Vedas are so meticulously designed and not just verses
1 Majority of our population do not know anything about our ancient
Vedic culture; among those who knew, many may think it only as a
yanjopaveeda, marriage and ritual mantras vadhyars do utter. West wrote
with scanty respects to our Vedas, unmindful of hurting someone who
practiced the tolerance. But many thought it as divine, not because they
are mantras, but showed the in-depth literacy of its structures, revealing
the way of life here, and the way TO REACH THE MUKTHI. Subash Kak wrote a
book on its wisdom; and an extract of its architecture is presented here.
It is long. It is difficult to understand. But doing it slowly, trying top
pick up, will in the long run, would show that it is really divine.
*II Numerical Considerations*
2 Here we speak of the style of writing in the Brahmanas in which many
statements are justified in a numerological manner. Cambridge came 10000
years later. But this style should not be taken to mean that a deeper
understanding was lacking.
Consider, for example, the number 360, the days in the year,
which forms a starting point in the design of the altars of SB (Shatapata
brahamana) that were used to represent various astronomical facts about the
year.
3 SB 10.4.2.1-18 points out that 720, the nights and days in the
nominal year, has exactly 15 factors that are smaller than the companion.
These divisors are stated to be: 1, 2, 3, 4, 5, 6, 8, 9, 10,12, 15, 16, 18,
20, 24. The numbers in this sequence which do not divide 720 (that is the
numbers 7, 11, 13, 14, 17, 19, 21, 22, 23) are also explicitly mentioned.
(KR: Pl do remember my notes on maths wizard Ramanujan on 2520)
4 The fact that there exist 15 such factors was taken to explain
why the moon waxes for 15 days and wanes for 15 days. The next passage
claims that 24, the largest of these numbers, represents the number of half
months in the year, which is a reiteration of 15 x 24 = 360.
5 This implies the thesis that the moon's circuit around the earth is 30
days because 720, the number of days and nights in the year, has exactly 30
different divisors. In other words, numbers are used to relate a
characteristic of the motion of the sun to another related to the moon's
orbit around the earth. An astronomical fact is explained" based on an
abstract numerical property. (KR: when I was young in Chennai B station
there will be English Music by V Chakrapani (the news reader); in that in
1960s, there will be a voice of prose which will read interpretations of
the 52 playing cards; I used to wonder; but when reading through the
treatise of how the Veda Vedangas were framed so as to line up with the
astronomy and astrology with the reason explicit, well they were really
genius)
6 It appears that the authors did not rather consider the number 360,
which has 12 divisors, which could have also been taken to correspond to
the 12 months of the year, yielding, in turn, the 30 day duration of the
month, because the largest of these divisors which is less than its
companion, 18, has no direct correspondence with the basic facts of the
year. The concern with the number of divisors implies finding out what
numbers do not have divisors, or are prime. We know, that for number *n *=
*p*1*a*1 x* p*2*a*2, the number of divisors *d*(*n*) is given by:
*d*(*n*) = (*a*1 + 1) (*a*2 + 1)
The pairs of these divisors, in the manner of counting by the
Vedic authors, is *±*(*n*) = *d*(*n*)*=*2.
7 The Vedic authors were also interested in the largest divisor,
whose companion is smaller than itself. If this divisor is called
*¹*(*n*), we have *¹*(720) = 24.
*III The six day Vedic week*
8 One would expect that paralleling a justification of the thirty days
month based on the number of factors of 720, an argument would have been
used to define divisions of the month. The argument would look at the 60
days and nights of the month and determine the number of divisors that,
paralleling the procedure in SB, are less than the companion. These
divisors are 1, 2, 3, 4, 5, and 6.
9 This suggests a week of six days. We do get references to the six- day
week called sadaha in the Vedic texts. Five sadahas made a month. This
defined a symmetry with the year of five seasons and the yuga of five
years. Although it has often been assumed that the seven-day week was a
later innovation, it is quite possible that it was the older tradition and
that the six-day week got mentioned in the texts because of the \theory"
behind its derivation. The seven-day week is a more natural, system because
it divides the lunar month into four equal parts.
