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'''''Vedi''''' is the term for "yajnika [[altar]]" in the [[historical Vedic religion|Vedas]]. Such altars were an elevated enclosure, generally strewed with [[Kusha grass]], and having receptacles for the [[yajnika fire]]; it was of various shapes, but usually narrow in the middle.

'''Vedi''' is the term for "yajnika altar" in the Vedas. Such altars were an elevated enclosure, generally strewed with Kusha grass, and having receptacles for the yajnika fire; it was of various shapes, but usually narrow in the middle.

*''mahavedi'', the great or entire altar

*mahavedi, the great or entire altar

*''uttaravedi'', the northern altar made for the sacred fire (''agnyayatana'')

*uttaravedi, the northern altar made for the sacred fire (agnyayatana)

*''dhishnya'',  a sort of subordinate or side-altar, generally a heap of earth covered with sand on which the fire is placed

*dhishnya,  a sort of subordinate or side-altar, generally a heap of earth covered with sand on which the fire is placed

*''drona'', an altar shaped like a trough (Shulbas. 3.216)

*drona, an altar shaped like a trough (Shulbas. 3.216)

*''adhvaradhishnya'',  a second altar at the [[Soma yajna]]

*adhvaradhishnya,  a second altar at the Soma yajna

The ''uttaravedi'' was in the shape of a [[falcon]] (''alajacita'' = "piled up in the shape of the bird Alaja"), and was piled up with bricks in the [[Agnicayana]] ritual.

The uttaravedi was in the shape of a falcon (alajacita = "piled up in the shape of the bird Alaja"), and was piled up with bricks in the Agnicayana ritual.

Vedic altars are described in the circum-Vedic texts dealing with [[Kalpa (Vedanga)|Kalpa]] (the proper performance of yajna), notably the [[Satapatha Brahmana]], and the [[Sulbasutras]] say that the [[Rigveda]] corresponds to an altar of mantras.<ref>BSS 7, ASS 14.</ref>

Vedic altars are described in the circum-Vedic texts dealing with Kalpa (the proper performance of yajna), notably the Satapatha Brahmana, and the Sulbasutras say that the Rigveda corresponds to an altar of mantras.<ref>BSS 7, ASS 14.</ref>

Fire altars are already mentioned in the Rigveda. According to [[Taittiriya Samhita]] 5.2.3., they are made of twenty-one bricks.

Fire altars are already mentioned in the Rigveda. According to Taittiriya Samhita 5.2.3., they are made of twenty-one bricks.

In ŚBM 10.4.3.14-20, the altar is made of 396 (360 + 36) yajusmati (special) bricks, and of 10,800 lokamprna (ordinary) bricks. 10,701 lokamprna bricks belong to the ahavaniya altar, 78 to the dhisnya hearths and 21 to the garhapatya.  Around the altar are 360 parisrita stones (261 around ahavaniya, 78 around dhisnya, 21 around garhapatya).   

In ŚBM 10.4.3.14-20, the altar is made of 396 (360 + 36) yajusmati (special) bricks, and of 10,800 lokamprna (ordinary) bricks. 10,701 lokamprna bricks belong to the ahavaniya altar, 78 to the dhisnya hearths and 21 to the garhapatya.  Around the altar are 360 parisrita stones (261 around ahavaniya, 78 around dhisnya, 21 around garhapatya).   

ŚBM 10.3.1. describes that the altar is symbolically built with [[gayatri]] (24 syllables), usnih (breath, 28  syllables), pankti (mind, 40 syllables), [[tristubh]] (ear, 44 syllables), jagati (48 syllables) and generative breath.  The gayatri altar's height is to the knees, the tristubh's to the navel and the jagati's to a man's height.  

ŚBM 10.3.1. describes that the altar is symbolically built with gayatri (24 syllables), usnih (breath, 28  syllables), pankti (mind, 40 syllables), tristubh (ear, 44 syllables), jagati (48 syllables) and generative breath.  The gayatri altar's height is to the knees, the tristubh's to the navel and the jagati's to a man's height.  

