ELUSIVE 33 ODD AND 48
EVEN NUMBER ENDINGS IN CHAMAKAM
(COMPILATION
FOR A DISCOURSE BY N. R. SRINIVASAN, BRENTWOOD,
USA, APRIL 2014)
Vedas
mention of “Ritagam Satyam Parabrahma” meaning
universal orderliness (rita) and Truth (Satyam) are Parabrahma (Paramaatman or
Supreme Principle). Chamakam found in
Srirudram of Rigveda presents a grand vision of Universal and Eternal orderliness
which is maintained by all the Vedic Gods indicated somewhat by what we call in
arithmetic as Progression in Chamakam. Human
being’s duty is to observe and reflect that kind of orderliness in his or her own life. Closely related to and mostly identical with rita was Satyam (Truth). Satyam was
declared as Sun (soorya or Savitar) in early upanishadic thoughts whose very nature
is this Satya. Satya in later period got mixed up with rita as creation progressed and was identified not only with
Brahman (Supreme Principle) also called Paramaatman but also with the person of
body-mind-complex referred as Jeevaatman or individual Self. It is therefore no
wonder that even and odd numbers are presented to us as Mantras (Vedic text or
hymn) in strange orderly fashion with no explanation abounding in mystery of
life and its yearning for liberation.
This order also ended abruptly with 33 in odd series and 48 in steps of
four in the even series. Mystery contained in this limited orderliness is
speculative with the only restriction being it is meditation oriented on
Supreme Principle.
We
find references to numbers ranging from Soonya (0) to Infinity all over in our
Srutis (Vedas and Upanishads) and Puranaas. Brahman is described as anoraneeyan mahato maheeyaan—smaller than the smallest
and larger than the largest and Brahman is ever full or poornam. Poornam is identified as Soonya also. Our rishis (Vedic sages) had very sound
knowledge of mathematics which has been at length described in the discourse
“Early and Medieval Hindus Contribution to Science and Technology” (Hindu
Reflections-September 2011). Vedic altar is geom.
etrical.
So is Srichakra. Srichakra is divine. It
defies all attempts to reach the divine center Bindu to construct a figure of
two dimensions as well as pyramidal three dimensions accurately with present
day knowledge of mathematics and computers because of the transcendental Pi, a
transcendental number of unending decimals about which our Rishis too had
knowledge. It mixes mathematics with transcendent and mysticism. Chamakam
further indicates how these numbers could be arranged in some sort of
sequential order as well as used to reflect divine thoughts. We have in the past discussed about these in
the discourses “What do Even and Odd Numbers in Chamakam signify” (Hindu
Reflections--January 2012) and “Visualizing Divinity in Numbers” (Hindu
Reflections--September 2012). Chamakam mentions of paying obeisance to numbers
in odd series starting with 1 and ending abruptly with 33. It also mentions of
even numbers in steps of four starting with 4 and ending with 48 for that
purpose. This abounds in divine mystery which may have several explanations. Here
are some new reflections on the subject based on my thoughts of Sanskrit
letters as divine.
Why
should the normal and regular odd series in Chamakam end abruptly with 33? Why
should the even numbers start with 4 and end abruptly end with 48? Why not have
the regular series of even numbers of 2, 4, 6….etc., and not 4, 8, 12 etc., in the even series in the same mantra since
odd series started withone ? The sole purpose of Chamakam is intended for
intense meditation which is clear if we
go through the message conveyed in the last Anuvaka (segment) of Chamakam, the
text and meaning of which can be found
in the Appendix below. Evidently Rishi
of this Chamakam wants to say to us that these two odd and even series are divine
influenced by the reference to 0, 1, 3, 4, 48, 50 in Vedas.
One
of the most interesting as well as intriguing aspect of Hindu thinking is
divinity of numbers and letters. 0 or 1
(Purusha) represents Brahman as revealed in Vedas. It also says that ONE is
Brahman—Tadekam: Tad Brahma. Bhagavadgita says Aksharaanaam Akaarosmi–among alphabet I am the first vowel a.
Bhagavdgeeetaa is a compendium of
Upanishads and its opinion is as good as Upanishads. This akshara is Sanskrit alphabet only as the language of Vedas and Geeta
is Sanskrit and not any other language.
Sanskrit
language begins with short vowel a and
ends with the aspirant ha. There are 33 consonants and 13 vowels and two
sounds known as anuswara (period over
letter) and Visarga (:) in Sanskrit
Grammar making it 48. According to
Srividya and Brahmachakra of Svetavatara Upanishad Sanskrit alphabet of 48 or
50 represents the entire Universe or Ksehtra while Brahman is Kshetrajna which
view is also expressed in Bhagavadgeetaa. According to Srividya a represents Siva and ha represents Sakti as well as Purusha
and Prakriti. (Please refer to my discourse on Sanskrit as divine language).
The first letter a and the last
letter ha with the unmodified m (Ardha
Chandra Bimbam or half-moon nasal sound as in Om) constitutes aham (ahamta). im+a=ma in Sanskrit language as
consonants need the help of vowel to have their existence as consonant to get
the full sound with closed lips. Brahman is often referred as Aham in Vedas. The Universe bound by the dimension of its un-manifest
origin, Siva or Purusha on one hand, and
by the dimensions of its manifest passing out and absorption, Sakti or Prakriti
on the other hand are illustrated by scriptures
by the letters of the alphabet beginning with short vowel a
and ending with consonant ha.
Chamakam’s
ending with the number 48 can be identified with the
48 letters in the Sanskrit language. Both Srichakra and Brahmachakra mention
the same. The 50 spokes of Brahma chakra
are 50 letters of scriptural Sanskrit which adds cerebral la and the conjunct sound ksha. Srividya calls Sanskrit letters as Maatrikas
or Mother Nature making them divine.
33
are the consonants which need the support of vowels. 33 are the divine guards
of Brahman or Vedic deities—12 Adityas, 11 Rudras, 8 Vasus, Indra and with
Supreme Principle as the overlord. The consonants themselves are impossible
meaningfully vocalize without the help of vowels. The vowels are said to
provide power (sakti) to the consonants, which are in the nature of Beeja or
seed. That is why Chamakam ends in 33.
In the odd series 1 siginfies beginning of Rudras and 11
the end of Rudras ; adding 12 to
this 11 it is 23 which shows the end of
12 Aadityas; adding eight to this becomes 31 which shows the end of Vasus; adding Indra and Prajapati this becomes 33
the end of the series. So the odd series is complete for its ending.
