1. The essay discusses what counts as knowledge in the arts by comparing it to knowledge in mathematics. Knowledge in art includes an artist's intentions in creating a work, as well as audience interpretations, which can vary unlike the fixed truths in mathematics. 2. Cultural and historical context also provide knowledge in art by revealing aspects of societies and traditions. In contrast, mathematics is a more universal language where concepts remain the same across cultures. 3. Emotions may result from artistic works but are not knowledge in mathematics, which is about tangible discoveries rather than intangible human experiences captured by art.

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Theory of Knowledge
Essay
Essay Question:
What counts as knowledge in the arts?
Discuss by comparing to one other
area of knowledge.
Report word count: 1598
Number of pages: 9
Done by: Sarah Lee Shan Yun
School: ACS (International), Singapore

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Art, the expression of creative skill, comprises a vast selection of genres,
medias, forms, periods and movements. Forms comprise of anything from visual arts
(paintings, installations, photography, etc.) to sound or written performances (music,
theatre, dance, film, literature, etc.). Knowledge in art is an understanding or the
presence of an opinion about a piece of art in the knower. It is assumed that
knowledge in art exists, though this knowledge may be implicit, particularly because
there is no ‘right’ or ‘wrong’ way to interpret a piece of art. The question in this
exploration would thus be: what is the nature of the information acquired from
experiencing art, regardless of its source? Mathematics, by contrast, has a reputation
for being explicit and discernable from the other areas of knowledge. Knowledge in
mathematics, ostensibly, equates to an understanding of theories and formulas, as well
as the methods of applying those devices in problem solving. The knowledge in
mathematics contrasts significantly with the knowledge in art, although surprisingly,
there are similarities, which will be discussed later in this essay. This investigation
explores the following notions: that the artist’s intent (to communicate the brilliance
of the human mind, societal meaning, culture, emotion) and the audience’s response,
all count as knowledge in the arts.
Intentionalism is the thesis that an artist’s intent possesses a determining role
in the creation of an artwork (Livingston, 1951). To know what an artist is aiming to
achieve in an art piece is to have knowledge of the artwork. For example, in the
conceptual installation entitled ‘One and Three Chairs’ by Joseph Kosuth, the artist
strives to encourage ‘an inquiry into the nature of art’ (MoMA, 1999), the implication
Picture 1 – Joseph Kosuth, 1965, One and Three
Chairs. Installation. The Museum of Modern Art.

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being that the same object can be comprehended both visually, verbally or
organically. Because the artist was successful in deciding and disseminating his
intentions, the audience thus achieves knowledge in the artwork. By contrast, the
theory of intentionalism does not occur in mathematics because mathematicians
discover knowledge, rather than create it. For example, the ancient Babylonians
discovered the Pythagoras theorem through measurements and recordings of the
lengths of right-angled triangles on ancient clay tablets (Smoller, 2001). It is
impossible for mathematicians to elect the answer that they expect. The knowledge of
the equation a2
+ b2
= c2
is the output or result of the process of investigation,
whereas in art, knowledge in the form of intention is the input in the process of
expression.
What, therefore, do artists intend to
convey? Take for example Leonardo Da
Vinci’s acclaimed portrait of ‘Mona Lisa’.
Technical mastery was undoubtedly an
intention of his – to capture the precise
countenance on the subject’s visage. Could
the mastery of skill or ability of the human
mind, be counted as knowledge in the arts?
From the painting, the knower
acknowledges the level of competence of
its creator and thus the intellectual
capability of human beings to create.
Personally, because I take Art as a subject
in school, I understand how an artistic skill,
just like any other skill, such as that of
solving mathematical problems, contributes
to an individual’s overall ability. Da Vinci, himself, has long been revered as the most
diversely gifted genius in history – an artist, philosopher, inventor, scientist, architect,
and most appropriately, a mathematician (Vasari, 1946). Up to this day
mathematicians are constantly uncovering new theories and solutions to problems
(e.g., the mapping of E8 lead by mathematician Jeffrey Adams in 2007 (Tune,
2007.)), imparting on us the knowledge that mathematics, just like the arts, reveals the
perpetual brilliance of the human mind.
Picture 2 – Leonardo Da Vinci,
1503-07, Mona Lisa. Oil on wood.
The Louvre Museum.