The number 7 plays an important number in Vedic cosmology
since it appears in conjunction with the name of the entire country, Sapta
Sindhu, with the additional ideas of seven rivers, seven continents, seven
islands, seven mountains, seven rsis (the Pleiades), seven musical notes,
and seven worlds.
The division of the year into 10,800 muhurtas SB 10.4.2.36 speaks of the
division of the year into 10,800 muhurtas.
It is further stated that the divisors of this number go into 30
arrangements, implying that it has 30 pairs of divisors or *d*(10800) =60,
or *±*(10 800) = 30.
*d*(10 800) = *d*(24 x 33 x 52) = (4 + 1)(3 + 1)(2 + 1) = 60
The text further relates the 30 pairs of divisors to the 30 nights
of the month.
The calculation of the 30 pairs of divisors of 10,800 suggests that
similar calculation was made for other numbers also, increasing our
confidence in the belief that the Vedic rishis knew primality.
IV Equivalence and Altars
`10 The notion of equivalence (*bandhu*) amongst the *adhidaiva *(*devas *or
stars), *adhibh¹uta *(beings), and *adhy¹atma *(spirit) plays a central
role in the Vedic system of knowledge (e.g., BG 8.1-2). The Vedic altar,
*adhiyajna*, shows these equivalences symbolically at different levels
including that of the individual himself (BG 8.4). Not only was
astronomical knowledge represented in the design of these altars but the
designs also mapped characteristics of the individual's inner sky. The
astronomy of the altars was tersely spelled out as
in the tenth chapter of the Satapatha Brahmana entitled *Agnira-*
*hasya*. The Rgveda itself is viewed as an altar of mantras in the
Sulbasutras (BSS 7.17, ASS 14.11).
11 Altars were used for two types of Vedic ritual: *Shrauta *and
*Gryha*, which marked specific points in the year or during the day.
Two important Soma rituals are agnisthoma and agnicayana. The
Shatapata Brahman a describes the twelve-day agnicayana rite that takes
place in a large trapezoidal area, called the mahavedi, and in a smaller
rectangular area to the west of it, which is called the pracnavamsa or
pragvamsa. SB 10.4.3.9 reasserts that agnicayana represents ritual as well
as knowledge.
The mahavedi trapezium measures 30 prakrama on the west,
24 prakrama on the east, and 36 prakrama lengthwise. The choice of these
numbers is related to the sum of these three equalling one fourth the year
or 90 days (SB 10.2.3.4). The nominal year of 360 days is used to reconcile
the discrepancies between the lunar and solar calendars, both of which were
used.
12 In the mahavedi, a brick altar is built to represent time in the
form of a falcon about to take wing, and in the pracnavamsa
three fire altars are built in specified positions, the garhapatya,
ahavanya, and daksinagni. The garhapatya, which is round, is
the householder's fire received from the father and transmitted to the
descendants. It is a perpetual fire from which other fires are lighted. The
daksinagni is half-moon shaped; it is also called the anvaharyapacana where
cooking is done. The ahavanya is square.
13 Between the ahavanya and the garhapatya a space of a rough hour-glass is
dug out and strewn with grass; this is the *vedi *for the godsto sit on.
During the agnicayana ritual the old ahavanya serves the function of the
original garhapatya. This is the reason why their areas are to be
identical, although one of them is round and the other square. In addition,
eight dhisnya hearths are built on an expanded ritual ground. Agnicayana
altars symbolize the universe. The garhapatya is the earth (SB 7.1.1.13),
the dhisnya hearths are space (SB 7.1.2.12),and the ahavanya altar, which
is made in five layers, is sky (SB8.2.1,2). Since the sky represents the
universe, it includes space and earth. The first layer represents the
earth, the third the space, and the fifth the sky. The second layer
represents the joining of the earth and space, and the fourth layer
represents the joining of space and sky. The SatapathaBrahmana (10.4.3.9)
asserts that knowledge is gained through altar construction.