The
vowels can be considered as 17 if we add to thirteen 3 sounds Anuswara,
Visraga, half nasal and long vowel lrr.,
which is also included along with lr (r., rr.. lr., lrr.), often.
We
can mathematically create a table of orderliness arbitrarily linking 33 with 17
as follows:
Odd Number
arrangement corresponding Square root
(1) (2) (3) (4)
0+0=0 0
1+ 0=1 1
3+ 1= 4 2
5+ 4= 9 3
7+ 9= 16 4
9+ 16=25 5
11+ 25=36 6
13+ 36=49 7
15+ 49=64 8
17+ 64=81 9
19+81=100 10
21+100=0121 11
23+121=144 12
25+144=169 13
27+169=196 14
29+196=225 15
31+225=256 16
33+256=0289 17
We
may add 0 before all these numbers without changing value. It then signifies the pervading Brahman
without actual involvement and as silent observer.
If
we add to first number in any column the
second number in the previous column we get a sum total in 3rd column
whose square root is in the 4thn column. This series could be taken to in 33
and 17 for our limited purpose.
The
first row of all zero represents Brahman.
Applying our knowledge of elementary arithmetic we could
possibly find an explanation as to why 0 is Brahman. Poornam represents Nirguna
(un-manifested) Brahman which is also represented as zero. Please recall the
famous Vedic mantra: “Poornamadah
poornamidam poornaat poornamad-uchyate poornasya poornamaadaaya poornameva
avashishyate—(Br. Up. 5.1). 0 in mathematics is indispensable and controls
the world of mathematics and computers. Nirguna Brahman is indispensable and is
inner controller of all beings. This mantra goes well with the mathematical
concept of zero for e.g., If we remove 0 from 0 what remains is also 0 etc.,
There is the other spiritual meaning: That which lies beyond is Plenum, (full
and undiminished). That which appears as this here (i.e., as the universal) is
also Plenum, equally full and undiminished. Out of Plenum, Plenum arises.
Plenum having been taken away out of Plenum, what remains is still the same
(undiminished) Plenum.
We
stopped the above table at 33 to
represent 33 deities which can be related to 17 representing Jeevatama, A b body-life-mind complex of
seventeen entities (five Praanas (vital forces) + five organs of action +five sense organs + mind +
Intellect).
Third
mundaka Of Mundakopanishad describes Jeeva and Iswara (the Supreme Soul) as two
birds perching on the same tree (the human body). While the former is eating
the sweet and bitter fruits of the tree, the latter is sitting majestically
looking at the other bird, itself not
eating any fruit that bringing associate ship
between the two birds.
Column
one has its free existence as divinity. All the thirty three deities are
Vyahritis of Brahman. The last column 4 of body-mind- complex is dependent or
generated out of column 1. Body-mind-complex or Jeevaatman is dependent on
Brahman. That calls for the table to be in odd series of 1 to 33. But
in order to link with column four it ends up as an odd series or as part for
the whole not referring to all the thirty three Vedic deities.
Numbers
in column 1 shows the Paramaatman represented by its Vyahritis.
Jeevaatman is the spark of Paramaatman clouded by Maaya (ignorance). Therefore
Chamakam conveys the message to Jeevaatman to meditate upon Paramaatman for its
Sreyas (Eternal Bliss) towards Liberation called Moksha in this prayer which
can also be done through the 33 vyahritis of Brahman. That is what this
mystical table reveals. It also shows how Jeevatman in the last column can
attain divinity meditating on deities like Rudra, Aaditya in the first column
and ultimately reach Brahman. This can be direct meditation or circuitous route
of worship. To lay man it means turn
inwards and meditate on Self.
There
is yet another interesting explanation. By some divine purpose Lalita Sahasra-naamam
out of the 50 letters of the Sanskrit alphabet has selected only 32 letters leaving
the rest to address Lalita by different names. Unlike Vishnu Sahasranaama
Lalita Sahasranaama does not repeat any name. Among the vowels only the first five, ae, o
and am (8) are only
selected. So it does not follow any
order in selecting the first letter of the names. Saktaas explain this as, 32
letters selected here only represent Maatrikaa or the letter of divinities. These
letters are for the devotees to approach Paraasakti. The letters that are
omitted are regarded as harmful in Nrisimha Paribhaasha. The 32 numbers are then the divinities like
Vedic deities. These 32 letters include the last consonant ha which is always surmounted by half-moon period as in Om. That makes the count as 33. Sanskrit language has 50 letters with the
addition of ksha and hard la. That leaves behind 17 (50 – 33=17) signifying
non divine numbers of Jeevatma (five motor organ + five sense organs + five
vital forces + mind + intellect). Hence it is reasonable to assume that
Jeevaatman of 17 numbers needs to meditate on 33 divinities as per the directions
of Chamakam.
Let
us now turn our thoughts on even numbers prayed upon in Chamakam. This series
begins with 4 and ends with 48 with steps of four in the Arithmetic series of
Even numbers. This needs a little bit
deeper understanding of Upanishads. Upanishads include Vishnu Gaaytree Mantra
as follows: “Naaraayanaaya vidmahe,
vaasudeevaaya dheemahi tannoe vishnuh prachoedayaat”. Let us know
Naaraayana. For that may we meditate on Vaasudeva! May Lord Vishnu invigorate us
towards the same! ”Svetaavataara Upanishad says Naaraayana is Paramaatman or
Supreme Being which has been adopted by the followers of Vishishtaadwaita of
Ramanuja and Dwaita of Madhva. Among the eulogized in Rig veda, Vishnu is
prominent one and is popular to-day amongst Vishitaadvaita, Dvaita, Gaudiya,
Smaarta, Bhaagavata and other Traditions of Hinduism. Some of these are
referred as cult by many Hindu authors as well as Westerners. The Vishnu of
Rigveda is celebrated for his three feet encompassing the entire Universe for
the welfare of worlds. Exposition of the
four aspects of Vishnu known as Vyoohas, results in twenty-four forms of Vishnu
popular worship in which some avatars
are included. All these are even numbers
multiples of four dominating. The order of four (4) weapons (conch, discus,
mace and lotus) held in 4 hands of Vishnu varies giving rise to twenty-four
(24) forms in modern iconography employed in Moorti Upaasana. The
identification of parts of the devotee’s body with the names of Vishnu results
in twelve forms (dwaadasa Moortis in standing stance seen in modern
iconography.
