From: kak@MAX.EE.LSU.EDU (Dr. S. Kak)
Newsgroups: soc.culture.indian
Subject: Decipherment of a Rigvedic code
Date: 23 Jul 92 16:08:02 GMT


The Astronomical Code of the Rigveda. I have recently discovered an
astronomical code in the organization of the Rigveda. Other scholars
have termed this discovery as being "revolutionary" and "monumental".
I have been pressed by scholars to describe this to a wider audience
before the results appear in journals. Below is a LSU technical report
dated May 5, 1992 that provides an overview.
 
 
-----------------------------------------------------------
The Architecture of the Rigveda and Other Vedic Books

by
Subhash C. Kak
Louisiana State University Baton Rouge, LA 70803-5901, USA Tel:
(504) 388-5552; Fax: 504-388-5200

copyright Subhash Kak

1. Introduction

The R gveda has come down to us in the S a kala recension and it
consists of 1017 main hymns and an additional 11  khila  hymns that
are called the Va lakhilya hymns.  Several indexes or Anukraman i
s to the R gveda were written quite early.  S aunaka in his Anuva
ka Anukraman i describes the number of words in the R gveda to be
153,286 but this does not include the khilas, and this suggests
that the 1017 hymns formed the main book, and the rest served as
an appendix.  The Ba s kala recension, according to S aunaka,
consisted of 8 more hymns, but this recension has not survived.

The hymns are divided into 10 man d alas (books) of varying lengths.
The question that we raise in this paper is whether there is a
definite design to the organization of the hymns.  In fact this is
an old question and an answer is implicit in the statement in S
atapatha Bra hman a 10.4.2.23 that describes the number of syllables
in R gveda to be 432,000 which equals the number of muhu rtas (1
day = 30 muhu rtas) in 40 years.  The number of muhu rtas in a year
is 10,800.  This suggests that the organization of the R gveda
reflects some astronomical facts.  This also raises questions about
the significance of the number 108 that occurs often in Vedic texts.

Antiquated theories of recent decades about the structure and the
internal chronology of the R gveda will not be reviewed in this
paper.  We will show that several astronomical numbers underlie
the structure of the book.  This should also put to rest the theory
about a gradual accretion of the hymns.  This theory has been
popular for some time in spite of the contrary internal evidence.
This is not to deny that there are hymns are of varying antiquity,
but our analysis will show that the whole framework has a unity.

As is well known the Vedic synthesis of knowledge was based on the
postulation of a correspondence between the cosmic, the terrestrial,
and the physiological.  This equivalence may be seen as the common
thread that permeates all the Vedic literature.  For examples of
equations between the cosmic and the physiological one may see S
B 8.1.1.6-2.6, AA 3.2.2.2-7, BU 2.2.4.  One might ask what cosmic
facts would be most apparent to the Vedic r s is.  The evidence
for the knowledge of a year which is between 365 and 366 days is
strong.  This is reflected in the 371 or 372 tithis (lunar days);
where there is a specific mention of 371 tithis in terms of the
3339 bha m s as (Kak 1991).  The nominal division of the year into
360 days is widely encountered.  The Sam hita s and the Bra hman
as speak of ceremonies that depend on precise knowledge (Sengupta
1938) of the solstice days (e.g. AB 18.18, TS 4.4.10, KB 19.3, KB
5.1, PB 5.9, S B 2.6.4.11).  Clearly there existed a careful
observation of the celestial phenomena.

2. Two Fundamental Numbers: 108 and 339

In the context of the other information it is reasonable to assume
that the Vedic r s is had found the fundamental astronomical numbers
108 and 339.  That this was so is corroborated by the R gveda
itself.

The number 108 is roughly the average distance that the sun is in
terms of its own diameter from the earth; likewise, it is also the
average distance that the moon is in terms of its own diameter from
the earth.  (The true averages obtained using modern instruments
are 107.6 and 110.6 respectively, but 108 should be considered an
excellent early approximation.) It is owing to this marvellous
coincidence that the angular size of the sun and the moon, viewed
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 confirm
that the angular measurement is the same.  Nevertheless, the
computation of this number would require careful observations.
Furthermore, 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 may be noted that the sky was divided into 180 degrees, a division
that is at the basis of the nominal representation of the year by
360 days.  It turns out that the angular measurement of the sun or
the moon is about 0.54 degree.  That this number is 1/200 of 108
invests both the numbers with enhanced significance.  Furthermore,
108 is  , where the mapping of the sky into 27 naks atras goes back
to at least TS 4.4.10.1-3.

