VEDANGA
VEDANGA
VEDANGA
FOR
THE FIRST TIME READER
BY
N.KRISHNASWAMY
PANINI
AS REPRESENTED ON A
COMMEMORATIVE POSTAGE STAMP
ISSUED BY THE GOVERNMENT OF INDIA
`
AUM
IS THE SYMBOL OF
THAT
ETERNAL CONSCIOUSNESS
FROM WHICH SPRINGS
THY
CONSCIOUSNESS OF
THIS
MANIFESTED EXISTENCE
THIS IS THE CENTRAL TEACHING OF THE UPANISHADS
EXPRESSED IN THE MAHAVAKYA OR GREAT APHORISM
Dedicated to
Natesan
who lived the life of a Jeevanmukta
ACKNOWLEDGEMENT
This book is less a fresh composition than a compilation of relevant information derived from
tht the Internet, specially those wonderful compilations of the Wikipedia, and writings of authors
Fri like Fruits Staal and others. I have not sought prior approval from them or their publishers as
thi this book is intended for free distribution to and for the benefit and pleasure of a small circle
of first time readers among my friends and well-wishers. For these trespasses I seek the pardon
of of the authors and publishers and I express my gratitude to them.
And I must also acknowledge the support of Alamelu and C.L.Ramakrishnan to whom I have
al always been always been able to refer both facts and logic of my narrative. Errors in these
are all of course, entirely mine, and for these, I seek the indulgence of the reader.
THE VEDANGAS
FOR
THE FIRST TIME READER
LIST OF CONTENTS
PREFACE
Chapter 1 :
Introduction
Chapter 2 :
Jyothisha - jaEtx
PAGE
Kalpa kp
- Ritual & Sacrifice - Activity
Chapter 4 :
Siksha - SXa
SXa
Learning - Sound & The Syllable
Chapter 5 :
Nirukta - n|
Etymology The Word
Chapter 6 -
Vyakarana - yakrN|
Grammar & Syntax The Sentence
Chapter 7 -
Chandas - Cds
Poetry - Rhythm
Chapter 8 - Semantics Communication & Meaning
Chapter 9 - Language & Knowledge
Chapter 10 - Perception - Truth & Reality
ANNEXURE 1 : OVERVIEW OF SACRED TEXTS OF INDIA
---------------------------------------------
These skills lead him into deep understanding and great accomplishments
of knowledge of both the external world of Nature and internal world of
the human Nature. And given the duration and rhythm of the breathing
process, when the Rishis committed all this knowledge to the word in the
Rig Veda and Sama Veda, it seemed just natural that they should set the
word to poetry and music in the rhythms of metre and tala
A sound when the mouth was opened, automatically became the sound of
the letter A or its equivalent in all languages. As the mouth started closing,
the sound gradually morphed into the sound of U, and when the mouth
was closed with the sound continuing, became the hum of the silent M, a
hum that even then, retained its capacity for music ! Here then was the first
word AUM proclaimed by the Vedas as the very first manifestation of the
Divine as the Word ! Of course, the mouth continued to use the different
parts of its anatomical structure to give further shapes and stresses to
these basic vowel sounds. It used the throat, palate, tongue, teeth and lips
to create the guttural, cerebral, palatal dental and labial consonants that
could then create all the possible basic sound components of speech, not
surprisingly, common to virtually every language spoken by man. The
pure sounds that originated in the vocal chords were the Svaras or vowels
and when these were shaped by the different parts of the mouth, they
became the Vyanjanas or consonants of the Sanskrit alphabet. It is of
special interest that the shaping of sound as it emerged from the throat to
the lips should be reflected correspondingly in the Ka-Cha-Ta-Tha-Pa
syllabic groups of the consonants, five in number, called the Vargas. What
should surprise the first time reader is that these components were first
suggested in the Vedas and clearly elaborated later by the Shiksha, one of
the six Vedangas, constituting a masterly exposition of the disciplines of
Phonology and Phonetics developed in India, long before any other culture
of the world had anything comparable to show for itself.
Again, early language often used letters of the alphabet for numeric
representation, till the appearance of specific symbols and words standing
for numbers. The external world needed to be understood as much in
quantitative as in qualitative terms. Time and distance required to be
expressed in units. One early device was to embed numeric codes through
letters in texts. A typical example was the Katapayadi scheme where one
could derive the numeric position of a Raga in the 72- Melakarta Raga
scheme of Carnatic music, from the letters that figured in the name of the
Raga. That scheme that tabulates the system of 72 basic ragas derives
from a permutation and combination of the 12 half-tone intervals that
comprise the octave and that figures so universally as to suggest an
almost natural endowment or inheritance of all mankind. One can
recognize in these devices, the concepts could have led inevitably to the
development of mathematical symbols and skills, and on the later
This brings us squarely into the discussion of what Words mean and
indeed to the philosophical question of what Meaning itself means. A
fundamental question then is, where does meaning come from ? From the
thought, the word, from the choice or sequence of words, the whole
sentence, or even the silent expression of what is not spoken ? Is there a
gap between what is said and what is meant, and if so, how is it bridged ?
These are the central concerns of language, communication and meaning.
And it is these questions that are addressed by the Vedangas. These
disciplines of the Vedangas were later elaborated, codified and presented
in extraordinary range and depth by a succession of the early brilliant
scholars like Yaska, Panini and Patanjali and the later ones like Bhartrhari.
Their concepts reach down today in every significant work of modern
linguistics Paninis central work, the Ashtdhyayi, so named after the eight
chapters that comprise the work, has the totality of the Sanskrit language
corpus, analysed and presented as rules of grammar in a total of 3998
Sutras or aphorisms of phenomenal brevity. It has indeed been considered
a masterpiece of encapsulation of the entire science of linguistics in a way
that George Cardona says : Panini's grammar . merits asserting ... that
it is one of the greatest monuments of human intelligence.
An enormous amount of scholarly writing has been addressed to the
chronology of development of the various disciplines covered by the
Vedangas. Much of this seeks to place the origins of these disciplines in
various points of time three or more millenia ago and various places like
Egypt, Greece, Asia Minor, Mesopotamia and India, with passionate claims
for each location. Early Western scholars tended to say everything
originated in Greece, till investigations started unveiling incontrovertible
evidence from other locations. Claims of India remained unrecognized for a
long time, simply because of want of physical recorded material such as
were available in other locations, and simply because the significance of
the what was derived from a largely oral tradition, in Sanskrit could not be
understood or evaluated. Texts and scholars from India were simply not
heard.
While Western scholars began to see significances in the Indian tradition in
the 19th Century, it was really in the next century that showed great
advances in Western scholarship in Sanskrit, when the traditional Western
biases started wearing down, and a true understanding and evaluation of
the ancient tradition began to be realized. They began indeed to recognize
an extraordinary commonality binding languages across the cultures of
SANSKRIT
PERSIAN
GREEK
LATIN
LITHUANIAN
CELTIC
GOTHIC
GERMAN
ONE
EKA
YAK
ELS
UNUS
VINAS
ONE
AINS
EINS
TWO
DVA
DU
DUO
DUO
DVY
DAU
TWAI
ZWEI
THREE
TRI
SIH
TRELS
TRES
TRYS
TRI
THREIS
DREI
FOUR
CATUR
CHAHAR
TERSSARES
QUATTAR
KETURI
CETHIR
FIDWR
VIER
FIVE
PANCA
PANJ
PENTE
QUINQUE
PENKI
COIC
FIMF
FUNF
SIX
SHAT
SHASH
EZ
SEX
SZEZI
SE
SAIHS
SECHS
SEVEN
SAPTA
HAFT
EPTA
SEPTEM
SEPTYNI
SECHT
SIBUN
SIEBEN
EIGHT
ASHTAU
HASHT
OKTO
OCTO
ASZTUANI
OCHT
AHTAU
ACHT
NINE
NAVA
NUH
ENNEA
NOVEM
DEVYNI
NOI
NIUN
NEUN
TEN
DASHA
DAH
DEKA
DECEM
DESZIMT
DEICH
TAIHUN
ZEHN
Even so, many Western biases persisted, and even today, scholarly
opinion remains divided on the origin in place and time, not only the Vedic
civilization, but of many ancient knowledge disciplines that formed part of
it, especially in the areas of astronomy and mathematics. The conflict of
scholarly opinions, such as those of Shrikant Talageri and Michael Witzel,
have indeed taken extreme positions of hostility. It is possible however,
that all findings or points of view of scholars still rest on inadequate and
inconclusive evidence, if we consider that only physical evidence is
acceptable. It does not however make sense to quarrel over such issues. It
matters little whether the theorem on the right-angled triangle originated
from Pythagoras or from the Shulba Sutras. We need to be generous
enough to accept it as wonderful human contribution of fellowhuman
beings, often concurrent or consecutive by accident, and not get drawn
into an East versus West song and dance. There seems however, to be one
point on which there is general agreement across all shades of opinion :
that among all the known cultures of the world, the Indian contribution to
an understanding of the philosophy of Language and the mechanics of
Linguistics is the oldest and most pre-eminent. And this a position
obtaining today that surely originates from the Vedangas.
