Examples from Chapter 1 Remarkable benefits emerged from fresh understanding of the abstract principle of similar triangle
geometry. Thales applied it to new circumstances, for example, to determine the distance of ships from the shore, providing great benefits to a maritime culture. Centuries later, Aristarchus of Alexandria
used similar triangle geometry to estimate lunar and solar diameters as compared to earth diameter, as well as the relative earth-sun and earth-moon distances.
Thales was not alone in his foray into the new world of geometry. Geometrical forms prevailed in Greek art and architecture of his time and well before. Consider the example vases from the Greek geometric
period, amply decorated with triangles, squares and circles.. Artists employed compass-like devices to draw precise, concentric circles as we know from tiny holes at the center. But emergence of new ideas in
science was not directly influenced by artists or vice versa. The commonality is that artistic thinking and scientific thinking were products of a shared culture, with different manifestations like different
fruits from a common soil. http://www.perseus.tufts.edu/cgi-bin/imbrow?query=a.typekey%20%3D%20%27Relatio n%27%20and%20a.valueid%3D%27Perseus%3Acoll%3Aim1990.24%27
http://www.perseus.tufts.edu/cgi-bin/image?lookup=Perseus:image:1990.24.0265
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http://www.perseus.tufts.edu/cgi-bin/image?lookup=Perseus:image:1990.24.0277
To Pythagoras, symmetry is one of the most appealing aspects about the way nature is shaped and ordered. In symmetry there is simplicity; relationships do not change. Besides emerging as a way to
understand nature, symmetry shaped expression in Greek art. Both front and back, the human exterior has bilateral symmetry about the mid-plane, emphatically demonstrated by the Greek Kouros of Anavysos. In
this archaic statue of a youth who died heroically in battle, the artist simultaneously expresses order, symmetry and proportion. A pottery vase shows underlying spatial symmetry in the positioning of human
figures.
http://www.usc.edu/schools/annenberg/asc/projects/comm544/library/images/832.html
http://www.marquette.edu/history/Slides/Greek/pages/Greek%20Slide%20%23118%20A navysos%20Kouros_jpg.htm
http://employees.oneonta.edu/farberas/arth/images/109images/greek_archaic_classical/scu lpture/kouros_kroisos.jpg
http://www.metmuseum.org/collections/view1zoom.asp?dep=13&full=0&mark=1&item= 31%2E11%2E10
http://www.metmuseum.org/collections/view1zoom.asp?dep=13&full=0&mark=1&item= 1989%2E281%2E69 To make observations one has to rely on the accuracy
of senses. When we look down upon surface of a calm pond we see an identical twin staring at us through the water. But we know it is an illusory image; we find no one when we dive into the pond. Our senses can betray and play tricks on us. A modern painting by M. C. Escher. provides a striking illustration of Parmenides' concern about misleading perceptions. With one swift glance, some of us tend to see only white angels in a black background while others may see black bats. But a closer look reveals how there are two interweaving patterns.
http://www.metmuseum.org/collections/view1zoom.asp?dep=13&full=0&mark=1&item= 1989%2E281%2E69 Even though the Parthenon temple is in ruins, we can appreciate its timeless beauty in the order of marble columns, the symmetry of its structure and the balance of its
proportion. Front and the back are identical; so are the two sides, as if reflected in a mirror. A comforting rhythm prevails through the repetition of columns. Through its commanding presence,
architects express geometric principles that rule exploration of spatial dimensions. Architect Callicrates, proportioned the front of the Parthenon, but not in a square outline. That would be perfectly
symmetric, too rigid and unlifelike. Instead he extended the square by an elegant geometrical construction to provide an aesthetically proportioned, golden rectangle, signature for the golden age.
http://academic.reed.edu/humanities/110Tech/graphics/ParthenonFromNW.htmlhttp://www.willamette.edu/cla/wviews/parthenon/ Raphael captures the critical distinction between the disparate approaches of Plato and
Aristotle in the School of Athens (see also the details). Emphasizing the primacy of reason and higher ideal principles, Plato points up, toward the world of ideas, perhaps toward the heavens. He
learned much from his master Socrates, who, even with his last breath, emphasized higher ideals. But Aristotle gestures downward toward earth, stressing the importance of paying attention to the more mundane, but
tangible evidence that surrounds us.