14 Time is represented by the bird. The months of the year were
ordinarily divided into six seasons unless the image of the bird for the
year was used, when Hemantha ritu and Śiśira ritu were lumped together.
The year as a bird had the head as 1 Vasanta, the body as 2 Hemantha and 3
Śiśira, the two wings as 4 Sarada and 5 grsma, and the tail as 6 varsha (TB
3.10.4.1, SB 10.4.5.2).
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V The Architecture of the Rigveda
15 According to tradition, the Rigvedic hymns, assembled by Paila un-
der the guidance of Vy¹asa, formed the Samhit¹a and the authors of
the Brahmana a literature described and interpreted the Vedic ritual.
Y¹aska was an early commentator of the Rgveda and he discussed
the meanings of many difficult words. In the 14th century, Sayana
wrote an exhaustive commentary on it.
A number of other commentaries were written during the medieval period,
including the commentaries by Skandasvamin (roughly
of the Gupta period), Udgtha, Venkata Madhava (ca. 10th to 12th
century) and Mudgala (after Sayana who did an abbreviated version of
Sayana's commentary).
16 Vyasa assembled the hymns of the Rgveda out of the many
circulating at the time. We are interested in determining the logic
that was used by him to assemble the collection. This would not
only throw light on the collection but also reveal attitudes about
the world and the sciences that existed at that time. Specifically, we
hope to ¯find the organization of the text based on the cosmology
of the Vedic system. Traditionally, scholars have only wondered
about the hymn counts of Books 1 and 10 being the same. In this
chapter we will show the deeper order of the text.
17 To study the design of the Rgveda it is essential to make a
distinction between its index tradition and the text itself. It is also
essential to recognize that in spite of the astonishing fidelity with
which the Vedic text has been passed down, the same fidelity may
not be true for the index tradition.
18 There are many references to the larger plan of the texts.SB
10.4.2.23-24 describes that the Rgveda has 432,000 syllables; The
Yajurveda has 288,000 and the Samaveda has 144,000 syllables.
These round numbers are ample evidence indicating a numerical
principle at work in the design of the texts. The syllable count of
the canonical text of the Rgveda has only 394,221 syllables, how-
ever.1 This syllable count is for the Samhita Patha where some-
times syllables in sequence coalesce due to rules of sandhi. But
this suggests that there could be a deference between the \ideal"
syllable count and the actual count of the syllables. The Rgveda
Pratisakhya 17.14 explains:
“To get the correct count for the total, resolve the coalesced combinations
in the incomplete padas."
19 Thus, Raster2 shows how the syllable count of the first hymn, which has
9 verses in the gayatri meter, can be restored
from its actual 210 to the correct 216 which is 9 x 24.
When the correct count for all the meters is made the syllable
count increases to 394,317. However, such exercises are somewhat
futile in estimating the size of the Rgveda because the meters can
be defined in a variety of ways and this restoration would then
depend on the description of the meters in the less reliable index
tradition.
20 According to Saunaka's Anuvaka Anukramana, the Rgveda of
the Sakala recension consists of 1017 main hymns, divided into 10
mandalas (books) of varying lengths, and an appendix of 11 khila
hymns that are called the Valakhilya hymns.3
21 The Baskala recension, according to Saunaka, consisted of 8
more hymns, but this recension has not survived. It is believed
that the 8 additional hymns of the Baskala recension consisted of
7 Valakhilya hymns and the Samjnana hymn. In other words,
the two recensions differ only in the arrangement of the khilas.
This fact also suggests that the various recensions referred in the
Pur¹an. as might have had very little differences.
