DIVINE POMEGRANATE

Daniel R. Kirk

Assistant Professor

Department of Mechanical and Aerospace Engineering

Florida Institute of Technology

Tuesday, December 5, 2006

HUM 2052: Western Civilization II

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MOTIVATION

• “In both secondary and higher education there is an abrupt dichotomy between the sciences and the humanities, the mathematician and the poet. ”

• A scientist worthy of his name, above all a mathematician, experiences in his work the same impression as an artist; his pleasure is as great and of the same nature.

- Jules Henri Poincaré (1854 - 1912) in N. Rose, Mathematical Maxims and Minims, Raleigh

NC:Rome Press Inc., 1988

• Accelerating Universe, Mario Livio, discusses “beauty” as an essential ingredient in fundamental theories of universe

• Paintings, like novels and poems, can have different layers of meaning

• Experiential test of whether this art is great or good, or minor or abysmal is the effect it has on your own sense of the world and of yourself. Great art changes you. – Sister Wendy Beckett

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HUM 2052: WESTERN CIVILIZATION TIMELINE

• Renaissance Europe ~(14th → 16th century)– Niccolò di Bernardo dei Machiavelli, (May 3, 1469 – June 21, 1527)

• Il Principe (1532)• Discorsi sopra la prima deca di Tito Livio (1531)

• Age of Reason (17th Century) – John Milton (December 9, 1608 – November 8, 1674)

• Paradise Lost (1667, 1674)• Enlightenment (18th Century)

– François-Marie Arouet (Voltaire), (November 21, 1994 – May 30, 1778)• Candide andrew, ou l'Optimisme (1759)

• Industrialism / Imperialism (late 18th and early 19th century) – Fyodor Mikhailovich Dostoevsky (November 11, 1821 – February 9, 1881)

• Crime and Punishment (1866)• Founder of existentialism (?)

• Modernity (1870 and 1910 → present)– Teodor Józef Konrad Korzeniowski (Joseph Conrad), (December 3, 1857 – August 3, 1924)

• Heart of Darkness (1899)• Postmodern (modern historical period has passed)

– Thomas Pynchon (born May 8, 1937)• The Crying of Lot 49 (1966)

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RENAISSANCE / REALISM: OVERVIEW• High Renaissance (1495-1525) short-lived (Da Vinci, Michelangelo, Raphael)

– Renaissance art is more lifelike than in art of Middle Ages– Work drew heavily from art of ancient Greece and Rome– Contrasts of light and dark (chiaroscuro) and smokey atmosphere (sfumato)– Perspective, study of human anatomy and proportion, refinement in techniques

• Flemish, Dutch, and German (Dürer, Cranach, Grünewald, Bosch, Brueghel) – More realistic and less idealized– New verisimilitude in depicting reality– Stylistic residue of sculpture and illuminated manuscripts of Middle Ages

• Renaissance painting reflects– Revolution of ideas and science (astronomy, geography)– Reformation– Painters are not mere artisans but thinkers as well (Dürer)– Painting gained independence from architecture– Not dominated religious imagery, secular subject matter returned

(imagination)– Movable pictures

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MIDDLE AGES → RENAISSANCE

The Mourning of Christ (1305)Giotto di Bondone

(1st Renaissance painter (?))

Byzantine: Eastern Roman Empirefrom ~ 5th century until

fall of Constantinople in 1453

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SAINT CATHERINE OF SIENA RECEIVING THE STIGMATADomenico Beccafumi , 1513-1515

Getty Museum, Los Angles

• Minimum of detail• Striking pose to demonstrate ecstasy, she bends forward as if to meet tilting crucifix

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LA GIOCONDA (LA JOCONDE, MONA LISA)Leonardo da Vinci (1503-5)

Musée du Louvre, Paris• Lisa Gherardini (24), wife of Florentine Francesco del

Giocondo• ‘Mona’ Italian contraction of ‘madonna’, meaning ‘my

lady,’ English ‘Madam,’ → ‘Madam Lisa’• Giocondo also means 'light-hearted' ('jocund' in

