB, one is picked
randomly to initiate the process of generating a tree. The system then grows the
tree of relatedness, connecting pairs, individual paintings and groups of two or
more, or groups. The node involving more than two paintings is computed as the
arithmetic mean of the SABs between the pictures
connected. This process continues until all pictures are connected to form a
relatedness tree (dendrogram). The accuracy of the dendrogram has been assessed
by goodness of fit (i.e., whether the distance in the dendrogram approximates
the SABs in the matrix (Avis, J.C. 1994. Molecular
numbers, natural history and evolution. Chapraon and Hull, New York, NY). By
using completely different methods to assess genetic relatedness between the
same collection of strains of an infectious fungus, the accuracy of the DENDRON
program was previously verified (Pujol, C., joly, S., Lockhart, S.R., Sebastian,
N., Tibayrenc, M., and Soll, D.R. 1977. J. Clin Microbiol, 2348-2358; Soll D.R.
2000. Clin Microbiol Rev 13, 332-370). The robustness of DIAS/DENDRON ART (DDA)
in clustering was also verified by the addition of the restored Les Noces de Cana to the Cézanne collection and the
unrestored Les Noces de Cana, as described in
Appendix II.
Appendix II
A comparison of the Cézanne Galerie Vollard collection with the unrestored
(Appendix II A) and restored (Appendix II B) versions of Veronese’s Les Noces de Cana, using all parameters but green.
Greenness was removed because in the restored version, a man’s cloak, which was
red, was converted by restoration to green. Both Cézanne’s Baigneuse debout, s’essuyant les cheveux and Veronese’s Les Noces de Cana reside in the same cluster with the
restored and unrestored Les Noces de Cana. It
should be noted that the alternative clusters in the three dendrograms share a
majority of other related Cézanne pictures, as is evident in lists of the
paintings in the alternative clusters, presented in Appendix II D. These results
also demonstrate the accuracy of the clustering method of DIAS/Dendron, given
that the addition of different versions, in this case the unrestored and
restored Les Noces de Cana, or the addition of
both, does not disrupt relationships, even though each dendrogram is generated
independently, using the unweighted pair-group method employing arithmetic
averages, as described in Appendix I.
Appendix II. A
Figure 14.
The Cézanne Galerie Vollard collection with the unrestored versions of
Veronese's Les Noces de CanaAppendix II. B
Figure 15.
The Cézanne Galerie Vollard collection with the restored versions of
Veronese's Les Noces de CanaAppendix II. C
Figure 16.
Lists of the paintings in the alternative clustersAppendix II. D
| Unrestored (Louvre) Cana | Restored (Venice) Cana | Unrestored and Restored Cana |
| Baigneuse | Baigneuse | Baigneuse |
| Les Bégonias | Les Bégonias | Les Bégonias |
| La Baignade | La Baignade | La Baignade |
| Pommes | Pommes | Pommes |
| Nature Morte | Nature Morte | Nature Morte |
| Esquisse de M. Cézanne | Esquisse de M. Cézanne | Esquisse de M. Cézanne |
| La Jas de Bouffan | La Jas de Bouffan |
Table 1.
Comparison of pictures in the resident clusters of Cézanne’s Baigneuse debout, s’essuyant les cheveux and either the unrestored
or restored versions of Veronese’s Les Noces de
Cana. Only the first word of the titles of the paintings are
included.Appendix III. Further demonstration of clustering Veronese’s Les Noces de Cana and Cézanne’s Baigneuse debout, s’essuyant les cheveux
To further demonstrate the similarity of Veronese’s Les
Noces de Cana and Cézanne’s Baigneuse debout,
s’essuyant les cheveux, we generated a dendrogram based on the SABs between these two paintings and nineteen paintings
Cézanne would have viewed in the Louvre between 1861 and 1906. The artists
include Delacroix (green), Rubens (black), and Tintoretto (blue). Les Noces de Cana and Baigneuse
debout, s’essuyant les cheveux again clustered, supporting the
relationship and accuracy of the dendrography program.
Figure 17.
A dendrogram featuring the SABs between
Les Noces de Cana and Baigneuse debout, s’essuyant les cheveux. The artist Delacroix
is shown in green; Rubens is shown in black; and Tintoretto is shown in
blue.Appendix IV. How to identify a golden window
Figure 18.
A detailed graphic showing the steps to identify a golden window. Image
1 says “The cursor is manually moved in a diagonal from
the upper left to lower right corner of the painting.” Image 2
says “DDA automatically computes phi along the upper and
left hand borders, and draws the golden rectangle.” Image 3 says
“DDA then bisects the picture in four equal
quadrants by drawing a vertical line and a horizontal line, and defines
the exact center of the painting.” Image 4 says “Steps one through three are performed regardles of the
dimensions of the picture.” Image 5 says “DDA
then identifies and color codes the golden window, and the horizontal
golden strip and the vertical golden strips.” Image 6 says “DDA then isolates the golden window for independent
analysis of parameters and comparison through dendrography.”
