Constructing DIVINE
Abstract:
This paper
describes initial research on a project designed to understand the experiences
of past generations of constructors and make that knowledge accessible to
future generations of engineering students and construction practitioners. Much
in the same way as medical students can trace their lineage back to
Hippocrates, this project aims to provide architecture, engineering, and
construction students, and professionals alike, a sense of their professional
history. The project was developed around three time epochs, four geographic regions,
and three different project types. I investigated issues such as the flow of
money, training of workers, sharing of design knowledge, and nature of
contracts and agreements.
The central question posed by this work is how should
knowledge of the history and evolution of construction practices be
incorporated in the dialog that educators have with students and with the
larger professional community? This research has led to multifaceted results.
On the one hand, the message to students should be pride in their professional heritage
because throughout time constructors and designers have used knowledge,
perseverance, and innovation to accomplish remarkable projects.
“Who knows only his own generation remains
always a child”
It is certainly true that all can benefit from the wisdom
and experience of past generations. This paper describes initial
research on a project designed to understand the experiences of past generations
of constructors and make that knowledge accessible to future generations of
engineering students and construction practitioners.
Interstellar Cosmology in the Hindu Temple
According to the Sthapatya Veda (the Indian tradition of
architecture), the temple and the town
should mirror the cosmos. The temple architecture and the city plan are,
therefore, related in their conception. Volwahsen (2001) has remarked on the continuity
in the Indian architectural tradition. The Harappan cities have a grid plan,
just as is recommended in the Vedic manuals. The square shape represents the
heavens, with the four directions
representing the cardinal directions as well as the two solstices and the equinoxes
of the sun’s orbit.
The monument that has been studied most extensively for
its cosmological basis is the Angkor Wat
temple. Although it is located in Cambodia, it was built according to the principles
of Indian architecture.
This paper presents the basis of the Hindu temple design
going back to the earliest period. We trace this design back to the fire altars
of the Vedic period which were themselves designed to represent astronomical
knowledge. An assumed equivalence between the outer and the inner cosmos is central
to the conception of the temple. It is because of this equivalence that numbers
such as 108 and 360 are important in the temple design.
The number 108 represents the distance from the earth to
the sun and the moon in sun and moon diameters, respectively. The diameter of
the sun is also 108 times the diameter of the earth, but that fact is not
likely to have been known to the Vedic rishis. This number of dance poses
(karanas) given in the Natya Shastra is also 108, as is the number 1o f beads
in a rosary (japamala). The “distance” between the body and the inner sun is also
taken to be 108, and the number of marmas in Ayurveda is 107. The total number
of syllables in the Rigveda is taken to be 432,000, a number related to 108. The
number 360, the number of days in the civil year, is also taken to be the
number of bones in the developing foetus, a number that fuses later into the
206 bones of the adult.
The centrality of this number in Vedic ritual is stressed
in the Shatapatha Brahmana. The primary Vedic number is three, representing the
tripartite division of the physical world into the earth, the atmosphere, and
the sky and that of the person into the physical body, the pranas, and the
inner sky. The Hindu temple also represents the Meru mountain, the navel of the
earth. The Brihat Samhita 56 lists the many design requirements that the temple
building must satisfy. For example, it says “the height of the temple should be
double its width, and the height of the foundation above the ground with the
steps equal to a third of this height. The sanctum sanctorum should be half the
width of the temple” and so on. It also lists twenty types of temples that
range from one to twelve storeys in height.
(a) An exotic depiction of the temple of Angkor Wat in Garnier's 1873 publication Voyage d'exploration en Indo-Chine; (b) The first photograph of Angkor Wat ever taken, by John Thomson 1866 (Source: (a) Francis Garnier, Voyage d'exploration en Indo-Chine effectué pendant les années 1866, 1867)
We first summarize some relevant characteristics of the
Angkor Wat temple that emphasize the relationship of the design to astronomy.
This will be followed by sections on the Vedic antecedents of the temple and
the medieval expression of the philosophy behind its design. We will also
consider the question of the chaitya hall with its pointed arch as an alternate
tradition within India that has been connected to the Lycian arch which may
have influenced the design of the cathedral.