Paancharaatra
texts declare that four Vyoohas are in fact four aspects of the same god-head.
These are four emanatory forms in the context of creation—Vaasudeva, Sankarshana,
Pradyumna and Aniruddha. These names are celebrated as heroes in
Bhaagavata. Four hands of Vishnu
represent Srishti (emergence, Sthiti (maintenance), Samhaara (dissolution) and
Mukti (emancipation). These four forms are also ritualistically named as
Paramahamsa (Purusha or manifest), Vyoema (Satya or Truth), Naada (Achyuta) and
Hamsa (Naaraayana). They are also said to represent the four great time
intervals (Yugas)—Krita, Treta, Dvaapara and Kali. (Please also refer to my
discourse on Exposition of Vishnu).
According
to Paancharatra doctrine each of the four vyoohas (primary emanatory forms of
Vishnu) bring forth three other forms called Vyoohantakas. 1) From Vaasudeva
emanate Kesava, Naaraayana and Maadhava; 2) from Sankarshana emanate Govinda
Vishnu and Madhusoodana; 3) from Pradyumna emanate Trivikrama, Vaamana and
Sreedhara; 4) from Aniruddha emanate Hrisheekesa, Padmanaabha and Daamoedara.
These secondary emanations are known as Dvaadasamoortee (12 images). From these
twelve secondary emanations arise eight other forms which are but further
manifestations of the four primary Vyoohas. These are: Purushoettama,
Adhoekshaja; Naarasimha; Achyuta, Janaardhana, Upendra, Hari and Krishna. Thus
the four primary Vyooha forms, the twelve Moortyaantara forms and the eight
further emanatory forms together constitute twenty four (24) forms known as
Chaturvimsati moorti (24 images form). Gaayatri Saara Sangraha identifies the
twenty-four syllable/letters of the Gaayatree mantra with the 24 deities mentioned
above as presiding deities over the letters (Abhimaana Devata) and 24 names of
Vishnu. While performing the daily ritual of Sandhyaavandana it is sometimes customary
to recite these twenty four names of Vishnu and consecrate the twenty-four (24)
parts of our body. The same is arranged in a tabular form below for easy
reference:
Gayatri Letter
|
Abhimaani Devata
|
Name of Vishnu
|
Ta
|
Agni
|
Kesava
|
tsa
|
Prajapati
|
Narayana
|
vi
|
Soma
|
Maadhava
|
tu
|
Eesana
|
Govinda
|
rva
|
Savitr
|
Vishnu
|
re
|
Brihaspati
|
Madhusoodana
|
ni
|
Paitr-deva
|
Trivikrama
|
yam
|
Bhaga
|
Vaamana
|
bha
|
Aaryama
|
Sreedhara
|
rgoe
|
Savitr
|
Hrisheekesa
|
dey
|
Tvashtr
|
Padmanaabha
|
va
|
Pushan
|
Daamoedara
|
sya
|
Indra
|
Sankarshana
|
dhee
|
Agni
|
Vaasudeva
|
ma
|
Vaayu
|
Pradyumna
|
hi
|
mitra-varuna
|
Aniruddha
|
dhi
|
Bhavatri
deva
|
Purushoettama
|
yoe
|
Vasudeva
|
Narasimha
|
yoe
|
Vishnu
|
Adhoekshaja
|
naha
|
Vaasava
|
Achyuta
|
pra
|
Tushtaba
|
Janaardhana
|
choe
|
Kubera
|
Upendra
|
da
|
Dasra
|
Hari
|
yat
|
Brahma
|
Sri
Krishna
|
[Gayatree-tantra insists that each
letter should be contemplated upon: “Varnaanaam
chintanam dhyaanam samyak paapapranaasanam- meditation on Gaayatree letters
is the complete path for eradicating sins]
In
Vishnu Sahasranaaama of Bheeshma, which is the pioneer of all Sahasranamaavalis,
he addresses Vishnu with lot of epithets which
all include four things as in the sloka:
“Chatutmoortih
chaturbahuh chaturvyoohah chaturgatih | Chaturaatmaa chatubhaavah chaturvedah
videkapaat ||”
·
Chatur moortih: The
Infinite is considered as having four forms—Viraat, Hiranyagarbha, Easwara and
Paramaatman. Puraanas mention about
different colors of the incarnations in different Yugas—White in Kritayuga; Red
in Tretaayuga; Yellow in Dvaaparayuga and Black in Kaliyuga. Incidentally these
are the colors found on the image of Lord Jagannath. In Vedanta Lord has four
expressions in the subjective life of each individual; the Waker (Viswa), the
Dreamer (Taijasa), the Deep-sleeper
(Praajna) and the Pure Self (Tureeya)
·
Chaturvyoohah—Pancharaatra
Aagama describes these as Vaasudeva, Sankarshana, Pradyumna and Aniruddha. They
are celebrated Heroes in Mahabharata. Aitreya Upanishad describes four types of
Purusha—Saareera Puusha (the person in the body); Chhandas purusha (the person
of Vedic meters of Mantras); Veda Purusha (the person in the Vedas) and Mahaa
Purusha (the Great Person)
·
Chaturgatih:
4 pursuits of man, Braahmana (Person with spiritual goal); Kshatriya (Warrior
pursuit to preserve Dharma); Vaisya (Commercial pursuit to distribute wealth in
Dhaarmic way); and Soodra (Manual work pursuit to serve the dharmic society
physically) or four Varnas. The Lord is also the consummate of four walks of
life—Celibacy (Brahmacharya); House holder (Grihasta); Retirement (Vaanaprstha)
and Renunciation (Sanyaasa).
·
Chaturaatma:
One who expresses himself as four inner aspects (antahkarana) in all of us.
·
Chaturbhaavah:
One who is the source of following four human aspirations—Dharma
(Righteousness); Artha (Wealth); Kaama
(Pleasure) and Moksha (Liberation). [Note
Dharma leads the rest.]
·
Chaturvedah;
one who is the author of four Vedas—Rigveda; Yajurveda; Saamaveda; and
Athrvaveda
Gaayatree
Mantra has 24 syllables/letters and is the most celebrated meter in Vedas. It
has 24 Abhimaana Devatas (sought after deities and is represented by 24 forms
of Vishnu as in the chart above. As per Vedic injunctions a spiritual speaker
must meditate upon 24 names of Vishnu with the help of 24 letters of Gayatree.