22 The Anukramanas ascribe books 2 to 7 to the rsis Grtsamada,
Visvamitra, Vamadeva, Atri, Bharadvaja, and Vasistha or their
families respectively. Book 9 is a collection of hymns by several
rsis to Soma Pavamana, or Soma poured through the filter. Book
1 which consists of 191 hymns is classed into 15 groups of hymns by
different rsis. Book 10 also has 191 hymns and its first 84 hymns
are classed into 25 groups based on rsis, and its remaining 107
hymns are counted singly. The Anukramanas give the authorship
for the individual hymns, but we will not have occasion to analyze
that information in this book.
23 The classification of the family books 2 to 7 is based on hymns
to different gods and these groups are 5, 4, 11, 7, 5, 12 respectively.
Book 8 hymns are grouped according to the particular rsis of the
Kanva family. Including the Valakhilya hymns these constitute 19
groups. The hymns of Book 9 are grouped into 7 according to the
meter. These meters are gayatri, jagati, tristubh, anustubh, usnih.
pragatha, and miscellaneous. These hymns are by a host of rsis
including Bhrgu, Kasyapa, and Kavi Usanas. This information is
summarized in Table 5.1.
Table 5.1: Hymns and groups
Mandalas 1 2 3 4 5 6 7 8 9
10***
Hymns 191 43 62 58 87 75 104 92 114 191***
Groups 15 5 4 11 7 5 12 18 7
132***
Anuvakas 24 4 5 5 6 6 6 10 7
12***
*** We see that the number of hymns in the different books (mandalas)
Satisfies the following relationships:
Books [1+2+3+4] = 354 (Lunar year)
Books [4+7] = Books [5+6] = 162 (1/2 Nakshatra year)
Books [4+5+6+7] = 324 (Nakshatra year)
Books [6+7] = Books [5+8] = 179 = 1/2 Books [1+6+8] = 1/2 Books
[5+6+7+8]
Books [5+7] = Book [1] = Book [10]
Note further,
1/2 nakshatra year + 21 = 1/2 year of 366 days.
The number of hymns in Books 1 and 10 is 191 each. This
number satisfies the interesting equality:
191 = 113 + 78 where 113 is one ninth of the total number of hymns in the
Rgveda and 78 is the atmosphere number of the fire altars. These
relationships highlight their astronomical basis.
24 The Anuvaka Anukramana says that the total number of Anuvakas is 85,
the number of adhyayas is 64, and the number of Vargas is 2,006. The total
number of verses is declared to be 10,580&1/2; the number of half-verses is
21,232 and of the words 153,826.
25 According to Sada-guru-sisya the half verse comes from RV 10.20.1.
Saunaka also declares that the number of syllables is 432,000.
How is one to explain the discrepancy between the numbers
of Saunaka and that of the canonical text? One cannot assume
that the canonical text is much smaller than the text available to
Saunaka because there exists perfect agreement in the number of
hymns, the meters of the various verses, and so on. The average
per verse based on Saunaka's verse numbers should be 40.83 to
yield the syllable count of 432,000. The actual average is however
37.65 because although “tristubh” (44 syllables) is the most common
meter, the second most common meter is gayatri (24 syllables).
The only conclusion that is open to us then is that the number 432,000 is
the ideal number of syllables. Considering that RV 1.164.45 declares that
speech is of four kinds, three of which are unmanifest, then the shortfall
of 37,779 syllables must be in terms of unmanifest syllables.
VI *The Rgvedic Index Related To The Other Vedas Samaveda*
26 The two main extant recensions of the Samaveda are Kauthuma
(Considered the vulgate) and the Jaiminya; a third recension called
the Ranayanya is very similar to Kauthuma. The Kauthuma recension consists
of 1810 verses in two main books called the Purvarcika (585 single verses)
and the Uttararcika (1225 verses); in addition, there are 54 verses in the
¹Aranyaparvan which belongs to the Purvarcika, which in turn has an
appendix of 11 mahanaman verses. The mahanaman verses may also be found in
the fourth Aranyaka of Aitareya Aranyaka Altogether, therefore, the
recension has 1875 verses.