Image 7 concludes by saying “DDA can expand independent
golden windows or archive for rapid comparison.”Supplementary Table I: List of Works
| Name of Artist | Title of Work | Medium | Size | Year | Location | Link to artwork used for analysis |
| Paul Cézanne | La Maison abandonnée | Oil on Canvas | 19 5/16 x 23 in | 1878-79 | Private Collection, New York | https://uploads7.wikiart.org/images/paul-cezanne/ |
| Paul Cézanne | La Baie de Marseille, avec vue sur le village | Oil on Canvas | 26 3/16 x 32 11/16 in. | 1877-79 | Vollard Archives, Photo No. 604 | https://www.moma.org/collection/works/80302?locale=en |
| Paul Cézanne | L'Estaque | Oil on Canvas | 31 1/2 x 39 1/16 in. | 1879-83 | The Museum of Modern Art, New York | https://www.moma.org/meetme/artwork/index |
| Paul Cézanne | La Campagne à Pontoise, près du Valhermeil | Oil on Canvas | 36 3/8 x 28 7/8 in. | 1881-82 | Fondation Sirina, Vaduz | http://www.cezannecatalogue.com/catalogue_images/main |
| Paul Cézanne | Marronniers et ferme du Jas de Bouffan | Oil on Canvas | 25 13/16 x 32 in. | 1885 | Private Collection, New York | https://uploads1.wikiart.org/images/paul-cezanne/ |
| Paul Cézanne | Gardanne (vue verticale) | Oil on Canvas | 31 1/2 x 25 5/16 in. | 1886 | The Metropolitan Museum of Art, New York | http://images.metmuseum.org/CRDImages/ep/original/DT1941.jpg |
| Paul Cézanne | Gardanne (vue horizontale) | Oil on Canvas | 25 X 39 in. | 1885 | Barnes Foundation, Philadelphia (BF917) | http://www.cezannecatalogue.com/catalogue_images/ |
| Paul Cézanne | Le Grand Pin | Oil on Canvas | 33 1/16 x 36 3/16 in. | 1887-89 | Museu de Arte de São Paulo Assis | https://uploads2.wikiart.org/images/paul-cezanne/the-great-pine-1889.jpg |
| Paul Cézanne | Maison au bord de la Marne (l'Île Machefer) | Oil on Canvas | 28 11/16 x 35 13/16 in. | 1888-94 | White House Collection, Washington, D.C. | http://www.cezannecatalogue.com/catalogue_images/ |
| Paul Cézanne | Le Chemin de halage sur les bords de la | Oil on Canvas | 24 13/16 x 31 1/8 in. | 1888 | Art Gallery of New South Wales, Sydney | https://www.artgallery.nsw.gov.au/media/collection |
| Paul Cézanne | Le Jas de Bouffan | Oil on Canvas | 29 3/8 x 21 1/2 in. | 1890-94 | Private Collection, Japan | https://uploads2.wikiart.org/images/paul-cezanne/jas-de-bouffan-1887.jpg |
| Paul Cézanne | Au bord de l'eau | Oil on Canvas | 28 11/16 x 36 3/16 in | 1890-92 | National Gallery of Art, Washington, D.C. | https://images.nga.gov/en/search/do_quick_search.html?q=%221972.9.1%22 |
| Paul Cézanne | Le Pont sur la Marne à Créteil | Oil on Canvas | 28 x 35 3/8 in. | 1894 | Pushkin Museum, Moscow | https://uploads0.wikiart.org/images/paul-cezanne/bridge-over-the-marne- |
| Paul Cézanne | Sous-bois | Oil on Canvas | 45 11/16 x 31 7/8 in. | 1893-94 | Los Angeles County Museum of Art | https://collections.lacma.org/node/172409 |
| Paul Cézanne | Le Nègre Scipion | Oil on Canvas | 42 1/8 x 32 11/16 in. | 1867 | Museu de Arte de São Paulo Assis | https://uploads4.wikiart.org/images/paul-cezanne/the-negro-scipio-1867.jpg |
| Paul Cézanne | Portrait de Victor Chocquet (buste) | Oil on Canvas | 13 13/16 x 10 11/16 in | 1877 | Virginia Museum of Fine Arts, Richmond | https://uploads6.wikiart.org/images/paul-cezanne/ |
| Paul Cézanne | Portrait de l'artiste | Oil on Canvas | 10 3/16 x 5 7/8 in. | 1877 | Musée d'Orsay, Paris | https://uploads7.wikiart.org/images/paul-cezanne/self-portrait-3.jpg |
| Paul Cézanne | Portrait de Louis Guillaume | Oil on Canvas | 22 x 18 1/5 in. | 1879-80 | National Gallery of Art, Washington, D.C. | https://images.nga.gov/en/search/do_quick_search.html?q=%221963.10.101 |
| Paul Cézanne | Portrait de l'artiste | Oil on Canvas | 18 1/8 x 15 in. | 1882 | Pushkin Museum, Moscow | http://www.arts-museum.ru/data/fonds/europe_and_america |
| Paul Cézanne | Madame Cézanne en robe rayée | Oil on Canvas | 22 3/16 x 18 1/5 in. | 1883-85 | Yokohama Museum of Art | https://uploads5.wikiart.org/images/paul-cezanne/ |
| Paul Cézanne | Esquisse d'un portrait de madame Cézanne | Oil on Canvas | 8 x 5 1/2 in. | 1883 | Richard Gray, Chicago | https://uploads5.wikiart.org/images/paul-cezanne/ |