The most impressive aspect
of the temple representation is that it occurs both at the level of the part as
well as the whole in a recursive fashion, mirroring the Vedic idea of the microcosm
symbolize the macrocosm at various levels of expressions. This is done not only
in the domain of numbers and directions, but also using appropriate
mythological themes, and historical incidents. The mythological scenes skillfully
use the oppositions and complementarity between the gods, goddesses, asuras,
and humans defined over ordinary and sacred time and space
Speaking just of numbers, the various lengths and circumferences of units representing the motion of the moon may equal 27, 28, 29 (nakshatras or days of the month), 354 (days of the lunar year), or 360 (tithis of the lunar year). Other lengths represent the solar year (360, 365, or 366) or larger time cycles. For example, the west-east axis represents the periods of the yugas. The width of the moat is 439.78 cubit; the distance from the first step of the western entrance gateway to balustrade wall at the end of causeway is 867.03 cubit; the distance from the first step of the western entrance gateway to the first step of the central tower is 1,296.07 cubit; and the distance from the first step of bridge to the geographic center of the temple is 1,734.41 cubit. These correspond to the periods of 432,000; 864,000; 1,296,000; 1,728,000 years for the Kali, Dvapara, Treta, and Krita yuga, respectively. It has been suggested that the very slight discrepancy in the equations might be due to human error or erosion or sinking of the structure.
In the central tower, the topmost elevation has external axial dimensions of 189.00 cubit east-west, and 176.37 cubit north-south, with the sum of 365.37. This division of the almost exact length of the solar year into unequal halves remained a mystery for some time until it was found to be connected with the Shatapatha Brahmana numbers for the asymmetric motion of the sun. Over the half-millenia of Khmer rule, the city of Angkor became a great pilgrimage destination because of the notion of Devaraja, that has been explained by Lokesh Chandra as a coronation icon. Jayavarman II (802-850) was the first to use this royal icon. According to Lokesh Chandra (1995), “Devaraja means `King of the Gods' and not `God-King'. He is Indra and refers to the highly efficacious aindra mahabhisheka of the Rigvedic rajasuya tradition as elaborated in the Aitareya-brahmana. It was not a simple but a great coronation, a mahabhisheka. It was of extraordinary significance that Jayavarman II performed a Rigvedic rite, which lent him charismatic authority.”The increasingly larger temples built by the Khmer kings continued to function as the locus of the devotion to the Devaraja, and were at the same time earthly and symbolic representations of mythical Mt. Meru, the cosmological home of the Hindu gods and the axis of the world-system. The symbol of the king's divine authority was the sign (linga) of Shiva within the temple's inner sanctuary, which represented both the axes of the physical and the psychological worlds. The worship of Shiva and Vishnu separately, and together as Harihara, had been popular for considerable time in southeast Asia; Jayavarman's chief innovation was to use ancient Vedic mahabhisheka to define the symbol of government.
To quote Lokesh Chandra further, “The icon used by Jayavarman II for his aindra mahabhisheka, his Devaraja = Indra (icon), became the symbol of the Cambodian state, as the sacred and secular sovereignty denoted by Prajapatishvara/Brahma, as the continuity of the vital flow of the universal (jagat) into the stability of the terrestrial kingdom (raja = rajya}). As the founder of the new Kambuja state, he contributed a national palladium under its Cambodian appellation kamraten jagat ta raja/rajya. Whenever the capital was transferred by his successors, it was taken to the new nagara, for it had to be constantly in the capital.”
Angkor Wat is the supreme masterpiece of Khmer art. The descriptions of the temple fall far short of communicating the great size, the perfect proportions, and the astoundingly beautiful sculpture that everywhere presents itself to the viewer. Its architecture is majestic and its representation of form and movement from Indian mythology has astonishing grace and power. The inner galleries of the temple have depiction of the battle of Kurukshetra, procession of King Suryavarman and his ministers, scenes from heavens and hells, churning of the sea of milk, the battle of Vishnu and the asuras, victory of Krishna over Bana, battle of the devas and asuras, Ravana shaking Kailasa with Shiva and Parvati atop, and the battle of Lanka between Rama and Ravana. These and other scenes are drawn with great artistic beauty. No wonder, the temple ranks amongst the greatest creations of human imagination.