That constitutes 48 inputs or means for effective meditation. Perhaps that is
why Chamakam ends with the number 48.
You also see how all the things explained above as powerful tools for
meditation are 4 and its multiples only. That is why Chamakam’s exposition of
Mantras is in numbers of 4 and its multiples and not any other even arithmetic
series.
You
will also see Rita or orderliness in many creations of Supreme Principle.
Supreme principle is meditated upon as Samvatsara (year) in Mantrapushapa (Samvatsaroevaa apaam pushpam), meaning
He is Kaalapurusha or embodiment of Time. There are 12 months in a year which
is 4 Chaturmaasaa (4x3=12). There are 24 fortnights (pakshas) in a year like 24
letters in Gaayatree. There are 4
quarters; 8 directions; 8 Vasus; 8 Direction deities (Ashta-dikpalakas);
Ashtaksharee mantra (Om Namoh Naaraayanaaya) of 8 letters; Dwaadasaaksharee (12
letters) Mantra (Om namoh bhagavate Vaasudevaaya); Shoedashaaksharee (16
letters) Mantra of (Hare Rama Hare Krishna). Each one of these is directed
towards the base figure of 4 mentioned in Vishnu Sahasranaama. Vishnu is identified
as Naarayana who is the Paramaatman (Supreme Principle) mentioned in
Svetaavataara Upanishad.
An orthodox Brahmin wears 12 naamams
(Srivaishnava religious mark on twelve parts of the body using the Mantra; 1. Om Kesavaaya Namah; 2. Om Naaraayanaaya
Namah; 3. Om Maadhvaaya Namah; 4. Om Goevindaaya Namah; 5. Om Vishnave Namah;
6. Om madhsoodanaaya Namah; 7. Om Trivikramaaya Namah; 8.Om Vaamanaaya Namah;
9. Om Sreedharaaya Namah; 10. Om Hrisheekesaaya Namah; 11. Om Padmanaabhaaya
Namah; 12. Om Daamoedaraaya Namah. Orthodox
Saivites also wear Vibhooti on 12
parts of the body daily. You may ask here why Vishnu in instead of Brahman. Vishnu
is one of the aspects among the three aspects of Brahman. In Vedas we have
another example Praana which is a group name as well as praana appearing as a
constituent of Pancha Praanaas or Life’s Vital Forces about which we have
talked about a lot. This is the Vedic way of description like part for the
whole in Grammar. So Vishnu is Brahmanso also Rudra—Tvam rudrastvam, vishnustvam—Brahman
is Vishnu; Brahman is Rudra (MNU)
In
Daily worship we use the Japa containing 12 names whatever may be our
tradition, Saiva, Vaishnava, Sakta or Smaarta. These are Kesava, Narayana,
Govinda, Madhava, Vishnu, Madhusoodana, Trivikrama, Vamana, Sridhara, Hrisheekesa and
damodara. Let us consider Kesava as
poornum or Plenum in the context of Vedic Mantra. The first mantra Kesava is
then 4 =4; the second Mantra becomes more powerful with the support of first
mantra; 4+4=8 where Plenum enlarges but still remains Plenum, again with no
perceptible change. So the series
continues till the 12th mantra assumes the power of 48, 4x12=48 and
still with no perceptible change. Still the Plenum remains Plenum though enlarged
48 times. The basic figure 4 represents the basic principle; Vaasudeva, Sankarshana;
Aniruddha; Pradyumna form which all other 12 names draw power increasingly.
This series and the power associated with the names could continue to infinity.
The above assumption also fits in well with
the famous Shanti Mantra: Poornamadah
poornamidam poornaat poornamduchyate | Poornasya poornamaadaya poornameva
avasishyate ||--that which lies beyond is Plenum (full and undiminished).
That which appears as this here (i.e. as the universal) is also Plenum, equally
full and undiminished. Out from Plenum, Plenum arises. Plenum having been taken
away out of Plenum, what remains is still the same (undiminished) Plenum. Brih.
Up. 5-1). So It is all Brahmamayam. Here
the Chamakam stops with 48 to focus our thoughts on Brahmachakra or Srichakra
which is a Kshetra(field ) for 48 divine letters in a mandala or circular form
whose Kshetrajna (or master)is Brahman. A circle is again Poornam with its cycle of
srishthi (creation), sthiti (sustenance) and laaya repeatedly also represented by AUM. The preference
to 4 and its multiple is amply explained above which cannot be justified by 2,
4, 6, 8 or any other even series.
Also
we know there was no such thing as Vaishnavism or Saivism in the Vedic period.
In the worship of Panchanana, five faced Siva in present day practice, he is
meditated upon as Panchabrahman with Panchabrahma mantras which contain the
five names of Panchanana popular with Saivites. The same
mantras are also addressed to Narasimha with the same epithets of Panchaanana
contained in Vedic mantras. This has been explained in previous discourse
“Mantras from Mahaanaaraayana Upanishad”.
Rudram and Chamakam only refer to Brahman. With sectarian doctrine these
are used in worship for Siva only. So the above contention of Chamakam numbers
are directed towards meditation on supreme Principle is no exaggeration. It was
all one universal prayer to that One Supreme Principle (tadekam); the Chamakam prayers are secret Mantras with hidden
secret of these odd and even numbers which is the Vedic way which leave mantras
to be expounded with the help of learned Gurus. The justification of 4 series
referring to Vishnu manifestation for Rudra Chamakam should not confuse or give
rise to conflicts. Rudra means rutaat
trayate iti, one who protects you from all miseries and that Vishnu means vyapyate iti vishnush, one who pervade
all entities sentient and non- sentient, both Rudra and Vishnu being the
aspects of Brahman in the role of srishthi, sthiti and laya.
Let
us summarize our thoughts on the meditation of odd numbers of 33 in a regular
odd series and even numbers 48 in a series starting with 4 and in steps of 4.
We are justified in our meditation on 33 as thirty three Vedic deities who are
all Vyahrities or emanations of Brahman and in Puranic terms subordinates of
Brahman which the body mind complex has to focus in meditation by turning
inwrads. 48 is substantiated by our Varnamala named after Japamala by which
term Sanskrit language is often referred to. I have explained elsewhere how
Hindu Japamala containing 54 beads represents full compliments of Sanskrit
letters as visualized by Swami Dayananda Saraswati unlike Grammar which is
content with 48 letters.