English), so "gioconda" means "light-hearted woman“• Not well-known until mid-19th century, Symbolist

movement began to appreciate it, and associated it with their ideas about feminine mystique

– Mythic embodiment of eternal femininity, Pater– “older than the rocks among which she sits”– “has been dead many times and learned the secrets

of the grave”• 2004: guarnello, pregnant or after giving birth• Pyramid shape places ML simply and calmly in space• Armrest dividing element between ML and us

– Attracted to mysterious woman but have to stay at a distance, ‘as if she was a divine creature’

• One of first to depict sitter before imaginary landscape– Represents rather an ideal than a real woman

• Smile mostly drawn in low spatial frequencies, best seen from a distance or peripheral vision (Livingstone)

• ML has no visible facial hair

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WHERE IS LISA?

The Salon Carre and the Grand Galerie of the LourveJohn Scarlett Davis, 1831, British Embasy, Paris

Le Salon CarréGiuseppe Castiglione, 1865

Gallery of the LouvreSamuel F. B. Morse, 1831-1833Musee americain, Giverny

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Cecilia Gallerani (Lady with an Ermine) Leonardo da Vinci (1483-90)

Czartorychi Muzeum, Cracow, Poland

La belle Ferronière Leonardo da Vinci (1490)Musée du Louvre, Paris

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GINEVRA DE' BENCILeonardo da Vinci, (1474-76)

National Gallery of Art, Washington, D.C

• Portrait of Ginevra de' Benci in commemoration of marriage to Luigi Niccolini

• Directly behind is juniper tree

• Reverse of portrait is decorated with a juniper sprig encircled by a wreath of laurel and palm and is memorialized by phrase VIRTUTEM FORMA DECORAT ("Beauty adorns Virtue")

• Italian word for juniper is "ginepro", which leads many to believe that juniper motif is a symbolic pun on Ginevra's name. Fittingly, juniper was also a Renaissance symbol for chastity.

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HONEST APPROACH TO ART

‘Ginevra is beautiful but austere; she has no hint of a smile and her gaze,though forward, seems indifferent to the viewer’

‘There are three things I have always loved but never understood; art, music, and women.’ - Bernard de Fontenelle

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RENAISSANCE / REALISM

• Pope Julius II (December 5, 1443 – February 21, 1513), National Gallery, London• Giuliano della Rovere, Pope from 1503 to 1513, ‘Warrior Pope’• Intimacy of image indicates that Raphael has progressed from narrative compositions to full

dominance of individual subjectivity• Raphael: dated by Julius's beard, which he grew as a token of mortification at having lost

city of Bologna in 1511 and had shaved off by March 1512

• Cappella Sistina• Michelangelo

Buonarroti (1508 – November 1, 1512)

• Special scaffold• 1st plaster layer

began to grow mold because too wet. Intonaco, created by Jacopo l'Indaco, and is still in use today

• Intense understanding of geometry to paint curved vaults

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NO PICTURES PLEASE

Without having seen the Sistine Chapel one canform no appreciable idea of what one manis capable of achieving – Goethe

… before Michelangelo no one had ever articulated and depicted human pathos as he did in those paintings. Since then all of us have understood ourselves just that little bit deeper, and for this reason I truly feel his achievements are as great as the invention of agriculture – Werner Herzog

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The School of AthensRaphael, 1509-1510

Stanze di Raffaello, Apostolic Palace, Vatican City

Plato(portrait of Leonardo da Vinci holding Timaeus)Plato points to heaven

Aristotle(holding a copy of

Nichomachean Ethics)Aristotle point to Earth

Diogenes

Michelangelo

Hypatia of AlexandriaFrancesco Maria I

della RovereMagherite

Raphael

Pythagoras

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THE ENTOMBMENTMichelangelo Merisi da Caravaggio, 1602-03

Pinacoteca Vaticana, Vatican City• Diagonal cascade of mourners

sliding downward to dead, limp Christ and bare stone

• Italian Christs die generally bloodlessly

• Where do arms point?– Dead God → stone– Mary → heaven– Message of Christ: God

come to earth, and mankind reconciled with the heavens

• Theory: cryptic depiction of resurrection

– Westerner's eye typically reads artwork from top left to bottom right much same way it reads printed text

– If painting were reversed it would show an obvious descending line from left to right. But as painting is it shows a prominent ascending line from left to right. Thus showing resurrection.