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As observed from Joseph Kosuth’s conceptual installation, not all artists
resolve to exhibit great technique. Another renowned artist, whom I have done
extensive research on during my IB course, is Andy Warhol, a man celebrated as one
of the most influential pop artists of all time. Often criticized for his ‘lack of talent’
(Colacello, 1990), Warhol aimed to distance himself from traditional ideals of
proficiency in skill, placing more emphasis on the essence of his work – the hyperbole
of the mass produced, popular culture of America in the 1950s to 1960s (Rosenberg,
2001). In any case, the knowledge consists of suggestions regarding society in
general. Can mathematics, too, reveal knowledge concerning society? The Sistine
Chapel in Vatican, designed by the architects Baccio Pontelli and Giovannio de Dolci
between 1475 and 1481 (Sacred Destinations, 2010.), is an example of a masterpiece
of both mathematics and art. One prominent element of the building would be the
proportions of it’s length to breadth to height in the ratio 3:1:2 respectively. When
interpreted mathematically, this knowledge reports the physical volume, structure and
size of the design. When an artistic approach is taken into consideration, however, the
refinement and magnificence of renaissance architecture is expressed, hence the
notion that the knowledge in mathematics pertains to the tangible aspects of society
whilst knowledge in the arts pertains to the more intangible psyche of mankind.
Picture 3 – Andy Warhol, 1962, Soup Cans. Synthetic polymer paint on canvas.
The Museum of Modern Art.

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Expressionism is a
style of art that seeks to
express emotional experience
rather than impressions of
the external world. Edvard
Munch’s ‘The Scream’ was
sold for a hefty price of $120
million in May 2012
(Hayden, 2012), making the
knowledge within the work
relatively significant.
Expressionism also prevails
in music. One notable figure
in the movement was Arnold
Schoënberg, who
experimented with
unorthodox free atonality in
his piano works (Schirmer,
2010). His composition
entitled “Three Piano Pieces,
No.1” expresses erratic variations in mood through abrupt shifts in tempo, dynamics,
harmony and discordance. The artist’s emotions can therefore serve as knowledge in
the arts, comprehended by the audience through sensory perception of the artist’s use
of elements, principles and devices. How does this compare with mathematics as an
area of knowledge? Emotion, as a way of knowing, is hardly associated with
mathematics. Although, when one mentions the moment where Archimedes cried
“eureka” and charged down the streets naked in excitement upon discovering the
buoyancy principle (Russel, 2001), this hypothesis does not seem to be true. Whilst
emotions may result from the revelation of knowledge, it is not however, the
knowledge attained from the actual investigation. Emotions are learnt through the
experiences of life, even before an understanding of simple reasoning is grasped (e.g.,
an infant’s cry upon the absence of a parent). Therefore, unlike in the arts, emotion is
probably not knowledge in mathematics.
Picture 4 – Edvard Munch, 1893, The Scream. Oil,
tempera and pastel on cardboard. National Gallery,
Oslo, Norway.

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In the anthropology of art, the socio-cultural context of aesthetics (be it objects
used in beliefs and rituals or sculptural materials) is studied (Coote, 2009). Cave
paintings in the Paleolithic era were the earliest form of art known to man
(Encyclopedia of Art, 2012). The lion dance, performed in my country during the
Chinese New Year period, forms a prominent element of Chinese culture. These are
examples of art forms that reflect traditions and the customs of life surrounding the
environment of the artist or performer. Through the analysis and examination of these
crafts, we gain a better awareness the heritage and history of communities, old and
new, therefore culture is knowledge in art. Can mathematics relate to culture as well?
Mathematics is often described to be a ‘universal language’ (Annenberg Foundation,
2012) because in today’s world, most countries use the same symbols and numbers to
communicate concepts through formulas and equations. However, this notion cannot
be generalized because some populations in countries, such as China, still utilize
different mathematical systems (i.e., the abacus, which I learned to use in primary
school (Zhou, 2012)). Yet the number ‘1’, though communicated using different
languages, fundamentally means the same thing. In essence, the concepts of
mathematics remain the same (e.g., π will always equal 3.142… no matter how it is
written) and thus culture is unlikely to be knowledge in mathematics.
Picture 5 – Unknown, 2500000 – 10000 BCE, Paleolithic Cave Paintings.
Minerals, ochres, burnt bone meal and charcoal mixed with water.
UNESCO world heritage site.

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So far the theory of
intentionalism has been discussed, but
on the other hand, does unintentional
art exist? If so, does it still possess
knowledge? Elephant art is an example
of anti-intentionalism, allowing the art
piece to take on a life of its own. For
my theory of knowledge presentation,
Jackson Pollock, an abstract
expressionist, was the focus of
investigation, where a survey was
conducted amongst my peers to
determine the effect his paintings had
on emotion. To some, his paintings
reminded them of fabric, whilst to
others, of vegetation and chaos. I came
to realize that knowledge in art does
not necessarily have to be inclined by
the artist, but rather, may arise from
the audience. The viewer’s own interpretation, be it the painting’s significance, value,
meaning, emotion or culture, creates interest in the art piece, and thus knowledge,
regardless of the artist’s intent. This explains how Jackson Pollock’s action paintings
have long survived as a topic of discussion, fetching high prices in art auctions ($140
million (Vogel, 2006)), even though he does not provide much insight into the
intentions of his paintings. Knowledge in mathematics, however, cannot vary because
there is always a truth – i.e., the answer to a mathematical problem is always the
same, regardless of the individual attempting to solve it.
Though it may be evident that there is knowledge in art, it is difficult to define
this knowledge, let alone ‘count’ or list it down. Perhaps there is no knowledge in art
at all or perhaps the knowledge in art is limitless. However, a general idea of the
information garnered through experiencing art tells us that the knowledge in art
differs greatly from that of the other areas of knowledge, particularly in mathematics.
It is only upon appreciating these differences that we get closer to understanding the
theory of knowledge.
Picture 6 – Nong Bank (Elephant), 2012,
Untitled. Acrylic on canvas. Samutprakan
Zoo, Thailand.