The
divine 33 consonants of Sanskrit Grammar represent 33 subordinates of Brahman
or Vedic Gods or 33 Matrikas. They need to be meditated upon as seen in our
practice of normal worship and rituals with Veda Mantras. Hindus always consider odd numbers 1, 3, 5, 7, 9 as sacred as explained in my
discourse on Divinity of Numbers. The reason why we think of 4 to start with
has also been adequately explained. The world started from four faced Brahma
with four directions and four Vedas. We also learnt that it ends in 48 because
Sanskrit alphabet ends in 48 with first vowel a representing Siva
and last consonant ha representing
Sakti. In Vishnu Chakra Siva is replaced by Purusha and Sakti by Prakriti.
Pancharatra concept projects Chaturvimsati (24) Moorti and Gayatree mantra of
24 letters. Together they add up to 48 on both of which we meditate. Further in
the even series of 48 there are 12 numbers (48/4=12). But by a strange divine
intuition in spite of our puranic differences among Siva, Vishnu Sakti etc., we
all employ twelve names of Brahman in his Omnipresence Vishnu form in our daily
Japa. These are Kesava, Narayana, Govinda, Madhava, Vishnu, Madhusudana,
Trivikrama, Vamana, Sridhara, Hrishikesa, Purushottama and Damodara. These are emanations of four Vyuhas of Vishnu
Vasudeva, Sankarshana, pradyuman and Aniruddaha. That explains in the nut shell
why Chamakam which is a Mantra of Brahman asks all to meditate on odd numbers 1--33
in regular series and 4—48 in even series in steps of four starting with 4 and
ending in 48 keeping that a mystery for the real spiritual seeker to reveal its
exposition. Chamakam shows Rhythm,
Orderliness in its odd and even series;
it shows Satyam, Truth as it starts with 1 Tadekam, That One supreme reality; it shows Parambrahma, Supreme Reality in revealing 48 which is the number of
alphabets in Sanskrit with a as the Purusha and ha as
the Prakriti in the Brhamchakra . [rita(ga)m satyam parabrahma].
Thus meditation on all these numbers leads to
Paramaatman only.
Chamakam is a mantra on Parabrahman, a mantra for all--Saivites,Vaishnavites,
Saktites and even non-believers who believe in nature and its natural
phenomenon regulated by it. Sankara did not explain why Chamakam 33 odd and 48 even numbers are meditation mantras but established Panchanana pooja which is all
directed to Siva, Sakti, and Vishnu that is Smarta Sampradaya. Everything is
created by Siva and Sakti combining and pervaded by Vishnu and guarded by 33
bodyguards of Brahman, Vedic deities. 33 Vedic deities include Brahma as Prajaapati, Indra as the ruler. 33
represents natural phenomenon and 48 represents universe to non-believers. To believers
48 means Siva and Sakti or Purusha and Prakriti overlord of the Universe represented
by 48 letters of divine language Sanskrit. First letter a represents Siva
or Purusha and last letter ha with half-moon period (Ardha Chandra Bimba) represents Sakti
or Prakriti. 48 letters representing Universe as 50 spokes of Brahmachakra of Upanishads with two
additions of Glutaral la and combined consonant Ksha. So last Anuvaka
of numbers of Chamakam is for meditation by all. Sarvam Vishnumayam jagat | Sarvam Sivaarpanamastu || May all be pervaded by Vishnu! May all dissolve in Siva or merge in Siva!
Vidhartaara(ga)m
havaamahe vasoeh kuvidvanaati Nah| Savitaaram Nrichakshasa
---(MNU)
We
invoke the Creator of the Universe
Who
sustains the creation in many ways and
Who
witnesses the thoughts in many ways and deeds of men
May
He grant us plenty of excellent wealth!
REFERENCES:
1)
Ramachandra Rao, Vishnu Kosha, Kalpataru Research academy, Sankara Math,
Bengaluru, India.
2)
Swami Devaswarupananda, Mantrapushpam, Ramakrishna Math, Kolkota, India.
3)
Swami Chinmayaananda, Vishnu Sahasranama, Central Chinmaya Mission Trust,
Mumbai, India.
4)
Srnivasan N.R., Some Vedic Mantras used in Hindu Worship and Rituals, Hindu
Reflections, Internet.
5)
Srinivasan N.R., What do Odd and Even Numbers in Chamakam Signify, Hindu
Reflections, Internet.
6)
Srinivasan N.R., Visualizing Divinity in Numbers, Hindu Reflections, Internet.
7)
Swami Vimalananda, Mahaanaaraayan Upanishad, Ramkrishna Math, Chennai, India.
8)
Ramachandra Rao, S.K., Srividya Kosam,
Sri Satguru publications Delhi, India.
9)
Sastry K.L.V., R.S. Vadhyar & Sons, Palghat, Kerala, India.
10)
Ramachandra Rao, S.K., Srividyaa-Kosa, Sri Sadguru Publications, Delhi, India.
APPENDIX
ELEVENTH ANUVAAKA PRAYER FROM
CHAMAKAM
Shiva Rudram Chamakam- Science explained
Chamakam is a sanskrit hymn dedicated to Rudra (an epithet of Lord Siva), taken from the Yajurveda (Taittariya Samhita (TS) 4.5, 4.7).
The 11th Anuvaka of Sri Rudram Chamakam (चमकम्) describes complex mathematics behind formation of different molecules by combination different number of atoms.
This
hymn is referred to in the Siva Purana and recitation of the
Śatarudrīya is claimed, in the Jābala Upanishad, to lead to immortality.
Rudram
chanting can be done with or without the accompaniment of a Vedic yagna
ritual. When accompanied with the Vedic fire ritual, it is called the
Rudra Yagnam. It is said that Lord Siva, after Bhasmasura was killed with the help of Lord Maha Vishnu, performed the Tandava Dance and then performed the “Rudra Yagna” for the betterment of humanity.
The place where first Rudra Yagna was performed is where the “Sri Kalahasti” Temple stands now; this temple also has one of the 5 (Pancha bhootha – Vayu, Agni, Jala, Akash, Prithvi) lingas called Vayu linga.
It consists of two texts from book four of the Taittiriya Samhita (TS 4.5, 4.7), which is a recension of the Krishna Yajurveda.