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MADONNA WITH THE LONG NECKGirolamo Francesco Maria Mazzola (1534-40)

Uffizi, Florence

• Mannerism: late Renaissance art (1530-1580), whose proponents sought to create dramatic and dynamic effects by depicting figures with elongated forms and in exaggerated, out-of-balance poses in manipulated irrational space, lit with unrealistic lighting

• Mannerism appealed to knowledgeable coterie audiences with its arcane iconographic programs and exaggerated new sense of an artistic "personality", an exciting new development at a time when primary purpose of art was to inspire awe and devotion, to entertain and to educate

• Michelangelo displayed tendencies towards Mannerism

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EXECUTION OF LADY JANE GREYPaul Delaroche, 1833 - 1834National Gallery, London

• Jane Grey (1537 - 54) nominated by Edward VI to be next Protestant monarch

• Catholic Mary I, who had a greater claim to throne

• Reigning only nine days, deposed by Mary and executed following year

• Tragic figure alive in British consciences

• Led to block by Sir John Brydges (Lieutenant of Tower)

• Pure historical nonsense– Executed in open air– More than 4 people– Dress not white married– Hair would be tied up

Experiment: look for 20 seconds and monitor focus of attentionBlindfolded face → length of arm to executioner's block → tableau → axe → executioner's faceLieutenant hardly scanned. Of two weeping ladies, woman with back to audience (nape of neck)

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SURREALISM

• Surrealist movement (1920s) based on images from world of dreams and subconscious

– ‘… liberation of our mind, and subsequently the liberation of the individual self and society, can be achieved by exercising the imaginative faculties of the “unconscious mind” to the attainment of a dream-like state different from, or ultimately truer than, everyday reality.’

• Surrealists believe more truthful reality can bring about personal, cultural, and social revolution, and a life of freedom, poetry, etc.

– “Beauty will be convulsive or not at all.” – André Breton

• Juxtaposing common objects in unexpected contexts

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GUERNICAPablo Picasso, 1937

Museo Reina Sofia, Madrid

• Picasso's horror at Nazi bombing of Guernica, Spain on April 26, 1937 during the Spanish Civil War• My life as an artist has been nothing more than a continuous struggle against reaction and the death of

art. How could anybody think for a moment that I could be in agreement with reaction and death?• Task of interpreting the specific meaning of the bull and the horse very tough. Their relationship is a

kind of ballet that was conceived in a variety of ways throughout Picasso's career." When pressed to explain them in Guernica, Picasso said, "...this bull is a bull and this horse is a horse... If you give a meaning to certain things in my paintings it may be very true, but it is not my idea to give this meaning. What ideas and conclusions you have got I obtained too, but instinctively, unconsciously. I make the painting for the painting. I paint the objects for what they are."

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LA PERSISTENCIA DE LA MEMORIASalvador Dalí (1944)

Museum of Modern Art, New York City

• Soft watches: suggest Einstein's theory that time is relative and not fixed• Ants: point to death, decay, and immense sexual desire• Snail :connected to human head (saw a snail on bicycle outside Freud’s house)• Locusts: are a symbol of waste and fear• Egg: to prenatal and intrauterine, thus using it to symbolize hope and love

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DREAM CAUSED BY THE FLIGHT OF A BEE AROUND A POMEGRANATE ONE SECOND BEFORE WAKING UP

Salvador Dalí (1944)Museo Thyssen-Bornemisza, Madrid

• Elephant: inspired Bernini's sculpture (Rome) of elephant to carry an ancient obelisk

• Coupled with image of their brittle legs create a sense of phantom reality

• “The elephant is a distortion in space, its spindly legs contrasting the idea of weightlessness with structure.”

