1. Introduction

Archaeoastronomy in India has the benefit of ancient texts that describe cosmological ideas, their basis in astronomy, and their representation in architecture. These texts provide us crucial understanding of the astronomy and cosmology of the historical period.

In the Indian view, the cosmos is seen as being tripartite and recursive (see Kak, 2000a and Kak, 2008 for review and additional references). The universe is viewed as three regions of earth, space, and sky (Dumézil, 1988) which in the human being are mirrored in the physical body, the breath (prāna), and mind. The processes in the sky, on earth, and within the mind are taken to be connected.

Indian narratives about the cosmos are characterized by the central role of the observer. The cosmos is seen both as real and arising out of the phenomenal contents of the mind. At a practical level, agreement on the phenomenal contents of many minds is taken to imply real existence, and the question of the nature of the qualities of the objects is raised. The question that is asked in the Indian narrative is: Do these attributes or concepts have a real existence or do they arise from the intuition of the observers?

The examination of this and related questions leads to theories of the cosmos, both at the universal and personal levels, that form part of the philosophical systems of Sānkhya and Vaiśeshika. The Vedic view of India (spanning a long period that goes back to at least 2000 BCE) classifies knowledge in two categories: the higher or unified and the lower or dual. Higher knowledge concerns the perceiving subject (consciousness), whereas the lower knowledge concerns objects. Higher knowledge can be arrived at indirectly through intuition and contemplation on the paradoxes of the outer world. Lower knowledge is analytical and it represents standard science with its many branches. There is a complementarity between the higher and the lower, each being necessary to define the other. This complementarity mirrors the one between mind and matter.

The Vedic thinkers were aware that formal descriptions of the universe lead to logical paradox. The one category transcending all oppositions is Brahman. Figure 1 represents this world-view schematically. In this figure, logic is shown as a subset of the capacities of the mind, and likewise models of reality (which are based on logic) do not capture all aspects of the material world. Machines have been grouped together with logic in the figure since they must be constructed according to a logical framework. This figure may be viewed as a representation of the incompleteness of formal systems of knowledge. Vedic ritual is a symbolic retelling of this conception. Notable features of this world view that are relevant here are (Basham, 2004):

With the above as background to the general ideas regarding the cosmos current in ancient India, we come to the discussion of archaeoastronomy in ancient India. A considerable part of the archaeoastronomy of this period is based on the author's research (see, e.g., Kak, 1992, 1993, 2000a, 2000b, 2005a, 2009). Due to the importance given in Indian culture to the abstract and the symbolic, many of the archaeoastronomical sites are temples. The king was consecrated at the temple. The consecration served to confirm the king as foremost devotee of the chosen deity, who was taken to be the embodiment of time and the universe (Kak, 2002).

The Indian sacred city has been viewed as a structured mesocosm, situated between the microcosm of the individual and the macrocosm of the culturally conceived larger universe (Levy, 1991). Such a city is constructed of spatially connected and recursively layered circles, each of which is sustained by its own culture and performance. Although Levy's city is not very ancient, it is built according to an old tradition (Volwahsen, 2001). The Harappan city of Dholavira (Bisht, 1997) is also recursively structured. Furthermore, temples were taken to be define the meeting ground between the macrocosm and the microcosm, and, therefore, they provide much information on the relationship between astronomy and cosmology.

India's archaeological record has unbroken continuity going back to about 7500 BCE at Mehrgarh (Kenoyer, 1998, Lal, 2002), and it has a rock art tradition, next only to that of Australia and Africa in abundance, that is much older (Pandey, 1993, Bednarik, 2000). Some rock art has been assigned to the Upper Paleolithic period. There is surprising uniformity, both in style and content, in the rock art paintings of the Mesolithic period (10,000 – 2500 BCE) (Wakankar, 1992).

