MATHEMATICS IN CHAMAKAM

[K.N.RAMESH]

Courtesy: Sri.G.Balasubramanian

MATHEMATICS IN CHAMAKAM

Mathematics is a part of our daily life in several ways. Hence, it is no wonder that it has come to occupy an important place in religious rituals also. This is what we find particularly in the Hindu way of life or the Hindu religion.

Worshippers of Lord Siva recite Rudram with 11 sections followed by Chamakam with 11 sections as a routine prayer every day. This is called the daily nyasam or mode of worship. In the Rudram part, the devotee pays repeated obeisance to Lord Siva and prays for his blessings for human well being. But on special occasions, the number of times the recitation is done is increased.

In Rudra Ekadasi, Rudram is recited 11 times and Chamakam is recited once. After Rudram is recited once, one section or anuvaka of Chamakam is recited in order.

In Laghu rudhram, Rudra Ekadasi is done 11 times, that is, Rudram is recited 112 or 121 times and Chamakam is recited 11 times.

In Maharudram, 11 Laghurudrams are recited; that is, Rudram is recited 113 = 1331 times and Chamakam 112 = 121 times.

In Atirudram, 11 Maharudrams are recited; that is, Rudram is recited 114 = 14641 times and Chamakam is recited 113 = 1331 times.

The Chamakam mentions completely the ideal of human happiness and defines in the highest degree the desires to be fulfilled without delimiting those to be asked for or to be granted.

In the Chamakam, in anuvakas or sections 1 to10, the devotee prays for almost everything needed for human happiness and specifies each item. But in the 11th anuvaka or 11th section of Chamakam, the devotee prays for the desired things not specifically but in terms of numbers, first in terms of odd numbers from 1 to 33 and later in multiples of 4 from 4 to 48, as follows:

“Eka cha me, thisrascha may, pancha cha may, sapta cha may, Ekadasa cha may, trayodasa cha may, panchadasa cha may, saptadasa cha may, Navadasa cha may, ek trimshatis cha may, trayovimshatis cha may, Panchavimshatis cha may, saptavimshatis cha may, navavimshatis cha may, Ekatrimshatis cha may, trayatrimshatis cha may, panchatrimshatis cha may, Chatasras cha may, ashtou cha may, dwadasa cha may, shodasa cha may, Vimsatis cha may, chaturvimshatis cha may, ashtavimshatis cha may, Dwathrimashatis cha may, shatstrimshas cha may, chatvarimshas cha may, Chatuschatvarimshas cha may, ashtachatvarimshas cha may”

which means:

“Let these be granted to me. One, three, five, seven, nine, eleven, thirteen, seventeen, nineteen, twenty one, twenty three, twenty five, twenty seven, twenty nine, thirty one and thirty three as also four, eight, twelve, sixteen, twenty, twenty four, twenty eight, thirty two, thirty six, forty, forty four and forty eight”.

Traditional scholars and pandits explain the significance of these numbers as follows:

ODD NUMBERS:

1 = Nature or Prakriti

3 = The three gunas, namely sattwa, rajas and tamas

5 = The five mahabhutas, or the five basic elements, that is, prithvi, ap, tejas, vayu and akasha, (earth, water, energy or agni or fire, wind and space).

7 = The five sensory organs and the mind and intellect

9 = The nine openings in the human body, called the navadwaras.

11 = The ten pranas and the Sushumna nadi

13 = Thirteen Devas

15 = The nadis or nerve centres in the human body

17 = The limbs of the human body

19 = Medicinal herbs

21 = Important vulnerable parts of the body

23 = Devas controlling serious diseases

25 = Apsaras in heaven

27 = Gandharvas

29 = Vidyut Devas

31 = Worlds

33 = Devas

MULTIPLES OF FOUR:

4 = The four ideals of human life, namely dharma, artha, kama and moksha,

(righteous way of life, wealth, desire, and salvation)

8 = The four Vedas and the four upavedas

12 = Six vedangas and six shastras.

16 = Knowledge to be obtained from God

20 = The Mahabhutas

24 = The number of letters in the Gayatri metre

28 = The number of letters in the Ushnik metre

32 = The number of letters in the Anushtup metre

36 = The number of letters in the Brihati metre

40 = The number of letters in the Pankti metre

44 = The number of letters in the Trushtup metre

48 = The number of letters in the Jagati metre

One great scholar says these numbers represent a polymer chain of molecules that form apa or water that enables evolution of life and intelligence, and apa is nothing but the nitrogenous base pairs of the DNA. The numbers 1 to 33 represent the 33000 base pairs of mitochondrial base pairs of DNA. The numbers 4 to 48 represent the 48 million nuclear bases of DNA. The two sets of DNA bases combine to provide sustenance of human wellbeing and onward evolution of human life. When the devotee prays for the blessing of these numbers, actually he is praying for bestowing on him all these DNA bases which conduce to sustenance of human wellbeing and happiness.

