Sunday, March 28, 2010

Third Iteration

Trigram Influence

Sephirot and Trigram [source]

Separation and Replacement

Third Iteration

Notes on Lost Civilization: Maya

  • Time-Life - access to archival footage - redeems production style of documentary
  • Tikal
  • Palenque
  • The Temple of Inscriptions - Alberto Ruz Lhuillier
  • Ruined skeleton and precious jade mask - Pacal
  • Eric Thompson - People Who Worshiped Time
  • El Castillo at Chitzen Itza
From Wikipedia: Chitzen Itza:

Dominating the center of Chichén is the Temple of Kukulkan (the Maya name for Quetzalcoatl), often referred to as "El Castillo" (the castle). This step pyramid has a ground plan of square terraces with stairways up each of the four sides to the temple on top. On the Spring and Autumn equinox, at the rising and setting of the sun, the corner of the structure casts a shadow in the shape of a plumed serpent - Kukulcan, or Quetzalcoatl - along the west side of the north staircase. On these two annual occasions, the shadows from the corner tiers slither down the northern side of the pyramid with the sun's movement to the serpent's head at the base.

Mesoamerican cultures periodically built larger pyramids atop older ones, and this is one such example. In the mid 1930s, the Mexican government sponsored an excavation of El Castillo. After several false starts, they discovered a staircase under the north side of the pyramid. By digging from the top, they found another temple buried below the current one. Inside the temple chamber was a Chac Mool statue and a throne in the shape of Jaguar, painted red and with spots made of inlaid jade.

Composite Laser scan image of Chichen Itza's Cave of Balankanche, showing how the shape of its great limestone column is strongly evocative of the World Tree in Maya mythological belief systems.

Demise of Hun Hunahpú and Vucub Hunahpú and origin of hero twins Hunahpú and Xbalanqué. They are summoned to the underworld of Xibalbá for playing their ball game too noisily. They are killed; Hun Hunahpú's head is placed in a calabash tree. This skull later impregnates Xquic, daughter of a Xibalbé lord, by spitting into her hand. She flees the lords and lives with Xmucané where she gives birth to "Hero Twins" Hunahpú and Xbalanqué. Mistreated by their half-brothers Hunbatz and Huchouén, Hunahpú and Xbalanqué trick them into climbing a tree. Hunbatz and Huchouén transform into monkeys.

A tableau from the Western Mexico shaft tomb tradition, showing a multi-layered tree with birds. It has been proposed that the birds represent souls who have not yet descended into the underworld,[1] while the central tree may represent the Mesoamerican world tree.[2] 

World trees are a prevalent motif occurring in the mythical cosmologies, creation accounts, and iconographies of the pre-Columbian cultures of Mesoamerica. World trees embodied the four cardinal directions, which also serve to represent the four-fold nature of a central world tree, a symbolic axis mundi which connects the planes of the Underworld and the sky with that of the terrestrial realm.[3]

Depictions of world trees, both in their directional and central aspects, are found in the art and mythological traditions of cultures such as the Maya, Aztec, Izapan, Mixtec, Olmec, and others, dating to at least the Mid/Late Formative periods of Mesoamerican chronology. Among the Maya, the central world tree was conceived as or represented by a ceiba tree, and is known variously as a wacah chan or yax imix che, depending on the Mayan language.[4] The trunk of the tree could also be represented by an upright caiman, whose skin evokes the tree's spiny trunk.[5]

Directional world trees are also associated with the four Yearbearers in Mesoamerican calendars, and the directional colors and deities. Mesoamerican codices which have this association outlined include the Dresden, Borgia and Fejérváry-Mayer codices.[6] It is supposed that Mesoamerican sites and ceremonial centers frequently had actual trees planted at each of the four cardinal directions, representing the quadripartite concept.[citation needed]

Izapa Stela 5 is considered a possible representation of a World Tree.

World trees are frequently depicted with birds in their branches, and their roots extending into earth or water (sometimes atop a "water-monster", symbolic of the underworld).

The central world tree has also been interpreted as a representation of the band of the Milky Way.[7]

 An 1847 depiction of the Norse Yggdrasil as described in the Icelandic Prose Edda by Oluf Olufsen Bagge. [source]

  • Mayan Calendar
  • Gears within gears
  • 23 December 2012

  • God of Decapitation:
  • Giles Healey
  • Discovery of Bonampak

    •  Skeleton With the Jade Mask
    • Lord Pacal
    • Source of Authority
    • Trail of Blood
    • Rope of Thorns
    • Stingray Spine / Knife
    • Blood of Kings
    • Blood is the price of power
    • Debt to the Gods
    • Soul resides in the blood
    • No surrogate sacrifice
    • skull racks
    • ball game
    • sacramental blood still feed the mayan imagination
    • Christianity made perfect sense - Blood shed by king/christ insures stability of world
    • asdfasd

    Notes on Lost King of the Maya

    From Nova: Lost King of the Maya:

    Edgar Allan Poe called it "perhaps the most interesting book of travel ever published." The historian David McCullough deemed it "a classic, thrilling piece of work [that] can be seen as the beginning of American archeology." It is Incidents of Travel in Central America, Chiapas, and Yucatán, by John Lloyd Stephens. A lawyer ostensibly on a mission for the U.S. State Department, Stephens, in 1839, went in search of Mayan ruins, which were then all but unknown. He was accompanied by architect Frederick Catherwood, whose meticulous drawings grace both Stephens' book and the passages excerpted below. Here, in introspective and highly impassioned prose, Stephens describes coming upon the ruined city of Copan, which he found so captivating that he promptly purchased the site—today owned by the Honduran government—from its then owner, an Indian named Don Jose Maria.



    From Stephens:

    We followed our guide, who, with a constant and vigorous use of his machete, conducted us through the thick forest, among half-buried fragments, to 14 monuments of the same character and appearance, some with more elegant designs, and some in workmanship equal to the finest monuments of the Egyptians; one displaced from its pedestal by enormous roots; another locked in the close embrace of branches of trees, and almost lifted out of the earth; another hurled to the ground, and bound down by huge vines and creepers; and one standing, with its altar before it, in a grove of trees which grew around it, seemingly to shade and shroud it as a sacred thing; in the solemn stillness of the woods, it seemed a divinity mourning over a fallen people. The only sounds that disturbed the quiet of this buried city were the noise of monkeys moving among the tops of the trees.