The setting for the hymns of the Rigveda, which is India's most ancient literary text, is the area of Sapta Saindhava, the region of north India bounded by the Sindh and the Ganga rivers although regions around this heartland are also mentioned. The Rigveda describes the Sarasvati River to be the greatest of the rivers and going from the mountains to the sea. The archaeological record, suggesting that this river had turned dry by1900 BCE, indicates that the Rigveda is prior to this epoch.

The Rigveda and other early Vedic literature have astronomical references related to the shifting astronomical frame that indicate epochs of the fourth and third millennium BCE which is consistent with the hydrological evidence. The nakshatra lists are found in the Vedas, either directly or listed under their presiding deities, and it one may conclude that their names have not changed. Vedic astronomy used a luni-solar year in which an intercalary month was employed as adjustment with solar year.

The foundation of Vedic cosmology is the notion of bandhu (homology or binding between the outer and the inner). It was estimated correctly that the sun and the moon were approximately 108 times their respective diameters from the earth (perhaps from the discovery that the angular size of a pole removed 108 times its height is the same as that of the sun and the moon), and this number was used in sacred architecture. The distance to the sanctum sanctorum of the temple from the gate and the perimeter of the temple were taken to be 54 and 180 units, which are one-half each of 108 and 360 (e.g. Kak, 2005a). Homologies at many levels are at the basis of the idea of recursion, or repetition in scale and time. The astronomical basis of the Vedic ritual was the reconciliation of the lunar and solar years.

2. The Cosmological Plan of the City and the Temple

According to the Vāstu Śāstra, manual of sacred architecture, the structure of the building mirrors the emergence of cosmic order out of primordial chaos through the act of measurement. The universe is symbolically mapped into a square that emphasizes the four cardinal directions. It is represented by the square vāstupurushamandala, which in its various forms is the basic plan for the temple, the house, and the city. There exist further elaborations of this plan, some of which are rectangular.

Yantric buildings in the form of mandalas, dated to about 2000 BCE, have been discovered in North Afghanistan that belong to a period that corresponds to the late stage of the Harappan tradition (Kak, 2005b, 2010) providing architectural evidence in support of the idea of recursion at this time. Although these building are a part of the Bactria- Margiana Archaeological Complex (BMAC), their affinity with ideas that are also present in the Harappan system shows that these ideas were widely spread..

Recent studies haves shown that the unit of dhanus has been used consistently in India in town planning and architecture for over 4,000 years, going back to the Harappan period. By considering the largest measure which leads to integer dimensions for the various parts of the Harappan age city of Dholavira, which was excavated in the 1990s (Bisht, 1997, Bisht, 1999), it was found that this measure is the same as the Arthaśāstra (300 BCE) measure of dhanus (bow) that equals 108 angulas (fingers) (see Kak, 2009, 2010, for details).

The measure of dhanus is seen to apply not only to the Mauryan and Gupta era structures, but even to more recent grid and modular measures in the town planning of Kathmandu Valley. The measures used in ancient India are summarized in the table below.

The three different hasta measures have been called the Prājāpatya (P-hasta), commercial (C-hasta), and forest (F-hasta) by Balasubramaniam (2008), and used variously in different situations. Here we are concerned primarily with dhanus, although we will also encounter pāda and aratni.

With the measure of dhanus (D) of 1.9404 m, the dimensions of Mohenjo-Daro's acropolis turn out to be 210 x 105 D, Kalibangan's acropolis turn out to be 126 x 63 D. The dimensions of the lower town of Dholavira are 405 x 324 D, the width of the middle town is 180 D, and the inner dimensions of the castle are 60 x 48 D (Danino, 2008). The sum of the width and length of the lower town comes to 729 which is astronomically significant since it is 27 x 27, and the width 324 equals the nakshatra year 27 x 12 (Kak, 2009).