| Paul Cézanne | Esquisse d'un portrait du fils de l'artiste | Oil on Canvas | 7 11/16 x 4 1/2 in. | 1883-85 | Von der Heydt Museum, Wuppertal | http://www.cezannecatalogue.com/catalogue_images/main_lg/R534.jpg |
| Paul Cézanne | Madame Cézanne au chapeau vert | Oil on Canvas | 38 1/2 x 31 1/2 in. | 1891-92 | Barnes Foundation, Philadelphia (BF141) | https://uploads8.wikiart.org/images/paul-cezanne/ |
| Paul Cézanne | Le Garçon au gilet rouge | Oil on Canvas | 31 7/8 x 25 5/8 in. | 1888-90 | The Museum of Modern Art, New York | https://www.moma.org/collection/works/79086?locale=en |
| Paul Cézanne | Le Garçon au gilet rouge | Oil on Canvas | 31 5/16 x 25 3/16 in. | 1888-90 | Foundation E.G. Bührle Collection, Zürich | https://uploads5.wikiart.org/images/paul-cezanne/boy-in-a-red-vest-1889.jpg |
| Paul Cézanne | Le Garçon au gilet rouge | Oil on Canvas | 36 3/16 x 28 11/16 in. | 1888-90 | National Gallery of Art, Washington, D.C. | https://images.nga.gov/en/search/do_quick_search.html?q=%221995.47.5%2 |
| Paul Cézanne | Madame Cézanne dans la serre | Oil on Canvas | 36 3/16 x 28 11/16 in. | 1891-92 | The Metropolitan Museum of Art, New York | http://images.metmuseum.org/CRDImages/ep/original/DP317780.jpg |
| Paul Cézanne | Cézanne coiffé d'un chapeau mou | Oil on Canvas | 23 5/8 x 19 5/16 in. | 1894 | Bridgestone Museum of Art, Tokyo | https://uploads0.wikiart.org/images/paul-cezanne/ |
| Paul Cézanne | Jeune fille à la poupée | Oil on Canvas | 36 3/16 x 28 11/16 in. | 1895 | Private Collection, New York | https://uploads5.wikiart.org/images/paul-cezanne/young-girl-with-a-doll.jpg |
| Paul Cézanne | Le Festin – L'Orgie; Le Banquet de | Oil on Canvas | 51 3/16 x 31 7/8 in. | 1867 | Private Collection, France | https://uploads4.wikiart.org/images/paul-cezanne/the-feast-the-banquet-of |
| Paul Cézanne | Le Pêcheur à la ligne | Oil on Canvas | 10 5/8 x 14 3/16 in. | 1868-70 | ? | Unable to locate color version |
| Paul Cézanne | Le Déjeuner sur l'herbe | Oil on Canvas | 23 5/8 x 31 7/8 in. | 1870 | Private Collection, New York | https://uploads0.wikiart.org/images/paul-cezanne/luncheon-on-the-grass- |
| Paul Cézanne | Au bord de l'étang | Oil on Canvas | 17 1/2 x 21 1/16 in. | 1876-77 | Museum of Fine Arts, Boston | http://www.mfa.org/collections/object/download/50439 |
| Paul Cézanne | Le Déjeuner sur l'herbe | Oil on Canvas | 13 3/8 x 15 3/8 in. | 1878-80 | ? | Unable to locate color version |
| Paul Cézanne | La Lutte d'amour | Oil on Canvas | 14 7/8 x 18 5/16 in. | 1880 | National Gallery of Art, Washington, D.C. | https://images.nga.gov/en/search/do_quick_search.html?q=%221972.9.2%22 |
| Paul Cézanne | Les Moissonneurs | Oil on Canvas | 10 3/16 x 16 1/8 in. | 1880 | Private Collection, Switzerland | http://www.cezannecatalogue.com/catalogue_images/main_lg/454.jpg |
| Paul Cézanne | Léda au cygne | Oil on Canvas | 23 x 28 7/8 in. | 1880 | Barnes Foundation, Philadelphia (BF36) | https://uploads0.wikiart.org/images/paul-cezanne/leda-and-the-swan.jpg |
| Paul Cézanne | Le Vase rococo | Oil on Canvas | 28 11/16 x 23 5/8 in. | 1875-77 | National Gallery of Art, Washington, D.C. | https://images.nga.gov/en/search/do_quick_search.htm |
| Paul Cézanne | Deux poires | Oil on Canvas | 6 1/2 x 9 3/8 in. | 1875 | Christie's, New York | https://www.ecosia.org/images?addon=chrome&addonversion= |
| Paul Cézanne | Cinq pommes | Oil on Canvas | 5 x 10 in. | 1877-78 | Mr. and Mrs. Eugene V. Thaw, New York | https://www.ecosia.org/images?addon=chrome&addonversion |
| Paul Cézanne | Pommes | Oil on Canvas | 7 1/2 x 10 1/2 in. | 1878 | The Fitzwilliam Museum, Cambridge | https://uploads3.wikiart.org/images/paul-cezanne/apples-1878.jpg |
| Paul Cézanne | Pommes et linge | Oil on Canvas | 9 13/16 x 17 5/16 in. | 1879-80 | Private Collection, Japan | http://www.cezannecatalogue.com/catalogue/entry.php?id=335 |
| Paul Cézanne | Bol et boîte à lait | Oil on Canvas | 7 7/8 x 7 1/16 in. | 1879 | Bridgestone Museum of Art, Tokyo | https://uploads2.wikiart.org/images/paul-cezanne/still-life-bowl-and-milk- |
| Paul Cézanne | Verre et pommes | Oil on Canvas | 12 3/8 x 15 11/16 in. | 1879-80 | Collection Rudolf Staechelin, Basel | http://www.cezannecatalogue.com/exhibitions/entry.php?id=52 |