    Architecture, sculpture, and painting, all the arts which embellish life, had flourished in this overgrown forest; orators, warriors, and statesmen, beauty, ambition, and glory, had lived and passed away, and none knew that such things had been, or could tell of their past existence. Books, the records of knowledge, are silent on this theme. The city was desolate.

    Catherwood's Map
    Like all his work, Catherwood's map of Copán is exquisitely drawn (though, strangely, north lies in the direction south should be and vice versa). 

    No remnant of this race hangs round the ruins, with traditions handed down from father to son, and from generation to generation. It lay before us like a shattered bark in the midst of the ocean, her masts gone, her name effaced, her crew perished, and none to tell whence she came, to whom she belonged, how long on her voyage, or what caused her destruction; her lost people to be traced only by some fancied resemblance in the construction of the vessel, and, perhaps never to be known at all. The place where we sat, was it a citadel from which an unknown people had sounded the trumpet of war? or a temple for the worship of the God of peace? or did the inhabitants worship the idols made with their own hands, and offer sacrifices on the stones before them? All was mystery, dark, impenetrable mystery, and every circumstance increased it.


    • K'inich Yax K'uk' Mo'
    • Founder of Copan
    • 400 year dynasty
    • 200 to 900 C.E.
    • Copan = Athens of C. America
    • The Acropolis at Copan
    • Altar Q


    • David Stuart
    • History written in the Stone
    • Hieroglyphic Stairway
    • Eye Goggle - Rain God - Tlaloc

      • Find K'inich Yax K'uk' Mo's Bones
      • Sacred Geography
      • Legitimize power by linking to dynastic founder
      • Invoke his bones
      • Rosalila Temple

      Notes and Hieroglyphs: Cracking the Maya Code

      From Wikipedia: Mayan Script [emphasis mine]:

      The Maya script was a logosyllabic system. Individual symbols ("glyphs") could represent either a word (actually a morpheme) or a syllable; indeed, the same glyph could often be used for both. For example, the calendaric glyph MANIK’ was also used to represent the syllable chi. (It's customary to write logographic readings in all capitals and phonetic readings in italics.) It is possible, but not certain, that these conflicting readings arose as the script was adapted to new languages, as also happened with Japanese kanji and with Assyro-Babylonian and Hittite cuneiform. There was ambiguity in the other direction as well: Different glyphs could be read the same way. For example, half a dozen apparently unrelated glyphs were used to write the very common third person pronoun u-.

      Maya was usually written in blocks arranged in columns two blocks wide, read as follows:
      Maya inscriptions were most often written in columns two glyphs wide, with each such column read left to right, top to bottom

      Within each block, glyphs were arranged top-to-bottom and left-to-right, superficially rather like Korean Hangul syllabic blocks. However, in the case of Maya, each block tended to correspond to a noun or verb phrase such as his green headband. Also, glyphs were sometimes conflated, where an element of one glyph would replace part of a second. Conflation occurs in other scripts: For example, in medieval Spanish manuscripts the word de 'of' was sometimes written Ð (a D with the arm of an E). Another example is the ampersand (&) which is a conflation of the Latin "et". In place of the standard block configuration Maya was also sometimes written in a single row or column, 'L', or 'T' shapes. These variations most often appeared when they would better fit the surface being inscribed.

      Maya glyphs were fundamentally logographic. Generally the glyphs used as phonetic elements were originally logograms that stood for words that were themselves single syllables, syllables that either ended in a vowel or in a weak consonant such as y, w, h, or glottal stop. For example, the logogram for 'fish fin' (Maya [kah] — found in two forms, as a fish fin and as a fish with prominent fins), came to represent the syllable ka. These syllabic glyphs performed two primary functions: They were used as phonetic complements to disambiguate logograms which had more than one reading, as also occurred in Egyptian, and they were used to write grammatical elements such as verbal inflections which did not have dedicated logograms, as in modern Japanese. For example, b'alam 'jaguar' could be written as a single logogram, BALAM, complemented phonetically as ba-BALAM, or BALAM-ma, or ba-BALAM-ma, or written completely phonetically as ba-la-ma.

      Phonetic glyphs stood for simple consonant-vowel or bare-vowel syllables. However, Maya phonotactics is slightly more complicated than this: Most Maya words end in a consonant, not a vowel, and there may be sequences of two consonants within a word as well, as in xolte’ [ʃolteʔ] 'scepter', which is CVCCVC. When these final consonants were sonorants (l, m, n) or glottals (h, ’) they were sometimes ignored ("underspelled"), but more often final consonants were written, which meant that an extra vowel was written as well. This was typically an "echo" vowel that repeated the vowel of the previous syllable. That is, the word [kah] 'fish fin' would be written in full as ka-ha. However, there are many cases where some other vowel was used, and the orthographic rules for this are only partially understood. Here's our current understanding:

      * A CVC syllable was written CV-CV, where the two vowels (V) were the same: yo-po [yop] 'leaf'
      * A syllable with a long vowel (CVVC) was written CV-Ci, unless the long vowel was [i], in which case it was written CiCa: ba-ki [baak] 'captive', yi-tzi-na [yihtziin] 'younger brother'
      * A syllable with a glottalized vowel (CV’C or CV’VC) was written with a final a if the vowel was [e, o, u], or with a final u if the vowel was [a] or [i]: hu-na [hu’n] 'paper', ba-tz’u [ba’tz’] 'howler monkey'.

