Chamakam & its numbers

WHY DID CHAMAKAM END IN 33 AND 48 IN ODD AND EVEN SERIES?

(DISCOURSE BY N. R. SRINIVASAN, BRENTWOOD, USA)

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 order 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.

We find references to numbers ranging from Soonya (0) to Infinity all over in our Srutis (Vedas and Upanishads) and Puranaas. This indicates that 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). 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.

Applying our present day knowledge of elementary arithmetic we could possibly find an explanation. 0 represents Nirguna (un-manifested) Brahman which is also represented as Poornam as expressed in Vedic Mantra "Poornamadah poornamidam poornaat poornamaduchyate poornasya poornamaadaaya poornameva avashishyate—Br. Up. 5.1).

0 in mathematics is indispensable. Nirguna Brahman is indispensable and is inner controller of all beings. If we remove 0 from 0 what remains is also 0. 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.

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 the regular series of even numbers 2, 4, 6….etc. is not seen as in the even series in the same mantra? The sole purpose of Chamakam is intended for intense meditation which would be 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. Evidently Rishi of this Chamakam wants to convey to us the divine purpose behind these numbers and their arrangement? A mantra has three stipulations to distinguish it from a normal hymn--it has a Rishi as its author, a Chhandas, meter or prosody and a deity to contemplate upon.

To our Rishis Supreme Brahman was Nirguna Brahaman complete in all respects as Poornam, symbolically Soonyam represenrted by "0". Then Saguna Brahman is represented by "1", which Nasadeeya sookta mentions as Tadekam (that One). It will not be wrong to conclude then "01" will be full representation of Brahman as Nirguna and Saguna standing side by side. Square root of 01 is 1. With this base we could arrive at a progressive picture for all numbers up to 33 as seen in the chart below as well as corresponding square roots in a divine orderly pattern which Vedas call as ritam. Surprisingly odd number 33 ends with the square root 17 in this representation; the same is illustrated as follows in a tabular format:

Odd Number arrangement corresponding Square root

(1) (2) (3) (4)

01+00=01 1

03+01=04 2

05+04=09 3

07+09=016 4

09+016=025 5

011+025=036 6

013+036=049 7

015+049=064 8

017+064=081 9

019+081=100 10

021+0100=0121 11

023+0 121=0144 12

025+0144=0169 13

027+0169=0196 14

029+0196=0225 15

031+0225=0256 16

033+0256=0289 17

[In the sequence above column 1 shows odd number series beginning with 1. Column 2 shows the total of previous line total of 1 and 2. Column 3 shows the total of column 1 and 2. Column 4 shows the square root of column 3. Thus there is an orderliness shown in this pattern, call it ritam or arithmetical progression or by any other name that may be given to it; I would like to call it divine progression.]

First column of numbers ends in 33. We all know that there are 33 divine guards described in Vedas who are responsible for the orderliness of the Universe. These are 11 Rudras, 12 Aaadityas, 8 Vasus, Indra and Prajaapati. Hindu Theology mentions them as 33 Vedic deities. There is also 0 in front of every number. 0 represents Nirguna Brahman who watches over everything without actively participating and being invisible. Supreme Being watches over all activities without involvement. This column therefore represents the domain of Brahman. Fourth column ends in 17. We learn from Upanishads that human being is intellect-mind-sense-vital force-complex called Jeevatman. Jeevaatman constitutes 5 motor organs (Karmendriyas) +5 sense organs (Jnanendriyas) +5 vital forces (Pancha Praanas) +mind (Manas) + Intellect (Buddhi). Brahman Assembly of 33 of column 1 keeps watch on 17 faculties of Jeevaatman represented by column 4. This is what Svetaavataara Upanishad describes as follows: "Dvaa suparnaa sayujaa sakhaayaa samaanam vriksham parishasvajaate | tayor-anyah pippalam svaadvatti anasna-annayoe abhichaakaseeti || Two birdsa (Jeevaatman and Paramaatman) of similar qualities which are inseparable from each other are perched on the same tree. Of these two, one (Jeevaatman) tastes the sweet pippala fruit (eats the fruit of the Karma) and the other (Paramaatman) is witnessing without eating (shines even without eating). Higher value numbers found in column 1 compared to less numbers in column 4 shows the Superiority of Paramaatman over Jeevatman as the over-lord. 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. It is therefore no surprise why Chamakam abruptly ends in 33 to convey this powerful message. It simply says silently in a hidden voice to Jeevaatman (derived square roots) to pay obeisance to Paramaatman (the odd numbers) to get relieved of its clouded Maaya or Avidya (illusion) without any explanation.