| Paul Cézanne | Les Bégonias | Oil on Canvas | 18 1/8 x 21 1/4 in. | 1879-80 | Private Collection | http://www.cezannecatalogue.com/catalogue_images/ |
| Paul Cézanne | Deux fruits | Oil on Canvas | 7 1/2 x 9 1/8 in. | 1885 | Private Collection, Japan | http://www.cezannecatalogue.com/exhibitions/entry.php?id=52 |
| Paul Cézanne | Grenade et poires dans une assiette | Oil on Canvas | 10 5/8 x 14 3/16 in. | 1885 | Private Collection, New York | https://uploads7.wikiart.org/images/paul-cezanne/ |
| Paul Cézanne | Nature morte | Oil on Canvas | 13 13/16 x 18 1/8 in. | 1890 | The State Hermitage Museum, St. Petersburg | https://uploads7.wikiart.org/images/paul-cezanne/still-life-with-apples-1.jpg |
| Paul Cézanne | Fruits et cruchon | Oil on Canvas | 13 x 16 1/8 in. | 1893-94 | Museum of Fine Arts, Boston | http://www.mfa.org/collections/object/fruit-and-a-jug-on-a-table-33253 |
| Paul Cézanne | La Corbeille de pommes | Oil on Canvas | 25 5/8 x 31 1/2 in. | 1893 | The Art Institute of Chicago | https://uploads0.wikiart.org/images/paul-cezanne/ |
| Paul Cézanne | Nature morte | Oil on Canvas | 17 5/16 x 24 in. | 1895 | Sammlung Esther Grether, Basel | http://www.cezannecatalogue.com/exhibitions/entry.php?id=52 |
| Paul Cézanne | La Baigneuse debout, s'essuyant les cheveux | Oil on Canvas | 11 3/8 x 5 1/8 in. | 1869 | Private Collection | https://uploads1.wikiart.org/images/paul-cezanne/ |
| Paul Cézanne | La Baignade | Oil on Canvas | 7 1/2 x 10 5/8 in. | 1875-77 | Private Collection, New York | http://www.cezannecatalogue.com/exhibitions/entry.php?id=52 |
| Paul Cézanne | Baigneur aux bras écartés | Oil on Canvas | 13 x 9 3/8 in. | 1877-78 | Jasper Johns, Sharon, Conn. | https://uploads2.wikiart.org/images/paul-cezanne/ |
| Paul Cézanne | Les Baigneurs au repos | Oil on Canvas | 31 1/8 x 38 3/16 in. | 1876-77 | Barnes Foundation, Philadelphia (BF906) | https://uploads3.wikiart.org/images/paul-cezanne/bathers-at-rest-1877.jpg |
| Paul Cézanne | Quatre Baigneuses | Oil on Canvas | 13 13/16 x 15 5/8 in. | 1880 | Private Collection | https://uploads0.wikiart.org/images/paul-cezanne/four-bathers-1878.jpg |
| Paul Cézanne | Baigneuses devant une tente | Oil on Canvas | 24 13/16 x 33 1/16 in. | 1883-85 | Staatsgalerie, Stuttgart | http://www.cezannecatalogue.com/exhibitions/entry.php?id=52 |
| Paul Cézanne | Le Baigneur au Rocher | Oil on Canvas | 66 x 44 1/2 in. (part | 1867-1869 | Chrysler Art Museum Norfolk, VA | http://www.cezannecatalogue.com/exhibitions/entry.php?id=52 |
| Paul Cézanne | Baigneuses | Oil on Canvas | 13 x 15 11/16 in. | 1870 | Private Collection | http://www.cezannecatalogue.com/exhibitions/entry.php?id=52 |
| Paul Cézanne | Homme Etendu et Baigneuses | Oil on Canvas | 10 1/2 x 13 3/4 in. | 1868-1870 | Private Collection | Private Collection. |
| Paul Cézanne | Baigneur et Baigneuses | Oil on Canvas | 7 7/8 x 15 3/4 in. | 1870-1871 | Travis Hanson, Fine Art, New York | http://www.cezannecatalogue.com/exhibitions/entry.php?id=52 |
| Paul Cézanne | Baigneuse au bord de la mer | Oil on Canvas | 9 1/4 x 8 5/8 in. | 1875 | Barnes Foundation, Philadelphia | http://www.cezannecatalogue.com/exhibitions/entry.php?id=52 |
| Paul Cézanne | Baigneuse assise | Oil on Canvas | 7 5/8 x 4 3/4 in. | 1875 | Columbus Museum of Art | http://www.cezannecatalogue.com/exhibitions/entry.php?id=52 |
| Paul Cézanne | La Baignade | Oil on Canvas | 7 1/2 x 10 5/8 in. | 1875-1877 | Private Collection, New York | http://www.cezannecatalogue.com/exhibitions/entry.php?id=52 |
| Paul Cézanne | Baigneur aux bras écartés | Oil on Canvas | 9 1/2 x 5 1/2 in. | 1876 | Rose Art Museum, Brandeis University | http://www.cezannecatalogue.com/exhibitions/entry.php?id=52 |
| Paul Cézanne | Baigneur aux bras écartés | Oil on Canvas | 9 x 6 in. | 1876-1877 | Private Collection, France | http://www.cezannecatalogue.com/exhibitions/entry.php?id=52 |
| Paul Cézanne | Cinq Baigneurs | Oil on Canvas | 9 3/8 x 9 13/16 in. | 1876 | Musee d'Orsay, Paris France | http://www.cezannecatalogue.com/exhibitions/entry.php?id=52 |