The layout of Dholavira is unique in that it comprises of three "towns," which is in accord with Vedic ideas (Bisht, 1997, Bisht, 1999). The feature of recursion in the three towns, or repeating ratios at different scales, is significant. Specifically, the design is characterized by the nesting proportion of 9:4 across the lower and the middle towns and the castle. The proportions of 5/4, 7/6, and 5/4 for the lower town, the middle town, and the castle may reflect the measures related to the royal city, the commander's quarter, and the king's quarter, respectively, which was also true of Classical India (Bhat, 1995).

The Somapura Mahāvihāra of Pāhārpur has dimensions of 280x281 m, which when converted to dhanus become nearly 147x147 D, or 49x49 with the units of three times dhanus, which would be a natural plan for a vāstupurushamandala. The base of the temple was generally in a square grid of 8 or 9 units (64 or 81 squares) in the Brihat Samhitā (Bhat, 1995), but according to other texts it could range from one to 1024 square divisions. Another text gives special importance to the 7x7 plan. The Brihadīśvara temple (which was completed in 1010 CE), has a sanctum tower of 30.2x30.2x66 and it is within an enclosure of 240x120 m. In dhanus units, this amounts to 16x16 D plan in an enclosure of 126x63 D, where the error is less than one percent in the sanctum and almost zero for the enclosure. This indicates that the sanctum used a vāstupurushamandala of 64 squares where each square had a length of one-fourth dhanus. The dhanus unit also explains the chosen dimensions of Angkor Wat and Prambanan temples in Southeast Asia.

3. More on Harappan and Vedic Records

In this section we consider additional evidence from Harappan and Vedic periods. The absence of monumental buildings such as palaces and temples makes the Harappan city strikingly different from its counterparts of Mesopotamia and Egypt, suggesting that the polity of the Harappan state was de-centralized and based on a balance between the political, the mercantile, and the religious elites. The presence of civic amenities such as wells and drains attests to considerable social equality. The power of the mercantile guilds is clear in the standardization of weights of carefully cut and polished chert cubes that form a combined binary and decimal system.

Mohenjo-Daro and other sites show slight divergence of 1° to 2° clockwise of the axes from the cardinal directions (Wanzke, 1984). It is thought that this might have been due to the orientation of Aldebaran (Rohinī in Sanskrit) and the Pleiades (Kritikkā in Sanskrit) that rose in the east during 3000 BCE to 2000 BCE at the spring equinox, the word "rohinī" literally means rising. Furthermore, the slight difference in the orientations amongst the buildings in Mohenjo-Daro indicates different construction periods using the same traditional sighting points that had shifted in this interval due to precession of the equinoxes (Kenoyer, 1998).

Mohenjo-Daro's astronomy used both the motions of the moon and the sun (Maula, 1984). This is attested by the use of great calendar stones, in the shape of ring, which served to mark the beginning and end of the solar year.

The seal of Figure 3 has been viewed by many as representing the Pleiades. The conjunction of this constellation with the sun at the vernal equinox marked the New Year around 2400 BCE. The Pleiades, the wives of the seven sages, are important in Vedic mythology as representing the seven mothers who nurse the war-god Skanda.

The seal of Figure 4 is taken to represent the opposition of the Orion (Mrigashiras, or antelope head) and the Scorpio (Rohini of the southern hemisphere which is 14 nakshatras from the Rohini of the northern hemisphere) nakshatras. The arrow near the head of one of the antelopes could represent the decapitation of Orion. It is generally accepted that the myth of Prajapati being killed by Rudra represents the shifting of the beginning of the year away from Orion and it places the astronomical event in the fourth millennium BCE (Kak, 1996, 2000a).

Figure 5 presents the 27 nakshatras of the Indian astronomy together with the 12 solar segments (rāshis). It is significant that the 27 nakshatras contain 24 names together with three which are further subdivided. This indicates that the 24 divisions may have preceded the 27 divisions of the Vedic astronomy.