4Numbers at Angkor Wat
The temple has 1300-m north-south axis and 1500-m west-east axis. The temple faces toward the west because that situates it to the east with respect to the worshiper, the appropriate direction for Vishnu who is a solar deity. At the heart of the temple are three rising, concentric galleries. Bordering these is further space, and a rectangular moat.
About 40 m in from the moat is a laterite wall, 4.5 m high, with large single entrances from the east, north, and south, and five entrances on the west. Mannikka has suggested that the Vastupurusha mandala at Angkor Wat forms a grid of 49, rather than the standard of 64 or 81. Various numbers from the Vedic astronomy are encountered at Angkor Wat as simple counts, or measurements in cubits, or phyeam = 4 cubits. Some of these represent just the basic constants of the system, while others provide specific information related to the orientation of the temple related to the nakshatras and the positions of the planets. For an example of the latter, consider that the length of the north-south axis, door to door, in the sanctuary is 13.41 cubits, which according to Mannikka represents the fact that the north celestial pole is 13.43 degrees above the northern horizon at Angkor. This number is also basic to the second gallery, devoted to Brahma who is ``situated'' at the north celestial pole.
The order in which the planets rose over the eastern horizon at the end of July 1131 is represented in the bas-relief of the northwest corner pavilion: Saturn (Agni), Jupiter (Indra), Venus (Kubera), Mars (Skanda), and Mercury (Varuna).
According to Mannikka, the design of the temple can be seen in three architectural units:
1. Central sanctuary: Mount Meru, with 45 gods, the north celestial pole, the centre of the mandala, the spring equinox, the axis of the earth, Vishnu, Brahma, and King Suryavarman
2 Circumferences: the ecliptic, the moon and lunar periodicity, the constellations, the planets, the celestial year, the krita yuga, the grid of the mandala, the history of King Suryavarman
3 Axes: the building blocks of time (60, 108), the yuga cycles, the solar year, the lunar year, historical dates in Suryavarman's reign, the mandala and its transformation of time, and, finally, the solar year and lunar time cycles from the vantage point of Mount Meru.
Some basic numbers that we encounter frequently in the architectural plan are given below. For more examples see the book by Mannikka which, however, does not recognize the special place of the altar numbers 78 and 261. Neither does it know the correct significance of the number 108. 21 The earth number shows up as the number of steps to the libraries.
27/28 This count of nakshatras is represented at numerous places; the total inner axes of the sanctuary.
32/33 This represents the number of devas and it is found as the number of pillars, windows and various lengths.
44/45 The number of divinities of the Vastupurusha mandala is shown in the total number of steps, main entrance and flanking Central Western entrances. As 450 cubits, various axial entrances and circumference of gallery.
54 As half of the distance in sun- or moon-diameters to the sun or the moon, 54 cubits or
54 phyeam are encountered several places on the Western bridge and the outer enclosure.
78 The atmosphere number is found in the central cruciform, inner axes as 20.08 phyeam, which equals 80.32 cubits. The 20 steps in several of the stairways to the libraries may also represent the same number divided by 4. Further evidence for that comes from the distance of 19.42 phyeam = 77.68 cubits each library, west-east outer axis. Since books represent the `atmosphere' in reaching the `sky' of knowledge, its use in the context of library is very appropriate.
108 In-and-out circumambulation of four corner towers together; circumambulation of the central Vishnu image from three axial entrances; inner axes of all four corner towers without images; full vertical distance above and below central sanctuary.
130.5/261 As half of the sky number 261, we find it in the circumambulation path to north end chamber, each end gateway. The number is 32.74 phyeam which equals 130.96 cubits.
354 The length of the lunar year in days, it is the distance between naga balustrade and first step at end of walkway to upper elevation.
360 In phyeam, the circumambulation path around the Cruciform Terrace.
366 Solar axes of gallery from walkway on west to bases on each side.
371 This is the solar year in tithis, and it is found in an in-and-out circumambulation of all four corner towers.
Solar and lunar measurements; Temple Antecedents
The solar and lunar numbers that show up in the design of the Angkor Wat temple are the number of nakshatras, the number of months in the year, the days in the lunar month, the days of the solar month, and so on. Lunar observations appear to have been made from the causeway.