| Paul Cézanne | Baigneur aux bras écartés | Oil on Canvas | 9 3/8 in. x 6 5/16 in. | 1875-1876 | Private Collection | http://www.cezannecatalogue.com/exhibitions/entry.php?id=52 |
| Paul Cézanne | Baigneuses | Oil on Canvas | 15 x 18 1/8 in. | 1875 | The Metropolitan Museum of Art | http://www.cezannecatalogue.com/exhibitions/entry.php?id=52 |
| Paul Cézanne | Cinq Baigneuses sous des arbre | Oil on Canvas | 23 5/8 x 28 11/16 in. | 1875 | Private Collection | http://www.cezannecatalogue.com/exhibitions/entry.php?id=52 |
| Paul Cézanne | Trois Baigneuses | Oil on Canvas | 7 1/2 x 8 11/16 in. | 1874-1875 | Musee d'Orsay, Paris France | http://www.cezannecatalogue.com/exhibitions/entry.php?id=52 |
| Paul Cézanne | Baigneurs au repose I | Oil on Canvas | 15 x 18 in. | 1875-1876 | Musee d'Art et d'Histoire, Geneva | http://www.cezannecatalogue.com/exhibitions/entry.php?id=52 |
| Paul Cézanne | Baigneurs au repose II | Oil on Canvas | 15 x 18 1/8 in. | 1875-1876 | Location Unknown | http://www.cezannecatalogue.com/exhibitions/entry.php?id=52 |
| Paul Cézanne | Baigneur debout | Oil on Canvas | 11 13/16 in. x 6 11/16 in. | 1876 | Sotheby's New York | http://www.cezannecatalogue.com/exhibitions/entry.php?id=52 |
| Paul Cézanne | Baigneur assis au bord de l'eau | Oil on Canvas | 11 3/8 x 8 5/16 in. | 1876 | Obersteg Collection, Basel | http://www.cezannecatalogue.com/exhibitions/entry.php?id=52 |
| Paul Cézanne | Trois Baigneuses | Oil on Canvas | 9 3/8 x 12 1/2 in. | 1876-1877 | Barnes Foundation, Philadelphia | http://www.cezannecatalogue.com/exhibitions/entry.php?id=52 |
| Paul Cézanne | Trois Baigneuses | Oil on Canvas | 9 13/16 x 13 1/5 in. | 1876-1877 | Elliott Wolk, Scarsdale | http://www.cezannecatalogue.com/exhibitions/entry.php?id=52 |
| Paul Cézanne | Trois Baigneuses | Oil on Canvas | 20 1/2 x 21 3/8 in. | 1876-1877 | Private Collection | http://www.cezannecatalogue.com/exhibitions/entry.php?id=52 |
| Paul Cézanne | Trois Baigneuses | Oil on Canvas | 12 x 13 in. | 1875 | Private Collections | http://www.cezannecatalogue.com/exhibitions/entry.php?id=52 |
| Paul Cézanne | Quatre Baigneuses | Oil on Canvas | 10 5/8 x 13 5/8 in. | 1876-1877 | Barnes Foundation, Philadephia | http://www.cezannecatalogue.com/exhibitions/entry.php?id=52 |
| Paul Cézanne | Quatre Baigneuses | Oil on Canvas | 15 x 18 1/8 in. | 1877-1878 | Pola Museum of Art, Kanagawa | http://www.cezannecatalogue.com/exhibitions |
| Paul Cézanne | Cinq Baigneuses | Oil on Canvas | 15 1/2 x 16 1/2 in. | 1877-1878 | Barnes Foundation, Philadephia | http://www.cezannecatalogue.com/exhibitions |
| Paul Cézanne | Cinq Baigneuses | Oil on Canvas | 17 7/8 x 21 5/8 in. | 1877-1878 | Musee Picasso, Paris | http://www.cezannecatalogue.com/exhibitions |
| Paul Cézanne | Cinq Baigneuses | Oil on Canvas | 15 x 16 1/8 in. | 1877-1878 | Private Collection | http://www.cezannecatalogue.com/exhibitions |
| Paul Cézanne | Baigneuse | Oil on Canvas | 8 5/8 x 5 1/2 in | 1877-1878 | Kuboso Memorial Museum of Arts | http://www.cezannecatalogue.com/exhibitions |
| Paul Cézanne | Baigneur vu de dos | Oil on Canvas | 9 3/8 in. x 7 1/2 in. | 1877-1878 | Private Collection | http://www.cezannecatalogue.com/exhibitions |
| Paul Cézanne | Baigneur aux bras écartés | Oil on Canvas | 28 3/4 x 23 5/8 in. | 1877-1878 | Private Collection | http://www.cezannecatalogue.com/exhibitions |
| Paul Cézanne | Cinq Baigneurs | Oil on Canvas | 13 5/8 x 15 in. | 1879-1880 | The Detroit Institute of Art | http://www.cezannecatalogue.com/exhibitions |
| Paul Cézanne | Cinq Baigneurs | Oil on Canvas | 23 5/8 x 28 3/4 in. | 1880-1882 | Private Collection | http://www.cezannecatalogue.com/exhibitions |
| Paul Cézanne | Baigneur | Oil on Canvas | 12 5/8 x 8 5/8 in. | 1877-1878 | Private Collection | http://www.cezannecatalogue.com/exhibitions |
| Paul Cézanne | Le Bain | Oil on Canvas | 13 13/16 in. x 8 11/16 in. | 1880-1882 | Staatsgalerie, Stuttgart | http://www.cezannecatalogue.com/exhibitions |
| Paul Cézanne | Baigneur debout vu de dos | Oil on Canvas | 13 in. x 8 11/16 in. | 1879-1882 | The Art Institute of Chicago | http://www.cezannecatalogue.com/exhibitions |