http://www.kfki.hu/~arthp/html/r/raphael/4stanze/1segnatu/1/athens.html Detail http://www.kfki.hu/~arthp/html/r/raphael/4stanze/1segnatu/1/athens1.html
Chapter 2Archimedes success with densities and
buoyancy showed that to understand nature one must pay close attention to details that may at first seem irrelevant. In his famous eureka moment, he took heed of the trivial displacement of water as he sank into
his bath-tub. Interest in detail is similarly evident in the evolution of the artistic world of the Alexandrian era. Examine the bulging muscles of the Discobolus
as compared to the simple and dignified Greek athlete. The rippling veins and the precarious poise convince us that action is imminent. Details of the world absorbed the kindred minds of scientists and artists.
http://www2.rgu.ac.uk/subj/eds/staff/mmc/art/seminar1/pictures/discobolus.htmhttp://www.udel.edu/PR/duPontFamily/internal_pages/discus.html Chapter 3Adopting St. Francis as a key figure, Renaissance artists began to
appreciate God's handwork in the beauty of nature. In the Ecstasy, Giovanni portrays how the saint gives up a monk's ascetic life of isolation to emerge from the cave and gaze in rapture at the sun,
marveling at the surrounding world of plants and animals. http://www.kfki.hu/~arthp/html/b/bellini/giovanni/1480-89/098ecsta.html Chapter 4For Galileo, it was not enough to think about the cosmos in limited terms of geometric order and harmony. Transcending the longing to recreate
glories of the ancient past, Galileo investigated motion with imaginative freedom. By challenging old habits with inquisitive bent of mind, by devising fresh experiments with bubbling imagination, Galileo turned a
historical corner into a new era. We can see a parallel development in the artistic world during the Baroque era dawning at the culmination of the Renaissance. Coined by art critics to characterize the new
style, the word "baroque" signifies "absurd" and "willful" - a wanton defiance of classical rules. Instead of calm, poised subjects set within a static, symmetric background, as
exemplified by Michelangelo's Delphic Sibyl, Baroque art teemed with motion. Exuberance and frenetic energy charge the works of Rubens and El Greco. After two centuries of classical revival, the
organized form and geometric clarity of the late Renaissance was ready to yield to a new dynamic. Both Rubens and El Greco studied in Venice, a city in constant motion, floating on a sparkling sea. Day and
night, bustling gondolas ferried their way to and fro across canals. Sibyl http://www.kfki.hu/~arthp/html/m/michelan/3sistina/4sibyls/01_7si1.html Rubens, coronation http://cgfa.sunsite.dk/rubens/p-rubens47.htm
lEl Greco: adoration http://www.kfki.hu/~arthp/html/g/greco_el/1611-/06shephe.html Special relativity plays havoc with our classical intuition of time and the absolute meaning it has assumed for all. Time no longer means the same thing for everyone,
everywhere. If a group of travelers synchronize their watches at a common starting point and proceed on separate high speed journeys through space, each participant's clock will read different times if their
speeds are different. When they meet up again, their clocks will no longer read the same time. Each person carries their own time. In a powerful
metaphor for the breakdown of conventional notion of time, the surrealist painter, Salvador Dali surprises and destabilizes the spectator, preparing him for enlightenment. Dali imposes a new vision of time.
Instead of showing clocks as icons of stability, he depicts limp, malleable clocks suspended from dead trees wrapped around lifeless creatures, and hung over the sides of tables like wet napkins. One of Dali's
most familiar works, the Persistence of Memory is a vast barren dreamscape without horizon, where time has come to a stop. Ants are eating a flipped-over dead clock. Looking at Dali's work in
terms of how special relativity has altered our concept of time, we can appreciate how the artist's vision embraces not only the physically possible world, but also the conceivable world. Relative to an observer
at rest, all time-dependent processes on a moving vessel slow down. Biological processes slow down. The heart beats slower. Pulse rate, thought processes, cancer growth rates, all proceed at a slower
pace. To a stationary observer, the moving person appears to be living life in slow motion. Dali http://www.ratbags.com/rsoles/artworks/dalimemory.html
http://www.mystudios.com/treasure/dali/dali.html Chapter 5The changing monthly residence of the sun among the zodiac constellations inspired artists through the ages. In some of the most picturesque portrayals, medieval artists illustrated calendars and
prayer books in the belief that the sun's zodiac position controlled seasonal activities. In the upper tier of April from Tres Riches Heures, the sun traverses the heavens in a celestial
chariot, rising in spring between Aries and Taurus. Down on earth, courtiers decked out in colorful garments for an April spring betrothal, exchange rings and vows. Beyond the landscape of trees looms a
lavish medieval castle. Reviving mythical themes from the classics, Renaissance artists painted imaginative connections. On the eastern
wall of the Room of the Months
at the Palazzo Schifanoia, Francesco del Cossa painted twelve, three-tiered allegorical frescoes. The middle tiers show the sun rising in the appropriate constellation, Taurus, the Bull, for the
Allegory of April. One of the oldest, most commonly recognized constellations, it symbolizes strength and fertility in many civilizations. The maidens, Hyades and Pleiades, accompany Taurus.