What then is unique about the Indian contribution ? One of the most
crucial starting points was the unquestioned sanctity of the word of the
Veda, which presented mans inner and outer world as an indivisible
continuum of a Reality that was Infinite and Eternal, and that the best that
man could do to understand this Reality was through finite bits of this
Reality symbolized by the word. The early scholars started looking at the
word of the Veda as something that originated from the intuitive,
perceptive mind of the Seer, become a vehicle of meaning, and lend itself
to articulation in speech to enable a sharing of all that it was intended to
convey. The mind then, clearly bore the faculty, that could just with a
thought, initiate the chain of inner events that culminated in the spoken
word. The scholars reflected deep on these inner sequences and named
the starting point the Sabda, the pure sound or wordless language,
originating in turn from an Ultimate Reality called the Sabda Brahman. The
Sabda carried the creative energy to shape an intent or meaning into a
word and transfer its energy to the vocal chords and cause the word to be
articulated. The meaning could come from a recall of an earlier experience
stored in their original words, or a new thought or a new experience or
meaning, and clothe it in one of the older words, creating addittional
meanings for the same word, or create a new words derived from the old
words or create new words altogether.
The early scholars who first received and reflected on the text of the
Vedas were clearly overawed by the range, depth and value of knowledge
that was embedded in their hymns. They saw that the Rishis were persons
of extraordinary vision, intellect and intuition who set their inspired visions
to words. It was inevitable therefore to invest the content and intent of
these hymns with an authority and a sanctity of Sruthi, or divinely inspired
works and canonize them as a sacred scripture. It became their sacred
responsibility to establish every possible discipline, organization and
method to ensure that they would be maintained in their pristine purity for
all time.
The first step was to establish an iron disciple for the recitation of the texts,
and this became the Siksha Vedanga. A basic step was to compile
authoritative lists of the words of which the texts were composed, lists
later referred to as the Nighantu, on which the onward related disciplines
could then be built. A clear understanding was set out on how basic
sounds were physically generated and then shaped by time intervals and
stresses and euphonic considerations into the basic components of
speech. We see here the first formulations of sound into the gutturals,
cerebrals, palatals, dentals and labials; the rising, falling and modulating
stresses, analogous to the modern diacritic variations of the accent, grave
and circumflex; and the euphonic changes at word junctions, typified in
variations in the use of the indefinite article in English as between say, a
ball and an apple. All these formulations represented the oldest known
compilations of Phonology and Phonetics presenting concepts that remain
valid to the present day.
To explain the Vedas the ancient scholars had obviously to start with the
words of the Vedas, and then start looking at the words that had
By the time of Panini, the structure and vocabulary of Sanskrit had greatly
expanded and it was to this expanded word Universe that he addressed
himself. He not only established a rule base governing their totality but
went on to state the rule base in terms that would apply to the future
growth of Sanskrit, and state these in generalized terms that had obvious
applicability to the growth of languages in general even extending to
computer languages of today. The first major developments in the
progressive evolution of modern Linguistics, in the works of Saussure,
Bloomfield and Naom Chomsky were greatly inspired by the work of
Panini, which they acknowledged in glowing terms.
--------------------------------------------------------------
CHAPTER 1 : INTRODUCTION
The word Vedanga means a limb or aid or auxiliary of the Veda. The word
Veda means Knowledge, being derived from Vid, which means to know.
And the Knowledge that Veda stands for, refers to the Knowledge of the
One Reality, the One Absolute, the One Truth. Not just the reality of
existence as it appears within our cognition, that is Transient, Relative or
Partial, but that is Knowledge of the One behind the Many. In this search
for the One Truth we subject everything that we know to the unrelenting
questions : What, How, When, Where and Why.
The first reference to Vedangas is made in the Mundaka Upanishad in the
following words :
meaning at both levels requires two levels of vision, sight on one, insight
on the other. The ancient Rishis presented the Vedas in words representing
a total vision of all existence. The scholars who followed later, and who
realized their true meaning and value, felt it necessary to establish
mechanisms for their preservation, transmission and understanding
through time, for the benefit of posterity. It was their effort that resulted in
the six Vedangas.
Four of the Vedangas were addressed to the structure and function of the
word content of the Vedas : Shiksha or Phonetics for their correct
articulation; Nirukta or Etymology, on how the words originated;
Vyakarana or Grammar, on how words should be used in sentences to
convey meaning; and Chandas how sentences should be rendered as
music or poetry through metrical structures, The other two Vedangas went
beyond the realm of the word, to address the realm of activities and
objects : Kalpa or Ritual, on how and with what objects and actions,
sacrificial rituals should be conducted; and Jyotisha or Astronomy on how
time and place for the conduct of the sacrifices should be determined. The
first four Vedangas present a remarkable treatment of the entire spectrum
of the discipline Linguistics, that are recognized today as directly relevant
to the formulations of modern linguistics. The last two are also seen to
have a remarkable conceptual anticipation of many aspects of Astronomy
and Mathematics of the present day.
Even a cursory reflection on the idea of existence will tell anyone at once
that it is whatever is set in a framework of Space and Time. Existence also
has two. basic dimensions : the external physical, and the internal mental.
The deeper reflections of the ancient Seers reflected probed far beyond
and deep into these two dimensions, both within the internal world of the
individual and the external reaches of the cosmos. Looking at the heavens
they saw massive units of distance and time at work, which seemed to be
vastly scaled down to reach down into the internal consciousness of the
individual. The energies and configurations of the planets and stars
seemed to have their counterparts in the energies and the cells that
supported life in the individual and share in what could best be described
by a continuum of a single vast consciousness that was presented as
existence. Time too, seemed to share the same quality of presenting vast
units of aeons scaled down to the time rhythms of the years, seasons and
days and nights, which invested the planets and stars with the same
regularity as the heart-beat and breath of the individual, giving them the
same sense of belonging to a single continuum of systemic existence.
From these concepts the Seers drew the inspiration of the highest values
relevant to a spiritual life and the knowledge of the most practical values
to a physical life : the first, finding expression in the Vedas and the second,
leading to the Vedangas.
passage and finally emerged from the mouth to launch the process of
communication. And that chain became complete with a corresponding,
complementary process in the person receiving the communication. Taking
the words of the Vedas as the first sacrosanct starting point, each of the
above link sequences in this long chain from thought to speech, were then
analysed in depth and expressed in terms of principles and rules which
went on to form the disciplines of the Vedangas. The ancient scholars who
later built on the word foundations of the Vedas, saw too, that its words to
had to submit to the compulsions imposed by of the physical speech
mechanisms on modulations, stresses and articulation and also and the
time limits of the exhalation phase of respiration, when alone these could
occur. This led them clearly to the rules of recitation, especially the
euphonies of smooth transitions between words that determined the rules
of Sandhi referred to in the Shiksha and the Nirukta and the metric
measures of the Chandas.
The Vedangas are thus, the six auxiliary disciplines for the understanding
and tradition of the Vedas. Traditionally, Vyakarana and Nirukta are shared
across all four Vedas, while each Veda has its own Siksha, Chandas, Kalpa
and Jyotisha. Later, they developed into independent disciplines, each with
its own corpus of Sutras.These ancient disciplines became the foundations
of virtually all the disciplines that obtain today, of Phonology, Phonetics,
Etymology, Philology, Semantics, Syntax, Grammar, Aesthetics, or the
History, Psychology and Philosophy of language, or any aspect indeed of
Linguistics.
----------------------------------------------------
between 1727 and 1734, having been requested to undertake this by the
then Mughal Emperor, Muhammed Shah.
The name Jantar Mantar is derived from the words Yantra and Mantra of the
ancient scriptures.
The fixed stars are divided into two sets, one of twelve groups and another
of twenty-seven groups. The twelve groups, based on the motion of the
Sun are called Signs or Ris; the twenty-seven groups of stars are called
Nakatras, stellar mansions or asterisms. This imaginary belt, with 12 Ris
and 27 Nakatras ranged along on it, is called the Zodiac.