== Agnicayana ==

== Agnicayana ==

{| class="wikitable"

{| class="wikitable"

|-

|-

|''Layer''

|Layer

|''Number of yajusmati bricks in SB''

|Number of yajusmati bricks in SB

|-

|-

|5

|5

|}

|}

In the Agnicayana ritual, the mahavedi (great altar) has a length of 24 [[prakrama]] in the east, 30 in the west and 36 in the north and south.<ref>With 24+30+36=90.</ref> Inside the mahavedi, an altar is placed. In the smaller ritual space to the west of the mahavedi (pracinavamsa, pragvamsa), three altars are placed: the garhapatya (earth, W), ahavaniya (sky, E) and daksinagni (or anvaharyapacana, SW). The round garhapatya and the square ahavaniya have the same area.<ref>(one square vyama/purusa)  SB 7. TS 5.</ref> The [[Squaring the circle]] problem was also investigated because of such ritualistic considerations.<ref>Kak (2000)</ref>  The ahavaniya altar has five layers (citi), representing earth, space and the sky.

In the Agnicayana ritual, the mahavedi (great altar) has a length of 24 prakrama in the east, 30 in the west and 36 in the north and south.<ref>With 24+30+36=90.</ref> Inside the mahavedi, an altar is placed. In the smaller ritual space to the west of the mahavedi (pracinavamsa, pragvamsa), three altars are placed: the garhapatya (earth, W), ahavaniya (sky, E) and daksinagni (or anvaharyapacana, SW). The round garhapatya and the square ahavaniya have the same area.<ref>(one square vyama/purusa)  SB 7. TS 5.</ref> The Squaring the circle problem was also investigated because of such ritualistic considerations.<ref>Kak (2000)</ref>  The ahavaniya altar has five layers (citi), representing earth, space and the sky.

== Archaeology ==

== Archaeology ==

At [[Kalibangan]] (at the [[Ghaggar]] river) the remains of what some writers claim to be [[fire]] [[altar]]s have been unearthed.<ref>B.B. Lal. Frontiers of the Indus Civilization.1984:57-58</ref> S.R. Rao found similar "fire altars" in Lothal which he thinks could have served no other purpose than a ritualistic one.<ref>S.R. Rao. The Aryans in Indus Civilization.1993:175</ref>

At Kalibangan (at the Ghaggar river) the remains of what some writers claim to be fire [[altar]]s have been unearthed.<ref>B.B. Lal. Frontiers of the Indus Civilization.1984:57-58</ref> S.R. Rao found similar "fire altars" in Lothal which he thinks could have served no other purpose than a ritualistic one.<ref>S.R. Rao. The Aryans in Indus Civilization.1993:175</ref>

Refer

Refer

*[[Subhash Kak]]. ''Birth and Early Development of Indian Astronomy''. In ''Astronomy across cultures: The History of Non-Western Astronomy'', [[Helaine Selin]] (ed), Kluwer, 2000

*Subhash Kak. Birth and Early Development of Indian Astronomy. In Astronomy across cultures: The History of Non-Western Astronomy, Helaine Selin (ed), Kluwer, 2000

*Subhash Kak, ''The Astronomical Code of the Rigveda'', Delhi, Munshiram Manoharlal, 2000, ISBN 81-215-0986-6.

*Subhash Kak, The Astronomical Code of the Rigveda, Delhi, Munshiram Manoharlal, 2000, ISBN 81-215-0986-6.

*Sen, S.N., and A.K. Bag. 1983. ''The Sulbasutras''. New Delhi: Indian National Science Academy.

*Sen, S.N., and A.K. Bag. 1983. The Sulbasutras. New Delhi: Indian National Science Academy.

== Ritual, Geometry and Astronomy<ref name=":0">Subhash Kak (2000), [http://www.ece.lsu.edu/kak/ast.pdf Astonomy and its Role in Vedic Culture], Chapter 23 in Science and Civilization in India, Vol.1, The Dawn of Indian Civilization, Part 1, edited by G. P. Pande, Delhi: ICPR/Munshiram Manoharlal, pp. 507-524.</ref> ==

== Ritual, Geometry and Astronomy<ref name=":0">Subhash Kak (2000), [http://www.ece.lsu.edu/kak/ast.pdf Astonomy and its Role in Vedic Culture], Chapter 23 in Science and Civilization in India, Vol.1, The Dawn of Indian Civilization, Part 1, edited by G. P. Pande, Delhi: ICPR/Munshiram Manoharlal, pp. 507-524.</ref> ==

We have mentioned that the altars used in the ritual were based on astronomical numbers related to the reconciliation of the lunar and solar years. The �fire altars symbolized the universe and there were three types of altars representing the earth, the space and the sky. The altar for the earth was drawn as circular whereas the sky (or heaven) altar was drawn as square. The geometric problems of circulature of a square and that of squaring a circle are a result of equating the earth and the sky altars. As we know these problems are among the earliest considered in ancient geometry.

