Math, Krishna and Shiva

[Vidya R]

गोपीभाग्यमधुव्रातशृङ्गिशोदधिसन्धिग ।

कलजीवितखाताव गलहालारसंधर ॥

namassarvebhyaH |

It is said that the above verse has 3 meanings -> 

1.  descriptive of Krishna

2.  descriptive of Shiva

3.  a mathematical formula

While the mathematical aspect is well explained, the first two are not.  My sister's elderly neighbor is very desirous of knowing 1 and 2.  Can somebody offer those 2 interpretations?

I found an online, a translation as follows:

"O Lord anointed with the yogurt of the milkmaids' worship (Krishna), O savior of the fallen, O master of Shiva, please protect me."

The verse is quoted in a book on Vedic Mathematics.

Thanks in advance, from me, my sister and her elderly neighbor :)

Vidya

[Arvind_Kolhatkar]

Vidya,

<The verse is quoted in a book on Vedic Mathematics. >

1) Can you explain the mathematical meaning of the verse?

2) The following is for the learned Group as a whole.

I believe that the phrase Vedic Mathematics has its origin in a book
of that title written by Swami Bharati Krishna Tirtha and published
posthumously in 1965 after Swamiji’s demise in 1960 due to old age.
It was going to be the first among 16 such books that Swamiji was
going to write but unfortunately he died just after completing the
first book. Swamiji claimed to have rediscovered the sutras of Vedic
Mathematics by his deep study of the Vedas, especially Atharva Veda.

Do we know anything about the process by which Swamiji reached these
secrets and can we identify the exact sources or words underlying
them? Otherwise, it is just an ‘ipse dixit’ of Swamiji. Absence of
these may well lead to the suspicion that these sutras were Swamiji’s
own creations, masqueraded as ‘Vedic’ to gain wider acceptance and
instant belief from the believers.

Also, I wonder what is ‘mathematics’ about the sutras? They are
basically complex ways of computing arithmetical numbers and, because
of that reason, do not rise above the level of school arithmetic.
Mathematics is much more than that. It generalizes from the
particular and identifies common elements between apparently disparate
things, which are not necessarily numbers only.

This reminds me of a performance of Shakuntala Devi that I had
witnessed several decades ago as a post-graduate student of
mathematics. For that performance, we had created in advance many
problems of arithmetical calculations and painstakingly found the
answers. Armed with this elaborate preparation, we threw the problems
at her one after the other. When a problem was posed to her she would
close her eyes, think for a few seconds and dictate the answer off the
bat! It was amazing. She certainly had a gift of an intuition with
arithmetical numbers but nobody called her a mathematician for that
reason.

I know that the above may sound sacrilegious to some but I believe, in
the modern times it is our right to demand reasoned answers and not
just be invited to rely on श्रद्धा, which is not an acceptable
standard of proof. Please notice the word परिपृच्छति in the श्लोक
below:

यः पठति लिखति पश्यति परिपृच्छति पण्डितानुपाश्रयति।
तस्य दिवाकरकिरणैर्नलिनीदलमिव विकास्यते बुद्धिः॥

Arvind Kolhatkar, Toronto, March 16, 2011.

[Arvind_Kolhatkar]

I have now found the arithmetical meaning of this verse, as extracted
by Vidya, with the help of the internet. For this, assign values to
letters as under. Ignore vowels and take only consonents

क ट प य = १
ख थ फ र = २
ग द ब ल = ३
घ ध भ व = ४
ञ (ज्ञ?) न म श = ५
च त ष = ६
छ थ स = ७
ज ड ह = ८
झ थ = ९
क = ०

The verse reads

गोपीभाग्यमधुव्रातशृङ्गिशोदधिसन्धिग ।
कलजीवितखाताव गलहालारसंधर ॥

Now write the verse as

गो पी भाग् य/ म धुव् रा त/ शृङ् गि शो द/ धि सं धि ग
क ल जी वि/ त खा ता व/ ग ल हा ला/ र सं ध र

and assign numerical values as in the table. What you get is

3 1 4 1/ 5 9 2 6/ 5 3 5 3/ 9 7 9 3/
1 3 8 4/ 6 2 6 4/ 3 3 8 3 /2 7 9 2

which is almost the expansion of pi/10 upto 28 decimal places. The
difference is only in one digit in the first line and two digits in
the second

3 1 4 1/ 5 9 2 6/ 5 3 5 8/ 9 7 9 3/
2 3 8 4/ 6 2 6 4/ 3 3 8 3/ 2 7 9 5

The value of pi/10 upto the first 28 places, as ascertained from two
different internet sources, is
.3141 5926 5358 9793 2384 6264 3383 2795

An inteellctual tour de force indeed...

That leaves the second question. How do you construe the verse to
apply to Krishna and Shiva? Can some among the learned members
explain?