• “...I am painting pictures which make me die for joy, I am creating with an absolute naturalness, without the slightest aesthetic concern, I am making things that inspire me with a profound emotion and I am trying to paint them honestly.” – Salvador Dalí.

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CERVANTES' DON QUIJOTE I.9 AND THE POMEGRANATE

• 2 meanings: geopolitical and moral• Symbol of kingdom of Granada• Ferdinand of Aragon (1492), "I will tear out one

by one the seeds of that pomegranate“• Estandarte de Caballeria [Cavalry Banner] 1580• Pomegranate of Chapter 9 → type of symbolism

that abounds in this town → Toledo.• "Then I went off with the Morisco into the cloister

of the main church …• Created a linguistic, cultural, and geopolitical

emblem of entire history of Spain• Moral symbolism dating from medieval times.

According to J. E. Cirlot, "the pomegranate is a perfect illustration of multiplicity because it is internally subdivided into a multitude of cells“

• Womb: its biblical name rimmon derives from rim, "to bear a child", and its association with Virgin Mary and the Christ child is common in medieval art

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DREAM CAUSED BY THE FLIGHT OF A BEE AROUND A POMEGRANATE ONE SECOND BEFORE WAKING UP

Salvador Dalí (1944)Museo Thyssen-Bornemisza, Madrid

• Geopolitical and moral symbolism in compositions– Dali: Postmodern surrealism of Dali– Cervantes: Renaissance Christian humanism

1. Combination of ancient and contemporary history– Dali frames his surreal event with elephant

invasion of Hannibal and Spanish Civil War– Cervantes moves between Castilian / Basque

conflict of medieval period and tensions in southern Spain during Renaissance

2. Masculine rivalry and female in jeopardy– Threatened female figure positioned at

endpoint of historical & geopolitical trajectory– Dali's Gala-Venus-Humanitas is Proserpine

with pomegranate offering salvation to a Spain that has just suffered a civil war

– Cervantes' Zoraida-Mary-Humanitas offers peaceful resolution to Spanish labyrinth of 16th century

– Each expresses hope that if we can imagine a better world, then we can also make one.

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FINAL THOUGHTS ON POMEGRANATES•

"The pomegranate can be a symbol for a republic whose inhabitants are very much in agreement and united."

— Sebastián de Covarrubias    Tesoro de la lengua castellana o española, 656

• Cervantes use of pomegranate as potentially split open by intercultural violence between Basques and Castilians

• Symbolism associated with imperial conquest of kingdom of Granada

• Political harmony among the diverse citizens of a republic.

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TIME TRANSFIXEDRené Magritte, 1938

The Art Institute of Chicago

• In explaining Time Transfixed, Magritte said: “I decided to paint the image of a locomotive . . . In order for its mystery to be evoked, another immediately familiar image without mystery — the image of a dining room fireplace — was joined.”

• Surprising juxtaposition and scale shift of common and unrelated images that their mystery and magic arises

• Locomotive’s smoke neatly floating up chimney, suggesting in turn smoke of coal in stove

• French title, La Durée poignardé, which literally means “ongoing time stabbed by a dagger.”

• Magritte hoped that it would be installed at the bottom of the collector’s staircase so that the train would “stab” guests on their way up to the ballroom. Ironically, was installed it over his fireplace instead.

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THE GULF STREAMWinslow Homer, 1899

Metropolitan Museum of Art, New York

• The world is cruel and batters one about • Aesthetic Realism: "All beauty is a making one of opposites, and the making one of opposites is what we

are going after in ourselves." → Repose and energy do not have to fight• Racism, Segregation, and the Spanish American War in the 1890s• Look at desperate and controlled sea painting of Homer, can see passion and control given to muscles

Mouth of Shark

Mouth of boat hold

Curvature of shark’s fin

Curvature of boat’s stern

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, e, and WHICH IS MOST BEAUTIFUL?• If you scorn painting, which is the sole imitator of all manifest works of nature, you will

certainly be scorning a subtle invention, which with philosophical and subtle speculation considers all manner of forms: sea, land, trees, animals, grasses, flowers, all of which are enveloped in light and shade. Truly this is science, the legitimate daughter of nature, because painting is born of that nature; but to be more correct, we should say the granddaughter of nature, because all visible things have been brought forth by nature and it is among these that painting is born.