| Paul Cézanne | Baigneur debout vu de dos | Oil on Canvas | 10 13/16 in. x 6 13/16 in. | 1879-1882 | Henry and Rose Pearlman Foundation | http://www.cezannecatalogue.com/exhibitions |
| Paul Cézanne | Quatre Baigneuses | Oil on Canvas | 13 13/16 in. x 15 5/8 in. | 1880 | Private Collection | http://www.cezannecatalogue.com/exhibitions |
| Paul Cézanne | Baigneurs et Baigneuses | Oil on Canvas | 7 1/2 in. x 8 5/16 in. | 1880 | Ohara Museum, Kurashiki | http://www.cezannecatalogue.com/exhibitions |
| Paul Cézanne | Cinq Baigneuses | Oil on Canvas | 25 5/8 x 25 5/8 in | 1885 | Kunst Musuem, Basel | http://www.cezannecatalogue.com/exhibitions |
| Paul Cézanne | Le Grand Baigneur | Oil on Canvas | 50 x 38 1/8 in. | 1885 | The Museum of Modern Art, New York | http://www.cezannecatalogue.com/exhibitions |
| Paul Cézanne | Six Baigneuses also known as Les Ondines | Oil on Canvas | 13 x 17 3/8 in | 1887 | Private Collection, Geneva | http://www.cezannecatalogue.com/exhibitions |
| Paul Cézanne | Baigneurs | Oil on Canvas | 23 5/8 x 31 7/8 in. | 1890 | Musee d'Orsay, Paris France | http://www.cezannecatalogue.com/exhibitions |
| Paul Cézanne | Baigneurs | Oil on Canvas | 20 11/16 in. x 25 5/16 in. | 1890-1892 | Saint Louis Art Museum | http://www.cezannecatalogue.com/exhibitions |
| Paul Cézanne | Quatre Baigneuses | Oil on Canvas | 28 3/8 x 36 1/4 in. | 1888-1890 | Ny Carlsberg Glyptotek, Copenhagen | http://www.cezannecatalogue.com/exhibitions |
| Paul Cézanne | Baigneuses | Oil on Canvas | 11 in. x 17 5/16 in. | 1890 | Musee D'Orsay, Paris France | http://www.cezannecatalogue.com/exhibitions |
| Paul Cézanne | Baigneuses | Oil on Canvas | 11 1/4 x 20 in. | 1890-1895 | Stiftung Langmatt Sidney and Jenny Brown | http://www.cezannecatalogue.com/exhibitions |
| Paul Cézanne | Baigneurs | Oil on Canvas | 15 3/8 x20 7/8 in | 1890 | Private Collection | http://www.cezannecatalogue.com/exhibitions |
| Paul Cézanne | Baigneurs en plein air | Oil on Canvas | 21 1/4 x 25 5/8 in. | 1890-1891 | The State Hermitage Museum, St. Petersburg | http://www.cezannecatalogue.com/exhibitions |
| Paul Cézanne | Baigneurs | Oil on Canvas | 8 5/8 x 13 in. | 1892 | Musee de Beaux-Arts, Lyon | http://www.cezannecatalogue.com/exhibitions |
| Paul Cézanne | Baigneurs et Baigneuses | Oil on Canvas | 8 7/8 x 13 15/16 in | 1890 | The Art Institute of Chicago | http://www.cezannecatalogue.com/exhibitions |
| Paul Cézanne | Groupe de Baigneuses | Oil on Canvas | 18 1/2 x 30 1/4 in. | 1895 | Ordrupgaard Collection, Copenhagen | http://www.cezannecatalogue.com/exhibitions |
| Paul Cézanne | Baigneurs | Oil on Canvas | 7 1/2 x 10 1/4 in. | 1890-1895 | Private Collection | http://www.cezannecatalogue.com/exhibitions |
| Paul Cézanne | Groupe de Baigneurs | Oil on Canvas | 11 1/2 x 15 1/2 in. | 1892-1894 | Barnes Foundation, Philadelphia | http://www.cezannecatalogue.com/exhibitions |
| Paul Cézanne | Le Bain | Oil on Canvas | 10 1/4 x 15 3/4 in. | 1892-1894 | Pushkin Museum, Moscow | http://www.cezannecatalogue.com/exhibitions |
| Paul Cézanne | Groupe de Baigneurs | Oil on Canvas | 8 1/2 x 12 1/8 in. | 1895 | Philadelphia Museum of Art | http://www.cezannecatalogue.com/exhibitions |
| Paul Cézanne | Les Grandes Baigneuses | Oil on Canvas | 53 1/2 x 75 1/4 in. | 1894-1905 | National Gallery, London | http://www.cezannecatalogue.com/exhibitions |
| Paul Cézanne | Les Grandes Baigneuses | Oil on Canvas | 52 3/8 x 81 1/2 in. | 1895-1906 | Barnes Foundation, Philadelphia | http://www.cezannecatalogue.com/exhibitions |
| Paul Cézanne | Les Grandes Baigneuses | Oil on Canvas | 82 x 98 in. | 1906 | Philadelphia Museum of Art | http://www.cezannecatalogue.com/exhibitions |
| Paul Cézanne | Baigneuses | Oil on Canvas | 11 x 14 1/4 in. | 1900-1904 | Private Collection | http://www.cezannecatalogue.com/exhibitions |
| Paul Cézanne | Baigneuses | Oil on Canvas | 20 1/8 x 24 1/4 in | 1899-1904 | The Art Institute of Chicago | http://www.cezannecatalogue.com/exhibitions |
| Paul Cézanne | Groupe de Sept Baigneurs | Oil on Canvas | 14 5/8 x 17 3/4 in. | 1900 | Fondation Beyeler, Riehen, Basel | http://www.cezannecatalogue.com/exhibitions |