The Zodiac and its divisions of Ris and Nakatras is the reference for
establishing the position of any planet or star in the sky. Since it encircles
the earth, it is comprised of 360 degrees. The twelve Ris each occupy 30
of arc along the Zodiac, and the twenty-seven Nakatras, being equal in
size, each span 1320'.
The heavenly bodies called planets or Grahas move, generally from west to
east, in the foreground of the fixed Ris and Nakatras. The name Graha
(graha = Sanskrit to grasp) derives from the fact that while moving against
the background of the Nakatras, they appear to get control of one
Nakatra after the other. Vedic astrology recognizes nine Grahas: Sun,
Moon, Mars, Mercury, Jupiter, Venus, Saturn, Rahu and Ketu. Of course,
the Sun is a star, the Moon is a satellite of the earth, and Rahu and Ketu are
mathematical points on the Zodiac, but Vedic astronomy and astrology
refer to all of them as Grahas. The Grahas (appear to) revolve around the
earth along the path of the Zodiac.
The terrestrial phenomena of day and night spring from the relative
rotation around its own axis with reference to the Sun, while the changes of
seasons comes from a skewed revolution of the Earth with reference to the
Sun, that shifts the direct overhead position of the Sun over the Earth over
the Tropic of Cancer and Tropic of Capricorn to occur on the 20th March
and the 21st September, referred to as the Vernal and Autumnal Equinoxes
and over the Equator on the 21st June and 21st December, referred to as
the Summer and Winter Solstices which can be visualized from the above
image.
From this description of Space in terms of the cosmos, we may now move
on to a consideration of Time. The ancients devised several systems of
time units for different purposes. Time was of course considered
fundamental to all Knowledge. All different branches of knowledge and all
phenomena are under the supreme control of kla, the personification of
the Supreme Godhead as Eternal Time. The astrological signs represent
the bodily parts of His celestial form, called the Kala-Purua. So ultimately
all aspects of Space and Time are but different manifestations of the Lord
as in the image below.
The Vedic seers had an elaborate method of reckoning time and expressed
it in terms that carried appeal to both intellectual and the devotee alike. The
following table compares some Vedic units of time with their
correspondence to present measures of time, which we may compare out
of curiosity, with our units of time of today ranging say, from the nanosecond to the light year
The earth revolves around the Sun once in 365 days, 5 hours, 48 minutes
and 46 seconds. Considered from the earth, the Sun appears to complete
one round of the ecliptic during this period, which is called a tropical year.
The earth regains its original angular position with the Sun in the span of a
tropical year. A tropical year is also called a year of seasons, since
occurrence and timing of the seasons depend on this annual Earth-Sun
cycle. If we consider the revolution of the Sun around the earth from one
vernal equinox to the next, it takes exactly one tropical year.
However, if we consider the position of the earth with reference to a fixed
star of the Zodiac such as first degree of Mea (Aries) or the end of Revati
Nakatra, at the end of a tropical year, the earth appears to lie some 50.26
seconds of celestial longitude to the west of its original position. In order
for the earth to attain the same position with respect to a fixed star after
one revolution, it takes a time span of 365 days, 6 hours, 9 minutes and 9.5
seconds. This duration of time is called a sidereal year. The sidereal year is
just over 20 minutes longer than the tropical year; this time difference is
equivalent to 50.26 seconds of celestial longitude. The difference between
the tropical year and the sidereal year is similar to the difference between
the solar day and the sidereal day. Each year, the Vernal equinox will fall
short by 50.26 seconds along the Zodiac reckoned along the fixed stars.
This continuous receding of the Vernal equinox along the Zodiac is called
the Precession of the Equinoxes.
Cause of the precession: The earth rotates around its axis like a spinning
top. In doing so, its north pole (and, therefore, the celestial pole), describes
a circle of some 47 degrees around the pole of the ecliptic. In other words,
the point where the plane of the equator intersects the plane of the ecliptic
is constantly shifting. This point, 0 Aries corres ponding to the Vernal
Equinox, moves westward at approximately 50.26 seconds of arc each
year. The result of this precession of the equinoxes is a slow increase in
the right ascensions of the Zodiac. This precession takes 25,800 years to
complete one circle. An appreciation of this precession is of great
importance in understanding the basic concepts of Vedic astrology and is
perhaps relatable to the ancient Indian celestial Yuga calendar.
An interesting point that emerges from all this is that the shifting of the
equinoxes has been noted by the star-gazers of ancient times and their
timing by the ascendant star or sign of the zodiac, finds explicit reference
in the Vedas and other ancient texts. These references provide unequivocal
proof of the chronology and historicity of the related events, in a measure
that is as reliable, if not indeed more reliable than any amount of
archeological or other material evidence. The following is a brief summary
of such findings on the timing of such ancient events :
-3928 July 25th: the earliest eclipse mentioned in the Rig Veda (according
to Indian researcher Dr. Sri P.C. Sengupta).
-3200 In India, a special guild of Hindu astronomers (nakshatra darshas)
record in Vedic texts citations of full and new moon at winter and summer
solstices and spring and fall equinoxes with reference to 27 fixed stars
(nakshatras) spaced nearly equally on the moons ecliptic (visual path
across the sky). The precession of the equinoxes (caused by the mutation
of the Earths axis of rotation) makes the nakshatras appear to drift at a
constant rate along a predictable course over a 25,000-year cycle. Such
observations enable specialists to calculate backwards to determine the
date the indicated position of moon, sun and nakshatra occurred.
date of roughly 8000 years ago or about 6000 BC. (There are other
scholars who give this date.)
If we take it that the winter solstice occured in Dhanistha Nakshatra in
Vedic times and that it slipped back to Moola Nakshatra now, I am looking
at a date of roughly 4000 years ago or about 2000 BC. There are many
people who believe that the Harappan civilization was about 2000 BCE.
----------------------------------------------------
The altar is seen to be comprised of two areas, one the Prachinasala, and the
other the Maha Vedi, The first area is earmarked for everyday rituals, generally
domestic, and the second special rituals, that formed large public events.
Different areas called citis were set aside within these two large areas of the altar,
for different purposes, and of these the Uttara Vedi was where the main ritual was
performed. It came in different shapes and sizes, (Baudhayana lists as many as
21) and is seen as circular in the above picture on the eastern end of the Maha
Vedi. It was situated in the east, because, as stated in the Satapatha Brahmana,
the gods reside in the east. (Of course the East was where the sun rose, relative
to mans own location and perception, though in the totality of Space pervaded
as it might be by the gods, the East could have no meaning).The standard unit of
measure of length, was the Prakrama, made up of 30 Angulas, as stated in
Baudhayanas Shulba Shastra (1-15). The Angula, which literally means finger,
itself was defined as the length occupied by 34 grains of Sesamum, where this
number was seen to even out small differences in individual grain size and yield
a fairly reliable standard unit of length. Clearly, the earliest concepts of counting
for any form of quantification may have derived from the fingers, and perhaps the
10 fingers became the fore-runners of the decimal system or numbers.
It is important to note here that though this Shulba is placed early in the first
millenium BC, some of the concepts and terms used in them go back to one
millenium or more and found in the Rig Veda. The Maha Vedi is a trapezium
shaped area, 36 prakrama long with two sides of length 30 and 24 prakrama,
making a total area of 972 square prakrama. The original first Vedi was said to be
a trapezium, 12 prakrama long with sides of length 10 and 8 prakrama, making for
an area of 108 square prakrama, and we have already seen where the figure 108
came from. Beyond this, one needs to note that the basic stipulation was that the
size of the Uttara Vedi could be 324, which was one third of 972, the area of the
Maha Vedi, or 108 which in turn, was one third of 324 square prakrama. One also
needs to note that the Uttara Vedis precise compliance of these shape and area
stipulations were generated on the ground from right angled triangles with length
of their sides conforming to what were later described as Pythagorean triples,
number sets like 3-4-5, 12-5-13, 15-8-17 7-24-25 and 15-16-35. (the sum of the
squares of two was equal to the square of the third figure in the triple) One had
also to note that points to mark lines that enclosed such areas were fixed on the
ground with wooden pegs and the distances between them were fixed by ropes
with that ended in loops that marked their standard lengths. And finally detailed
specifications were prescribed for the sizes, numbers and placement of clay
bricks to be used in brick structures of the altars showing a complete grasp of
the geometry and three dimensional computation.