We have mentioned that the altars used in the ritual were based on astronomical numbers related to the reconciliation of the lunar and solar years. The fire altars symbolized the universe and there were three types of altars representing the earth, the space and the sky. The altar for the earth was drawn as circular whereas the sky (or heaven) altar was drawn as square. The geometric problems of circulature of a square and that of squaring a circle are a result of equating the earth and the sky altars. As we know these problems are among the earliest considered in ancient geometry.

The �fire altars were surrounded by 360 enclosing stones, of these 21 were around the earth altar, 78 around the space altar and 261 around the sky altar. In other words, the earth, the space, and the sky are symbolically assigned the numbers 21, 78, and 261. Considering the earth/cosmos dichotomy, the two numbers are 21 and 339 since cosmos includes the space and the sky.

The fire altars were surrounded by 360 enclosing stones, of these 21 were around the earth altar, 78 around the space altar and 261 around the sky altar. In other words, the earth, the space, and the sky are symbolically assigned the numbers 21, 78, and 261. Considering the earth/cosmos dichotomy, the two numbers are 21 and 339 since cosmos includes the space and the sky.

The main altar was built in fi�ve layers. The basic square shape was modifi�ed to several forms, such as falcon and turtle (Figure 2). These altars were built in �five layers, of a thousand bricks of specifi�ed shapes. The construction of these altars required the solution to several geometric and algebraic problems.

The main altar was built in five layers. The basic square shape was modified to several forms, such as falcon and turtle (Figure 2). These altars were built in five layers, of a thousand bricks of specified shapes. The construction of these altars required the solution to several geometric and algebraic problems.

Two different kinds of bricks were used: the special and the ordinary. The total number of the special bricks used was 396, explained as 360 days of the year and the additional 36 days of the intercalary month. By layers (25), the fi�rst has 98, the second has 41, the third has 71, the fourth has 47 and the fi�fth has 138. The sum of the bricks in the fourth and the �fth layers equals 186 tithis of the half-year. The number of bricks in the third and the fourth layers equals the integer nearest to one third the number of days in the lunar year, and the number of bricks in the third layer equals the integer nearest to one fi�fth of the number of days in the lunar year, and so on.

Two different kinds of bricks were used: the special and the ordinary. The total number of the special bricks used was 396, explained as 360 days of the year and the additional 36 days of the intercalary month. By layers (25), the first has 98, the second has 41, the third has 71, the fourth has 47 and the fifth has 138. The sum of the bricks in the fourth and the fifth layers equals 186 tithis of the half-year. The number of bricks in the third and the fourth layers equals the integer nearest to one third the number of days in the lunar year, and the number of bricks in the third layer equals the integer nearest to one fifth of the number of days in the lunar year, and so on.

The number of ordinary bricks equals 10,800 which equals the number of muhurtas in a year (1 day = 30 muhurtas), or equivalently the number of days in 30 years. Of these 21 go into the garhapatya, 78 into the eight dhishnya hearths, and the rest go into the ahavaniya altar.<ref name=":0" />

The number of ordinary bricks equals 10,800 which equals the number of muhurtas in a year (1 day = 30 muhurtas), or equivalently the number of days in 30 years. Of these 21 go into the garhapatya, 78 into the eight dhishnya hearths, and the rest go into the ahavaniya altar.<ref name=":0" />

# Lunar, which is a fraction more than 354 days (360 tithis); and  

# Lunar, which is a fraction more than 354 days (360 tithis); and  

# Solar, which is in excess of 365 days (between 371 and 372 tithis).  

# Solar, which is in excess of 365 days (between 371 and 372 tithis).  

A well-known altar ritual says that altars should be constructed in a sequence of 95, with progressively increasing areas. The increase in the area, by one unit yearly, in building progressively larger �fire altars is 48 tithis which is about equal to the intercalation required to make the nakshatra year in tithis equal to the solar year in tithis. But there is a residual excess which in 95 years adds up to 89 tithis; it appears that after this period such a correction was made. The 95 year cycle corresponds to the tropical year being equal to 365.24675 days. The cycles needed to harmonize various motions led to the concept of increasing periods and world ages.<ref name=":0" />