Arvind Kolhatkar, March 16, 2011.

[Sunder Hattangadi]

This is known as the "kaTapayAdi" algorithm or system.   The following and many more reference would be useful: (traced upto Aryabhatta).   http://en.wikipedia.org/wiki/Bharati_Krishna_Tirthaji   He gives a poem in Anustub metre, couched in the alphabetic Code-Language [15] that has three meanings, a hymn to Lord Srī Kṛṣṇa, a hymn in praise of the Lord Shri Shankara, and the third the value of pi/10 to 32 decimal places, pi/10 = 0.31415926535897932384626433832792... with a "self-contained master-key" for extending the evaluation to any number of decimal places.[16] 15.^ pages 294-195, 209-210 16.^ Pages 362-363, Vedic Mathematics Sri Bhārāti Kṛṣṇa Tīrtha - Vedic Mathematics, Motilal Banarassidas Publications, Delhi, (1992) ISBN 81-208-0164-4 ================================ http://www.hindupedia.com/en/Mathematics ================================ http://www.namboothiri.com/articles/katapayaadi.htm         Regards,   sunder --- On Wed, 3/16/11, Arvind_Kolhatkar <kolhat...@gmail.com> wrote:

[Jay Dave Zoom]

There is a book which tabulates words used for numbers. For example, it is known that Trigonometry originated in India. How were the sin, cos and tan values tabulated? A book has a Stotra like collection of verses and it was the Sine Table!   I am away from my desktop that I usually usea nd has my bookmarks. I will be able to send that once I am back in 2/3 days. If that is little long, you may find it by googling enough.   Meaning leading to shiva may be some powerfull Yamak if the Shloka starts with Gopi....   --- On Wed, 3/16/11, Vidya R <imar...@yahoo.com> wrote:

namassarvebhyaH |

1.  descriptive of Krishna 2.  descriptive of Shiva 3.  a mathematical formula

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[Vasu Srinivasan]

katapayaadi system is not attributed to Aryabhatta. It is attributed to vararuchi and the earliest reference found is said to be in chandravaakya.

Aryabhatta had a completely different system that is fantastically suited to represent astronomical (literally) numbers. I have blogged about it in http://vagartham.blogspot.com/2008/09/aryabhattas-numerical-encoding.html

coming back to the sloka - shiva krishna reference.. i dont know the word-by-word meaning but the word references are enough to suggest praisings to shiva and krishna (gopi, madhu, srngi, galahaala, kalajIvita etc).. Likely the first line is Krishna, second line is Shiva.

--
Regards,
Vasu Srinivasan
-----------------------------------
vagartham.blogspot.com
vasya10.wordpress.com

[Arvind_Kolhatkar]

The above verse

गोपीभाग्यमधुव्रातशृङ्गिशोदधिसन्धिग ।
कलजीवितखाताव गलहालारसंधर ॥

How is it construed to describe Krishna and Shiva?

[Sunder Hattangadi]

http://www.indiadivine.org/audarya/vedic-astrology-jyotisha/583815-fwd-vakya-panchangas-vararuchi.html   The Vakyas used in South India for computation of planetary longitudes is usually ascribed to Vararuchi. If we review the astronomical tradition of South India, we could locate 3 Vararuchis...............................................   Another reference gives Vararuchi as one of 9 gems in Vikarmaditya court (3rd cent. A.D.)     Regards,   sunder           --- On Wed, 3/16/11, Vasu Srinivasan <vas...@gmail.com> wrote:

[Sunder Hattangadi]

Venturing a wild guess here:   gala + hAlA + rasaM + dhara  refers to Shiva, holder of a snake round his neck.       Regards,   sunder

[Vidya R]

"Meaning leading to shiva may be some powerfull Yamak if the Shloka starts with Gopi...."

Thank you.  This is one clue, but, not sufficient for me to pick up and follow.  I hope you, or others, can take this further.

To address other questions / points:

1.  Mathematical aspect is well documented and analyzed - my question does not pertain to it.

2.  My first guess was that the first quarter was on Krishna, the second on Shiva, the last 2 being the mathematical stuff.  But, it turns out that the first is also mathematical, and the last line has some comprehensible meaning.  So, I have to go with the original expectation that all whole verse can be parsed in 3 different ways to resolve into 3 interpretations.

"gala + hAlA + rasaM + dhara  refers to Shiva, holder of a snake round his neck."

Vidya

---

From: Jay Dave Zoom <zoom...@sbcglobal.net>
To: sams...@googlegroups.com
Sent: Wed, March 16, 2011 1:38:37 PM
Subject: Re: [Samskrita] Math, Krishna and Shiva

[Sunder Hattangadi]

The book is titled: Tarkasamgraha  by   Neelakantha. It is available in Digital Library of India (171 pages).   Att. file shows the cover page of the book.     Regards,   sunder

[hnbhat B.R.]