The Indian ancients were thus clearly and completely at home with many of the
key concepts of mathematics, though it is possible that they used them for their
application to specific purposes, particularly religious purposes, rather than as
formal stand alone academic disciplines supported by algorithmic proofs, as the
Greeks did in the style of Euclid. Their tools were mainly thought and intuition,
the outer eye and the inner eye, and at a physical level, simple devices like ropes
and pegs which anyone could make or use. They were at home with numbers,
integers or fractions, all the way from Zero to Infinity, but they were more clearly
concerned with their practical uses for computing length and area, as could be
applied to counting cows and horses, or building houses or altars, or
demarcating plots of land for crops or making spoked wheels and chariots. They
understood and used gravity to stop river flows enough to divert the rising
waters into systems of canals, with principles and mechanisms that remain
relevant to the present day. One sees references in the Rig Veda to Rhbus or
artisans engaged in these activities as a profession. In these areas of application,
where ratio and proportion became more relevant than mere numbers, geometry
seemed to prevail over arithmetic, perhaps because they provided more vivid
symbols of the
physical relevance, not to speak of the relativities and
compulsions of physical existence. Who discovered the numeric triples earlier,
Baudhayana or Pythagoras is really irrelevant when we could more charitably
see and accept this as the similar progress of the human mind irrespective of
time and place. It is the historian and politician who misinterpret or misuse
history who are apt to survive and thrive by bringing such issues of time and
place of origins into contention.
It would now be useful to provide a broader perspective of the textual basis of
the Kalpa discipline. Tradition does not single out any special work in this branch
of the Vedanga; but sacrificial practice gave rise to a large number of systematic
sutras for the several classes of priests. A number of these works have come
down to us, and they occupy by far the most prominent place among the literary
productions of the sutra-period. The Kalpa-sutras, or rules of ritual ceremonial,
are of two kinds: (1) the Shrautasutras, which are based on the shruti, the Vedas,
and teach the performance of the great sacrifices, requiring three or five
sacrificial fires; and (2) the Smartasutras, or rules based on the smrti or tradition,
which again includes two kinds of treatises: (a) the Grhyasutras, or domestic
rules, treating the rites of passage, such as marriage, birth, namegiving, etc.,
connected with simple offerings into the domestic fire; and (b) the Dharmasutras,
which treat of customs and social duties, and have formed the chief sources of
the later law-books, the Dharma Sastras. Further, the Shrauta-sutras of the
Yajurveda include a set of so-called Shulba-sutras, i.e. rules of the cord, which
treat of the measurement by means of cords, and the construction, of different
kinds of altars required for sacrifices. These treatises are of special interest as
supplying important information regarding the earliest geometrical operations in
India. Along with the Sutras may be classed a large number of supplementary
treatises, usually called Parishishta on various subjects connected with the
sacred texts and Vedic religion generally.
The Shrauta Sutras ( rautas tra)
tra form a part of the corpus of Sanskrit Sutra
literature. Their topic are the instructions relating to the use of the Shruti corpus
in ritual ('kalpa') and the correct performance of rituals as such. Some early
Shrauta Sutras were composed in the late Brahmana period (such as the
Baudhyanana and Vadhula Sutras), but the bulk of the Shrauta Sutras are roughly
contemporary to the Grhya corpus of domestic Sutras, their language being late
Vedic Sanskrit, dating to the middle of the first millennium BCE, generally
predating Panini). There are Sutra compilations associated with different
composers but specific to each of the four Vedas.
The Grhya Sutras "domestic sutras" are a category of Sanskrit texts prescribing
Vedic ritual, mainly relating to rites relevant to life activities or events like birth,
death, marriage etc. . Their language is late Vedic Sanskrit, and they date to
around roughly 500 BCE, contemporary with the Shrautasutras. They are named
after Vedic shakhas and are also specific to each of the four Vedas.
The Dharma Sutras are Sanskrit texts dealing with custom, rituals and law. They
include the four surviving written works of the ancient Indian tradition on the
subject of dharma, or the rules of behavior recognized by a community. Unlike
the later Dharma Shastra, the Dharmasutras are composed in prose. The oldest
Dharmasutra is generally believed to have been that of Apastamba, followed by
the Dharmasutras of Gautama, Baudhayana, and an early version of Vasishtha. It
is difficult to determine exact dates for these texts, but the dates between 500-300
BCE have been suggested for the oldest Dharma Sutras. The Dharma Sutras are
also specific to each of the four Vedas.
The hulba Stras that deal with laying out the offering ground and altar geometry
are part of the Shrauta Sutras and are set in both the Krishna Yajur Veda and the
Shukla Yajur Veda. The Shulba Sutras are part of the larger corpus of texts called
the Shrauta Sutras, considered to be appendices to the Vedas. They are the only
sources of knowledge of Indian mathematics from the Vedic period. Unique firealtar shapes were associated with unique gifts from the Gods. The four major
Shulba Sutras, which are mathematically the most significant, are those
composed by Baudhayana, Manava, Apastamba and Katyayana, about whom very
little is known. The texts are dated by comparing their grammar and vocabulary
with the grammar and vocabulary of other Vedic texts. The texts have been dated
from around 800 BCE to 200 CE,[2] with the oldest being the sutra that was written
by Baudhayana around 800 BCE to 600 BCE.
The Baudhayana Shulba Sutra gives the construction of geometric shapes such
as squares and rectangles. It also gives, sometimes approximate, geometric areapreserving transformations from one geometric shape to another. These include
transforming a square into a rectangle, an isosceles trapezium, an isosceles
triangle, a rhombus, and a circle, and transforming a circle into a square.
As an example, the statement of circling the square is given in Baudhayana as :
2.9. If it is desired to transform a square into a circle, [a cord of length] half the diagonal [of the
square] is stretched from the centre to the east [a part of it lying outside the eastern side of the
square]; with one-third [of the part lying outside] added to the remainder [of the half diagonal], the
[required] circle is drawn. (This construction leads to a value of 3.088)
How did the various geometric procedures originally come to be associated with
sacrificial rituals ? There are competing theories about the origin of the geometry
that is found in the Shulba sutras, and of geometry in general. Kim Plofker says
Various theories of the ritual origin of geometry infer that the geometrical
figures symbolized religious ideas, and the need to manipulate them ritually
inspired the development of the relevant mathematics. It seems at least equally
plausible, though, that the beauty and mystery of independently discovered
geometric facts were considered spiritually powerful, and were incorporated into
religious ritual on that account." We may thus how see the fascination of the
Indian ancients for space and time, and relationships between shape and size
and thought and symbol and how they could represent all facets of human or
cosmic existence, must have led them to a congruence of ritual and geometry
The Vedas are indeed replete with use of numerical, astronomical and other data
to express relationships, encoded in a surprising number of ways for different
purposes. The use of the number 108 to express a cosmic relation for a
ritualistic purpose has already been shown. This is but one of many more
numbers and numeric and functional relationships. The number of hymns in
books 1, 2, 3 and 4 of the Rig-Veda adds up to 354, the number of days in the
Lunar year. Similarly, the total number of hymns in books 4, 5, 6 and 7 is 324, the
number of days in the so-called Nakshatra year, being the duration of the sun's
stay in 24 of the 27 lunar mansions. One sees a choice of numbers in a
cosmically meaningful way is also present in the construction of the Vedic altar,
such as the numbers of bricks in each layer being equal to the number of days in
given planetary cycles. It involves fairly complicated arithmetic, and shows the
kind of concern which the Vedic seers had for the harmony between their own
religious practices and the astronomical cycles. That approach led logically to
insightful Mathematics based on painstakingly accurate observations and
calculations.
---------------------------------------------------------------------
ka
ca
a
kha
cha
ha
ga
ja
a
gha
jha
ha
a
a
a
ta
pa
tha
pha
da
ba
dha
bha
na
ma
What is more interesting is that these five groups appear in the same order
in which the sounds are generated as they emerge in the vocal passage, as
seen in the diagram below, starting with the throat, and through the palate,
tongue, and teeth and ending at the lips. This is why they are referred to
the gutturals, cerebrals, palatals, dentals and labials respectively. But what
is truly remarkable is that these concepts accepted as standard today in
modern linguistics, appeared for the first time nearly 3000 years ago in the
Shiksha texts of the Vedic corpus in India.
In this
matrix, the stress difference
between sounds is preserved whether you
recite it horizontally or vertically. This was
extended and completed with fricatives
and sibilants, semi-vowels, and vowels,
and was eventually codified into the
Brahmi alphabet, which is one of the most
systematic approaches of mapping sound
to writing. The varga system was clearly
the result of centuries of analysis. In the
course of that development, the basic
concepts of phonology were discovered
and defined
Svara akaras are also known as pra akara i.e. they are main sounds in
speech, without which speech is not possible. We find the same notation
used for referring the Tamil vowels calling them as Uyir ezhutthu, meaning
letters bearing life.