The division of the year into the two halves of 189 and 176.37 was recently explained by the author as being derived from the Shatapatha Brahmana. In layer 5 of the altar described in the Shatapatha, a division of the year into the two halves in the proportion 15:14 is given (Kak, 1998, 2000). This proportion corresponds to the numbers 189 and 176.4 used at Angkor Wat, where in the central tower the topmost elevation has dimensions of 189 east-west and 176.37 north-south.
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| (a) An elevation of the lower eastern section of the central tour of Angkor Wat and (b) a collage of original sculptures, plaster casts and photographs from the real site of Angkor Wat. |
The elliptical orbit of the earth together with the fact that the sun is at a slight offset is behind the asymmetry in the sun's orbit. The period from the autumnal equinox to the vernal equinox is smaller than the opposite circuit. The interval between successive perihelia, the anomalistic year, is 365.25964 days which is 0.01845 days longer than the tropical year on which our calendar is based. In 1000 calendar years, the date of the perihelion advances about 18 days. The perihelion was roughly on December 18 during the time of the construction of Angkor Wat; and it was on October 27 during early 2nd millennium BC, the most likely period of the composition of the Shatapatha Brahmana. In all these cases the perihelion occurs during the autumn/winter period, and so byKepler's 2nd law we know that the speed of the sun in its orbit around the earth is greater during the months of autumn and winter than in spring and summer.
During the time of the Shatapatha Brahmana, the apogee was about midway through the spring season, which was then somewhat more than 94 days. The extra brick in the spring quadrant may symbolically reflect the discovery that this quarter had more days in it, a discovery made at a time when a satisfactory formula had not yet been developed for the progress of the sun on the ecliptic. It is possible that the period from the spring equinox to the fall equinox was taken to be about 189 days by doubling the period of the spring season; 176 days became the period of the reverse circuit.
Why not assume that there was no more to these numbers than a division into the proportions 15:14 derived from some numerological considerations? First, we have the evidence from the Shatapatha Brahmana that expressly informs us that the count of days from the winter to the summer solstice was different, and shorter, than the count in the reverse order. Second, the altar design is explicitly about the sun's circuit around the earth and so the proportion of 15:14 must be converted into the appropriate count with respect to the length of the year. Furthermore, the many astronomical alignments of the Angkor Wat impress on us the fairly elaborate system of naked-eye observations that were the basis of the temple astronomy.
But since precisely the same numbers were used in Angkor Wat as were mentioned much earlier in the Shatapatha Brahmana, one would presume that these numbers were used as a part of ancient sacred lore. The count between the solstices has been changing much faster than the count between the equinoxes because the perigee has been, in the past two thousand years somewhere between the autumn and the winter months. Because of its relative constancy, the count between the equinoxes became one of the primary `constants' of Vedic/Puranic astronomy.
The equinoctial half-years are currently about 186 and 179, respectively; and were not much different when Angkor Wat temple was constructed. Given that the length of the year was known to considerable precision there is no reason to assume that these counts were not known. But it appears that a `normative' division according to the ancient proportion was used.
As it was known that the solar year was about 365.25 days, the old proportion of 15:14 would give the distribution 188.92 and 176.33, and that is very much the Angkor Wat numbers of 189 and 176.37 within human error. In other words, the choice of these `constants' may have been determined by the use of the ancient proportion of 15:14.