[Rajagopal Iyer]

namo namaH,

On Thu, Nov 13, 2014 at 11:48 AM, K.N.RAMESH <knra...@gmail.com> wrote:
> Courtesy: Sri.G.Balasubramanian
>
> MATHEMATICS IN CHAMAKAM
>
>

> “Eka cha me, thisrascha may, pancha cha may, sapta cha may, Ekadasa cha may,
> trayodasa cha may, panchadasa cha may, saptadasa cha may, Navadasa cha may,
> ek trimshatis cha may, trayovimshatis cha may, Panchavimshatis cha may,
> saptavimshatis cha may, navavimshatis cha may, Ekatrimshatis cha may,
> trayatrimshatis cha may, panchatrimshatis cha may, Chatasras cha may, ashtou
> cha may, dwadasa cha may, shodasa cha may, Vimsatis cha may, chaturvimshatis
> cha may, ashtavimshatis cha may, Dwathrimashatis cha may, shatstrimshas cha
> may, chatvarimshas cha may, Chatuschatvarimshas cha may, ashtachatvarimshas
> cha may”
>
> which means:
> “Let these be granted to me. One, three, five, seven, nine, eleven,
> thirteen, seventeen, nineteen, twenty one, twenty three, twenty five, twenty
> seven, twenty nine, thirty one and thirty three as also four, eight, twelve,
> sixteen, twenty, twenty four, twenty eight, thirty two, thirty six, forty,
> forty four and forty eight”.
>

> One great scholar says these numbers represent a polymer chain of molecules
> that form apa or water that enables evolution of life and intelligence, and
> apa is nothing but the nitrogenous base pairs of the DNA. The numbers 1 to
> 33 represent the 33000 base pairs of mitochondrial base pairs of DNA. The
> numbers 4 to 48 represent the 48 million nuclear bases of DNA. The two sets
> of DNA bases combine to provide sustenance of human wellbeing and onward
> evolution of human life. When the devotee prays for the blessing of these
> numbers, actually he is praying for bestowing on him all these DNA bases
> which conduce to sustenance of human wellbeing and happiness.
>

One more interesting aspect regarding the odd numbers here:
If you add seach subsequent number with the sum of previous numbers,
you will get a square upto 17
Number - Chamaka - Sum
1 - 1 - 1
2 - 3 - (1+3) = 4 =2^2
3 - 5 - (4+5) = 9 = 3^2
4 - 7 - (9+7) = 16 = 4^2

and so on upto 17.

I have not been able to figure out the even number suff sequence though.

Regards,
--
aa no bhadraaH kratavo yantu vishvataH
(Let auspicious come from the Universe)

Rajagopal

[G S S Murthy]

I do not understand anything of this and strictly have no business to make a comment. But if something stops at 17, it may be remarkable, in that there are only 17 pattern groups which cover an infinite plane. I just read about it.

Regards,

Murthy 

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http://gssmurthy.blogspot.com

[Arvind_Kolhatkar]

There is no mystery here and this 'trick' does not stop at 17 or any other odd number.  It is an inherent property that can be explained by school-level algebra.  I shall attempt to explain this in simple terms.

Set down all odd numbers in sequence, one below another, in a vertical column.  For any odd number in this column, write against it the total of all its previous odd numbers + that number itself.  You will see that the resulting sum is the square of (that odd number minus 1) / 2 + 1.

Thus, write the vertical column and the further algorithm:

1    1 + 0      = 1 = {(1 -1) / 2  + 1}^2

3    1 + 3      = 4 = {(3 - 1) / 2 + 1}^2 

5    4 + 5      = 9  = {(5 - 1) / 2 + 1}^2 

7    9 + 7      = 16 = {(7 - 1) / 2 + 1}^2

9    16 + 9    =  25 = {(9 - 1) / 2 + 1}^2 

11   25 + 11  = 36 = {(11 - 1) / 2 + 1}^2 

17   64 + 17  = 81 = {(17 - 1) / 2 + 1)^2

19   81 + 19  = 100 = {(19 - 1) / 2 + 1)^2

You can go on like this ad infinitum and the rule will always hold.

This happens because every odd number is expressible as (2n +1), 'n' taking values as 1,2,3 etc.  In the above algorithm, if you set down (2n +1) in its proper place, you shall have to write against it n^2 (being the total of all its odd predecessors) plus  that number itself i.e. (2n + 1).  The result is n^2 +2n + 1, which is the square of (n + 1).

This is an inherent rule built into the number system.  I do not know why it has been shown above as something unique to RudrasUkta.  It could be an attempt of retrofitting and reading into ancient scriptures things that were not intended by the original composers.

Arvind Kolhatkar.

[Arvind_Kolhatkar]

I could also have added in the above that it can be easily proved for any natural number 'n' that the sum of all odd numbers upto the odd number (2n +1) is equal to (n + 1)^2.

To see this, recollect the formula of the sum of all natural numbers upto the number 'n' = (n)(n +1) /2.  (This is an arithmetical progression with 1 as the first term and 1 as the common difference.)

Therefore, the sum of all natural numbers upto the number (2n + 1) will be (2n + 1)(2n + 2) /2 = (2n +1)(n + 1)

In this sum are included all even numbers starting from 2,4,6 and so on.  If we sum these up and deduct that sum from the sum of all natural numbers upto the number (2n + 1) , the remainder will be the sum of all odd numbers upto (2n +1).

