MAN IN NATURE
Cosmogony and the Elements...
The Intuition of Cosmos in Science and Myth...
John McKim Malville
Measurement in India
In Sanskrit, to measure, ma, is to give existence to a thing, to give it reality in our world, and to demonstrate relationship. The close connection in Hindu thought between measurement and creation is evidenced by the words mother, matir and mater which come from the same Sanskrit root, as does maya. Measurement separates and differentiates the elements of the world and thereby creates them. The first act of measurement in our universe, which occurred at the boundary between time and the timeless, wrested the elements of our world from the continuum of chaos. The ritual of measurement performed at the time of establishment of a temple or Vedic altar is a re-enactment of creation of the world (Malville 1992). Prajapati, who is the Year, measures the world, both in space and time, with his eye, the sun. Purusa, identified with Visvakarman, the architect of the universe, "bears the measuring rod (mana), knows divisions, and thinks himself composed of parts (Vayu Purana, IV.30-31: Kramrisch 1946:131). The world has resulted from the division of his parts.
Recognition of the cosmogonic aspect of measurement extends back to the time of the Vedas. The Vedic altar was reconstructed each year near the time of vernal equinox as a symbolic reconstruction of Prajapati, the year (Kramrisch 1981; Staal 1983). Built of five layers, representing the five seasons, five elements and five directions, the altar was surrounded by a wall of 360 bricks acknowledging that the year is bounded by 360 days. The fired bricks symbolized the elements of fire, earth, and water. The sun horse provided the element of air by breathing upon the bricks of the altar to bring them to life.
The importance of precise orientation and measurement in construction of the Hindu temple reveals the cosmogonic symbolism involved in the act. The Sanskrit term referring to the temple, vimana, means ‘well-measured’ or ‘well-proportioned’. Texts on temple architecture give extensive discussions of the system of proportional measurements and techniques for determining true north.
When laying out the design for a temple, the orientation of the site had to be established at a time when the sun was in the northern part of the sky, i.e., when it was above the cosmic ocean, and on a day when there were no sunspots disfiguring its visible surface. A pillar, the gnomon, was erected and used to cast measured shadows. At one level of meaning the gnomon represented the God Indra who "pillared apart" and therefore differentiated heaven and earth; the pillar supported the heaven and steadied the earth (Kramrisch 1991). The yupa, the sacrificial post, the lingam, the central pole of a tent used for dance, and the tree of life are other examples of sacred or ritual pillars (Vatsyayan 1983). The stalk of the lotus bearing Brahma, the four-faced creator of the universe, is another cosmogonic pillar from which creation emanates.
In the Indian gnomon we encounter the remarkable union of a technical and a ritual device (Ajitagama: Dagens 1984). It is placed in a square area, which had to be "as smooth as a mirror", checked with a water level. Around the gnomon is traced a circle with a radius equal to the height of the gnomon. In the simplest of approaches two points are marked on the circle where the shadow of the gnomon touches it at midmorning and midafternoon. These two points are joined by a straight line which is close to true east-west.
This method, often referred to as the Indian Circle method, produces an alignment to the true cardinal directions which is only approximately accurate during most of the year. Swinging between its winter and southern extremes at the solstices, the sun moves most rapidly at the equinoxes. At the time of vernal equinox, for example, since the sun moves northward between midmorning and midafternoon, the Eastern point, produced by the afternoon shadow is shifted slightly southward of the Western point. The line connecting the two points would thus be tilted south of east in the spring and north of east in the fall.
Brahmagupta (born ad 598) is credited with the first recorded recognition of this defect of the method (Yano 1986), although he did not give a formula for correction. Sripati (ad 1039) was the first who successfully versified the formula in Sanskrit, and after him the formula apparently became common knowledge among Indian architects and astronomers (Yano 1986):
s = h [sin(dec1 ) — sin(dec2 )]/cos(latitude)
where s is the distance of the tip of the shadow from the east-west line, h is the hypotenuse of the shadow, and dec1 and dec2 are the respective declinations of the sun at the time in the morning and afternoon when the shadows touch the circle. Similar to latitude of the earth which measures the angular distance from the earth’s equator, declination measures the angular distance from the celestial equator. Thus at equinox the declination of the sun is 0o and at summer solstice its declination is 23.5o.
Even on the days of equinox, the effects of the movement of the sun in declination are slight compared to the best measurement that could have been achieved before the invention of the telescope. During 6 hours from midmorning to midafternoon, the declination of the sun varies at most by 6' (1/10 of a degree), only 1/5 the angular diameter of the sun.
The amount by which the sun changes its declination during the day decreases as the sun moves away from equinox, and on the days of solstice the change is zero. For the two month period around solstice, the maximum error is only 3' and within 10 days of solstice, the maximum error has fallen to 1'.
A fascinating and impressive array of other methods were also available to achieve the same corrections (Yano 1986; Staal 1983). I have described this method in some detail to demonstrate the robust role of measurement within the Indian tradition. The resolution of the human eye is at best 1.5-2 minutes of arc, and the corrections achievable by these methods and computations exceed the highest precision that could have been achieved in pre-telescopic times.