      A more complex spelling is ha-o-bo ko-ko-no-ma for [ha’o’b kohkno’m] 'they are the guardians'. (Vowel length and glottalization are not always indicated in common words like 'they are'.) A minimal set, not fully translated, is,

      ba-ka [bak]
      ba-ki [baak]
      ba-ku [ba’k] or [ba’ak]
      ba-ke [baakel] (underspelled)


      It was until recently thought that the Maya may have adopted writing from the Olmec or Epi-Olmec. However, recent discoveries have pushed back the origin of Maya writing by several centuries, and it now seems possible that the Maya were the ones who invented writing in Mesoamerica.[14]

      Knowledge of the Maya writing system continued into the early colonial era and reportedly a few of the early Spanish priests who went to Yucatán learned it. However, as part of his campaign to eradicate pagan rites, Bishop Diego de Landa ordered the collection and destruction of written Maya works, and a sizable number of Maya codices were destroyed. Later, seeking to use their native language to convert the Maya to Christianity, he derived what he believed to be a Maya "alphabet" (the so-called de Landa alphabet). Although the Maya did not actually write alphabetically, nevertheless he recorded a glossary of Maya sounds and related symbols, which was long dismissed as nonsense but eventually became a key resource in deciphering the Maya script, though it has itself not been completely deciphered. The difficulty was that there was no simple correspondence between the two systems, and the names of the letters of the Spanish alphabet meant nothing to Landa's Maya scribe, so Landa ended up asking the equivalent of write H: a-i-tee-cee-aitch "aitch", and glossed a part of the result as "H".

      Landa was also involved in creating a Latin orthography for the Yukatek Maya language, meaning that he created a system for writing Yukatek in the Latin alphabet. This was the first Latin orthography for any of the Mayan languages,[citation needed] which number around thirty.

      Only four Maya codices are known to have survived the conquistadors. Most surviving texts are found on pottery recovered from Maya tombs, or from monuments and stelae erected in sites which were abandoned or buried before the arrival of the Spanish.

      Knowledge of the writing system was lost, probably by the end of the 16th century. Renewed interest in it was sparked by published accounts of ruined Maya sites in the 19th century.
      Wikipedia: Writing System:

      Writing systems were preceded by proto-writing, systems of ideographic and/or early mnemonic symbols. The best known examples are:

      * Jiahu Script, symbols on tortoise shells in Jiahu, ca. 6600 BC
      * Vinča script (Tărtăria tablets), ca. 4500 BC
      * Early Indus script, ca. 3500 BC

      The invention of the first writing systems is roughly contemporary with the beginning of the Bronze Age in the late Neolithic of the late 4th millennium BC. The Sumerian archaic cuneiform script and the Egyptian hieroglyphs are generally considered the earliest writing systems, both emerging out of their ancestral proto-literate symbol systems from 3400–3200 BC with earliest coherent texts from about 2600 BC.

      The Chinese script likely developed independently of the Middle Eastern scripts, around 1600 BC.

      The pre-Columbian Mesoamerican writing systems (including among others Olmec and Maya scripts) are also generally believed to have had independent origins.

      It is thought that the first true alphabetic writing appeared around 2000 BC, as a representation of language developed for Semitic slaves in Egypt by Egyptians (see History of the alphabet). Most other alphabets in the world today either descended from this one innovation, many via the Phoenician alphabet, or were directly inspired by its design.

      From Above Time: Emerson's and Thoreau's Temporal Revolutions by James R. Guthrie

      In Above Time, James R. Guthrie explores the origins of the two major transcendentalists' revolutionary approaches to time, as well as to other temporally related issues such as history, memory, and change. Most critical discussions of this period neglect the important truth that a good deal of the entire American transcendentalist project involved a transcendence not just of materiality, but also of time. Emerson concluded that time was a human invention contrived as a means of organizing, subduing, and owning a world of things. Nature, he agreed with Thoreau, did not need time, nor even acknowledge its existence. Like many other nineteenth-century observers, Emerson and Thoreau were compelled to see time in a new light by developments in contemporary science: geologists were debating the antiquity of the earth, archaeologists were making discoveries in Egypt, and zoologists were attempting to unravel the mysteries of speciation and heredity. The discoveries effectively enlarged the scope of time, and consequently, exacerbated existing tensions between religious orthodoxy and scientific rationalism. This tension culminated in the ambivalent public reception that greeted Darwin's Origin of Species when it first appeared in 1859. Thoreau and Emerson were thoroughly aware of these wider cultural developments; and both tried, with varying degrees of success, to integrate contemporary scientific thought with their preexisting late-romantic idealism. As romantics, the American transcendentalists regarded nature as a set of correspondences, formalized as symbols or hieroglyphics that could be decoded to discover the animating presence of eternal laws. Yet the transcendentalists hoped togo beyond merely understanding nature to achieving a kind of passionate identity with it, and this union could be achieved only by overcoming time. In their essays and poems, Emerson and Thoreau adopt a series of philosophical, rhetorical, and psychological strategies designed to jolt their readers out of time, often by attacking conventional and traditional notions about temporality.

      Personal Notes:

      • Nature of Hieroglyphs
      • de Landa - biography
      • only 4 codices survive
      • Mayan civilization at height of glory during the Dark Ages
      • 9th cen. abandoned
      • Dresden Codex

        • developed calendar - mark time
        • date universe was created: 13 August 3014 B.C. to 23 December 2012 "Long Count"
        • Eric Thompson: Mayan :: Focus :: Time
        • Tatiana Proskouriakoff - Story of Kings
        • Knorozov
        • Linda Schele 
        • David Stuart
        • Graphic component of Mayan Writing - letters and sounds conflate to create and art in addition to the meaning of the word

        Monday, March 22, 2010

        On Entering Dante's Cathedral

        Oft have I seen at some cathedral door
        A laborer, pausing in the dust and heat,
        Lay down his burden, and with reverent feet
        Enter, and cross himself, and on the floor
        Kneel to repeat his paternoster o'er;
        Far off the noises of the world retreat;
        The loud vociferations of the street
        Become an undistinguishable roar.
        So, as I enter here from day to day,
        And leave my burden at this minister gate,
        Kneeling in prayer and not ashamed to pray,
        The tumult of the time disconsolate
        To inarticulate murmurs dies away,
        While the eternal ages watch and wait.