Fire altars, with astronomical basis, have been found in the third millennium cities of India. Vedic texts describe the design and ritual of the fire altars which were oriented towards the east and whose design, using bricks laid in five layers, coded astronomical knowledge of its times (Kak, 2000a). The best known of the fire altars is the falcon altar of Figure 6. Texts that describe fire altar designs are conservatively dated to the first millennium BCE, but their contents appear to be much older.

Vedic ritual was based on the times for the full and the new moons, the solstices and the equinoxes. There were two years: the ritual year started with the winter solstice (mahāvrata), and the civil one started with the spring equinox (vishuva). The passage of the rising of the sun in its northward course from the winter solstice to the summer solstice (vishuvant) was called gavām ayana, or the sun's walk. The solar year was divided into two ayanas: in the uttarāyana the sun travels north, in the dakshināyana it travels south. The movement of the moon was marked by its nightly conjunction with one of the 27 or 28 nakshatras. The Rigveda 1.164 also speaks of another tradition of dividing the zodiac into twelve equal parts. It appears that these divisions were called the Ādityas. The incommensurability between the lunar and the solar reckonings led to the search for ever-increasing cycles to synchronize the motions of the sun and the moon. This is how the yuga astronomical model was born. In the lunar month, there were separate traditions of counting the beginning of the month by the full-moon day and the new-moon day.

4. Neolithic and Megalithic Sites

Sites of archaeoastronomical interest include the Neolithic site of Burzahom from Kashmir in North India, and megalithic sites from Brahmagiri and Hanamsagar from Karnataka in South India. The dates for these specific sites are provided in the text. The importance of these sites arises from the fact that they present astronomical knowledge that was most likely outside the literary tradition.

Burzahom, Kashmir

The Burzahom site is located about 10 km northeast of Srinagar in the Kashmir Valley on a terrace of Late Pleistocene-Holocene deposits. Dated to around 3000 - 1500 BCE, its deep pit dwellings are associated with ground stone axes, bone tools, and gray burnished pottery. A stone slab of 48 cm x 27 cm, obtained from a phase dated to 2125 BCE shows two bright objects in the sky with a hunting scene in the foreground. These have been assumed to be a depiction of a double star system (Rao, 2005).

Brahmagiri, Karnataka. The megalithic stone circles of Brahmagiri (latitude 14^o 73', longitude 76^o 77'), Chitradurga district of Karnataka in South India, that have been dated to 900 BCE, show astronomical orientations. Rao (1993) has argued that site lines from the centre of a circle to an outer tangent of another circle point to the directions of the sunrise and full moon rise at the time of the solar and lunar solstices and equinox.

Hanamsagar, Karnataka. Hanamsagar is a megalithic site with stone alignments pointing to cardinal directions. Since the megalithic period of Karnataka is believed to belong to the first millennium BCE, it may be assumed that this is the period of the site. The site is located on a flat area between hills about 6 km north of the Krishna river at latitude 16^o 19' 18" and longitude 76^o 27' 10". The stones, which are smooth granite, are arranged in a square of side that is about 600 meters with 50 rows and 50 column (for a total of 2,500 stones), with a separation between stones of about 12 m. The stones are between 1 to 2.5 m in height with a maximum diameter of 2 to 3 m. The lines are oriented in cardinal directions. There is a squarish central structure known as chakri katti.

It has been argued that the directions of summer and winter solstice can be fixed in relation to the outer and the inner squares. Rao (2005) suggests that it could have been used for several other kind of astronomical observations such as use of shadows to tell the time of the day, the prediction of months, seasons and passage of the year.

5. The Sanchi Stupas

The Sanchi Stupa, a hemispherical domed structure with a flattened top meant to contain the relics of the Buddha, is believed to have been built by King Aśoka in around 250 BCE, an enlargement to double the size was done by the Śungas (this dynasty ruled between 185 and 73 BCE). It is surrounded by a balustrade that represents the sun's circuit. The Buddha did on full moon day of the lunar month Vaiśākha, and this day is observed as the Buddha pūrnimā day. At full moon the moonrise and sunset are observed in the eastern and western horizons.