| Paul Cézanne | Baigneurs | Oil on Canvas | 10 5/8 x 18 1/4 in. | 1898-1900 | The Baltimore Museum of Art | http://www.cezannecatalogue.com/exhibitions |
| Paul Cézanne | Baigneurs | Oil on Canvas | 8 5/8 x 13 in. | 1899-1900 | Musee d'Orsay, Paris France | http://www.cezannecatalogue.com/exhibitions |
| Paul Cézanne | Baigneurs | Oil on Canvas | 10 5/8 x 8 5/8 in | 1900 | Location Unknown | http://www.cezannecatalogue.com/exhibitions |
| Paul Cézanne | Baigneurs | Oil on Canvas | 16 5/8 x 21 5/8 in. | 1900-1904 | Musee d'Orsay, Paris France | http://www.cezannecatalogue.com/exhibitions |
| Paul Cézanne | Baigneurs | Oil on Canvas | 11 7/8 x 17 3/8 in. | 1900 | Location Uknown | http://www.cezannecatalogue.com/exhibitions |
| Paul Cézanne | Esquisse deBaigneurs | Oil on Canvas | 7 7/8 x 13 in. | 1900-1902 | Private Collection | http://www.cezannecatalogue.com/exhibitions |
| Paul Cézanne | Baigneuses | Oil on Canvas | 11 1/2 x 9 1/4 in. | 1902-1906 | Private Collection | http://www.cezannecatalogue.com/exhibitions |
| Paul Cézanne | Esquisse de Baigneurs | Oil on Canvas | 12 5/8 x 15 3/4 in. | 1902-1906 | Private Collection | http://www.cezannecatalogue.com/exhibitions |
| Paul Cézanne | Esquisse de Baigneurs | Oil on Canvas | 25 5/8 x 31 7/8 in. | 1900-1906 | Fondazione Magnani-Rocca, Parma | http://www.cezannecatalogue.com/exhibitions |
| Paul Cézanne | Baigneuses | Oil on Canvas | 13 3/4 x 8 5/8 in. | 1900 | Private Collection | http://www.cezannecatalogue.com/exhibitions |
| Paul Cézanne | Esquisse de Baigneuses | Oil on Canvas | 9 x 6 5/8 in. | 1900 | Becon Collection, Greenwich | http://www.cezannecatalogue.com/exhibitions |
| Paul Cézanne | Baigneurs | Oil on Canvas | 9 x 10 1/2 in. | 1902-1904 | Barnes Foundation, Philadelphia | http://www.cezannecatalogue.com/exhibitions |
| Paul Cézanne | Etude de Baigneuses | Oil on Canvas | 8 3/8 x 12 3/4 in. | 1900-1906 | Museum Rosengart, Lucerne | http://www.cezannecatalogue.com/exhibitions |
| Paul Cézanne | Baigneuses | Oil on Canvas | 29 x 36 3/8 in. | 1902-1906 | Private Collection | http://www.cezannecatalogue.com/exhibitions |
| Paolo Veronese | Les Noces de Cana (before conservation) | Oil on Canvas | 22 ft.3 in. x 32 ft | 1563 | Louvre (unrestored) | https://www.wikiart.org/en/paol o-veronese/the-marriage-at-cana- |
| Paolo Veronese | Les Noces de Cana (digital facsimile) | Digital Reproduction | 22 ft. 3 in. x 32 ft. | 2006 | Fondazione Giorgio Cini, Venice | https://www.cineclubdecaen.com/peinture/peintres/veronese/nocesdecana.jpg |
Table 2.
SUPPLEMENTARY TABLE II: Golden Windows
Figure 19.
SUPPLEMENTARY TABLE III: Golden Strips
Figure 20.
Notes
[1] In A New
History of the Humanities: The Search for Principles and Patterns
from Antiquity to the Present (Oxford: Oxford University
Press, 2013), Rens Bod maps art history’s trajectory in the western
world. For Bod, the formal study of art history begins with Vitruvius’s
theory of harmonious proportion in On
Architecture (15 BCE) and continues with Pliny’s discussions
of illusionism in Natural History (77 CE).
Though China had a thriving field of art historical scholarship in the
Middle Ages, the western world produced few written discussions of art
between Pliny and Alberti’s works. Bod cites Alberti’s On Painting (1435) as the first theoretical
treatise on art, followed by Piero della Francesca’s “On the Perspective for Painting” (1435), A
Treatise on Painting, attributed to Leonardo da Vinci and compiled by
Francesco Melzi (1540), then Vasari’s Lives of the
Most Excellent Painters, Sculptors and Architects (1550).
Bod views the advent of the digital humanities as a natural extension of
the general search for principles and patterns that directs humanistic
inquiry. 311-325.
[2] Kugler divided art
history into pre-Greek, classical, romantic and modern periods.
Burkhardt identified the features of Renaissance art. Wölfflin
distinguished Baroque from Renaissance art through the relations of
differences principle employed in structural linguistics. In
analytically comparing paintings, Wölfflin showed that Renaissance art
is “linear, flat, and closed,” while Baroque art is “painterly,
deep, and open.”