        - Henry Wadsworth Longfellow, prefatory sonnet to his translation of the Commedia

        Thursday, March 18, 2010

        Cildo Meireles' Failed Attempt to Build a Cathedral Out of Coins, Bones and Communion Wafers

        How to Build Cathedrals | Cildo Meireles | 1987

        From the Blanton Museum of Art:

        Cildo Meireles has gained an international reputation for his effective combination of Conceptual art with explicit social and political critiques. In Missão/Missões he makes reference to the seventeenth- and eighteenth-century Jesuit missions in southern Brazil, Paraguay, and northern Argentina. The missions were established as communities to convert the indigenous Tupi-Guaraní people to Catholicism, and many of the Jesuit and Franciscan churches remain among the jewels of Latin American Baroque architecture. Meireles's evocative contemporary "cathedral" exposes the hidden agenda behind these missions, highlighting in particular the relationship between wealth (600,000 coins on the ground), agricultural exploitation (200 suspended cattle bones), and religion (a column of communion wafers connecting the "land" and the "heavens"). The installation draws attention to the fact that the conquest of the Americas was as much about economics as it was about religion or saving souls.

        Tuesday, March 16, 2010

        Building in the Name of God


        It is difficult to watch the History Channel appeal to the lowest common denominator, to make history "hip" by adding techno beats and fast cuts to all of its shows.

        Nevertheless, I endured Building in the Name of God.


        • Hagia Sophia
        • Notre Dame
        • St. Peter's
        • Sagrada Familia
        • Crystal Cathedral


        Hagia Sofia:

        • purpose built structures
        • altar / nave / vaults
        • idea of dome 
        • circle upon a square
        • most structurally deformed bldg after tower at pisa\
        • procopius: "Golden Thread"


        Notre Dame

        • construct a bldg that would reflect divine power and light
        • ribbed vaults acting like bones of a skeleton
        • mortar - glue that allows flexibility but holds cathedrals together
        • skeletal b/c of flying buttresses


        St. Peter's

        • build a new church
        • wonder of the world
        • largest Christian structure
        • tomb of st peter
        • largest cathedral in the world
        • importance of dome


        Sagrada Familia

        • scale is insane
        • framework = skelton
        • inside the skeleton of Moby Dick
        • cantenary parabolic arches
        • impossible to design a cathedral on the scale of S.F. if you lack the necessary spiritual and religious inspiration
        • begun by a bookseller
        •  From Wikipedia: Towers

          Every part of the design of La Sagrada Família is replete with Christian symbolism, as Gaudí intended the church to be the "last great sanctuary of Christendom". Its most striking aspect is its spindle-shaped towers. A total of eighteen tall towers are called for, representing in ascending order of height the Twelve Apostles, the four Evangelists, the Virgin Mary and, tallest of all, Jesus Christ. (According to the 2005 "Works Report" of the temple's official website, drawings signed by Gaudí found recently in the Municipal Archives indicate that the tower of the Virgin was in fact intended by Gaudí to be shorter than those of the evangelists, and this is the design — which the Works Report states is more compatible with the existing foundations — that will be followed. The same source explains the symbolism in terms of Christ being known through the Evangelists.) The Evangelists' towers will be surmounted by sculptures of their traditional symbols: a bull (St Luke), a winged man (St Matthew), an eagle (St John), and a lion (St Mark). The central tower of Jesus Christ is to be surmounted by a giant cross; the tower's total height (170 m) will be one metre less than that of Montjuïc (a hill in Barcelona), as Gaudí believed that his work should not surpass that of God. Lower towers are surmounted by communion hosts with sheaves of wheat and chalices with bunches of grapes, representing the Eucharist.


          The Church will have three grand façades: the Nativity façade to the East, the Glory façade to the South (yet to be completed) and the Passion façade to the West. The Nativity facade was built before work was interrupted in 1935 and bears the most direct Gaudí influence. The Passion façade is especially striking for its spare, gaunt, tormented characters, including emaciated figures of Christ being flogged and on the crucifix. These controversial designs are the work of Josep Maria Subirachs.


          Tree-like supporting pillars of roof

          The church plan is that of a Latin cross with five aisles. The central nave vaults reach forty-five metres while the side nave vaults reach thirty metres. The transept has three aisles. The columns are on a 7.5 metre grid. However, the columns of the apse, resting on del Villar's foundation, do not adhere to the grid, requiring a section of columns of the ambulatory to transition to the grid thus creating a horseshoe pattern to the layout of those columns. The crossing rests on the four central columns of porphyry supporting a great hyperboloid surrounded by two rings of twelve hyperboloids (currently under construction). The central vault reaches sixty metres. The apse will be capped by a hyperboloid vault reaching seventy-five metres. Gaudí intended that a visitor standing at the main entrance be able to see the vaults of the nave, crossing, and apse, thus the graduated increase in vault loftiness.

          The columns of the interior are a unique Gaudí design. Besides branching to support their load, their ever-changing surfaces are the result of the intersection of various geometric forms. The simplest example is that of a square base evolving into an octagon as the column rises, then a sixteen-sided form, and eventually to a circle. This effect is the result of a three-dimensional intersection of helicoidal columns (for example a square cross-section column twisting clockwise and a similar one twisting counter-clockwise).

          Geometric details

          Alpha and Omega carving at Sagrada Família entrance. 
          Key to the symbolism of the church. 
          The towers on the Nativity façade are crowned with geometrically shaped tops that are reminiscent of Cubism (they were finished around 1930), and the intricate decoration is contemporary to the style of Art Nouveau, but Gaudí's unique style drew primarily from nature, not other artists or architects, and resists categorization. Gaudí used hyperboloid structures in later designs of the Sagrada Família (more obviously after 1914), however there are a few places on the nativity façade—a design not equated with Gaudí's ruled-surface design, where the hyperboloid crops up. For example, all around the scene with the pelican there are numerous examples (including the basket held by one of the figures). There is a hyperboloid adding structural stability to the cypress tree (by connecting it to the bridge). And finally, the "bishop's mitre" spires are capped with hyperboloid structures[3]. In his later designs, ruled surfaces are prominent in the nave's vaults and windows and the surfaces of the Passion facade. Symbolism Themes throughout the decoration include words from the liturgy. The towers are decorated with words such as "Hosanna", "Excelsis", and "Sanctus"; the great doors of the Passion façade reproduce words from the Bible in various languages including Catalan; and the Glory façade is to be decorated with the words from the Apostles' Creed. Areas of the sanctuary will be designated to represent various concepts, such as saints, virtues and sins, and secular concepts such as regions, presumably with decoration to match.