These groups of bright stars were to play important roles in the future of astronomy. Upper tiers depict activities appropriate to the chosen month. We see, on the right, youths, maidens and musicians surrounding
two young lovers kneeling in embrace. Clearly, love is in the April spring air. Even rabbits huddle together. The lower tier represents courtly events for that time of the year. Limborg http://www.ibiblio.org/wm/rh/1.html Cosssa
http://www.kfki.hu/~arthp/highlight.cgi?file=html/c/cossa/schifano/2april/2april.html&find =room
http://www.kfki.hu/~arthp/highlight.cgi?file=html/c/cossa/schifano/1march/1march.html& find=room Chapter 6Eudoxus' approach to eclipses reflected an emerging cultural trend: realism through emphasis on detailed observation. Ideal principles aside, what
are the real movements of the heavens? Appealing to an audience wider than just the elite, Praxiteles, a dominant artist of the time, created sculptures of planetary gods in settings more typical for ordinary
people than for deities. In preparing for a bath, Aphrodite drapes her clothes over a water vase. Breathing life into marble, the artist is interested in hair curls, anatomical features, and articulation of
muscles. The goddess stands in a relaxed S-shaped pose, a spontaneous stance that contrasts with the rigid classical pose. This more realistic pose shows that the human body is flexible and moves
by continuously shifting weight from one supporting leg to another. Praxiteles was a penetrating observer. Legend has it that his nude Aphrodite was so realistic that the goddess herself exclaims upon seeing the
statue: "Where could Praxiteles have seen me naked?" Aphrodite praxiteles
http://itsa.ucsf.edu/~snlrc/encyclopaedia_romana/greece/hetairai/aphrodite.htmlhttp://www.roanoke.edu/gst/PraxitelesVenus.htm Chapter 7Reviving classical ideas, Renaissance artists of Copernicus' time
had built a bridge to the Golden Age of Greece. Mingling images of God with those of his creations, they resurrected the classical insight of humanity's position in the universe, showing a new intimacy between God
and humanity. On the ceiling of the Sistine Chapel, Michelangelo expressed humanity's special relationship with God by painting a lightning arc between God's finger and man's outstretched hand. Now in one
quick stroke, Copernicus knocked humanity off its special pedestal. But Copernicus was not alone. Parallel threads were emerging in the fabric of a culture under transformation. Instead of always
putting the clear and meaningful subject at the foreground, front and center, artists of the late Renaissance and Baroque periods strained to break free from classical traditions. In a unique interpretation of
Rest of the Flight into Egypt, Elsheimer's star-studded night-sky overwhelms the scene. Were it not for a divine light that softly illuminates the center, one can hardly find Mary, Joseph and baby Jesus.
They are fused into a harmonious unity with their landscape. It is a strong departures from core centrality and dominance. Michelangelo
http://www.kfki.hu/~arthp/highlight.cgi?file=html/m/michelan/3sistina/1genesis/6adam/06 _3ce6.html&find=adam
Elsheimer http://cgfa.sunsite.dk/e/p-elsheimer1.htm Chapter 8Poised to explore planetary system dynamics that emerged from the
luminous power of an eccentric sun, Kepler was among the Baroque innovators who broke out into unconstrained exploration of skewed forms that provided a new sense of vitality to describe planetary motion.