- Leonardo da Vinci (1452 - 1519), in M. Kemp, ed., Leonardo on Painting, Yale University Press, New Haven and London, 1989

• The most beautiful thing we can experience is the mysterious. It is the source of all true art and science.

- Albert Einstein (1879 - 1955), What I Believe

• It is possible to know when you are right way ahead of checking all the consequences. You can recognize truth by its beauty and simplicity.

- Richard Feynman (1918 - 1988), The Character of Physical Law, M.I.T. Press, Cambridge and London, 1965

• The scientist does not study nature because it is useful; he studies it because he delights in it, and he delights in it because it is beautiful. If nature were not beautiful, it would not be worth knowing, and if nature were not worth knowing, life would not be worth living.

- Jules Henri Poincaré (1854 - 1912)

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SOME FAMOUS NUMBERS

• Mathematicians

– Ancient Greece: Pythagoras and Euclid

– Medieval Italian: Leonardo of Pisa, Luca Pacioli's Divina Proportione, 1509

– Renaissance: Johannes Kepler

– Present-day: Roger Penrose (Oxford physicist)

• Not confined just to mathematicians

– Biologists, artists, musicians, historians, architects, psychologists, mystics

– Probably has inspired thinkers of all disciplines like no other number

• Phidias, a sculptor who is said to have employed it

091798057 6381177203 4586834365 4989484820 871.61803398

9572470936995266249775360287471384590452352.71828182e

1071693993757950288419462643383235897932383.14159265

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THE DIVINE RATIO

• Elements: Euclid (ca. 300 BC) defines a proportion derived from a division of a line into what he calls its "extreme and mean ratio."

A straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the greater segment, so is the greater to the lesser.

1. Begin with a line segment AB

2. Locate point C so ratio of AC to CB is equal to ratio of AB to AC

A B

A BC

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THE DIVINE RATIO

• Ratio of AC to CB is equal to ratio of AB to AC

A BC

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SOME INTERESTING RELATIONS FOR

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THE SACRAMENT OF THE LAST SUPPERSalvador Dali, 1955

National Gallery of Art, Washington DC

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THE SACRAMENT OF THE LAST SUPPERSalvador Dali, 1955

National Gallery of Art, Washington DC

• Dodecahedron: 12 faced Platonic solid in which each side is a pentagon

• Surface area and volume of a dodecahedron of unit edge length are simple functions of Golden Ratio

• Plato "which the god used for embroidering the constellations on the whole heaven"

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SEARCHING FOR

a = Top-of-head to chin = ___.__ cmb = Top-of-head to pupil = ___.__ cmc = Pupil to nosetip =        ___.__ cmd = Pupil to lip =                ___.__ cme = Width of nose =          ___.__ cmf = Outside distance between eyes = ___.__ cmg = Width of head =   ___.__ cmh = Hairline to pupil = ___.__ cmi = Nosetip to chin = ___.__ cmj = Lips to chin = ___.__ cmk = Length of lips = ___.__ cmI = Nosetip to lips = ___.__ cm

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ADDITIONAL EXAMPLES

Saint Jerome Leonardo da Vinci

Place de la Concorde by

Mondrian, 1872-1944

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FIBONACCI SEQUENCE

• Fibonacci sequence: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, etc

• Look at ratios:

– 1/1 = 1.0

– 2/1 = 2.0

– 3/2 = 1.5

– 5/3 = 1.666

– 8/5 = 1.6

– 13/8 = 1.625

– 21/13 = 1.615385

– 34/21 = 1.619048

– 55/34 = 1.617647

– 89/55 = 1.61812

• Australian sculptor Andrew Rogers's 50-ton stone and gold sculpture, entitled Golden Ratio, is installed outdoors in Jerusalem

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AND PENROSE TILES

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INSPIRATION COMES BY JIM T. HENRIKSENhttp://allpoetry.com/poem/1733415

I

am

sitting

quietly,

listening for the

quiet noises in the darkness,

ghostly images flying between the tall pine trees,

illusion created by the mind, made by shadows, the brain playing tricks on itself.