*27 Yajurveda: *According to tradition there were 101 schools of the
Yajurveda in two groups, viz., Krishna and Sukla. The surviving texts of
the Krishna Yajurveda are placed into four main groups: Taittireeya,
Kathaka, Kapisthala, and Maitrayani. The Taittireeya has the best pre-
served texts. The Sukla or the Vajasaneyi Yajurveda is represented
by the Madhyandina and the Kanva recensions. The Vajasaneyi Yajurveda5 is
organized in a more regular fashion. It appears that out of its 40 chapters
the first 18 form the core text; chapters 19-25 deal with souramana and
Aswamedha sacrifices; chapters 26-35 are called khilas or supplementary
material; chapters 36-39 are devoted to the pravargya ceremony and chapter
40 is the Isa Upanishad The total number of verses has been taken to be
1,975 or 1,984. The ¯first 18 chapters add up to 1,026 verses.
*28 Atharvaveda*
There are two extant recensions: the Paippalada and the Saunakya.
The Saunakya recension is much better preserved; it consists of 20
books of which the first 18 appear to be the core. Book 19 has material
arranged differently from the preceding books and book 20
is clearly supplementary. It will be shown later that the core text
consisted of 5,226 verses. According to *Satvalekar *the verse total
for the entire text is 5,977; the Paippal¹ada recension has about
8,000 verses.
*VII Analysis Of Hymn Numbers*
29 We begin with the analysis of the number 432,000. Shatapata Brahamana
SB 10.4.4.2 speaks of the number of stars in the sky being equal to the
number of muhurtas (1 day = 30 muhurtas) in 1,000 years or 1000*360*30 = 10,
800, 000.{KR: 360 was originally adopted as per then recensions which is
changed to 365.25 much later, when the planets moved otherwise; people
attribute it as a mistake; the planets change their movements every 26,500
years, when the south pole becomes north pole and vice-versa; Thus the
Vakya panchangam reflects errors if calculated our jadagams; Drig is a
variable and adjusted every year scientifically so Drig panchangam are the
authority} This means that the ideal number of syllables in the Rgveda
equals the number of muhurtas in 40 years. The number of days in 40 years
is 14,400 and if one took the identity of a day to a verse then this would
be the number of verses in the Rgveda. The average number of syllables per
verse is therefore 30, or the mean of gayatri and brhat Now we know that
sky (or heaven) is ascribed the number 261 in Vedic ritual. If we consider
the equation that the verse is to the sky-day what the syllable is to the
muhurta, then the number of verses in a span of 40 years, considering 261
sky days per year, equals 10,440. This is only two less than the actual
count obtained by Macdonell,6 and it appears that the canonical text had
two fewer verses by reorganizing, say, four shorter verses into two longer
ones. As argued by Macdonell his count of 10,442 for the Rgveda verses may
be reconciled with Saunaka’s figure by considering the 127 dvipadas twice;
this raises the count to 10569 verses which is only 11 verses less than
Saunaka’s figure. It is possible that the 11 hymns of the khila were
counted as the remainder in a count
across categories, evidence of which is common as in the number
17 counted as 12 months and 5 seasons in the brahmanas. One can propose
another theory that the Rgveda is ideally 10,800 verses with an average of
40 syllables per verse. The short-fall between this number and the actual
of 10,440 is exactly 360 verses. Since 10,800 {30*360d} are the muhurtas in
one year, the shortfall amounts to the muh¹urtas in 12 days.
30 We now come to another theory for the reconciliation of the
verse count of 10,580 to the actual count of 10,440. We propose
that the khila verses originally totalled 140, that is 60 more than
the current number. But such a possibility is unlikely since there
is no tradition that speaks of such a large number of lost verses.
We can also explain the significance of the actual count of syllables.