A well-known altar ritual says that altars should be constructed in a sequence of 95, with progressively increasing areas. The increase in the area, by one unit yearly, in building progressively larger fire altars is 48 tithis which is about equal to the intercalation required to make the nakshatra year in tithis equal to the solar year in tithis. But there is a residual excess which in 95 years adds up to 89 tithis; it appears that after this period such a correction was made. The 95 year cycle corresponds to the tropical year being equal to 365.24675 days. The cycles needed to harmonize various motions led to the concept of increasing periods and world ages.<ref name=":0" />

== Rgveda and the Vedi<ref name=":0" /> ==

== Rgveda and the Vedi<ref name=":0" /> ==

The number of syllables in the Rgveda con�firms the textual references that the book was to represent a symbolic altar. According to various early texts,(26) the number of syllables in the Rgveda is 432,000, which is the number of muhurtas in forty years. In reality the syllable count is somewhat less because certain syllables are supposed to be left unspoken.

The number of syllables in the Rgveda confirms the textual references that the book was to represent a symbolic altar. According to various early texts,(26) the number of syllables in the Rgveda is 432,000, which is the number of muhurtas in forty years. In reality the syllable count is somewhat less because certain syllables are supposed to be left unspoken.

The verse count of the Rgveda can be viewed as the number of sky days in forty years or 261 * 40 = 10,440 and the verse count of all the Vedas(27) is 261 * 78 = 20,358.

The verse count of the Rgveda can be viewed as the number of sky days in forty years or 261 * 40 = 10,440 and the verse count of all the Vedas(27) is 261 * 78 = 20,358.

The Rgveda is divided into ten books with a total of 1,017 hymns which are placed into 216 groups. Are these numbers accidental or is there a deliberate plan behind the choice? One would expect that if the Rgveda is considered akin to the fi�ve-layered altar described in the Brahmanas  then the fi�rst two books should correspond to the space intermediate to the earth and the sky. Now the number that represents space is 78. When used with the multiplier of 3 for the three worlds, this yields a total of 234 hymns which is indeed the number of hymns in these two books. One may represent the Rgvedic books as a fi�ve-layered altar of books as shown in Table 1.

The Rgveda is divided into ten books with a total of 1,017 hymns which are placed into 216 groups. Are these numbers accidental or is there a deliberate plan behind the choice? One would expect that if the Rgveda is considered akin to the five-layered altar described in the Brahmanas  then the first two books should correspond to the space intermediate to the earth and the sky. Now the number that represents space is 78. When used with the multiplier of 3 for the three worlds, this yields a total of 234 hymns which is indeed the number of hymns in these two books. One may represent the Rgvedic books as a five-layered altar of books as shown in Table 1.

{| class="wikitable"

{| class="wikitable"

|+Table 1: The altar of books

|+Table 1: The altar of books

|191

|191

|}

|}

The choice of this arrangement is prompted by the considerable regularity in the hymn counts. Thus the hymn count separations diagonally across the two columns are 29 each for Book 4 to Book 5 and Book 6 to Book 7 and they are 17 each for the second column for Book 4 to Book 6 and Book 6 to Book 8. Books 5 and 7 in the �rst column are also separated by 17; Books 5 and 7 also add up to the total for either Book 1 or Book 10. Another regularity is that the middle three layers are indexed by order from left to right whereas the bottom and the top layers are in the opposite sequence.

The choice of this arrangement is prompted by the considerable regularity in the hymn counts. Thus the hymn count separations diagonally across the two columns are 29 each for Book 4 to Book 5 and Book 6 to Book 7 and they are 17 each for the second column for Book 4 to Book 6 and Book 6 to Book 8. Books 5 and 7 in the first column are also separated by 17; Books 5 and 7 also add up to the total for either Book 1 or Book 10. Another regularity is that the middle three layers are indexed by order from left to right whereas the bottom and the top layers are in the opposite sequence.

Furthermore, Books [4+6+8+9] = 339, and these books may be taken to represent the spine of the altar. The underside of the altar now consists of the Books [2+3+5+7] = 296, and the feet and the head Books [1+10] = 382. The numbers 296 and 382 are each 43 removed from the fundamental Rgvedic number of 339.