Kahy
hya
Ka
hy
a : Velar; Tlavya : Palatal; rdhanya : Retroflex; Dantya : Dental;
and shtya : Labial. Apart from that, other places are combinations of the
above five places. They are:- Dantsthya : Labio-dental (Eg: v);
Kantatlavya : Eg: Diphthong e; and Kantsthya : Labial-velar (Eg:
Diphthong o)
The active places of articulation are classified as three, they are
Jihvmla : tongue root, for velar; Jihvmadhya : tongue body, for palatal;
Jihvgra : tip of tongue, for cerebral and dental; and Adha : lower lip, for
labial
word1word2;
word2word3,
word3word2,
In the dhvajadhvaja-ph
p ha (literally "flag recitation") a sequence of N words were
recited (and memorized) by pairing the first two and last two words and
then proceeding as:
word1word2, word(N-1)wordN;
word(N-1)wordN, word1word2
word2word3,
word(N-3)word(N-2);
...;
word3word2word1,
word2word3word4,
The world has no more fascinating story than that of the origin of
sound from the hour-glass shaped drum, the Damaru, played by
Shiva to provide the melodic beat of his celestial dance that
unleashed the energy of all Creation. It provided the rhythms of all
existence from the heart beat of living organisms to the motions of
the Sun and the stars, and all the sounds from which came speech
and song.
One detail of the story that is relevant here is that the Siva produced 14
sound sequences from the Damaru that formed the foundations for all
beats of dance, all notes of music and all phonemes of speech; that these
sounds appeared in Paninis mind and inspired him to set them down as
the Siva Sutras at the head of his great work, the Ashtadhyayi, the
foundational text of the worlds first scientific grammar and all the
grammars that later followed. The 14 sound sequences may be seen
clockwise from the arrow at the red line on the picture at the above right
Here is a sampling of a few verses quoted from a compilation of 60 verses
of Paninis Shiksha that illustrates the fundamental levels at which the
subject was treated by him :
Now, I shall give out the Siksha according to the views of Panini. In
pursuance of the traditional lore, one should learn it with reference to the
popular and the Vedic languages.
That speech-sounds in Prakrit and Sanskrit are sixty three or sisty four,
according to their origin, has been said by Brahman (Svayambhu) himself
One of the earliest philosophical texts of the Classical Greek period to deal
with etymology was the Socratic dialogue Cratylus (c. 360 BC) by Plato.
During much of the dialogue, Socrates makes guesses as to the origins of
many words, including the names of the gods. you know, says
Socrates in this dialogue, that the original names have long ago been
buried and disguised by people sticking on them, or stripping off letters
for the sake of euphony .. and the additions are often such that at last no
human being can possibly make out the original meaning of the word. ..
and first, remember that we often put in or pull out letters in words and give
names as we please nor does the addition or subtraction of a letter
make any difference so long as the essence of the thing remains in
possession of the name . Plato does not appear to subsribe to
operation of any principles in the evolution of words - something in sharp
contrast, as will become shortly apparent, to the Nirukta of Yaska, to
presenting the process as subject to clear-cut rules, showing that he was
really the worlds founder of Etymology as possessed of the discipline of
a science.
Etymology in the modern sense emerges in the late 18th century European
academia, within the context of the wider "Age of Enlightenment. The first
known systematic attempt to prove the relationship between groups of
European languages on the basis of similarity of grammar and lexicon was
made by two Hungarians, Jnos Sajnovics in 1770, and Samuel Gyarmathi
in 1799. The origin of modern historical linguistics is often traced back to
Sir William Jones, an English philologist living in India, who, in 1782
observed the genetic relationship between Sanskrit, Greek and Latin.
Jones published his The Sanscrit Language in 1786, laying the
foundation for the field of Indo-European linguistics. The study of
etymology in Germanic philology was introduced by Rasmus Christian
Rask in the early 19th century, and taken to high standards with the
German Dictionary of the Brothers Grimm. The philosopher Friedrich
Nietzsche used etymological strategies to argue that moral values have
definite historical relevance, where modulations in meaning in relation to
concepts like "good" and "evil" showed changes over time, reflecting
which value-system prevailed. From the 20th century on, philosophers like
Jacques Derrida started using etymologies to free them from the hold of
Western metaphysics and began an extraordinary commonality binding
languages across the cultures of East and West, to suggest a common
Indo-European heritage, that is easily recognIzable in the following table of
names of numbers
THE NAMES OF THE NUMERALS IN NINE INDO-EUOPEAN LANGUAGES
ENGLISH
SANSKRIT
PERSIAN
GREEK
LATIN
LITHUANIAN
CELTIC
GOTHIC
GERMAN
ONE
EKA
YAK
ELS
UNUS
VINAS
ONE
AINS
EINS
TWO
DVA
DU
DUO
DUO
DVY
DAU
TWAI
ZWEI
THREE
TRI
SIH
TRELS
TRES
TRYS
TRI
THREIS
DREI
FOUR
CATUR
CHAHAR
TERSSARES
QUATTAR
KETURI
CETHIR
FIDWR
VIER
FIVE
PANCA
PANJ
PENTE
QUINQUE
PENKI
COIC
FIMF
FUNF
SIX
SHAT
SHASH
EZ
SEX
SZEZI
SE
SAIHS
SECHS
SEVEN
SAPTA
HAFT
EPTA
SEPTEM
SEPTYNI
SECHT
SIBUN
SIEBEN
EIGHT
ASHTAU
HASHT
OKTO
OCTO
ASZTUANI
OCHT
AHTAU
ACHT
NINE
NAVA
NUH
ENNEA
NOVEM
DEVYNI
NOI
NIUN
NEUN
TEN
DASHA
DAH
DEKA
DECEM
DESZIMT
DEICH
TAIHUN
ZEHN
pray) got related through both sound and meaning to the English word
bead. Such combinations of sound change and semantic change make
etymological connections difficult to detect by merely looking at the
modern word-forms.
English is derived from Anglo-Saxon, a West Germanic variety, although its
current vocabulary includes words from many languages. The Anglo-Saxon
roots can be seen in the similarity of numbers in English and German,
particularly seven/sieben, eight/acht, nine/neun and ten/zehn. Pronouns are
also cognate like I/mine/me and ich/mein/mich or thou/thine/thee and
du/dein/dich. However, language change has impacted many grammatical
constructs, such as the noun-case system, which is greatly simplified in
modern English; and certain elements of vocabulary, much of which is
borrowed from French. Though more than half of the words in English
either come from the French language or have a French cognate, most of
the common words used are still of Germanic origin. Days of the week are
derived from old Norse: Monday [Moondg] Tuesday [Twiesdg]
Wednesday [Wodensdg] Thursday [Thorsdg] Friday [Friedg] Saturday
[Saternesdg] Sunday [Sunnandg]
When the Normans conquered England in 1066, they brought their Norman
language with them. During the Anglo-Norman period which united insular
and continental territories, the ruling class spoke Anglo-Norman, while the
peasants spoke the vernacular English of the time, as well as the native
Celtic languages. Anglo-Norman was the conduit for the introduction of
French into England. This led to many paired words of French and English
origin. For example, beef is cognate with the modern French buf, veal
with veau, pork with porc, and poultry with poulet. All these cognate words,
French and English, refer to the meat rather than to the animal. This
relationship carries over into the names for farm animals where the
cognate is with modern German. For example swine/Schwein; cow/Kuh;
calf/Kalb; sheep/Schaf. An explanation of this variant usage has been was
the Norman rulers mostly ate meat (an expensive commodity) while the
Anglo-Saxons reared the animals, an explanation that has passed into
common lore.
The search for meaningful origins for familiar or strange words is far older
than the modern understanding of linguistic evolution and the
relationships of languages, which has its roots no deeper than the 18th
century. The Sanskrit linguists and grammarians of ancient India were the
first to make a comprehensive analysis of linguistics and etymology. The
study of Sanskrit etymology has indeed provided Western scholars the
basis of both historical linguistics and modern etymology. Four of the most
famous Sanskrit linguists are:
Though they are not the earliest Sanskrit grammarians, they follow a line of
more ancient grammarians of Sanskrit dating back to several centuries
earlier. The earliest of attested etymologies can be found in Vedic
literature, in the philosophical explanations of the Brahmanas, Aranyakas
and Upanishads. The analyses of Sanskrit grammar of the previously
mentioned linguists involve extensive studies on the etymology (called
Nirukta or Vyutpatti in Sanskrit) of Sanskrit words, because the ancient
Indo-Aryans considered sound and speech itself to be sacred, and for
them, the words of the sacred Vedas contained a deep encoding of the
mysteries of the soul and God.