        Crystal Cathedral

        • Robert Schuller looks like a reptile: cold blooded, flicking his pink tongue out to smell the prey, talking about money money money money.
        • who truly believes that the aesthetic monstrosity of the Crystal Cathedral deserves to have a place amongst these mountains?

        The Riddles the Sphinx

        Why is it that sometimes we end up watching a sixteen year old on a talk show go on abou ther 16th birthday party rather than a documentary about the Riddle of the Sphinx?

        It seems, at times, unthinkable that we,  who have access vis the internet to huge databases of art, culture, history, etc., end up wasting so much time on trivia, superficiality, gossip.

        What are we living for? We wallow in an embarassment of riches that overwhelms our sense of focus.

        From Wikipedia:

        A sphinx (Ancient Greek: Σφίγξ / Sphinx, sometimes Φίξ /Phix) is a mythological figure which is depicted as a recumbent lion with a human head. It has its origins in sculpted figures of Old Kingdom Egypt, to which the ancient Greeks applied their own name for the male monster, the "strangler", an archaic figure of Greek mythology. Similar creatures appear throughout South and South-East Asia. In European decorative art, the sphinx enjoyed a major revival during the Renaissance. Later, the sphinx image, something very similar to the original Egyptian concept, was exported into many other cultures, albeit often interpreted quite differently due to translations of descriptions of the originals and the evolution of the concept in relation to other cultural traditions.
        Generally the role of sphinxes was as temple guardians; they were placed in association with architectural structures such as royal tombs or religious temples. The oldest known sphinx was found in Gobekli Tepe, Turkey and was dated to 9,500 B.C.[1] Perhaps the first sphinx in Egypt was one depicting Hetepheres II, of the fourth dynasty that lasted from 2723 to 2563 BC. The largest and most famous is the Great Sphinx of Giza, Arabic: أبو الهول, sited at the Giza Plateau on the west bank of the Nile River and facing due east, is also from the same dynasty (29°58′31″N 31°08′15″E / 29.97528°N 31.1375°E / 29.97528; 31.1375). Although the date of its construction is uncertain, the head of the Great Sphinx now is believed to be that of the pharaoh Khafra.
        What names their builders gave to these statues is not known. At the Great Sphinx site, the inscription on a stele erected a thousand years later, by Thutmose IV in 1400 BCE, lists the names of three aspects of the local sun deity of that period, Khepera - - Atum. The inclusion of these figures in tomb and temple complexes quickly became traditional and many pharaohs had their heads carved atop the guardian statues for their tombs to show their close relationship with the powerful deity, Sekhmet.
        Other famous Egyptian sphinxes include one bearing the head of the pharaoh Hatshepsut, with her likeness carved in granite, which is now in the Metropolitan Museum of Art in New York, and the alabaster sphinx of Memphis, currently located within the open-air museum at that site. The theme was expanded to form great avenues of guardian sphinxes lining the approaches to tombs and temples as well as serving as details atop the posts of flights of stairs to very grand complexes. Nine hundred with rams' heads, representing Amon, were built in Thebes, where his cult was strongest.

        Monday, March 15, 2010

        Google Earth and Sketch Up

        How to Build a Cathedral: With a square, a circle and a diagonal, you can generate an entire cathedral

          How To Build A Cathedral

        Notes from How to Build a Cathedral: BBC 4

        • Gates of Heaven
        • Everything in existence has symbolic value
        • Man's actions images of Divine Order
        • Architects = Master Masons
        • 1 : √2

        There are a number of algorithms for approximating the square root of 2, which in expressions as a ratio of integers or as a decimal can only be approximated. The most common algorithm for this, one used as a basis in many computers and calculators, is the Babylonian method of computing square roots, which is one of many methods of computing square roots.

        The square root of 2 is equal to the length of the hypotenuse of a right triangle with legs of length 1.

        Another proportioning system is the ratio of (Square root of 2) : 1. The simplicity of the derivation (square root of 2 is the diagonal through a square of side length 1) is paralleled by the ease of maintaining the proportion through division or multiplication of the proportioned rectangles. 




        Clearly the golden section proportion is closely connected with the square, the most neutral rectangular proportion (1 : 1) imaginable. (The "Modulor" books are square!) Compared with other proportions, the golden section rectangle is relatively long. That creates a certain tension between golden section and square, which may contribute to the interest that this proportioning scheme can maintain (see Corbu's Modulor), especially when compared to schemes that use the square as only proportioning scheme (see O.M.U.).

        Now, does that constitute any understandable reason to connect golden mean proportioning inseparable with beauty? Without doubt: No. Because of the non-linear nature of the golden section, as clearly demonstrated in the Modulor derivations, it is possible to find some base length and some subdivisions close enough to the ratio of the golden section in anything that may be perceived as beautiful. But that may have to do with the underlying structuring into non-equal divisions that establish scale and generate more interest because of the increased amount of detail that is generated or that is cause of the inequal divisions. 

        Another proportioning system is the ratio of (Square root of 2) : 1. The simplicity of the derivation (square root of 2 is the diagonal through a square of side length 1) is paralleled by the ease of maintaining the proportion through division or multiplication of the proportioned rectangles. The sum of two rectangles of proportion (Square root of 2) : 1 long side by long side is (Square root of 2) : 2. Divided by the square root of two we arrive at 1 : (Square root of 2), the same ratio as the two rectangles that were added together, only with a change of orientation. [source]

        \This is suggested by the Roman architectural forerunner Vitruvius and his discussion of the application of the side and diagonal of a square. He pays great homage to Plato for stating and showing in Meno that the square on the diagonal of another square has twice the area of the smaller square. Vitruvius emphasizes the great utility of this result. He notes that this surmounts an arithmetical impossibility (i.e., writing down the square root of two) with a geometric solution. This ascribes to the ratio of the side of the square to itsdiagonal a special status—it is a profound principle. Its profundity, association with Plato as noted by Vitruvius, and long-standing traditional use may have given a reverence and prestigeto this principle during the medieval period.