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. In the popular Vishnu Expositions the four aspects of Vishnu known as Vyoohas and the resulting twenty-four forms of Vishnu forms the theme besides the popular ten incarnations. All these are even numbers, even number of 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.

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 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:

No. Gaayatree letter Abhimana Devata Names of Vishnu

(Chosen deity)

1. ta Agni Kesava

2. tsa Prajaapati Narayana

3. vi Soma Maadhava

4. tu Easaana Govinda

5. va Savitar Vishnu

6. re Brihaspati Madhusoodana

7. ni Paitru-deva Trivikrama

8. yam Bhaga Vaamana

9. bha Aaryama Sreedhara

10. rgoe Saavitri Hrisheekesa

11. dey Tvashtr Padmanaabha

12. va Pooshan Daamodara

13. sya Indra Sankarshana

14. dhee Agni Vaasudeva

15. ma Vaayu Pradyumna

16. hi Mitra-varuna Aniruddha

17. dhi Bhraatrideva Purushoettama

18. yoe Visvedeva Adhoekshaja

19. yoe Vishnu Naarasimha

20. nah Vaasava Achyuta

21. pra Tushtaba Janaardana

22. choe Kubera Upendra

23. da Dasra Hari

24. yaat Brahma Sree 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. Vishnun is identified as Naarayana who is the Paramaatman (Supreme Principle) mentioned in Svetaavataara Upanishad.

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 Panchbrahma 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.

Smaarta Tradtion is more liberal, broad-based and non-sectarian tradition in Brahminism. Their philosophy is more suited to common form of worship conducted in Hindu temple-complexes popular outside India. They worship Ganesha, Siva, Sakti, Vishnu, Soorya and Skanda with equal importance, though all of them are not Vedic deities and even though the word Smaarta is derived from Smriti meaning strict adherence to Vedas. They give equal importance to all that is said in Vedas and accept all major Hindu deities also as forms of Brahman. They accept all the six manifestations of God as recommended by Sankara. They are known as Sanketis in Karnaataka. Most recent Upanishads like Ganesha Athrvaseershoepanishat and Kalisantarana Upanishad on Puraanic deities with lot of Phalasrutis (benefits derived by praying) fit into their philosophy including Bhajana Sampradaayam (prayer by singing hymns loudly).

Purushasookta says what humans know is only one fourth and what is hidden from them is three fourths. That concept is well demonstrated when we look at Linga images installed in temples. Only one third of the Linga is available for physical worship. On the dark but clear moonless night if we gaze at the wide expanse of the sky we see billons of star-clusters from millions of galaxies with their inscrutable silence. We live on a small-sized planet called earth which is almost comparable to a dot on the whole universe, which is again a planet of a medium sized star (Sun). We have limited knowledge of the Milky-way only amongst all galaxies. Our knowledge is mostly confined to Mother Earth and rest remains on speculation or mystery. Knowing the limitations of the human beings and the short span of life on this earth, Good Lord stopped at the odd number of 33 and even number of 48, without taxing us by extending it to infinity. Even here we do not know his original intentions. Hence I have speculated on these limited numbers like many others. May we therefore conclude this discourse with a prayer to the Supreme Principle for granting us that supreme Knowledge which can be attained only when Jeevaatman merges with Paramaatman in its final journey!

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.

APPENDIX

ELEVENTH ANUVAAKA PRAYER FROM CHAMAKAM

PRAYER OF SERIES OF ODD NUMBERS

" Ekaa cha may tisracha may pancha cha may sapta cha may nava cha may ekaadasa cha may trayodasa cha may panchadasa cha may saptadasacha may navadsas cha may ekavi(ga)msatischa may trayovi(ga)msatischa may panchavi(ga)msatischa may saptavi(ga)msatischa may navavi(ga)msatischa may ekatri(ga)msacha may trayastri(ga)msascha 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 prasavascaa-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.]