Construction of Odd and Even numbers in Chamakam

ऊँ ऋतं सत्यं परब्रह्म पुरुषं कृष्णपिंगलम्।
ऊर्ध्वलिंगं विरूपाक्षं विश्वरूपाय नमो नमः।।

Vedas mention of “Ritam Satyam Parabrahma” meaning universal orderliness (rita) and Truth (Satyam) are Parabrahma (Paramaatman or Supreme Principle). Chamakam found in Sri Rudram of Rig veda 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 अणोरअणीयान् महतो महीयान anoraneeyan mahato maheeyaan - smaller than the smallest and larger than the largest and Brahman is ever full or पूर्णं poornam. Poornam is identified as शून्यं Soonyam also. Vedic altar is geometrical. 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. 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 with one ? 

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 is given below. 

Prayer of series of Odd numbers 

एका॑ च मे ति॒स्रश्च॑ मे॒ पंच॑ च मे स॒प्त च॑ मे॒ नव॑ च म॒ एका॑दश च मे॒ त्रयो॒दश च मे॒ पंच॑दश च मे स॒प्तद॑श च मे॒ नव॑दश च म॒ एक॑विग्ंशतिश्च मे॒ त्रयो॑विग्ंशतिश्च मे॒ पंच॑विग्ंशतिश्च मे स॒प्त विग्ं॑शतिश्च मे॒ नव॑विग्ंशतिश्च म॒ एक॑त्रिग्ंशच्च मे॒ त्रय॑स्त्रिग्ंशच्च मे॒ 

“Ekaa cha may tisrascha may pancha cha may sapta cha may nava cha may ekaadasa cha may trayodasa cha may panchadasa cha may saptadasa cha may navadsasa cha ma ekavi(ga)msatischa may trayovi(ga)msatischa may panchavi(ga)msatischa may saptavi(ga)msatisacha may navavi(ga)msatischa ma ekatri(ga)msaccha may trayastri(ga)msasccha may 

Prayer of series of Even numbers

चत॑स्-रश्च मे॒‌உष्टौ च॑ मे॒ द्वाद॑श च मे॒ षोड॑श च मे विग्ंश॒तिश्च॑ मे॒ चतु॑र्विग्ंशतिश्च मे॒‌உष्टाविग्ं॑शतिश्च मे॒ द्वात्रिग्ं॑शच्च मे॒ षट्-त्रिग्ं॑शच्च मे चत्वारि॒ग्॒ंशच्च॑ मे॒ चतु॑श्-चत्वारिग्ंशच्च मे‌உष्टाच॑त्वारिग्ंशच्च मे॒ वाज॑श्च प्रस॒वश्चा॑पि॒जश्च क्रतु॑श्च॒ सुव॑श्च मू॒र्धा च॒ व्यश्नि॑यश्-चांत्याय॒नश्-चांत्य॑श्च भौव॒नश्च॒ भुव॑न॒श्-चाधि॑पतिश्च ॥ ११ ॥

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

ॐ इडा॑ देव॒हूर्-मनु॑र्-यज्ञ॒नीर्-बृह॒स्पति॑रुक्थाम॒दानि॑ शग्ंसिष॒द्-विश्वे॑-दे॒वाः सू॓क्त॒वाचः॒ पृथि॑विमात॒र्मा मा॑ हिग्ंसी॒र्-म॒धु॑ मनिष्ये॒ मधु॑ जनिष्ये॒ मधु॑ वक्ष्यामि॒ मधु॑ वदिष्यामि॒ मधु॑मतीं दे॒वेभ्यो॒ वाच॒मुद्यासग्ंशुश्रूषे॒ण्या॓म् मनु॒ष्ये॓भ्य॒स्तं मा॑ दे॒वा अ॑वंतु शो॒भायै॑ पि॒तरो‌உनु॑मदंतु ॥

ॐ शांतिः॒ शांतिः॒ शांतिः॑ ॥

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 Shantih Shaantih Shaantih ||

[May I be granted the odd numbers 1, 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 misdeeds 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.]

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 our ancient 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'. Bhagavdgita 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 Gita is Sanskrit and not any other language.

Vedic Sanskrit, Srividya and Brahma chakra

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 Brahma chakra of Svetasvatara Upanishad, Sanskrit alphabet of 48 or 50 represents the entire Universe or Ksehtra while Brahman is Kshetrajna which view is also expressed in Bhagavadgita. According to Srividya a represents Siva and ha represents Sakti as well as Purusha and Prakriti. 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 Brahma chakra 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 signifies 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:

Table of Orderliness

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=121	11
23+121=144	12
25+144=169	13
27+169=196	14
29+196=225	15
31+225=256	16
33+256=289	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 4th 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, 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 associateship  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:

Gaayatri Saara Sangraha

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 ||

• Chaturmoortih: 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.

Likewise, orthodox Saivites also wear Vibhooti on 12 parts of the body daily. You may ask here why Vishnu 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 Brahman so also Rudra—Tvam rudrastvam, vishnustvam—Brahman  is Vishnu; Brahman is Rudra (Mahanarayana Upanishad)

In Daily worship we use the Japa containing 12 names whatever may be our tradition, Saiva, Vaishnava, Sakta or Smaarta. These are Kesava, Narayana, Madhava, Govinda,  Vishnu, Madhusoodana, Trivikrama,  Vamana, Sridhara, Hrisheekesa, Padmanabha 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.

Smarta Sampradaya

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 Panchayatana 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 Brahma chakra 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!

Purushasooktam 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 like the symbol Pi. 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 kuvit vanaati nah | savitaaram nri-chakshasam |

- Mahanarayana Upanishad

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!

Courtesy: Sri Nadipuram Srinivasan (http://nrsrini.blogspot.in) 
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.