The Nirukta is attributed to Yska (Devanagari )),
a Sanskrit
grammarian who preceded Pnini (fl. 4th c. BC), believed to have been
active in the 5th or 6th century BC. He is thought to have succeeded
kayana, an anncient grammarian and expositor of the Vedas, who is
mentioned in his text. There are references to names of seventeen writers
on this subject as having preceded Yaska.
The Nirukta was developed around ancient collections of words referred to
as the Nighantu which were possibly the first efforts attempts to explain
how certain words get to have their meanings, especially in the context of
interpreting the Vedic texts. It includes a system of rules for forming words
from roots and affixes, and a glossary of irregular words, and formed the
basis for later lexicons and dictionaries. It consists of three parts, viz.:(i)
Naighantuka, a collection of synonyms; (ii) Naigama, a collection of words
peculiar to the Vedas, and (iii) Daivata, words relating to deities and
sacrifices.
The Nighantu represents the earliest known attempt at Lexicography in the
ancient Indian tradition. It presents a list of words from the Rig Veda, with
little or no attempt to provide meanings. It can only be described as
Vocabulary, rather than a Dictionary, though it may have been the forerunner of the Kosa or dictionary class of litterature. It is not ascribable to
any one author, and may have been a corpus developed by several
authors, perhaps spanning several generations. More importantly it
provided an
authoritative
basis on which the language related
disciplines of the Vedangas were later built.
The Nighantu has come down in two rescensions, one short and the other
a long one. The latter is longer because of listing a few more words, but
mainly because of a addition of a lot of explanatory and summarised
information. The Nighantu, according to the well documented and scholarly
book by Laksman Sarup, enumerates around 1926 words, listed out under
79 slokas, distributed over 5 Chapters which are set in 3 Kanda sequences
with contents as follows :
Sequence 1 : Naighuntaka Kanda covering the first three Chapters dealing
with synonyms (different words having the same or similar meaning) ; and
these chapters broadly deal with words related to Nature, to Man and to
abstract qualities respectively.
Sequence 2 : Naigama Kanda covering thee fourth Chapter dealing with
homonyms (the same word having different meanings) ; and
Sequence 3 : Daivata Kanda covering the fifth Chapter dealing with the
deities.
It is interesting and perhaps natural that the earliest words of languages
developed through an imitation of sounds encountered in nature, referred to
in the jargon of later linguistics as onomatopoeia. (From the Latin, "to make
names"). The first speech was considered onomatopoeic, marked by echoic
words such as moo, meow, splash, cuckoo, and bang. The role of
onomotopoeia is referred to in several Linguistic theories, variously called
the Bow-wow theory, the Ding Dong theory, etc Linguists generally begin
discussions about onomatopoeia with examples from different languages :
the snip of a pair of scissors is su-su in Chinese, cri-cri in Italian, riquiriqui in Spanish, terre-terre in Portuguese, krits-krits in modern Greek.
. . Use of ding dong to represent a bell ringing has been immortalized in
the My Fair Lady song, I'm getting married in the morning! Ding dong!
the bells are gonna chime."
Onomatopoeia may have had a limited influence in the early history of
language but of course, must have had little or no influence in the later
course of language development. The early onward stages may have seen
a development of homonyms, with a small number of available words
applied with different meanings to different objects. This would have
followed later by a rapid proliferation of a large number of words to attach
to different meanings, often to the point of different words sharing the
same or meaning or different shades of it. One sees this at an advanced
stage in the Nighantu in India, when many other societies in the world may
well have been in the bow-wow stage of onomatopoeia.
Yska takes his authority from the lost text of Sakatayana, an early
precursor, that etymologically, most nouns have their origins in verbs. An
example in English may be the noun origin, derived from the Latin
originalis, which is ultimately based on the verb oriri, meaning "to rise".
This view is related to the position that in defining agent categories,
behaviours are ontologically primary to, say, appearance. This was also a
source for considerable debate for several centuries.
Yska defines four main categories of words :
----------------------------------------------------------
IAST
Devangar
1. a i u
. |
2. K
. |
3. e o
4. ai au C
. |
5. h y v r
. & |
6. l
. |
7. m n M
. |
8. jh bh
. |
9. gh h dh
. |
10. j b g d
.
. |
11. kh ph ch h th ca t V
.
. |
12. k p Y
.
. |
13. s R
14. h L
.
. |
.
. |
pZy|!z&{vNSp&ziNgCDNSvp|!sn!
Be it noted that these rules that arise from derivation or inflection are
referred to Sandhi or junction or transition a change in meaning and
sound at the point of change and the change of sound is dictated by
considerations of euphony, a musical quality that is pleasing to the ear.
Both the pleasing poetic meter and the musical quality of a recitation of a
Vedic mantra, apart from the meaning content and intent, are thus integral
features the Sanskrit language and its Vedic usage, and all these features
come through clearly and in such phenomenal detail in the related
Vedangas. All that we can do is stand before this collosal corpus created
by the Indian ancients in silent awe.
---------------------------------------------------------------------
use of Time, with rules for the number of its syllables, and the patterns of
the alternation of their lengths and stresses. The foot is not only a limb
with which we traverse distance. It is also a measure of distance traversed
by every step we take, and also the distance traversed by a line of music
or poetry. It is these facets of music and poetry that add quality to the
words that they clothe, and it this essence of beauty that is personified by
the word triple that describes the Universal Mother in Her Sahasranama.
Nor is Chandas the exclusive domain of the Universal Mother.
Be it
remembered too, that in the Bhagavad Gita, (X-35) Krishna proclaims, that
among the highest forms of all Existence, He is also Chandas, the essence
of the Gayathri Mantra. To the ancients, then, the entirety of Existence was
woven in the warp and weft of Space and Time.
We may now examine some of the ways in which the subject of Chandas
was addressed by the ancients. While Chandas (
)
), the study of Vedic
meter, is one of the six Vedanga ("limb of the vedas"), no treatises dealing
exclusively with Vedic meter have survived. The basic rules go back as far
as the explanatory Vedic texts known as the Pratisakhyas (see Chapter 4). The oldest work preserved is Pingalas Chandas Shastra, dating back to
the period of transition from Vedic to Classical Sanskrit poetry. Later
sources are the Agni Purana, based on the Chandas Shastra, Chapter 15 of
Bharatas Natyashastra, and Chapter 104 of the Brihat-Samhita. These
works all date to roughly the Early Middle Ages. Later related works are the
Vritta Ratnakara of Kedarabhatta,, the Suvrittatilaka of Kshemendra etc,
dating to the 14th century or later.
At the outset, it may be noted that the Rishi composers of the Vedas
considered themselves to be Kavis or Poets. Poetry was therefore implicit
in their use of words, with attention to brevity, beauty and depth of
meaning within a strict adherence to patterns of meter. The words had the
number and syllabic content of a line set, with an alternation of their length,
stress and modulation that made them as musical as poetic. A verse had to
be set in a meter, divided into a set number of Padas, comprised in turn, of
syllables. In most of Sanskrit poetry the primary determinant of a meter is
the number of syllables in a unit of verse, called the pda ("foot"). The
common meters were : the jgat, with 4 padas of 12 syllables, the triubh,
with 4 padas of 11 syllables, the virj with 4 padas of 10 syllables, the
anuubh, with 4 padas of 8 syllables; and the gyatr, with 3 padas of 8
syllables A rik is a stanza of typically three or four padas, with a range of
two to seven found in the corpus of Vedic poetry. Stanzas may mix padas
of different lengths, and strophes of two or three stanzas are common.
Meters of the same length are distinguished by the pattern of laghu ("light")
and guru ("heavy") syllables in the pda. They can be summarized thus :
1.
A syllable is laghu if its vowel is hrasva ("short") and it is followed by
at most one consonant before another vowel is encountered, provided the
single consonant is not an anusvara ('') or a visarga (''). (These two
exceptions apply to word-final syllables only, as neither of them ever
precedes a vowel directly.)
2.
All other syllables are guru, either because the vowel is drgha
("long"), or because the hrasva vowel is followed by a consonant cluster or
an anusvara or a visarga.
3.
The hrasva vowels are the short monophthongs: 'a', 'i', 'u', '', ''
4.
All other vowels are drgha: '', '', '', '', 'e', 'ai', 'o' and 'au'.
(Morphologically, the last four vowels are actually the diphthongs 'ai', 'i',
'au' and 'u', as the rules of sandhi in Sanskrit make clear. So, while an
original 'ai', for example, had been shortened to an 'e' sound in practice, it
was still to be treated as long metrically.