The second number 339 is simply the number of disks of the sun or
the moon to measure the path across the sky:  This represents the
earliest approximation to   that takes it equal to 3.1389.  Another
way one might obtain the number 339 is:  The actual product is more
than 180 since 0.54 degree is slightly larger than the true angular
size of the sun or the moon.  Nevertheless, 183 is also of significance
since it represents half the number of days in the year.

Once 108 was arrived at 339 could be easily calculated.  These
estimates must have been refined through mutually related measurements.
For example, one could count the number of disks of the sun or the
moon that would go into an arc of a specified extent.

With 339 being the number of what one might call sun steps during
the day, the r s is would have liked to relate it to the 183 days
of the half-year.  This has an excess of 156 units, which when
divided into the 2 sandhya s of the dawn and the dusk apportion 78
to each.

The question might be asked as to what evidence supports such an
astronomical interpretation for the numbers 108, 339, and 78 in
the Vedic literature itself.  There are two kinds of evidence:
first, in the organization of the Vedic texts; second, in the
parallel with the details of agnicayana, or representation of time
by a fire altar (Kak 1991).  These will be described in the next
sections.

3. The Total Number of the Hymns

Note that in agnicayana (Tripa t hi  1990, Kak 1991) 21 bricks go
into the formation of the ga rhapatya altar.  At the same time 21
enclosing stones go around the ga rhapatya, whereas the number of
such stones around the dhis n ya and the a havani ya are 78 and
261 respectively making a total of 360.  The ga rhapatya represents
the earth, whereas the dhis n ya and the a havani ya represent the
space and the sky respectively.  In analogy 21 days of the year
may be called ga rhapatya days; the remaining 339 days of the year
represent the 78 days of the space and the 261 days of the sky.
This provides a corroboration of our interpretation of the number
339.

Many hymns are very brief whereas others are much longer.  This
suggests that when the compilation of the hymns into the R gveda
was made the total number must have played a role.  Now  .  Also
note that  .  The 1017 hymns then symbolize the   divine (space
and sky) days of the three worlds.

Recall again the theory of the Vedic knowledge based on a similarity
between the cosmic, the terrestrial, and the spiritual.  This is
why the geography of the R gveda counts just three sevens or 21
rivers in RV 10.75.

Also note that a lunar day, called a  tithi , was considered equal
to 9  bha m s as .  As explained in Kak (1991) the RV 3.9.9 and RV
10.52.6 reference to 3339 gods in a year, personified as Agni,
represents the 371 tithis in the year.  It is also quite possible
that this 3339 is coded doubly into the
  for the total number of hymns.

4. The Organization of the Books

The Anukraman i s ascribe books 2 to 7 to the r s is Gr tsamada,
Vis va mitra, Va madeva, Atri, Bharadva ja, and Vasis t ha or their
families.  Book 9 is a collection of hymns by several r s is to
Soma Pavama na, or Soma poured through the filter.  Book 1 which
consists of 191 hymns is classed into 15 groups of hymns by different
seers.  Book 10 also consists of 191 hymns and its first 84 hymns
are classed into 25 groups based on r s is, and its remaining 107
hymns are counted singly.
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 seers of the
Kan va family.  Including the Va lakhilya hymns these constitute
19 groups.  The hymns of Book 9 are grouped into 7 according to
the metre.  These metres are Ga yatri , Jagati , Tris t ubh, Anus
t ubh, Us n ih, Praga tha, and miscellaneous.  These hymns are by
a host of r s is including Bhr gu, Kas yapa, and Kavi Us anas.
This information is summarized in Table 1.