(d) The famous face towers of the Angkorian temples, depicted in (a) Thomson 1875, (b) Fergusson 1876, and Delaporte 1880 (Source: (a) John Thomson, The straits of Malacca, Indo-china and China, London 1875, p.151; (b) James Fergusson, History of Indian and Eastern architecture. Vol. 3 of History of architecture in allcountries, London 1876
The temple is considered in the image of the Cosmic Purusha, on whose body is displayed all creation in its materiality and movement. Paradoxically, the space of the Purusha (Rigveda 10.90) is in the sanctuary only ten fingers wide, although he pervades the earth. The prototype of the temple is the Agnikshetra, the sacred ground on which the Vedic altars are built. The Agnikshetra is an oblong or trapezoidal area on which the fire altars are built. Tripathi (1990) has argued that the agnichayana sacred ground provides the prototype, because in it is installed a golden disc (rukma) with 21 knobs or hangings representing the sun with a golden image of the purusha on it. Tripathi shows that the detailed ritual includes components that would now be termed Shaivite, Vaishnava, or Shakta. In Nachiketa Agni, 21 bricks of gold are placed one top of the other in a form of shivalinga. The disk of the rukma, which is placed in the navel of the altar on a lotus leaf is in correspondence to the lotus emanating from Vishnu’s navel which holds the universe.
Several bricks are named after goddesses, such as the seven krittikas.
The temple is the representation of the cosmos both at the level of the universe and the individual, making it possible for the devotee to get inspired to achieve his own spiritual transformation. The purusha placed within the brick structure of the altar represents the consciousness principle within the individual. It is like the relic within the stupa.
Complementing the tradition of the Vedic ritual was that of the munis and yogis who lived in caves and performed austerities. From this tradition arose the vihara, where the priests lived. The chaitya hall that also housed the stupa may be seen as a development out of the agnichayana tradition where within the brick structure of the altar were buried.
Concluding Remarks
This paper has shown how the Hindu temple represents the outer and the inner cosmos. The outer cosmos is expressed in terms of various astronomical connections between the temple structure and the motions of the sun, the moon, and the planets. The inner cosmos is represented in terms of the consciousness at the womb of the temple and various levels
of the superstructure that correspond to the states of consciousness. The position of the gods in the vastupurushamandala within the temple is a symbolic representation of the spatial projections of the cosmic purusha in his own body.
The temple must be seen as a structure that gives us considerable information about the science and cosmology of its times. Regarding technology behind the constructions, one must look at each structure separately and see how it fits in the evolving techniques of design and artistic representation across the region.
References
Kak, S., 1992. ``Astronomy of the Vedic altars and the Rigveda'', Mankind Quarterly, 33, 43-55.
Kak, S., 1993. ``Astronomy of the Vedic Altars," Vistas in Astronomy, 36, 117-140.
Kak, S., 1995. ``The astronomy of the age of geometric altars," Quarterly Journal of the Royal Astronomical Society, 36, 385-396.
Kak, S., 1998. ``The sun's orbit in the Brahmanas,'' Indian Journal of History of Science, 33, 175-191.
Kak, S., 1999. ``The solar equation in Angkor Wat,'' Indian Journal of History of Science, vol. 34, pp. 117-126.
Kak, S., 2000. The Astronomical Code of the Rgveda. Munshiram Manoharlal, New Delhi.
Kak, S., 2002. The Gods Within. Munshiram Manoharlal, New Delhi.
Kamiya, T. 2002. Lycian influence to Indian cave temples. http://www.ne.jp/asahi/arc/ind/lycia/liki_eng.htm
Kaulacara, R., 1966. Silpa Prakasa. Boner, A. and Rath Sarma, S. (eds.). E.J. Brill, Leiden, 1966.
Kramrisch, S., 1946. The Hindu Temple. The University of Calcutta, Calcutta, 1946; Motilal Banarsidass, Delhi, 1991, page 35-36.
Lokesh Chandra, 1995. ``Devaraja in Cambodian history'', In Cultural Horizons of India. Aditya Prakashan, New Delhi.
Mannikka, Eleanor, 1996. Angkor Wat: Time, Space, and Kingship. Univ of Hawaii Press, Honolulu
Millar, F.G. and Kak, S., 1999. ``A Brahmanic fire altar explains a solar equation in Angkor Wat,'' Journal of the Royal Astronomical Society of Canada, vol. 93, pp. 216- 220. Tripathi, V., 1990. Agnicayana. Sampurnanand Sanskrit University, Varanasi.
Volwahsen, A., 2001. Cosmic Architecture in India. Prestel, New York, and Mapin Publishing, Ahmedabad.
Nice blog on Prefabricated Structures . Its very informative !
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