Now, 2 + 4 + 6 +.....+ 2n = 2(1 + 2 + 3 +....+n) = 2(n)(n +1)/2 = (n)(n + 1).

Deduct this from the total of all numbers upto (2n + 1) thus:

(2n +1)(n + 1) minus (n)(n + 1) 

Take out the common factor (n + 1) .  You get

(n + 1) (2n + 1 minus n) = (n + 1)(n + 1) = (n + 1)^2.

Arvind Kolhatkar.

[G S S Murthy]

My point was just this: if the Vedic text refers only upto 17 and does not go beyond, 17 has a uniqueness mathematically.

Regards,

Murthy

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[Rajagopal Iyer]

On Sun, Nov 16, 2014 at 11:51 AM, G S S Murthy <murt...@gmail.com> wrote:
> I do not understand anything of this and strictly have no business to make a
> comment. But if something stops at 17, it may be remarkable, in that there
> are only 17 pattern groups which cover an infinite plane. I just read about
> it.
> Regards,
> Murthy
>

Kindly use bottom or interleaved posting style.

BTW can you provide a link for understanding pattern groups infinite plane

[Hnbhat B.R.]

I do not know algebra or mathematics. All the numerals are used in the
famine gender should denote some noun in feminine gender and here the
noun counted is missing.

Please explain what it is or is it generally referring the numbers
themselves, one, two, three. and it does not stop here only by 17 but
48 अष्टाचत्वारिंशच्च मे. beginning from चतस्रश्च मे, अष्टौ च मे,
gradually increased by 4. up to 48 with even numbers list.

As commented these two lists denote the numbers only. While all the
others words requested are only some thing material or subjective
things, why these numbers are requested? Please try to find the
answer. Anyhow, there are numbers beyond 48 and the need to divided
them into two separate lists? Any reason beyond teaching mathematics?
or just to teach mathematics?

[Hnbhat B.R.]

Oh sorry. I did not read completely the first post.

Here is a commentary explaining all the terms in terms of Philosophy
as already explained in the first post. Thanks for the information.

[Arvind_Kolhatkar]

I was not trying to explain any math at the bottom of the enumeration in Anuvaaka 11 of Chamaka but only answering to Rajagopal Ayer's (possible) suggestion that there was a mathematical mystery involved there.

As to what the sequence of odd numbers 1 to 33 and another sequence even numbers 4 to 48 mean in that Anuvaaka, I am too modest to hazard a guess.  It is a mystery to me, not resolved even by reading traditional commentators like SayaNa and Bhattabhaaskara.  SayaNa actually does not say anything about it beyond mentioning 'एकादिशब्दा: संख्यापरा:'.  (please see attachment below.)  The Anandashrama text that I have does not contain anything from Bhattabhaaskara.

I have a Marathi commentary called 'रुद्रार्थदीपिका' by श्रीपादशास्त्री किंजवडेकर, a well-known Maharashtrian scholar of the mid-20th century.  He explains these numbers in terms of traditional philosophy as 

एक - अविकृत, निर्गुण, निराकार ब्रह्म

तिस्र: - Three guNas as सत्त्व, रज, तम

पञ्च - पञ्चमहाभूतानि 

सप्त - ५ ज्ञानेन्द्रियs + मनस् + बुद्धि

नव - नवद्वारयुक्त मनुष्यदेह

एकादश - ५ प्रमुख प्राण (प्राण, अपान, समान, व्यान, उदान) + ५ subsidiaries as देवदत्त, धनंजय, नाग, कूर्म, कृकल + सुषुम्ना नाडी.

I am skeptical of this explanation couched in philosophical terminology because most of these concepts of philosophy were created in the post-Vedic period.  Explaining Rudraadhyaaya relying on them looks to me like retrofitting.  

Retrofitting has been going on with Rudraadhyaaya for the last 2000 years.  The Vedic deity Rudra has been totally identified with the post-Vedic deity of Shankara.  Terms such as नीलग्रीव, शिव, गिरिश, पशुपति, कपर्दिन् employed in Rudraadhyaaya have been made to agree with later-day mythology of Shankara consuming the Halaahala poison, living on Mount Kailasa.  So much so that while Vedic Aryans looked upon शिश्नपूजा with abhorance (Rigveda VII.21.5, X.99.3), लिंगपूजा has become the central tenet of Shaivism.

Arvind Kolhatkar.

[Taff Rivers]

Houston, we've had a problem here.

  Down on Earth, the problem remains:

While I have no problem with counting, even up to 33,000, should I have to, I am having a small problem with locating some Naiyāyikas here:

"The numbers 1 to 33 represent the 33000 base pairs of mitochondrial base pairs of DNA."

 

And an even larger problem as to where the great'* comes in, even when making allowance for what's hiding within the etc.'s?

I am able to resolve these issues when I look with eyes wide shut, but ...

  Taff Rivers

 great'*

–interj.

22. (used to express acceptance, appreciation, approval, admiration, etc.).

[G S S Murthy]

Pl visit 

http://en.wikipedia.org/wiki/Wallpaper_group

to know more about tiling pattern groups.

Regards

Murthy

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