DESMA 9: Art, Science and Technology

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DESMA 9Art, Science and Technology
Mathematics Perspective Time Space

• "Clouds are not spheres, mountains are not
  cones, coastlines are not circles, and bark is
  not smooth, nor does lightning travel in a
  straight line.
• - Benoit Mandelbrot

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• TODAY 4/9/07
• Quick Review of last weeks
• ZERO
• Perspective
• Escher
• Buckminster Fuller
• Mandelbrot

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ZERO
"zero" derives ultimately from the Arabic sifr
which also gives us the word "cipher"
Around 700 BC, uses three hooks to denote an
empty place in the positional notation. On a
tablet found at Kish, an ancient Mesopotamian
city located east of Babylon in what is today
south-central Iraq. Not used as a number but a
punctuation mark
Greek astronomers began to use the symbol O.
Some historians favor the explanation that it is
omicron, the first letter of the Greek word for
nothing -- "ouden". Zero appeared in India in
650 AD, and spread to China and Islamic
countries, It was not until the 1600s the zero
was used in the West, after encountering a lot
of resistance!
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ZERO
during the Middle Ages, zero was disparaged as a
mark of infidel sorcery, the sign of the Devil
himself, the canceller of all meaning. For the
Mayans, Zero was the Death God among their lords
of the underworld, and men adopting the persona
of Zero were ritualistically sacrificed in hopes
of staving off the day of zero, the time when
time itself would stop. Only much later was
zero reinterpreted as a symbol of God's power to
create a lot out of naught.
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Upanishads
zero infinity, as alluded to in the
Upanishads and reflected in the Sanskrit word
poornam which means both zero and full
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Y2K bug zero causes problemseven recently!
Recently many people throughout the world
celebrated the new millennium on 1 January 2000.
Of course they celebrated the passing of only
1999 years since when the calendar was set up no
year zero was specified. Although one might
forgive the original error, it is a little
surprising that most people seemed unable to
understand why the third millennium and the 21st
century begin on 1 January 2001.
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PERSPECTIVE
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al-Haytham
Al Haytham, around 1000 A.D. gave the first
correct explanation of vision, showing that
light is reflected from an object into the eye.
He studied the complete science of vision,
called perspectiva in medieval times, and
although he did not apply his ideas to painting,
the Renaissance artists later made important use
of his study.
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Duccio first attempt Annunciation 1316
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13th century GIOTTO The Visitation Not a
precise formulation Intuitive approach
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Albrecht Dürer (German, 1471-1528), Melancholia
1, 1514
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BRUNELLESCHI Credited with the first correct
formulation of linear perspective, about 1413
His perspective paintings were lost but a
Trinity fresco by Massacio from this same
period still exists. He used Brunelleschis
perspective principles.
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VANISHING POINT Developed by Brunellesci, Massacio
preserved Alberti described
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Albertis treatise On Painting, 1435 Written in
Latin for scholars and Italian for the general
audience
Perspective is necessary in order to understand
painting. It is completely mathematical,
concerning the roots in nature from which arise
this graceful and noble art. A painting is the
intersection of a visual pyramid at a given
distance, with a fixed centre and a defined
position of light, represented by art with lines
and colours on a given surface.
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If you place the intersection one metre from the
eye, the first object, being four metres from
the eye, will diminish by three-quarters of its
height on the intersection and if it is eight
metres from the eye it will diminish by
seven-eighths and if it is sixteen metres away
it will diminish by fifteen-sixteenths, and so
on. As the distance doubles so the diminution
will double.
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Piero de la Francesca leading artist of his
time, also leading Mathematician in 15tn century
Rennaisance
Pieros illustration of a dodecahedron
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Leonardo da Vinci Mathematics Art Fused into
a Single concept
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(No Transcript)
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GOLDEN RATIO
"Vitruvian Man" by Leonardo da VinciGallerie
dell'Accademia, Venice, Italy
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ARCHITECTURE
The Parthenon, Athens, superimposed with a
diagram demonstrating the use of the Golden Mean
in the design
Architect Charles E. Jeanneret, known as "Le
Corbusier" (French, 1887-1965), often used
golden rectangles in his designs for buildings.
One of these is the United Nations building in
New York. The proportions of its vertical and
horizontal dimensions correspond to the Golden
Mean.
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Golden ratio and Hollywood
Phi Nature of Growth
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DIMENSIONALITYMOVING AWAY FROMFLATLAND
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Maurits Escher
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In a lecture in 1953, Escher said I have often
felt closer to people who work scientifically
(though I certainly do not do so myself) than
to my fellow artists.
Circle Limit III
In 1958 he met mathematician Coxeter and they
became life-long friends. In 1995, Coxeter
published a paper which proved that Escher
reached mathematical perfection in one of his
etchings. Escher got it absolutely right to the
millimetre, absolutely to the millimetre ....
Unfortunately he didn't live long enough to see
my mathematical vindication.
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In mathematical quarters, the regular division of
the plane has been considered theoretically. ...
Mathematicians have opened the gate leading
to an extensive domain, but they have not
entered this domain themselves. By their very
nature they are more interested in the way in
which the gate is opened than in the garden
lying behind it.
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Buckminster Fuller
Octet Truss
Tensegrity
Geodesic dome
How they work
Synergetics
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Artists influenced by Buckminster Fuller John
Cage Joseph Albers Kenneth Snelson
Others impressed by him
Bucky class we Elaine de Kooning and Joseph
Albers, Black Mountain college, 1948
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Piet Mondrian
1926
1942
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Mandelbrot The Psychedelic world of FRACTALS
Fibonacci, Fractals and Financial Markets -
Socionomics.net
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Contemporary Artists using Mathematics http//www
.sciencenews.org/articles/20061118/mathtrek.asp
http//www.sciencenews.org/articles/20060506/matht
rek.asp
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Sol Lewitt
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John Sims
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Casey Reas Mark Pomilio
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MUSIC MATHEMATICS
MATH ROCK Gil Kuno presents on
Wednesday Yoshida Tatsuya, one of the
originators of the RUINS and the cited as the
"indisputable master drummer of the Japanese
underground"
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On campus
IPAM
In the city