The time duration of syllables was in units called morae, laghu syllables
counting as one unit, and guru syllables as two units.The standard unit of
grouping, analogous to the "foot" of Western prosody, is four morae (four
laghus, two gurus, or a guru and two laghus).
The rules distinguishing laghu and guru syllables go back as far as the
auxiliary Vedic texts known as the Pratisakhyas. Standard traditional
works on meter are Pingala's Chandastra and Kedra's Vttaratnkara .
Originally there were apparently no constraints on permissible patterns of
long and short syllables, the principle being purely quantitative. Vedic
prosody innovated a number of distinctive rhythms:
The last four syllables of a pada, termed the cadence by Indologists, are
usually in iambic (a short-long syllable alternation) or trochaic (a long-short
syllable alternation). This is mainly a strict alternation in the penultimate
and antepenultimate syllables, as the final syllable can be of either weight.
A caesura is found after the fourth or fifth syllable in triubh and jagat
padas, dividing the pada into an opening and break before the cadence.
The break very often starts with two short syllables. The opening shows an
iambic or trochaic tendency in keeping with the cadence, though the first
syllable can be of either weight, the alternation being in the second and
third.
1.
Syllabic verse (akaravtta): meters depend on the number of
syllables in a verse, with relative freedom in the distribution of light and
heavy syllables. This style is derived from older Vedic forms, and found in
the great epics, the Mahabharata and the Ramayana.
2.
Syllabo-quantitative verse (varnavtta): meters depend on syllable
count, but the light-heavy patterns are fixed.
3.
Quantitative verse (mtrvtta): meters depend on duration, where
each verse-line has a fixed number of morae, usually grouped in sets of
four.
The units:
The gaas:
k e iI l |
. ka la hr .
h s k h l |. ha sa ka ha la hr .
s k l |
. sa ka la hr .
torso and lower part of the body of the Devi, and these are directly referred
to in specific Names of the Lalitha Sahasranama. Other Names in the
Sahasranama also refer to the corresponding Chakras or vital energy
centres of the human body or as graphically represented in the Sri Chakra
Yantra that is special to worship of Lalitha Devi, and thereby establish
what might be called a living triple linkage between the Devi, the Sri
Chakra and the devotee, reflected in the Names Mahamantra, Mahatantra
and Mahayantra.
Again when go beyond the word to the realm of numbers and mathematics
we seem to be entering a new realm of symbol and meaning. Arithmetic
lets us express quantities from the very small to the very large. The number
5 by itself tells us nothing. We have a little more meaning when we say 5
apples but the meaning becomes complete when we say I have 5 apples
So is the case with Geometry that lets us relate to tangible size and shape.
But when we go to Algebra, we go into the realm of the intangible where
the symbol x may be any anything or any quantity; where the equation
y = f(x) may express any computation applied to the value x that would give
us the resulting value y; or where the equation e = mc2 expresses a
profound working principle of the cosmos that relates mass to energy. To
the stranger in mathematics, all this is babble, but to ear of the
mathematician it music, while for the scientist, this is the realm of truth, of
true meaning.
Next let us . proceed to realms that are even more intangible. Let us take
the sound modulations prescribed for recitation of Mantras or the musical
rendering of the Sama Veda Mantras, which are credited with being
vehicles of power extending beyond literal meaning. What then could the
content and intent be in the Mantra and what is the meaning that its sounds
are really communicating ? When we go beyond the word, to the realm of
music, of pure sound, we clearly experience specific auditory impacts,
beginning say, from the deep sonorous monotone chanting of AUM and
going on to the three tonal levels of chanting of the Sama Veda. Yet, are
we here in another word-neutral realm of communication operating through
a language and alphabet of a different genre ? It should be even more
interesting to the reader to shift attention from the word content of the
Vedas to more or less contemporaneous texts that addressed the nonlanguage communication media of song and dance.
Pride of place in this regard belongs to the Natya Shastra of Bharata Muni
from whom the ancient Indian tradition of Music and Dance is traced, and
who is placed in time between 200 BC and 200 AD. His work in turn is said
to come from an older tradition, of what is referred to as the Gandharva
Veda, said to have been provided by Brahma as an annexure to the Sama
Veda, and said to contain 36000 slokas and described as the Fifth Veda,
and that was meant for the lay, rather than the learned. The story goes
that enchanted by Bharata Munis first play, iva himself, the lord of the
Cosmic dance, sent his disciple Tandu to teach Bharata the authentic
principles of dance, which Bharata included in the chapter Tandava
Lakshana of his work, the Natya Shastra. Bharata Muni evolved ten basic
postures of the body, nine of the neck, thirty-six of the hand, and thirteen
poses of the headpostures that required the disciplined use of the entire
body and all of its potential for expression. Various schools of dance have
elaborated on these principal postures, each of which blossoms into an
exactingly coordinated repertoire of associated hand, facial, eye, foot, and
total body movements synchronized to the rhythm of intricate instrumental
and vocal music to communicate a telling story.
The Natya Shastra has a text of 6000 slokas and treats of all the arts of
dance, drama and music in astonishing technical detail. There is
considerable attention to the communication of meaning through every
possible mode of expression. These involve concepts of bhava and rasa
which give colour and impact to the communication. There is here a whole
world of communication of meaning through not only sound and word, but
of thought, action and feeling through bodily movements, poses, gestures,
and facial expressions. These are physical expressions laden with
overlays of bhava and rasa, form and essence, colour and taste to enrich
the communication. When one considers these different representations of
thought, action and feeling, one begins to see the significance of the Vedic
constructs of the Mantra, Tantra and Yantra as vehicles of great power
Bharata established the Shadja, as the first defining note of the musical
scale, where Shadja means six, that refers to its giving birth to the
remaining six notes together with which it forms the octave, and makes the
Grama or basic scale of music. Could these seven notes be indeed a
reference to the meeting together of the seven noisy birds in the Rig
Veda (X-71-3) Bharatas formulations provide the foundations for Indian
classical music system of today, though of course, the intervening
centuries since then have seen a great deal of sophistication and
development. The chief innovation of course, is a shift from the Grama
where the Shadja has a fixed absolute frequency level, to the Raga where
the Shadja can be fixed at any level that suited the singer. Music could
then be set in a variety of octaves of different frequencies, making for the
same musical patterns and impacts by different musicians with different
2
kha
Tha
pha
ra
3
ga
Da
ba
la
4
5
6
7
8 9
0
gha ~ma cha Cha ja jha ~na
Dha Na ta tha da dha na
bha ma
va
Sa sha sa ha
For example, Harikambhoji raga starts with syllables Ha and ri, which have
numbers 8 and 2 associated with them. Reversing them we get 28. Hence
Harikambhoji is the 28th Melakarta raga.
When we come to the medium of dance, we find the Mudra or a dance pose
is a physical action frozen in time, that expresses an object or an activity or
a quality, that replaces a whole string of words with as much if not
greater impact than the word itself, indeed side-stepping the need for the
word altogether. Consider the following sample examples of Mudras and
the meanings they communicate, of the Bharata Natya dance form, as
prescribed in the Natya Sastra.
Tripatka (Tree-pah-tah-ka)
on forehead : putting
on a crown
Utpalapadma
prohibiting something
Katakam ( Bangle)
Kartharee Mukham
(Scissor's sharp point)
Sukathundam
(Parrot's peek)
. Ardhachandram
(Half moon)
If these five letters were considered and articulated separately, they would
be mere sounds carrying no meaning. But put the letters together and you
get the word APPLE, which when articulated conveys the following
image in your mind of the word and the object it represents :
small element that has apparently has no meaning but does have a
potential to grow into wider meaning and finally complete meaning.
Now let us make a quantum jump to another level of abstraction : The
above sentence, if represented in braille, looks like this :
J!MJLF!UP!FBU!BO!BQQMF!
J!MJLF!UP!FBU!BO!BQQMF!
I
L I K E TO EA T AN A PPLE
What you now have in the braille alphabet is a single dot that generates all
three levels of communication with corresponding meanings, the letter, the
word and the sentence. So obviously a dot too has the same potential as a
letter to communicate meaning. Suppose we take this line of argument
beyond the dot, to its minute limits, namely, the point, with its geometric
definition as a circle with a diameter of zero. We then refer to this point, for
want of a better word, by the word nothing or the word zero. But its
potential still remains. We may then conceive of a minute germ of sound
bearing a minute germ of meaning with the potential to develop
progressively into the larger forms of speech and thought expressed as
words and sentences. Did not we not have modern physics tell us of a
similar point of existence, the electron, that marks that origin where
matter disappears, but remains as energy, with a potential for aggregation
into more matter or more energy in newer forms with added meaning.