It is likely that the astronomical basis of the Stupa was inspired by the Vedic altar that represented the circuit of the sun. It has been shown elsewhere (Millar and Kak, 1999) how this representation of the sun's motion remained common knowledge and it was used in Angkor Wat.

Two further Stupas were built by the Śunga kings and it is believed that they fixed the orientation of the Stupa. G.M. Ballabh and K.D. Abhyankar found that the Buddha pūrnimā occurred at Sanchi on April 28, 109 BCE with the sunset and moonrise of the full moon to the east-west orientation of the Stupa (azimuth of the Sun and Moon equal to 285.2 and 105 degrees, respectively, with an altitude of about 1 degree). This also corresponds to the setting and rising of the Pleiades (Krittikā) and δ Scorpii (Anurādhā) (Rao, 1992).

There is further astronomical significance to the design of the outer balustrade in the Stupas.

Great Stupa. The outer balustrade has 120 posts arranged in 4 quadrants and they are joined by three rows of 29 horizontal crossbars. Starting with the 30 posts in the first quadrant, 29 crossbars of the second quadrant, 30 posts of the third quadrant, and 29 crossbars of the fourth quadrant, we have a count of 118. Three such rounds correspond to the number of days in the lunar year. Rao (1992) adds that to arrive at an undistorted full circle it would require 108 (i.e. 120-16+4) posts, where the 16 entrance posts have been subtracted and 4 missing posts at each entrance required have been added for reasons of symmetry. We have already mentioned the significance of the count of 108 in Indian astronomy. Rao (1992) speculates that the total number of outer balustrade posts (120) and slabs (115) gives a count of 235 corresponds to the lunations of the Metonic cycle. The harmika balustrade at the top has 28 posts, which equals the number of nakshatras.

Stupa 2. The count according to Rao (1992) for the posts and the crossbars is also 354, the number of days in the lunar year. Rao further speculates that the location of Sanchi may have astronomical significance since its latitude is close to the declination of the sun on the summer solstice day.

6. Concluding Remarks

This paper presents a broad overview to the archaeoastronomy of ancient India. Indian archaeoastronomy provides unique insights into the nature of ancient science and society in India for this region has vast number of texts belonging to different ages. The assumed homologies between the outer and the inner cosmoses meant that the same vocabulary was used to speak of their respective structures. While this becomes an obstacle for those who do not understand the system, it has within it the potential to explain many attitudes in Indian mythology, religious practice, science, and art.

In concluding, there was continuity between the archaeoastronomy of the early period covered in this essay and that of the medieval period where pilgrimage and temple centers mirrored conceptions of the cosmos. Medieval sites of archaeoastronomical significance include Sisupalgarh, Chitrakut, Vijayanagara, Gaya, Konarak, Khajuraho, and the Suryapuja temples in Tamil Nadu (e.g. Malville, 1989, Malville and Gujral, 2000, Malville and Swaminathan, 2005, Singh, 2009). For example, the temple complex of Khajuraho in Madhya Pradesh, built in 9th -12th century CE by the Chandela kings, form three overlapping circles, with centers at the Lakshmana (Vishnu), the Javeri (Śiva), and the Duladeva (Śiva) temples. Their deviation from true cardinality is believed to be due to the direction of sunrise on the day of consecration (Singh, 2009). The Lakshmana temple, one of the oldest of the complex, is considered the axis mundi of the site and it is oriented to the sunrise on Holi.

The sun temples of Varanasi (Malville, 1985, Singh, 2009) are interesting in that six of these lie along one side of an isosceles triangle with a base of 2.5km. The triangle surrounds the former temple of Madhyameshavara, which was the original center of the city. Pilgrims walking along the triangle are symbolically circumambulating the cosmos. The subject of the medieval temples forms an important and fascinating chapter in India's archaeoastronomy that is beyond the scope of this paper.