        The rediscovery of the mathematical schema, including the side of the square and its diagonal, employed at a specific church is a challenging problem within architectural history. As an example, Durham Cathedral, an Anglo - Norman Romanesque church, built 1093–1130/1133, in the northeast of England has many mathematical points of interest. Consider the constructional- geometric procedure for the major lengths of the building and the widths of the transepts. A design motif that was common, though not standard, in the large Anglo-Norman Romanesque churches was basically, in terms of interior lengths, that the west tower/nave (HD in Figure 6) to the west tower/nave/crossing/choir up to the chord of the central east-end apse (HB in Figure 6) is in the same ratio as the side of the square to its diagonal or equivalently, the half-diagonal to the side of the square. A slightly different situation appears at Durham Cathedral. The “cut-point” possibly should be the interior east wall of the transept chapels (C in Figure 6), rather than using the interior west wall of the transept or the transept piers (D in Figure 6). The length of the choir up to the chord of the central east-end apse (BC in Figure 6) to the width of the choir (AB in Figure 6) are also in the ratio of the side to the half-diagonal of the square. One of the other common larger scale relationships, for Anglo - Norman churches with attached monasteries including Durham, is that the length of the cloister’s side adjoining the nave (DG in Figure 7) to the length of the tower and nave (HD in Figure 7) equals the ratio of the side of the square to its diagonal, or equivalently the ‘half-diagonal’ of the square to its side. The thorough application of the square’s side and diagonal also occurred in the ground plan of the south transept and suggests a relationship between the full interior width of the south transept and the interior width of the nave and its north and south aisles [Figure 8]. These relationships are examples of the application of practical or constructive geometry in the design and laying out of Durham Cathedral. [source .pdf]

        • Proportion, Ratio and Symmetry = spiritual qualities the reflected the harmony of creation
        • With a square, a circle and a diagonal, you can generate an entire cathedral
        • Arches = basic building block of cathedrals
        • Scared Theater: architecture, sculpture, music all combined in harmony
        • Sacred Scenes on facades, in windows
        • Skeletons of Stone 

          Cathedral by David Macaulay

          Just watched Cathedral (1985) by David Macaulay. As in introduction, I highly recommend it. An easy mix of walk around narration by Macaulay and Caroline Berg with an interesting animated story that brings a certain life to the building of a cathedral.

          It is worth noting that I also recently read Ken Follett's Pillars of the Earth (1989). Granted that there are common elements to the construction of cathedrals and Pillars of the Earth is much deeper in dimensionality, but there are striking similarities between the two works. So much so that I was inclined to do some cursory research to see of there was any acknowledgment on Follett's part of the influence of Macaulay. Found nothing.

          Anyway, this is besides my pupose here.

          Notes from Cathedral:

          The Cathedral is a single unified expression of God's hand in nature.
          The Cathedral is a physical representation of the Divine Order of Things.
           Iconography of cathdrals used to teach the pre-literate.
          Stained glass as a three-dimensional (sic) picture book of religious instruction.

          Second Iteration: Directions | Elements | Age | States of Being

          Sunday, March 14, 2010

          The Parthenon: an objective basis of beauty that mirrors the proportions of an ideal human body

          When the Parthenon was completed in 432 B.C., the gleaming marble temple atop the Acropolis would have been visible from almost anywhere in the ancient city. [source]

          Notes from the transcript (emphasis mine):

          •  NARRATOR: It is the Golden Age of Greece, a unique window of time that gives birth to Western ideals of beauty, science, art and a radical new form of government: democracy. To immortalize those ideals, the Greeks build what will become the very symbol of Western Civilization, the Parthenon.
          • JEFFREY M. HURWIT (University of Oregon): It was the physical embodiment of their values, their beliefs, of their ideology.
          •  The Parthenon is a 20,000 ton, 70,000 piece, three-dimensional jigsaw puzzle. And worse, it's a puzzle that doesn't include instructions. No one has found anything resembling architectural plans.
          •  JEFFREY M. HURWIT: The Parthenon was the greatest monument in the greatest sanctuary in the greatest city of classical Greece. It was the central repository of the Athenians' lofty conception of themselves and the physical—marble—embodiment of their values, their beliefs, their myths, their ideologies. It was as much a temple to Athens and the Athenians as it is to their patron goddess, Athena Parthenos.
          •  He [Pericles] spearheads an ambitious campaign to rebuild Athens and ushers in the Golden Age of Greece, a unique window of time that establishes Western ideals of beauty, science, art and a radical new form of government: "demos" meaning "people," and "cratos," "power"— people power, or democracy.
          • In a powerful statement of their self-confidence, the people of Athens vote to rebuild the Acropolis, and at its center, a building to embody their ideals, the Parthenon.