 Table 1: Hymns and groups

 Mandalas 1       2       3 4       5       6       7       8       9       10 =

Hymns   191  43      62      58      87      75      104     92+11   114 191

Groups  15      5       4       11      7       5       12 18+1    7      25+107

One would expect that if the R gveda is considered akin to the
five-layered altar described in the Bra hman as (Kak 1991) 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.  We find that is indeed the number of
hymns in these two books.  One may represent the R gvedic books as
a five-layered altar of mantras as shown in Table 2.

 Table 2: The altar of books

 Book 10 Book 9
 Book 7  Book 8
 Book 5 Book 6
 Book 3  Book 4
 Book 2  Book 1

Note that the structure of this representation has considerable
regularity.  In particular, Books [4+6+8+9] = 339.  Other relationships
are apparent from Table 3.

 Table 3: Hymns in the altar of books

 191     114
 104     92
 87      75
 62      58
 43      191

We see also that the number of hymns in the different books (man
d alas) satisfy the following relationships:

Books [1+2+3+4] = 354  (Lunar year)
Books [4+7] = Books [5+6] = 162  (1/2  Naks atra  year) 
Books [4+5+6+7] = 324  (Naks atra 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 naks atra year + 21 = 1/2 year of 366 days

The number of hymns in Books 1 and 10 is 191.  This number also
satisfies the interesting equality:

191 = 113 + 78

where the significance of 113 and 78 has already been explained.

5. More on the Astronomical Basis

The total number of groups, excluding the Va lakhilya hymns, is
216.  This is twice the 108 diameters of the sun that describe the
distance from the sun to the earth.  This is 1/2000 the fundamental
great yuga number of 432,000 which according to the S atapatha Bra
hman a equals the number of syllables in the R gveda.

PB 16.8.6, PB 21.1.9 speak of the sun being at a distance of a
thousand earths from the earth.  This statement is not factually
correct since the correct distance is more than 10 times greater
than this figure.  But the number of 432,000 may now be seen as a
product of the total units of the sun and the earth diameters that
are assumed to be separating the two.

6. On the Organization of the Atharvaveda

The Atharvaveda consists of 19 main books and an appendix (often
termed Book 20) called the Kunta pa-khila.  These main books fall
into 4 divisions.

The total number of hymns if 565 which is
 .
Note that 113 is 339/3.  Also note that the total number of hymns
in the R gveda is
 .
This establishes that the same person or tradition was responsible
for the organization of the two Vedas.

As in the R gvedic books, one may also view the Atharvaveda books
as a five-layered altar.

Note that the total number of verses of the four Vedas is by one
tradition taken to be 20358.  It is not surprising then that this
number is  , a product of two fundamental numbers in the design of
altars.  This confirms the unity in the arrangement of the four
Vedas.

One might ask what meaning the total number of verses in the
Atharvaveda might have.  When the verses of the Kunta pa-khila as
well as the parya ya hymns are added we get a total of 5226 verses.
This is exactly equal to  .  Once again we see the Vedic number 78
as a constituent of the total.

7. On the Structure of the Bhagavadgi ta

We now consider another canonical text and we will show how our
decipherment of the Rgvedic code is of significance here.
The text of the  Bhagavadgi ta  has four participants:  Dhr tara
s t ra, Sam jaya, Arjuna, and Kr s n a.  Of these Arjuna and Kr s
n a engage in a transcendental dialogue, whereas Dhr tara s t ra
and Sam jaya represent the observers of this dialogue.  A deliberate
design of the Bhagavadgi ta  might then reflect these numbers in
terms of the verses spoken by each.  The total number of verses
spoken by Arjuna and Kr s n a is 659.  As a fraction of the total
it equals 659/700 = 94.14%.  On the other hand the fraction 339/360
= 94.16%.  With the constraint of 700 as the total number of verses
this is as close as one can get to the basic R gvedic ratio of
339/360.

One might wonder if this is a coincidence.  The laws of probability
would rule against that, however.  Another reference to an astronomical
number is the sum of the first 9 chapters which equals 372 verses
or the number of
 tithis  (lunar days) in a year.