Not just temples, but cities in India have been built mindful of the importance of precise measurement. The greatest of medieval cities of India, Vijayanagara, echoes the symbolic seriousness of careful measurement. In a manner remarkably similar to the north-south axiality of Beijing, a north-south line extends from the summit of Matanga hill into the middle of the royal center passing through a major ceremonial gateway (Fig. 2.6). In the case of Beijing the north-south axis is a line of dominion extending from the Emperor of Heaven to his terrestrial counterpart. In Vijayanagara there are multiple levels of meaning contained in the axis, some of which may be related to our theme of cosmogony and the elements: (1) The north-south line crosses and is tangent to the Tungabhadra river just where it turn north, reminiscent of the northward flowing of the Ganga at Kashi. North is the direction of birth and the north-south axis of the City thus acquires a cosmic symbolism paralleling that of Kashi itself. (2) The axis crosses the remains of an artificial lake that was constructed just south of Matanga hill. This lake, which does not seem to have served any practical needs of the city, may have been a metonym for the Ocean of Milk, one of the great symbols of fertility and cosmogony in Hindu texts. The lake may have been involved in ritual processions between the summit of Matanga hill and the royal center. (3) The axis may be symbolic protection of the city by the sage Matanga (Malville and Fritz 1993), which figures prominently in the creation mythology of the city. (4) The axis establishes a well-defined symmetry by dividing the royal center into public/private, male/female dualities.
Standing at night in that ceremonial gateway of the royal center, looking north, one sees the North Star, fixed and unmoving, lying directly above the sikhara of the Virabhadra temple on the summit of Matanga hill. As viewed from that spot, the north pole of the celestial sphere is displaced from the sikhara by only 0.8'. The visual symbolism of that nighttime vista is forceful and commanding, and the cosmological symbolism actually works! The north celestial pole lies on the cosmic axis that passes through Matanga hill. Who could doubt that Matanga hill lies at the center of the universe or that Vijayanagara is a magical and powerful city?
To the south of the gateway is another remarkable example of precise measurement within the royal center. In this case measurement appears to legitimize with cosmic authority the two (public/private) realms of kingship. The largest palace in the Western area balances the 100 column audience hall in the east. The midpoint between their two centers, a fulcrum of kingship lies only a few meters from the north-south axis of the royal center which passes through the celestial north pole and Matanga hill (Fig. 2.7). The respective roles of the king and queen appear thus to be symmetrical and balanced. A symmetry is found in Beijing involving the temples of the sun and moon (Krupp 1989). But here it appears to speak to the fundamental role of the queen as developed in the Ramayana. It also symbolizes a refusal within Hindu mythology to grant precedence of the elemental Male over the Female Energy: the queen as Pakrti or Sakti energizes the ‘inert’ lump of matter that is the male, Purusa, and is just vital for the well-being of the empire as is the king.
Fig. 2.1: The interior of a massive star just before the collapse which triggers the supernova explosion showing the layers containing different elements.
Fig. 2.2: The Aztec sun stone. The sun god, Tonatiuh, is in the center. The next ring contains depictions of the four great ages of the world, destroyed successively by Jaguars, wind, rain of fire, and water. The next ring contains the twenty days of the week which comprise the 260 day sacred calendar. Cimi (Maya) or Miquiztli (Aztec) representing death is indicated (after Coe).
Fig. 2.3: Newgrange. The cross-section of the mound and a view from above showing the orientation of the passage to the rising sun at winter solstice (after O'Brien).
Fig. 2.4: Stonehenge, showing alignments to the major cyclic positions of the sun and moon (Griffith Observatory).
Fig. 2.5: Beijing's Imperial Palace (Griffith Observatory).
Fig. 2.6: The north-south axis of Vijayanagara, crossing the Tungabhadra River (T) where it turn north, the summit of Matanga hill (M), the artificial lake (L) which may symbolize the Ocean of Milk, and the ceremonial gateway (G) in the royal center.
Fig. 2.7: The north-south axis where it crosses the royal center through the ceremonial gateway (G). The symmetrical placement of the queen's palace (P) and the king's 100 column hall audience hall (A) are shown.
I started this discussion with astrophysics and, coming nearly full circle, I conclude with physics. There is an almost uncanny similarity between the role of Vedic measurement in evoking elements from primordial chaos and that of quantum mechanical measurement in ‘actualizing’ the objects of the world. According to the Copenhagen interpretation of quantum mechanics championed by Niels Bohr (1963), "discrete objects such as electrons do not come into existence until they are measured". Prior to the act of measurement, electrons exist only as probabilities. The Many Worlds Hypothesis, collapsing wave functions, and, even, the death of Schroedinger’s cat are various features of this insight of modern physics that the material world is created by the human act of measurement (Wigner 1961).
Both myth and science are human creations, and it should come as no surprise that they often converge with common insights (Malville 1975). The actors in our cosmogonic drama have had many roles and many costumes ranging from creation mythologies to quantum mechanics. Elements have come to us from all directions of space and time: falling from the sky, emerging out of earth and water, born of the union of Yin and Yang, and evoked in that mysterious yet simple act of making a measurement in this extraordinarily interconnected cosmos which we call home.
©1995 Indira Gandhi National Centre for the Arts, New Delhi