8. 8
Bibliography
Internet
• Annenberg Foundation, 2012. Man in daily life, The Universal Language.
<http://www.learner.org/interactives/dailymath/language.html> [7/08/12]
• Colacello, B., 1990. Holy Terror: Andy Warhol Close Up.
<http://www.warholstars.org/warhol/warhol1/andy/warhol/can/feld23.html>
[6/08/12]
• Coote, J., 2009. Anthropology of Art.
<http://www.discoveranthropology.org.uk/about-anthropology/specialist-
areas/anthropology-of-art.html?lang=> [7/08/12]
• Encyclopedia of art, 2012. Earliest art.
<http://www.visual-arts-cork.com/earliest-art.htm#first> [7/08/12]
• Hayden, E., 2012. Buyer of Edvard Munch’s $120 million ‘Scream’ Revealed.
<http://newsfeed.time.com/2012/07/12/buyer-of-edvard-munchs-120-million-
scream-revealed/> [7/08/12]
• Livingston, P., 1951. Intentionalism in Aesthetics.
<http://muse.jhu.edu/login?auth=0&type=summary&url=/journals/new_literar
y_history/v029/29.4livingston.html> [6/08/12]
• Rosenberg, J., 2001. Andy Warhol.
<http://history1900s.about.com/od/artists/p/warhol.htm> [6/08/12]
• Russel, D., 2001. Archimedes.
<http://math.about.com/library/blbioarchimedes.htm> [7/08/12]
• Sacred Destinations., 2010. Sistine Chapel.
<http://www.sacred-destinations.com/italy/rome-sistine-chapel> [6/08/12]
• Schirmer, G., 2010. Arnold Schoenberg.
<http://www.schirmer.com/default.aspx?TabId=2419&State_2872=2&Compo
serId_2872=1390> [7/08/12]
• Smoller, L., 2001. Isaac Newton (1642-1727).
<http://ualr.edu/lasmoller/newton.html> [6/08/12]
• The Museum of Modern Art, 1999, MoMA Highlights
<http://www.moma.org/collection/object.php?object_id=81435> [6/08/12]
• Tune, L., 2007. Math Breakthrough by UM-led Team Excites Congress and
the World.

9. 9
<http://www.newsdesk.umd.edu/scitech/release.cfm?ArticleID=1421>
[6/08/12]
• Vasari, G., 1946. Lives of the Artists: Biographies of the Most Eminent
Architects, Painters and Sculptors of Italy.
<http://www.ucmp.berkeley.edu/history/vinci.html> [6/08/12]
• Vogel, C., 2006. A Pollock is Sold Possibly for a Record Price.
<http://www.nytimes.com/2006/11/02/arts/design/02drip.html?_r=1>
[7/08/12]
• Zhou, R., 2012. The Chinese Abacus.
<http://www.chinahighlights.com/travelguide/culture/the-chinese-abacus.htm>
[7/08/12]
Pictures
1. Joseph Kosuth, 1965, One and Three Chairs. Installation. The Museum of
Modern Art.
<http://www.moma.org/collection/object.php?object_id=81435> [6/08/12]
2. Leonardo Da Vinci, 1503-07, Mona Lisa. Oil on wood. The Louvre Museum.
<http://www.davincithegenius.com/> [6/08/12]
3. Andy Warhol, 1962, Soup Cans. Synthetic polymer paint on canvas. The
Museum of Modern Art.
<http://farm2.static.flickr.com/1128/562288842_4317a25b67.jpg> [6/08/12]
4. Edvard Munch, 1893, The Scream. Oil, tempera and pastel on cardboard.
National Gallery, Oslo, Norway.
<http://www.arts-stew.com/wp-content/uploads/2012/05/The-Scream.jpg>
[7/08/12]
5. Unknown, 2500000 – 10000 BCE, Paleolithic Cave Paintings. Minerals,
ochres, burnt bone meal and charcoal mixed with water. UNESCO world
heritage site.
<http://leseyzies-tourist.info/tag/southwestern-france> [7/08/12]
6. Nong Bank (Elephant), 2012, Untitled. Acrylic on canvas. Samutprakan Zoo,
Thailand.
<http://news.xinhuanet.com/english/photo/2012-05/30/c_131620276_2.htm>
[7/08/12]