          • CATHY PARASCHI: On the beautiful island of Naxos, we see this temple which is one of the early archaic Greek temples, made of stone.
            NARRATOR: The temple of Demeter was constructed about 100 years before the Parthenon. It, too, was built with few right angles or straight lines.
          •  MARGARET LIVINGSTONE: This is another classical illusion. If you have two straight lines, if you add converging lines, these two lines seem to bow in the middle. So if the floor of the Parthenon has converging cues as to depth and perspective, you could have an illusory sag in the floor of the Parthenon. NARRATOR: Perhaps to compensate for the illusory sag, the builders left extra marble in the middle. The ancient Greeks realized that to construct a building that appears perfect, they would have to come up with a design that tricks the eye. What they invent is a system of optical refinements.
            CATHY PARASCHI: Their concern was the visual perfection of the building.
            NARRATOR: This small stone temple, on Naxos, provides evidence of the Greeks' keen observation over hundreds of years.
            CATHY PARASCHI: Here we can see the first optical refinements already experimented by the people building the temple. Here lies, literally, the D.N.A. of the Parthenon.
          •  Architect Mark Wilson Jones believes the enigmatic Salamis Stone, depicting an arm, hands and feet, may be a conversion table for the different measuring systems, Doric, Ionic and Common. MARK WILSON JONES (University of Bath): This is a tracing I've done that shows the stone, and you can immediately see how the main measures work. We have this foot rule here. That's 327 millimeters, more or less, the Doric foot. And here you have a foot imprint that's roughly a 307-millimeter-long foot, which we tend to call the Common foot. And there are, in fact other feet. For example, this dimension here is one Ionic foot. So there is a, kind of, whole network of different interrelated measurements here.
            NARRATOR: The Salamis Stone represents all the competing ancient Greek measurements: the Doric foot, the Ionic foot, and, for the first time, the Common foot—virtually the same measurement we use today.
            Wilson Jones finds evidence of all three measuring systems in the height of the Parthenon.
            MARK WILSON JONES: That distance is, at one and the same time, 45 Doric feet, that's the ruler on the relief; it's also 48 Common feet, which is the foot imprint; and it's 50 Ionic feet, all at the same time. And these are quite exact correspondences.
            NARRATOR: So the Salamis Stone may have provided a simple way for ancient workers from different places to calibrate their rulers and cross-reference different units of measurement.
            But the Salamis Stone may also be a clue to how the ancient Greeks were using the human body to create what we now regard as ideal proportions.
            MARK WILSON JONES: What's extraordinary about this, is that at the same time as being a practical device, it's also a kind of model of theory, architectural theory, that a perfect, ideal human body, designed by nature, is a kind of paradigm for how architects should design temples.
            NARRATOR: Among the first to record that Greek temples were based on the ideal human body was the Roman architect, Marcus Vitruvius. He studied the proportions of temples like the Parthenon, in the first century B.C.E., 400 years after it was built.
            MANOLIS KORRES: Vitruvius's work gives us the overall frame which is necessary to understand the system of proportions of the Parthenon.
            NARRATOR: According to Vitruvius, Greek architects believed in an objective basis of beauty that mirrors the proportions of an ideal human body. They observed, among many examples, that the span from finger tip to finger tip is a fixed ratio to total height, and height is a fixed ratio to the distance between the navel and the foot.
            Two thousand years after the Parthenon, another artist was also searching for an objective basis of beauty.

            MARK WILSON JONES: This is a very famous image. It's drawn by Leonardo da Vinci, in the Renaissance, and it's based on Vitruvius's description of the ideal the human body. And he encapsulates this idea of its theoretical importance. And what's really interesting for us is that when we superimpose the Salamis relief on this drawing, we see that there's a remarkable correspondence. There are differences, but it's the same principle. You have the same interest in the anthropomorphic principle of getting a kind of sacred fundamental justification for these measures.
            NARRATOR: Da Vinci's ideal Renaissance man famously stands in a circle surrounded by a square. Da Vinci named this image "Vitruvian Man" after the Roman architect.
            The ratio of the radius of the circle to a side of the square is 1 to 1.6. That ratio is sometimes attributed to the Greek mathematician, Pythagoras, who lived 100 years before the building of the Parthenon. In the Victorian age, it became known as the "golden ratio." It was a mathematical formula for beauty. For centuries many scholars believed the golden ratio gave the Parthenon its tremendous power and perfect proportions. Most notably, the ratio of height to width on its facades is a golden ratio.
            Today the golden ratio's use in the Parthenon has been largely discredited, but Manolis Korres and most scholars believe another ratio does in fact appear in much of the building.
            MANOLIS KORRES: The width, for instance is 30 meters and 80 centimeters; the length is 69 meters and 51 centimeters, the ratio being 4:9.
            NARRATOR: The 4:9 ratio is also found between the width of the columns and the distance between their centers, and the height of the facade to its width.
            JEFFREY M. HURWIT: The Parthenon, like a statue, exemplifies a certain symmetria, a certain harmony of part to part and of part to the whole. There's no question that the harmony of the building, which is clearly one of its most visible characteristics is dependent upon a certain mathematical system of proportions.
            MARK WILSON JONES: For the Greeks, there was nothing better than a design based on the coming together of measures, of proportions and harmonies and shapes. It's rather like an orchestrated piece of music in which the harmonies of the various instruments are, sort of, fused together in a wonderful, glorious, orchestrated symphony.
            NARRATOR: With something like the Salamis Stone's use of the human body as units of measure, and the idealized human form to define perfect proportions, the Parthenon literally embodies the words of the Greek philosopher Protagoras, who lived in Athens during the construction of the Parthenon, "Man is the measure of all things."
          •  NARRATOR: One of the subtlest of these curves can be found on the Parthenon's columns. LENA LAMBRINOU: If we pull a string, we can see that from the middle of the column and up, we can see a curve, a very slight curve.
            NARRATOR: The curve is gentle, starting a little less than halfway up and tapering again near the top. It's an optical refinement called "entasis."
            CATHY PARASCHI: Entasis means tension. It gives life to the column visually. It resembles an athlete trying to lift the weight, even the deep breadth of the swelling of its chest. It is no longer dead stone. It has life in it. It has pulse.
            JEFFREY M. HURWIT: These deviations from the straight, from the perfectly vertical, from the perfectly horizontal are analogous to the curvatures and the swellings and the irregularities of the human body. And in that sense the Parthenon strikes me as being a sculptural as well as an architectural achievement.
            NARRATOR: The entasis curve on the side of the column is so subtle and so slight, restorers can only draw it by computer. For the ancients to have drawn it at full scale, they would have had to set their compass at an impossible radius of nearly a mile. How they constructed the curved columns was one of the last great riddles left by the ancient Greek temple builders.
            The answer literally "came to light" at Didyma, 200 miles from Athens, in what is, today, Turkey. Here, a team of German archaeologists was exploring the ruin of the Temple of Apollo.
            Built at the time of Alexander the Great, 150 years after the Parthenon, it was the biggest Greek temple ever conceived: 120 columns, each one more than twice the height of the Parthenon's.
            The German team noted an optical refinement, a curvature, on the base of the temple, similar to that of the Parthenon.
          •  NARRATOR: The Parthenon was completed in 432 B.C.E. As the ultimate expression of Athenian ideals, the temple is adorned with mythological battles of victory: justice over injustice, civilization defeating barbarity, order prevailing over chaos. And, perhaps for the first time on a Greek temple, the Athenians, mere mortals, depict themselves alongside the gods. JEFFREY M. HURWIT: And so, if the human beings, the Athenians on the Parthenon frieze, are elevated near the rank of gods, the gods are represented in a way that makes them human. And the difference between gods and mortals, between Athenians and the Olympians is not one so much of kind, as of degree. This is an extremely humanistic way of representing themselves.