It sits there, the raven, black as night, looking at me with its dark eyes in the dark night. Inspiration comes. Words form in my head. Evermore.

1

1

2

3

5

8

13

21

34

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VILLA, BY LE CORBUSIER, 1887-1965

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IS THE GOLDEN RATIO HERE?

The Parthenon's facade showing an interpretationof golden rectangles in its proportions.

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IS THE GOLDEN RATIO HERE?

Each section of an index finger, from the tip to the baseof the wrist, is larger than the preceding one by about 1.618,fitting the Fibonacci numbers 2, 3, 5 and 8.

Lilies have 3 petalsButtercups have 5Many delphiniums have 8Marigolds have 13Asters have 21Daisies commonly have 13, 21, 34, 55 or 89

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IS PROBABLY NOT IN THE STOCK MARKET

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POMEGRANATES AND DODECAHEDRON

• Seeds of pomegranate are initially tiny spheres

• As seeds grow and expand fully into shape that skin will allow, sees grow into form of 12-sided dodecahedron

• Makes use of ‘optimal’ packing

NOW GO BACK AND LOOK AT EVERYTHING AGAIN

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Matthias Grünewald (1470-1528)

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CORPUS HYPERCUBUS

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FOLDING CUBES AND HYPERCUBES (TESSERACT)

?

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DALI: SCIENCE AND ART

• Dalí also had a keen interest in natural science and mathematics

– 1950’s: Painted his subjects as composed of rhinoceros horns, signifying divine geometry (as the rhinoceros horn grows according to a logarithmic spiral) and chastity (as Dalí linked rhinoceros to Virgin Mary)

– Dalí was also fascinated by DNA and the hypercube; the latter, a 4-dimensional cube, is featured in the painting Crucifixion

• All in Dali is indeed contrived, a brilliant illustration of his own psyche as he understands it, as opposed to how it truly may have been – Sister Wendy Beckett

• Cervantes underscores that history is experienced differently by different peoples (Basques, Castillians, Jews, Christians, Arabs, Moors, Moriscos, and Muslims) and so there can be no inherently "true" version of its events, only different perspectives on, and different translations of, said events.

• The set of events that are simultaneous to one observer are not simultaneous to another observer!

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AMEDEO CLEMENTE MODIGLIANI (JULY 12, 1884 – JANUARY 24, 1920)

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TEMPTATION OF ST. ANTHONYHieronymus Bosch, Jeroen Bosch or Jerome Bosch), 1505Museu Nacional de Arte Antiga, Lisbon (copy in Prado)

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TEMPTATION OF ST. ANTHONYMatthias Grünewald, 1513-15

Musée d'Unterlinden, Colmar, France

• Only about 13 of his paintings and some drawings survive. His present worldwide reputation, however, is based chiefly on his greatest masterpiece, the Isenheim Altarpiece (c.1513-15)

• Different from High Renaissance idealism and humanism

• Grünewald's uses of figural distortion to portray violence and tragedy, thin fluttering drapery, highly contrasting areas of light and shadow (CHIAROSCURO), and unusually stark and iridescent color

• Individualistic style most fully realized in his Isenheim Altarpiece.

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TEMPTATION OF ST. ANTHONYTENIERS, David the Younger

Wallraf-Richartz Museum, Cologne

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TEMPTATION OF ST. ANTHONYPaul Cézanne, 1875

Musée d'Orsay, Paris, France

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TEMPTATION OF ST. ANTHONYWilliam Roberts, 1951

Tate, London

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TEMPTATION OF ST. ANTHONYSalvador Dali, 1946

Musee d'Art Moderne, Brussels