Sri Rudram or the Namakam (chapter five) describes the name or epithets of Rudra, which represent his aspects. Additionally, the devotee asks for the benevolent aspect of Siva to be invoked rather than the terrible aspect and requests forgiveness of sins. The Chamakam (chapter seven) asks for the fulfilment of wishes. Each part consist of eleven anuvaka or hymns. Traditionally Rudra is assigned the number 11, and among the thirty three deities of the Vedic pantheon, eleven are considered forms of Rudra.
Sri Rudram
The anuvakas of Sri Rudram correspond to the eleven hymns of TS 4.5, with the final anuvaka extended by an additional eight verses, including the Mahamrityunjaya Mantra. The central Saivite mantra, Aum Namah Sivaya is also derived from the Sri Rudram, it appears (without the aum) in TS 4.5.8.l.
There are eleven hymns; each has its own purpose and meaning. For instance, the seventh anuvakam is for education, progeny; the eighth anuvakam is for destruction of enemies and possession of one’s own things from them.
Chamakam
Second part of the text, corresponding to TS 4.7, asks God for fulfillment of wishes. The repeated phrase, cha me literally means, “and to me [be this granted]“, accompanied by a list of desirables, which are primarily necessary appurtenances for Vedic sacrifices.
The original context of the Chamakam is the piling up of the fire-altar of the Vedic religion. The hymn invokes, apart from Agni and Vishnu at the beginning, a pantheon of Vedic deities that are successively linked with Indra to enable the yajamana or sacrificer/patron to successfully perform Vedic fire sacrifices or yagnyas, such as the Agnishthoma, Somayaga, and the Ashwamedha. The Chamakam can be interpreted both as a preparatory for a physical external sacrificial ritual, and the inner, possibly yogic sacrifice involving pranic control, since the yogic “vital airs” are explicitly mentioned as sacrificial adjuncts in anuvaka, or stanza 10.
11th Anuvaka of Chamakam
Eka
cha may, thisra cha may, panchas cha may, saptha cha may, nava cha
mayEkadasa cha may, tryodasa cha may, pancha dasa cha may, saptha dasa
cha may, Nava dasa cha may, eka trimsathis cha may, tryovimsathis cha
may,
Pancha vimsathis cha may, saptha vimsathis cha may, nava
vimsathis cha may, Eka trimsathis cha may, tryatrimsathis cha may,
pancha trimsathis cha may,Chathasras cha may, ashtou cha may, dwadasa
cha may, shodasa cha may,Dwathrimasthis cha may, shat trimsas cha may,
chatvarimsa cha may,
Chathus chathvarimsa cha may, ashta chatvarimsa cha may,
Vaajas cha prasavas cha pijascha kradis cha suvas cha moordha cha
Vyasniyas cha anthyayanas cha anthyas cha
Bhouvans cha bhuvanas chadhipadhis cha.
Eka cha may means 1,
Square root of 1 = 1.
thisra cha may means 1+3 = 4.
Square root of 4 = 2.
Panchas cha may means 5+4 = 9.
Square root of 9 = 3.
Sapta cha may means 7 + 9 = 16.
Square root of 16 = 4.
Nava cha may means 9 + 16 = 25.
Square root of 25 = 5.
Ekadasa cha may means 11 + 25 = 36.
Square root of 36 = 6.
Tryodasa cha may means 13 + 36 = 49.
Square root of 49 = 7.
This goes on till Nava ving satis cha may where ytou derive 361 + 39 = 400 and square root of 400 = 20.
The algorithm described in this 11th anuvaka of chamakam has odd numbers in them with hidden even numbers between them.
This description is about multiple combinations of atoms to form various molecules.
Siva is described to be in anu-poorva sthiti (pre-atomic state), which means electrons, protons and neutrons.
They combine to form atoms and these atoms when combine is different numbers will form molecules.
Vishnu (mean, the one who is spread all over) is such molecules which create elements and substances in this creation.
Acharya Kaṇāda used these concepts to Vaishesika Sutras, which describe Laws of Motion & Concept of Atom.
PRAYER OF SERIES OF ODD NUMBERS
“Ekaa cha may trisrascha may
pancha cha may sapta cha may nava cha
may ekaadasa cha may trayodasa cha may panchadasa cha may saptadasa cha may
navadsasa cha may ekavi(ga)msatischa may trayovi(ga)msatischa may panchavi(ga)msatischa may saptavi(ga)msatisacha
may navavi(ga)msatischa may ekatri(ga)msaccha may trayastri(ga)msasccha may ||
PRAYER OF SERIES OF EVEN
NUMBERS
Chatasrascha may ashtau cha may dvaadasa cha may shodasa cha may vi(ga)msatischa may chaturvi(ga)msatischa may
ashtaavi(ga)msatischa may dvaatri(ga)mscha may
shat-tri(ga)mscha may chatvaari(ga)mscha may chatus-chatvaari(ga)mscha
may ashtaa-chatvaari(ga)mscha may vaajascha prasavaschaa-pijascha kratuscha
suvascha moordhaa cha vysniyascha-antyaayanascha-antyascha bhouvanascha
bhuvanascha-adhipatischa ||11||
CONCLUDING PRAYER
Om Idaa devahoor-manur-yajneer-brihaspatir-ukthaamadaani
sa(ga)msishad-visvedevaah sookta-vaachah prithvimaatarmaa maa hi(ga)mseer-madhu
manishye madhu janishye madhu vakshyaami
madhu vadishyaami madhumateem devebhyo vaacham-udyaasa(ga)m
sushrooshenyaam manushebhyastam maa
devaa avantu sobhaayai pitaro-anumadantu || Om Shatih Shaantih Shaantih ||
[May I be granted the odd numbers1, 3, 5, 7,
9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, and 33 as well as even numbers
4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, and 48 to ensure food and its
continuity and the urge to enjoy the origin of all creation—the Sun, the
heaven, the head of all, the infinite, the all-pervading like the sky, time and
the like present at the end of total
consummation exists at the end of it on
the earth as universal form, the Antaryamin, the immortal, the inner ruler of
everything, the Omnipresent and
Omnipotent. May Peace prevail, in all our inner struggles, external conflicts
and Heavenly disturbances due to our own missdeeds disturbing the Universal
orderliness that was given to us!]