Modern epistemology which deals with the sources of knowledge and
modern semiotics which deals with signs or symbols, look at thought,
word or meaning developing in this way, but this is precisely the way of
thinking of the Indian ancients. These were remarkable methodologies of
men like Yaska and Panini, Patanjali and Bhatrhari who were at once
Linguists, Grammarians and Philosophers all rolled into one. These were
disciplines, never assigned a separate and unique identity as in modern
times, and though their contexts were broadly recognized by the
Vyakaranikas or Grammarians and the Darshanikas, or Philosophers, they
were always inter-meshed into a common over-arching visualization of one
ultiimate truth.
----------------------------------------------------------------
The European scientific revolution would not have spread as wide and fast
as it did, if mathematicians like Euler had not translated Newtons
cumbersome Latin, and obsolete Euclidian methods and unwieldy
formalizations into simple algebraic equations that everybody could learn
to understand.. The spectacular results of the so-called exact sciences are
largely due to mathematization. The adoption of an artificial language for
the expression of a fundamental truth, set out in a mathematical equation,
is not just an abbreviation of what may be expressed through a natural
language; it possesses a structure that may be called linguistic or syntactic
but is totally different from the syntactic structure of natural language. It
preserves the mathematical property that Chomsky called discrete
infinity and still rests on sentences that must be true or false. But it does
not consist of a subject and predicate .It lacks gender, mood, aspect or
tense and does not refer to "I" or "you." And yet, this grammar of artificial
languages developed from the syntax of the natural, incorporating other
symbolic systems such as expressions for numbers. The functional
expression f(x), for example, may in some simple cases be interpreted as
"x is f", which may in turn be read as a subject-predicate sentence.
The formal languages of mathematics have replaced natural language in all
the so-called exact sciences, and is now spreading to embrace the human
sciences, including linguistics. Although Chomsky seems to have gone
further in deriving the formal properties of natural language from abstract
principles than anyone else so far, there is a prehistory to it, In the
European tradition, in the formalization of natural language, starting from
Aristotle. An interesting anticipation of Chomsky dates back to 1660 when
two British grammarians, Arnauld and Lancelot, stated : this
marvellous invention of composing out of 25 or 30 sounds that infinite
variety of expressions, which, whilst having in themselves, no likeness to
what is in our mind, allow to disclose to others its whole secret, and to
make known to those who cannot penetrate it, all that we imagine and all
the stirrings of our soul
But Staal now takes us back 25 centuries to have a close look at the
corresponding explorations of the internal world of the human mind in
India, and how these led human language to a level of perfection in the
Sanskrit language. (Incidentally, the word Sanskrit itself means done to
perfection) The level of sophistication reached by then was such that it
needed a whole battery of sciences, the Vedangas, to explain, describe
and preserve the language of the Vedas. The level of sophistication
reached by the worlds first grammar of Panini, can be readily recognized
by one of its verses ( Panini 3.3.161 ) which lists the different forms that the
that a verb in the optative mood could take so many shades of meaning,
as illustrated by Staal in the examples below : (The optative means
injunction, invitation, permission, respectful command, deliberation, or
request).
The great contribution of Panini was to derive from the language corpus of
the Sanskrit of his time, virtually a meta language comprised of nearly 4000
Sutras in much the same way as Backus-Naur form has done for the
natural languages of today, paving the way to put hem to use on
computers. One may hearken back at this point to the examples given in
Chapter 6 of Paninis rules in encoded form for the constructions of
syllables, words and sentences. It would be of special interest to the reader
today to know that Paninis Ashtadhyayi is today available as a fine
Computer Software package, called the Ganakashtadhyayi developed Dr.
Shivamurthy Swamiji, a remarkable modern scholar who is also the
religious head of the Taralabalu Brihannmutt, Sirigere, Karnataka. (The
package is available as a free download on the Internet
at
www.taralabalu.org) While Paninis objective was primarily to establish a
strong and permanent foundation for the understanding and preservation
of the Vedic corpus of Knowledge, his work was recognized by Chomsky
as clearly providing a framework of principles from which any language,
Natural or Artificial, could be derived. Here then, was a unique example of a
work of the oldest grammarian of the world that was held in in the greatest
awe and admiration by the greatest linguist of the modern times !
--------------------------------------------------------------
The Indian ancients referred to Truth and Reality by a single word, Sat or
Satya. The Western tradition seems to prefer use of the word Truth to
Reality as more appropriate to the context of Science which was the focus
of their concerns. It is possible that in contradistinction, the Indian
approach may have considered Reality as better referring to their concerns
over Knowledge, in respect of which their approach had a wider sweep.
Their perspectives addressed Knowledge in terms of an over-arching
Existence that presented mans inner and outer world as an indivisible
continuum of a Reality that was Infinite and Eternal, and that the best that
man could do to understand this Reality was only through finite bits of this
Reality symbolized by the word. The early scholars started looking at the
word of the Veda as something that originated from the intuitive,
perceptive mind of the Seer. The word became a vehicle of meaning, that
lent itself to articulation in speech, to enable a sharing of all that it was
intended to convey. The mind then, clearly bore the faculty, that could just
with a thought, initiate the chain of inner events that culminated in the
spoken word.
The ancient scholars reflected deep on these inner
sequences and considered the pure sound emerging in the shape of
Sabda, the Word, from One Ultimate Reality called the Sabda Brahman.
The Sabda carried the creative energy to shape an intent or meaning into a
word and transfer its energy to the vocal chords and cause the word to be
articulated. The meaning could come from a recall of an earlier experience
stored in their original words, or a new thought or a new experience or
meaning, and clothe it in one of the older words, creating new meanings for
the same word, or create a new words derived from the old words or create
new words altogether.
Here then was a panorama that unfolded in the awesome reaches of the
minds of the ancient Rishis, which they reduced to the concept of the One
that becomes the Many, which the ancient Rishis reduced to one word
AUM, and Uddalaka Aruni put into the three words of the Great Saying,
the Mahavakya, Tat Tvam Asi. If words are meant to convey meaning,
there could clearly be no higher meaning than Reality. Through the ages,
man has engaged relentlessly in the search for Reality, and the Indian
ancients came as close to it as words would permit, yet at a point, they
were quick to add that words were not adequate to state or describe it.
tvms tkkEtaEn it
things that your mind makes you out to be, shaped by memories and
hopes, but one real thing that is in the present you are always are in, not
the unreal things of the past or the future, that are creatures of the mind.
Sound as the first manifestation of the Divine and its proliferation into
innumerable words, philosophically stated as the One becoming the Many,
becomes the central concern of the Philosophy of Language. Here then is a
vast spectrum of existence in sound, stretching all the way from the Eternal
to the Transient, and the Infinite to the Finite, that has been bridged and
brought into our consciousness and understanding and sensory reach,
and expressed by the word to express every experience of our external and
internal world. It thus became possible for the highest of human
experiences of the ancient Rishis to be set down in the Vedas in words that
they ascribed to the Divine, and for a succession of scholars to elaborate
and explain the esoteric meaning of words of the Vedas in the simpler
words of the Vedangas, that could be understood by and provide guidance
to men of lesser spiritual, intellectual or mental endowments.
Elaboration and explanation is by no means easy and required incisive
investigation and effort by minds gifted with deep insight and analytical
skills of the awesome calibre of scholars like Yaska, Panini and Patanjali. It
meant tracing the origin and course of words as they emerge from the
thought and throat of man, how they acquire their structure of language
and accomplish their
purpose of communication of meaning and
Knowledge. These great pioneers laid the foundations for every shade of
linguistic discipline, of Phonology, Phonetics, Etymology, Syntax and
Semantics, and built a vast super structure of the science of Linguistics
that embraced and articulated every shade of experience ranging from the
simplest physical facts to the highest philosophical truths.
One of the many consequences of this proliferation, driven by analytical
methods of astonishing acumen, was the classical schism between the
Darshanikas and Vaiyakaranikas, the philosophers and the grammarians,
who sought exclusive jurisdictions in their areas of thought, but
nevertheless had inevitably to borrow concepts from each other, clearly
because areas of thought could not easily be demarcated to serve any
claims of exclusivity. Even today, the philosopher at one end of the
spectrum, insists that the ultimate Reality is beyond words, while the
grammarian at the other end, insists that the Word itself is the Reality,
leaving us to wonder what they mean by what they say.
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Title:
THE VEDANGAS
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Creation Date:
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