[3] Wikipedia contributors, “Heinrich Wölfflin,” Wikipedia, The Free
Encyclopedia, (accessed September 13, 2017). https://en.wikipedia.org/wiki/Heinrich_W%C3%B6lfflin.
[4] Bod, p. 320.
“No matter how much the digital, computational
approach is in its infancy, it provides a powerful tool for testing
hypotheses relating to paintings.”
[5] Matthew Battles and Michael Maizels, “Collections
and/of Data: Art History and the Art Museum in the DH Mode”
in Debates in the Digital Humanities
(2016). http://dhdebates.gc.cuny.edu/debates/2.
[6] See also Vols. 7531 (2010) and 7869
(2011).
[7] The New York Times announced that The
Metropolitan Museum is making 375,000 images from its collections
available online “for however you want to use
them.” The National Gallery of Art in Washington, The
Rijksmuseum in Amsterdam, and the Museum of Modern Art in New York have
also made their collections freely available to the public for
downloading. Joshua Baron, “MET Museum Makes
350,0000 Images Free.”
New York Times, February 7, 2017.
[8] “It should be difficult today to conceive
of the computer as any more than a speedy idiot obeying a set of
precise instructions; but many in the humanities do indeed continue
to regard it as a black and magical (or black-magical) box — throw
the data at it, and somehow the computer will make sense of
them.” Michael Greenhalgh, A Companion
to Digital Humanities. http://www.digitalhumanities.org/companion/. Stephen Ramsay
in Humane Computation, summarizes
objections to DH: “There are many who think scatter
plots filled with data points drawn from, say, English novels, are
already a crime against the humanities — the death of all that is
good and pure about humanistic study. For them, the problem is
positivism in its properly technical sense. They fear an
epistemology that does not merely value empirical data, but which
(in its extreme philosophical forms) considers empirical data to be
the only valid form of evidence. They imagine a computationally
driven history or French literature curriculum that forsakes the
ancient circle of the seminar for the modern angles of the server
room. They imagine humanistic conversation debasing itself in the
form of technical cavils, humanistic ethics becoming nothing more
than ‘practical business ethics,’ and teaching degenerating
into mere training.”
[9] www.sciencedaily.com/releases/2019/01/190107131236.html.
Accessed 1/9/19.
[10] In the context of book history, and the shift from orality to
literacy, Marshall McLuhan discusses the way technology
“extends” the senses in The
Gutenberg Galaxy: The Making of Typographic Man. Toronto:
University of Toronto Press, 1965. 40.
[11] J.T.
Clark’s famous “Cézanne’s Freud”. Representations 52. Fall 1995 is
representative of this approach. Of Cézanne’s Baigneurs en repose he writes, “never,
for a start, has a picture declared itself so openly — so awkwardly
— made out of separate, overdetermined parts coexisting only in
sufferance.” 94.
[12] “The practices
include the embrace of minimal computing, small data sets, local
archives, and freely available platforms for creating small-scale
digital humanities projects while working with undergraduate
students.” Roopika Risam and Susan Edwards, “Micro DH: Digital Humanities at the Small
Scale”
https://dh2017.adho.org/abstracts/196/196.pdf.
[13]
In “Distant Reading and Intellectual
History”, Ted Underwood writes that distant reading “doesn’t overemphasize technology, and it candidly
admits that new methods are mainly useful at larger scales of
analysis.” Our work here scales down a distant reading
approach. 138 paintings is still more than the brain can handle in
making comparisons, nevertheless, the data set is small enough to allow
the researcher to toggle between the images and graphical output to
verify hypotheses and make discoveries.
[14] Can digital images replace
physical paintings as serious objects for study? Certainly, there are
irreducible elements to paintings that do not translate well
electronically or in print, and that demand first-person viewing, such
as the luminous and changing effects of varnishes and glazes on
paintings, and the layering and aging of paints. Whether in print or
online, all reproductions of paintings are
“approximations”. In even the most expensively
illustrated books, the same paintings may vary in color. Phillip Ball
discusses the limitations of print and the digital reproductions of
works of art in Bright Earth. He observes
how “for a coloristically complex picture like
Danae, no two reproductions will look the same.”
Nevertheless, “All written discourses of art must
rely on reproductions to make their point.” Art Historians
depend on approximations for their work, and computer-assisted systems,
though they convert these approximations into numbers, can provide us
with data that is inaccessible subjectively, data that the researcher
must interpret.
[15] The Louvre did not acquisition
Ingres’ La Source until 1878, nine years
after Baigneuse debout, s’essuyant les
cheveux was painted. Nevertheless, the painting was
exhibited in the official Paris Salon in 1856 and was famous when
Cézanne was a young student in 1861.
[16] On Cézanne’s famous
statement that he wished to bring “Poussin back to
nature” see Richard Shiff, “Introduction,”
Conversations with Cézanne, xxi. His
footnote, p. 217 provides valuable bibliography on this topic.
[17] Bruno Latour and Adam Lowe
have discussed of the painting’s history as a material object and as a
facsimile.
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Published by: The Alliance of Digital Humanities Organizations and The Association for Computers and the Humanities
Affiliated with: Digital Scholarship in the Humanities
DHQ has been made possible in part by the National Endowment for the Humanities.
Copyright © 2005 -
Unless otherwise noted, the DHQ web site and all DHQ published content are published under a Creative Commons Attribution-NoDerivatives 4.0 International License. Individual articles may carry a more permissive license, as described in the footer for the individual article, and in the article’s metadata.