[The sacred gods are implored by mantras on
Kamadhenu, the granter of all wishes. Manu does the sacrifices and Brihaspati
recites the pleasant Mantras. May these praises of Visvedevas and Mother Earth
save me from sufferings! May my pleasant thought bring forth pleasant actions
and resultant enjoyable fruits! May my joyous offerings bring forth fine and
worthy speech and my words please the divinity, make men turn their tears to
joy; May Gods enlighten me and invoke my speech very powerful and my ancestors
(Pitrus) feel extremely glad over it and bless me to perpetuate it.]
Vishnu in Rudram
This post
is a humble attempt to translate this brilliant article by Sri Hari
Sriramamurthy published in Rushipeetam monthly spiritual magazine in Feb 2007.
Rudram means Rudradhyayam (रुद्राध्यायं )[1]. This is also
referred to as Shatarudreeyam (शतरुद्रीयं), Rudropanishath (रुद्रोपनिशत्). It constitutes Namaka (नमक) and Chamaka (चमक)
Mantras. These are taken from Yajurvedam. They are used in Rudrabhiskeham[2]
(रुद्राभिषेकं). Sayana, Bhatta Bhaskara, Abhinava Shankara, Vishnu Suri wrote
commentaries[3] on these mantras. A study on these mantras and these
commentaries reveals that these mantras talk about Sun, Siva and Vishnu.
उतैनं
गोपा
अद्रुशन्नद्रुशन्नुदहार्यः |
उतैनं विश्वा भूतानिसदृष्टो मृढयातिनः ||
उतैनं विश्वा भूतानिसदृष्टो मृढयातिनः ||
- based on interpretation for Sun :
येनं = This Surya
उदहार्यः = उद – water, हार्यः – taking or absorbing i.e., absorbing water
गोपाः = gopikas ; गोपाः = गाः – Earth , पाः – Saving or protecting i.e., Sun Rays
अदृशन् = watched or saw or noticed - based on interpretation for Rudra (Siva):
येनं = This Rudra
उदहार्यः = (उत् – अहार्यः) whose souls were taken away (up)[2]
गोपाः = humans, living beings
अदृशन् = watched or saw or noticed - based on interpretation for Vishnu :
Three different interpretations have been proposed. - येनं = This Vishnu
उदहार्यः = fetching water
गोपाः = gopikas
अदृशन् = watched or saw or noticed - According to Vaijayanti Kosha, Harii (हरी) means jaarastri (जारस्त्रि)
i.e., woman who is corrupted/spoiled
कन्या प्रसूतिजा जारी हरी नाम्नैव दूषित
– वैजयन्ती कोश 87-96
So, haaryah (हार्यः) means women who are corrupted/spoiled. Thus “na haaryah” (न हार्यः) or ahaaryah (अहार्यः) meaning those women who are not corrupted/spoiled. (Since uth – उत् – means noble) So udahaaryah (उदहार्यः) means those women who are not corrupted but are noble women.
Gopaah (गोपाः) = Gopikas
Yenam (येनं) = This Krishna
Adrushannadrushan (अद्रुशन्नदृशन्) = (अदृशन् + अदृशन्; अदृशन् means watched, noticed or saw)[3] Noticed, watched or saw again i.e., Gopikas saw Krishna again and again and they felt blessed
This means
even though noble Gopikas were in rasaleela[4] (rasa dance) with Sri Krishna, they were not corrupted/spoiled but remained noble. - Ahaaryah (अहार्यः) means a mountain according to Amarakosha – आहार्य धर पर्वताः. Udahaaryah (उदहार्यः) means the one who lifted a mountain i.e., Govardhana mountain – Sri Krishna. Thus it means Gopaah (गोपाः) i.e., Gopikas adrushan (अदृशन्) i.e., saw, noticed or watched such a Krishna and felt blessed.
Narayana
Teertha (नारायण
तीर्थ)
called Gopikas as a manifestation of Vedas by referring to them as Srutayah (श्रुतयः). A similar reference to
Gopikas as manifestation of Vedas can be found in Bhagavata Puranam.
इति
गोप्यः
परानन्दं गायंतस्त्याः पृथक्
पृथक्
|
अपराः श्रुतयोः भूयो भूयो तत्रैव संगताः ||
अपराः श्रुतयोः भूयो भूयो तत्रैव संगताः ||
– कृष्णलीला तरंगीणि
This
summary comes from Narayana Teertha’s[4] observation on Mantras in
Yajurveda and Shlokas in Bhagavata Purana in Krishna Leela Tarangini.
Putting
all these interpretations in perspective,
येनं
= This Paramatma (supreme being) devoid of all attributes and properties
उदहार्यः = उत् – noble, good अहार्यः – that which cannot be taken away or stolen or doesn’t vane
गोपाः = Vedic Mantras
अदृशन् अदृशन् = noticing, watching or observing again and again
उदहार्यः = उत् – noble, good अहार्यः – that which cannot be taken away or stolen or doesn’t vane
गोपाः = Vedic Mantras
अदृशन् अदृशन् = noticing, watching or observing again and again
Vedic
Mantras, which are noble and which cannot be taken away, stolen or vane,
proclaim us to observe in them, a paramatma (supreme being) devoid of all
attributes i.e., Sun, Siva and Vishnu are manifestations of paramatma (supreme
being).
In Rudram,
नमो गिरिशायच शिपिविष्टायच |
Commentaries
indicate that “shipivishta” (शिपिविष्ट) is a reference to Sun, Siva and Vishnu. Sayana refers to
Vishnu as
विष्णुमूर्ति धारी
शिपिविष्टः |
which
means Shipivishta is a manifestation of Vishnu. Vedas refer to Shipivishta in a
similar way.
विष्णुः शिपिविष्टः |
In
Vishnu Sahasranamam, Shipivishta is referred to as
नैकरूपो बृहद्रूपः शिपिविष्टः प्रकाशनः |
In Siva
Sahasranamam, Shipivishta is referred to as
शिपिविष्टो अम्बिकानाधः |
In
Naanardha Sangraha Kosha, Vishnu and Siva are referred to as Hari and Shankara
respectively
शिपिविष्टस्तु दुश्चर्म खिल्वात हरिशन्कराः |
Vishnu
Suri’s commentary explains
शिपयो जीवाः,
तदनुसंधाता शिपिविष्टः सर्वसाक्षी रुद्रः
|
This
means “Shipis are living beings. Rudra as the all-pervading consciousness
protects them by being their conscience”
In
Taittriya Samhita,
यज्ञोवै विष्णुः, पशवः
शिपिः,
यज्ञ
येव
पशुषुः
प्रतितिष्ठति |
– तैत्त्रिय संहित 2-5-5
Adi
Shankaracharya in his commentary on Vishnu Sahasranama and Vishnu Suri in his
commentary proclaim
शिपयः पसवः,
तेषु
विशति
प्रतितिष्ठति यज्नरूपेण इति
शिपिविष्टः |
Cattle
are also called as Shipis. Vishnu in Yajna manifestation, enters their inner
consciousness and protects them as Shipivishta.