Knowing that the earth number is 21 and the sky number
is 261, it is likely that the actual syllables are (261-21) 240*=*261 of
the ideal number of 432,000. This amounts to 399,241 syllables. Now the
count of syllables for the Rgveda and the khila verses is 397,265.
Therefore, there must have been a modification suggested by actual
observations.
31 How do we explain the number 10,442 as the verse count in the
Rgveda? It appears that the knowledge that the year was actually
371.05 tithis was translated into a representation of the sky number
to 261.05. Over 40 years now we get 10,442 verses. If the other
numbers are proportionately changed to 77.96 and 20.99, then the
ratio 240*:*06 * 432, 000*=*261*:*05 = 397, 265*: *This is precisely the
number of syllables of the Rgveda. One may further assume that when the
Rgveda expanded from its core size of 10,440 verses, 2 more verses were
added to it. Paralleling this, 2 verses were added to the 78 original khila
verses.
32 We assume that the logic of considering the muhurtas of 40
years to represent the syllables of the Rgveda flows from the time
span of 100 years to represent all the four Vedas. As explained
above, Yajur and Samaveda taken together also get 40 years; the
remaining 20 years are assigned to the Atharvaveda. That such a
logic was at work is suggested by the fact that the total number
of hymns in the Saunakya recension, when considering only the
Kuntapa hymns of the Book 20 is 5,226, just six more than the
number of hymns according to this theory.
33 The total number of hymns in the Saunakya recension when
the remainder of the Book 20 is also considered is 5977 which equals
43 * 139. The distribution of all the verses of the Vedas as they have come
down to us is:7
Table 5.2:
Verses in the Vedic books
Rgveda 10522
Yajurveda 1984
Samaveda 1875
Atharvaveda 5977
Total 20358
That this total is exactly 261*78 implies that the verses were,
metaphorically, supposed to pervade the entire space of span 78
and breadth 261.
34 One might assume that the original structure started with 261*40 =
10,440 verses for the Rgveda corresponding to 40 years; the
Atharvaveda had 261 * 20 = 5, 220 verses for 20 years. The
Yajurveda and the Samaveda were assigned approximately 80 and
40 years, which arose from the space number of 78 and by its half
39. Also we believe that the Shatapata Brahmana reference to the
verses of the Yajurveda and Samaveda being in the proportion 2:1
is only approximately true; the correct proportion being 25:15.
This leads to the figure 78 * 25 = 1, 950 verses for the Yajurveda and 39 * 15
= 585 verses for the Samaveda. The figure for Yajurveda is very close to
the value leaving out the Isa Upanishad verses of chapter 40 and the
Samaveda figure is identical to the Purvarcika verses. Various
considerations, like the ones for the Rgveda verse totals outlined earlier,
led to modifications of these numbers with the constraint that the total
had to be 261 * 78 = 20, 358.
35 Other numerical and astronomical considerations played a role
in the modifications that were introduced. Is it possible that the
Atharvaveda number was first increased to 5,226 because it is 78*67?
36 From another perspective, we expect that the syllable count
for the Samaveda by the Shatapata Brahmana reference comes to
4,800 verses and that for the Yajurveda to 9,600 verses. Now note
that the 585 Purvarcika stanzas are in practice sung to double
the number of tunes; this allows us to modify the total count as
1225 + 2 * 585 + 54 + 11 = 2395.
37 This is just 5 short of the half of the total 4,800. Considering
still another angle, note that Samaveda has 1810 verses plus 5
hymns in the Aranyaparva and the 11 mahanaman verses. If we
add across categories we get a total of 1826, only one less than
261 * 7.
38 The basis behind the verse totals was forgotten quite early since
there is no mention of it in the various Anukramanas. But it survived in
certain circles as evidenced by its use in the Bhagavadgita.
The fact that the numbers, after the passage of millennia, still satisfy
the number relationships further attests to the amazing fidelity with which
the texts were preserved.
KR IRS 9123
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