Furthermore, Books [4+6+8+9] = 339, and these books may be taken to represent the spine of the altar. The underside of the altar now consists of the Books [2+3+5+7] = 296, and the feet and the head Books [1+10] = 382. The numbers 296 and 382 are each 43 removed from the fundamental Rgvedic number of 339.

The Brahmanas and the Shulbasutra tell us about the altar of chandas and meters, so we would expect that the total hymn count of 1017 and the group count of 216 have particular signifi�cance. Owing to the pervasive tripartite ideology of the Vedic books we choose to view the hymn number as 339*3. The tripartite ideology refers to the consideration of time in three divisions of past, present, and future and the consideration of space in the three divisions of the northern celestial hemisphere, the plane that is at right angle to the earth's axis, and the southern celestial hemisphere.

The Brahmanas and the Shulbasutra tell us about the altar of chandas and meters, so we would expect that the total hymn count of 1017 and the group count of 216 have particular significance. Owing to the pervasive tripartite ideology of the Vedic books we choose to view the hymn number as 339*3. The tripartite ideology refers to the consideration of time in three divisions of past, present, and future and the consideration of space in the three divisions of the northern celestial hemisphere, the plane that is at right angle to the earth's axis, and the southern celestial hemisphere.

Consider the two numbers 1017 and 216. One can argue that another parallel with the representation of the layered altar was at work in the group total of 216. Since the Rgvedic altar of hymns was meant to symbolically take one to the sky, the abode of gods, it appears that the number 216 represents twice the basic distance of 108 taken to separate the earth from the sky. The Rgvedic code then expresses a fundamental connection between the numbers

Consider the two numbers 1017 and 216. One can argue that another parallel with the representation of the layered altar was at work in the group total of 216. Since the Rgvedic altar of hymns was meant to symbolically take one to the sky, the abode of gods, it appears that the number 216 represents twice the basic distance of 108 taken to separate the earth from the sky. The Rgvedic code then expresses a fundamental connection between the numbers

from the earth, is about identical.

from the earth, is about identical.

It is easy to compute this number. The angular measurement of the sun can be obtained quite easily during an eclipse. The angular measurement of the moon can be made on any clear full moon night. A easy check on this measurement would be to make a person hold a pole at a distance that is exactly 108 times its length and confi�rm that the angular measurement is the same. Nevertheless, the computation of this number would require careful observations. Note that 108 is an average and due to the ellipticity of the orbits of the earth and the moon the distances vary with the seasons. It is likely, therefore, that observations did not lead to the precise number 108, but it was chosen as the true value of the distance since it is equal to 27*4, because of the mapping of the sky into 27 nakshatras.

It is easy to compute this number. The angular measurement of the sun can be obtained quite easily during an eclipse. The angular measurement of the moon can be made on any clear full moon night. A easy check on this measurement would be to make a person hold a pole at a distance that is exactly 108 times its length and confirm that the angular measurement is the same. Nevertheless, the computation of this number would require careful observations. Note that 108 is an average and due to the ellipticity of the orbits of the earth and the moon the distances vary with the seasons. It is likely, therefore, that observations did not lead to the precise number 108, but it was chosen as the true value of the distance since it is equal to 27*4, because of the mapping of the sky into 27 nakshatras.

The second number 339 is simply the number of disks of the sun or the moon to measure the path across the sky: � * 108 � 339.

The second number 339 is simply the number of disks of the sun or the moon to measure the path across the sky: � * 108 � 339.

We return to a further examination of the numbers 296, 339, and 382 in the design of the Rgvedic altar. It has been suggested that 339 has an obvious signi�ficance as the number of sun-steps during the average day or the equinox, and the other numbers are likely to have a similar signifi�cance. In other words, 296 is the number of sun-steps during the winter solstice and 382 is the number of sun-steps during the summer solstice.

We return to a further examination of the numbers 296, 339, and 382 in the design of the Rgvedic altar. It has been suggested that 339 has an obvious significance as the number of sun-steps during the average day or the equinox, and the other numbers are likely to have a similar significance. In other words, 296 is the number of sun-steps during the winter solstice and 382 is the number of sun-steps during the summer solstice.

There also exists compelling evidence, of a probabilistic sense, that the periods of the planets had been obtained and used in the setting up of the Rgvedic astronomical code.(28)<ref name=":0" />

There also exists compelling evidence, of a probabilistic sense, that the periods of the planets had been obtained and used in the setting up of the Rgvedic astronomical code.(28)<ref name=":0" />