Thus
one can see Vaishnavam in Rudram.
Also in
Rudram,
नमस्ताराय नमस्चंभवाय च |
Tarah (तारः) means that which blesses.
This mantra talks of Siva (Rudra) who blesses. In Vishnu Sahasranamam,
अशोकस्तारणस्तारः |
and
भूर्भुवः स्वस्तरुः तारः
|
Both
Bhatta Bhaskara’s commentary,
तारय प्राणव
रूपाय
|
and
Vishnu Suri’s commentary,
तारयति संसारदिति तारः
प्राणवः तद्रूपाय |
indicate
that tara (तार)
means Om (ॐ). Both
Siva and Vishnu are manifestations of Om.
Another
mantra
नमो ह्रस्वायच वामनायच |
clearly
talks of Vishnu’s reincarnation – Vamana.
Another
mantra in rudram says
नमो गोष्ठायच गृःयायच
Sayana
in his commentary explains
गोष्ठं गवाम्
स्थानम् तत्र
भवो
गोष्ठ्यः
Meaning
– Goshtam (गोष्ठं)
is the place where cows live i.e., a Byre and Goshtyah (गोष्ठ्यः) is Krishna, since he stays
with the cows. Vishnu Suri in his commentary says
श्रुतयो गवाः,
तासां
स्थानम् गोष्ठं
– मनोमय
कोशं
| तत्र
प्रकशमानः गोष्ठ्यः | तस्मै
नमः
|
Vishnu
Suri refers to Cows as Vedic Mantras. The place where cows stay is Goshtam (गोष्ठं). Vedic Mantras reside (in a
human) is mind or manas (Manomaya Kosham). One who resides there glowing
brightly is called Goshtyah (गोष्ठ्यः) and that is Go-pala i.e., Go-vinda, the one who takes care of Cows
which are manifestations of Vedic Mantras. That Go-pala is none other than
Krishna.
Similarly,
mantras like नमश्शोक्यायच, आशुषेनायच clearly refer to Vishwaksena or Krishna.
This
way, all mantras in rudram clearly refer to Sun, Siva and Vishnu. Finally,
नमो रुद्राय विष्णवे मृत्युर्मे पाहि
meaning
“I salute Siva who is manifestation of Vishnu and Vishnu who is manifestation
of Siva. May Vishnu who is manifestation of Siva protect me from death. May
Siva who is manifestation of Vishnu protect from death”. Such interpretation
would lead to unity between Siva and Vishnu.
Rudram
is also referred to as “Shata Rudreeyam” (Rudram of 100 mantras). In Drona
Parva (in Mahabharata), Vyasa taught Ashvatthama and Arjuna as an Upadesam.
Neela KanTa Deekshitulu in his commentary on Rudram, to show Vishnu in Rudram,
says that Shata Rudreeyam starts with non-duality of Siva and Vishnu.
“तदेवं विश्नोष्षिवमयत्वं व्याख्याय विष्णुत्राणात्
तन्मय स्वजगतः तराणमपि शिवमेव कर्मेत्युक्तं”
तन्मय स्वजगतः तराणमपि शिवमेव कर्मेत्युक्तं”
“यधा शिवमयो विष्णुरेवं विष्णुमयं जगत्”
–
Bharatam – NeelakaTa Vyaakhya – Drona Parvam.
By
explaining non-duality of Vishnu with Siva, it has also be summarized that like
Vishnu, protection of the worlds is Siva’s Karma.
पूर्वयोः पर्वणोः विश्नोर्विस्वरूप प्रकाषणेन व्याख्यातं| अथ
दृष्तांतीकृतं विश्निष्षिवमयत्वं व्याचिख्यासुः शतरुद्रीयमारभते |
–
Bharatam – Drona Parvam – 1201.
Meaning
“all smritis say that Siva is a manifestation of Vishnu and Vishnu is a
manifestation of Siva. In Drona Parvam, to show this non-duality, Shata
Rudreeyam is being started”
Explanatory
Notes:
[1]
Rudram is taken from Yajurvedam. It is also called as Rudradhyayam and Rudra
Prasnam. It is a great treatise to the properties of universal consciousness or
nirguna paramatma as explained earlier via an example from Chamakam here. Translators who came from
Europe saw Rudram as sacrificial hymns to Shiva but rather these are actually
properties of nature. This is probably the reason why so many commentators –
ancient and modern see that Rudram is actually a treatise not just to Shiva but
also Surya (Sun) and Vishnu –deities described by Adi Sankaracharya as three of
the six primary deities or Shanmatas.
[2]
Abhishekam is that process of worship in which a deity is anointed with some
nature’s products as a part of worship. Panchamritas (ghee, milk, curd,
sugar/jiggery syrup, honey), Sandalwood powder, leaves from different
trees/plants, rice grain and many more are generally used for this purpose. This
is treated as an offering made to the deity. Abhishekam is done to any deity
according to Hindu worship. When it is done while reciting Rudra Mantras, it is
called Rudrabhishekam. Rudram is generally most used in deity worship through
abhishekam.
[3]
Actually the Sanskrit word – Bhashyam cannot be translated to English
precisely. Commentary would be a misfit in many cases. We will however stick to
the word commentary in this translation.
[4] Narayana Teertha’s Krishna
Leela Tarangini is a literary work based on Dasama Skandam of Bhagavatam. The
work is represented in many forms in modern day – both in music, dance. The
lyrical beauty of in Krishna Leela Tarangini is something which has no parallel
in its genre. For instance, sample this – Alokaye Sri Balakrishnam.
[This is a prepared lecture compiled from
above references and others for a discourse at Sri Ganesha Temple, Nashville
and to benefit those who are not able to attend the same in person. You are
free to download and use it for your reading and reference as well as circulate
to others to spread the wisdom of Vedas and Hindu values which good act will be
appreciated. Any suggestion to add to the compilation to enhance its value will be appreciated. < nadipuram@hotmail.com>]
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