Renaissance and Baroque styles stand in dramatic contrast through a comparison of the Last Supper by Castagno with the Last Supperby Tintoretto. With architectural clarity, Castagno paints
Christ at the tranquil center of the drama of communion. But Tintoretto abandons left-right symmetry, straight edges, and the calm of the classical to create visual tension with diagonal lines. Instead of
placing the table parallel to the picture plane, the rebel skews it to thrust the dynamic of his mystical message onto the mind of the observer. In the Renaissance versions of the Last Supper, apostles sit
symmetrically on either side of Christ, except for Judas. Many artists of Castagno's period adopted this classical style and arrangement. Domenico del Ghirlandaio framed his symmetric work in circular
geometry instead of Castagno's rectangular panels. But such elements are nowhere to be seen in Tintoretto. Instead, there is a new dynamism in Tintoretto's subjects. Light energy blazes from the head
of Christ and the Holy Ghost, portrayed as a ceiling lamp, and illuminates the apostles' halos. Clouds of smoke transform into angels, rendering earthly to divine, natural to supernatural. A radiant Christ
stands off-center. da Vinci http://www.kfki.hu/~arthp/html/l/leonardo/05copies/7lastsup.html
Castagno
http://www.kfki.hu/~arthp/html/a/andrea/castagno/1_1440s/08lasts1.html Ghirlandao http://www.kfki.hu/~arthp/html/g/ghirland/domenico/4lastsup/2ogniss.html
Tintoretto http://www.kfki.hu/~arthp/html/t/tintoret/2religio/l_supper.html Chapter 9Galileo named the moons of Jupiter "Medicean stars," in honor of his financial sponsor, Cosimo de Medici, a generous supporter of arts and
sciences. Cosimo was delighted to be immortalized in the heavens. When he visited the Duke, Galileo personally showed him the new heavenly bodies. There
is another fascinating story behind the naming of Jupiter's now sixteen moons. For each, astronomers chose a name corresponding to one of the many lovers of Zeus: Io, Europa, Callisto, and so on. According
to Greek legendary myths, Jupiter assumed many disguises to hide his numerous liaisons from his jealous wife Juno. In the sensuous painting Jupiter and Io,
the king of gods appears as a cloud embracing the willing nymph Io, planting an ethereal kiss upon her sensual lips. Correggio – Io http://www.kfki.hu/~arthp/html/c/correggi/mytholog/io.html Chapter 10.Descartes was not alone in his inspiration to bring rational,
mathematical order into space. Geometrical framework ruled the design of architects commissioned to glorify the reigning French monarch, Louis XIV. In a bird's eye view, we can see the precise symmetric
layout of the sumptuous palace, gardens and adjacent buildings of the estate at Marly. Replete with fountains, artificial lakes, spacious lawns and flower gardens lined with sculptures, a Cartesian framework ruled
the grounds. Tamed and ordered, nature provided a vast palace of pleasure for king and court. Buildings, fountains, and garden paths spread outward from the center, in precise circular symmetry. Landscape artists
perfected the natural shape of each tree by trimming it to a precise cone. In the Garden of Oranges, they laid out groves in a rigid geometrical grid.
Orangerie
http://www.pyroscaphe.com/alienworkers/vuesdeparis/browse/133.htm
http://arts-sciences.cua.edu/ml/faculty/shoemaker/Versailles/pictures/versailles/orangerie.J PG
http://www.atkielski.com/inlink.php?/PhotoGallery/Versailles/Gardens/OrangerieSmall.ht ml Chapter 11How far Newton had progressed from simple reflections in the garden at Lincolnshire! How radically changed was Newton's dynamic universe from
Aristotle's static heavenly architecture of concentric spheres! Newton's imagination liberated artists to mingle heaven and earth. In the Glorification of St. Ignatius,
Pozzo continues the physical architecture of a beautiful Church in Rome right into a ceiling fresco. With masterly perspective he lifts the vault roof to reveal heaven. It is a Jesuit heaven full of religious tumult, one that would have appealed to Newton's religious side. But the smooth integration of celestial and terrestrial scenes is only visible from a singular location, marked by a metal plate on the church floor, as if Pozzo built a towering ladder from the plate straight up to the heavens, just as Newton built his bridge to the heavens from a singular place in the garden at Lincolnshire.
Pozzo
http://www.kfki.hu/~arthp/html/p/pozzo/apotheos.html A perfect
circular orbit right above earth's surface occurs at a fantastic launch speed of 8 km/sec (18,000 mph). At this tangential velocity, centripetal acceleration exactly balances earth's gravity force. In
comparison, earth's rotation speed is a mere 0.5 km/sec. But if earth were to miraculously speed up and spin 16 times faster, turning once every one-and-a-half hours, Newton's apples would no longer
"fall" to the ground. Acceleration due to gravity would be entirely centripetal, nullifying the familiar consequence of gravity. Defying customary
notions, Rene Magritte paints an imaginative scenario in the Castle of Pyrennes, floating effortlessly above a hypothetical earth! Even though it is unlikely that he knew how the physics of gravity and
rotation would permit such an incredible levitation, he had the intuitive foresight to impose such a vision of the world from the raw information. With suggestive pictures of reality, Magritte always tries to
disturb our thought habits and outsmarts our certitudes. Magritte http://web.tiscali.it/no-redirect-tiscali/G2000/GP_Magritte.htmlhttp://www.varietyartshop.com/scripts/prodView.asp?idProduct=2427
http://vaidro.tripod.com/edens/magritte.html |