Tradition ascribes the arrangement of the Vedas as well as the
authorship of the Bhagavadgi ta  to Kr s n a Dvaipa yana Vya sa.
The ratio of 339/360 is a commonality between the two.  Perhaps
one can consider it as a signature by Vya sa or by one that knew
of this tradition.  Another commonality amongst the books ascribed
to Vya sa is a division into 18 chapters.

Why 700 verses were chosen for the book is not clear.  But this
number is very close to the Vedic number 78, the number for space,
because  .  If 702 was the original number then 2 verses are now
lost.  It is possible that the book started out with 702 verses to
be consistent with the requirement that the total be a multiple of
78.  However, the imposition of the further requirement of the
ratio 339/360 then called for a pruning of two verses.

Another possibility is that  .  Here 21 would represent the earth
and 1 is representative of the transcending unity in a manner which
is quite commonly used in Vedic writing.  If the second explanation
is right then the Bhagavadgi ta  has retained the form in which it
was conceived.  The presence of the 339/360 ratio is another argument
that supports the 700 verse critical edition.

8. The Geography of the R gveda and the Sarasvati  Script

The geography of the R gveda is of enormous help in determining a
chronology of the hymns (e.g. Frawley 1991, Kak 1992).

RV 7.95 and RV 6.61 speak of Sarasvati  being the pre-eminent river
of that age, flowing from mountains to the sea.  RV 2.41.16 calls
it  nadi tama  , the best of rivers.  RV 6.61.14 indicates that
region around the river was the center of the Vedic people.  An
allusion to building a fire altar on the banks of Sarasvati  and
Dr s advati  to represent time is in RV 3.23.4.  Ma nava Dharma S
a stra MDS 2.17.19 defines Brahma varta, the land between Sarasvati
and Dr s advati , as being the most sacred.

After the R gvedic age, the Bra hman as speak of the disappearance
of the Sarasvati  in the desert.  PB 25.10.16 speaks of the source
of Sarasvati  in the mountains forty days on horseback from where
it is lost in the desert.  The source is called Plaks a Pra sravan
a, which is apparently a lake.

Archaeological research has established (Kenoyer 1991) that the
Sarasvati river dried up around 1900 B.C.E., when as a result of
tectonic shifts its tributaries S utudri  and Yamuna  were captured
by Sindhu and Gan ga .  Note also that most of the settlements of
the Harappan phase (2600-1900 B.C.E.) of the Indus tradition were
on the banks of the Sarasvati  river (Figure 1).  This tradition
goes back to at least 6500 B.C.E. (Kenoyer 1991, Kak 1992).  With
the settlements of r s is on the banks of the Sarasvati river it
is not surprising that the later tradition represents Sarasvati
as the goddess of learning.  It appears that this tradition alludes
to the development of writing in the Sarasvati  region.  This
suggests that perhaps the earliest script of India was called the
Sarasvati  script ; this is the script that is now popularly known
as the Indus script.  Recent analysis has shown (Kak 1988, Kak
1989, Kak 1990) that this script and the later Bra hmi  scripts
are related.  This squares with the tradition that the Bra hmi
script represents a renewal of a tradition of learning that had
been interrupted.

9. Discussion

One might assume that the compilation of the hymns was made based
on a large number of available hymns.  Just as the total number of
1017 was deliberately chosen, it is also likely that the number of
hymns in the individual books had astronomical significance.  This
may also have been true of the manner in which the hymns were
grouped.

The Va lakhilya hymns appear to have the significance of the 11
extra days that need to be added to the lunar year to obtain the
solar year.  At one level the entire R gveda appears to be a
representation in mantras of the agnicayana rite.

One reason why the syllables of the R gveda were preserved with
incredible fidelity is that the total represented measurements of
natural processes.


Abbreviations for Vedic Texts

AA      Aitreya A ran yaka

AB      Aitreya Bra hman a

AV      Atharvaveda

BU      Br hada ran yaka Upanis ad

KB      Kaus i taki Bra hman a

MDS     Ma nava Dharma S a stra

PB      Pan cavim s a Bra hman a

RV      R gveda

S B     S atapatha Bra hman a

TB      Taittiri ya Bra hman a

TS      Taittiri ya Sam hita

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1991.  Gods, Sages and Kings . Salt Lake City: Passage Press.

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