          A full-scale, 12-ton replica of the colossal Athena Parthenos is the centerpiece of a recreation of the Parthenon in Nashville, Tennessee. While the replica is gilded in gold leaf, the fifth-century statue was plated in some 2,400 pounds of solid gold. [source]

          Notes from the Interview with Jeffrey Hurwit, a professor of art history at the University of Oregon and expert on the architecture of the Acropolis:

          • Hurwit: I think the artists and the architects of any culture strive for what they consider the perfect expression of their ideas of beauty or their beliefs. Clearly the Athenians, and the Greeks in general, had notions of perfection; they had notions of what they called symmetria, the harmonious relationship of part to part and of the part to the whole. And the Parthenon, like certain statues created in the fifth century, is an expression of these ideas.
          • So the Parthenon was an attempt on the part of Pericles and Athens to assert the city's cultural, political, and military dominance over the rest of Greece and the Aegean. Pericles called Athens "the school of Hellas," an education unto Greece, and the Parthenon was intended to be the main text in the curriculum.
          • Hurwit: The Parthenon was built completely of marble from the base of the temple to its roof tiles. It had two large-scale pediments, each filled with over 20, larger-than-life-sized marble figures in compositions that extolled Athena and her power. It was adorned with 92 exterior sculptured metopes [decorated rectangular panels near the top of the temple]. It also had an Ionic frieze running around the top of the cella walls [the interior walls of the building] representing an idealized and pious Athenian citizenry. It had great roof ornaments, acroteria, in the form of victory figures, Nikai, alighting as if descending from heaven.
            And the great statue of Athena Parthenos inside the Parthenon, made of gold and ivory, held in the palm of her hand another image of Nike, some six feet tall, offering it to the Athenians as if to confirm their military predominance over the rest of Greece.
          • The statue had all kinds of sculptural decorations. She not only held in her hand a statue of victory, but the shield on which she leaned with her left hand was adorned on the outside with a battle of the Greeks against the Amazons. And on the inside, there was a representation of the gods fighting the giants. And on the sandals of the statue there was a representation of the Greeks fighting the centaurs. All of these mythological battles represent the struggle between the forces of justice and injustice, of civilization against barbarity, of order versus chaos.
            These three battles (as well as episodes from the Trojan War) were also represented on the outside of the Parthenon, on the metopes of the building. So there is a thematic unity from the exterior to the interior of the Parthenon. This theme of victory, of order over chaos, would have been drilled into any visitor to the Parthenon. These mythological battles between gods and giants, Greeks and centaurs, Greeks and Amazons were regarded as mythical allusions to historical victory, the recent victory of the Athenians over the Persians.
            One interesting thing about the Athena Parthenos, however, is that this glorious expression of Athens' patron goddess stood on a base decorated with a representation of the birth of Pandora. Pandora is best known through Hesiod, the epic poet, as responsible for letting loose evils from her famous box. It's curious that Pandora, whom Hesiod calls a beautiful evil, should adorn the base of a statue that otherwise expresses Athenian might, wealth, and power.
            I think an intellectual member of Athenian society might have wondered whether Pheidias wasn't attempting to perhaps slightly undercut the glorification of Athens, that this great statue hinted that Athens might have to deal with circumstances not of its own choosing.
          • Hurwit: There is no question that the Greeks conceived of their architecture in anthropomorphic terms. The most obvious expression of this is found on the Acropolis itself, where in the south porch of the Erechtheum, columns take the form of six maidens, or caryatids. Vitruvius, the Roman architect, talks about how the Doric order is masculine and the more elaborate, thinner Ionic order is feminine. There is no question that in the Greek mind, there was an analogy between the architectural form and the human form.
          • Q: Did the ancient Greek architects have a mathematical formula for beauty?
            Hurwit: Well, the idea of symmetria, the harmonious relationship of one part of a body or of a structure to another part of a body or a structure, seems to have been of paramount importance to the Greeks, not just architects but sculptors as well.
            In the middle of the fifth century, while the Parthenon was under construction, Polykleitos of Argos, a great sculptor, actually created a statue, which we call the Doryphoros, or Spear Bearer, to be the embodiment of a geometrical or mathematical system of proportion. It is likely that Greek architects also strove for an architectural symmetria—for some formula, some geometrical or mathematical proportional system that would enable them to achieve a perfect harmony of part to part and of parts to the whole.
            Q: So is it fair to say that the Parthenon's beauty comes from such a formula?
            Hurwit: The Parthenon, like a statue, exemplifies a certain symmetria. Its symmetria largely depends upon the 9:4 ratio, which is present in various dimensions of the building—the length of the stylobate [the platform that forms the base of the building] to the width of the stylobate, the width of the stylobate to the height of the column and entablature [the top section between the columns and roof] together. There's no question that the harmony of the building, which is clearly one of its most visible characteristics, is dependent on a certain mathematical system of proportions.
            Because we assume that the Parthenon was perfectly designed, we almost have a compulsion to focus on the basic mathematical ratio that governs the design. But I think it is the irregularities and variations that are the most interesting things about the Parthenon and that give it an organic feel. 

            Nashville, Tennessee is home to a full-scale replica of the Parthenon, including a recreation of its original Athena statue.