Thanks for the efforts.

I had seen this verse tossed in many other forms and without any successful explanation including this one too long ago, but no satisfactory explanation was offered in any. It is not expected too unless the commentator comments them himself.

The main purpose of the verse is astronomical calculation and it is served. Further, if it is not commented, as in the case of the most cases of Yamaka, it is hopeless to spend time with groping with it. I remember a verse I had in praise of Shiva:

त्वयि सति शिव दातर्यस्मदभ्यर्थिताना-

मितरमनुसरन्तो दर्शयन्तो ऽर्थिमुद्राम्।

चरमचरणपातैर्दुर्ग्रहं दोग्धुकामाः

करभमनुसरामः कामधेनौ स्थितायाम्।।

O Shiva, when you are here to bestow on us whatever we desire, we are following other deities stretching hand in begging mood. (This is like)

We desire to milk the camel which is difficult to achieve due to kicking with its hinder legs, while we have within our reach, the Kamadhenu itself (which is capable of bestowing us with whatever we desire.).

Just though of yamaka-s and other Citra-kavya-s available in Sanskrit poetical verses, while we are trying to solve this riddle. 15th Sarga of Magha (Shishupalavadha) and Kiratarjuniya, respectively be interpreted, as describing reproaches as well as praises of Krishna and Shiva respectively. There are commentaries available too. If we want to enjoy, that is always available so that we can build up our vocabulary too.

Hence I didn't try at all. Hope somebody would come up with proper solution.

Wish you all the best of luck.

--
Dr. Hari Narayana Bhat B.R.
EFEO,
PONDICHERRY

[hnbhat B.R.]

On Thu, Mar 17, 2011 at 8:03 AM, Sunder Hattangadi <sun...@yahoo.com> wrote:

The book is titled: Tarkasamgraha  by   Neelakantha. It is available in Digital Library of India (171 pages).   Att. file shows the cover page of the book.     Regards,   sunder

Does this Tarkasangraha contain Trigonometry? May be. 

But the work as can be seen from the image, is entitled Tantra-Sangraha, a work on Ganita and not on Tarka.

Tarka-sangraha is another work by Annambhatta, a primer to both Indian Nyaya and Vaisheshika system. I was confused to read the title.

Anyhow, thank you for the information on Ganita. Lilavati, is the popular one for Ganita.

With regards

[hnbhat B.R.]

गोपीभाग्यमधुव्रात - शृङ्गिशोदधिसन्धिग

खलजीवितखाताव गलहालारसंधर|

Anyhow, here is not much to be achieved by the grammatical analysis as the Translation somehow is imaginary from the obvious words. I could not follow the translation at all.

If we take the grammatical analysis for the translation, it would some how applicable for both Shiva and Vishnu too common adjectives for both. But nowhere on the pages I found on the net, this verse has been commented differently in its mathematical value which is the main objective. The remaining can be made out from your imagination. 

गोप can mean Krishna as the cowherd and also Shiva in his capacity as पशुपति, and his wife can be गोपी = पार्वती, and the rest common for both. भाग्यमेव मधु, तस्य व्रातः = समूहः, तत्सबुद्धौ गोपीभाग्यमधुव्रात - common address in the vocative case ending.

शृङिशो दधिसन्धीन् गच्छति इति शृङ्गिशो दधि-सन्धि-ग =

Following each cow, one who goes the cowpen  or the hut where curd is kept for selling. दधि-सन्धि; 

शृङिणि = गिरौ शेते इति शृङ्गिश, vocative of Shiva, who is called गिरिश elsewhere. Now remaining will be उदधि-सन्धिं गच्छति इति उदधिसन्धिग; It may refer somehow, mean his presence at the churning of Milk Ocean. I don't have a clear idea, by splitting this 

way. उदकानि धीयन्ते अत्रेति उदधिः, सन्धीयते इति सन्धिः = juncture;

Any suggestion on this point is welcome.

खलजीवितखात = खलानां जीवितानि खातानि येन सः, खलजीवितखात;

One who has uprooted the lives of wicked persons;

(khan = to root up (Monier-Williams, Sir M. (1988));

which can be commonly applicable for both Shiva and Krishna.

अव = please protect. 

 

गलहालारसंधर = गले हालारसं धरतीति गलहालारसंधर;

In the first Krishna's case, गले हाला यस्य सः, गलहालः, कालियः, तस्मिन् रसं धरतीति विनोदं करोतीति गलहालारसंधर;

In the case of Shiva, it is he himself, carry the हालाहल venom during the churning of the Milk Ocean, हालाहलरसं धारयतीति It can be also as denoting Shiva as carrying the serpent, which is having हाला venom as suggested by Vidya.

This much can be got out of Grammatical Analysis of the structure. But in the third linke, it is found as खल in all the web pages, instead of कल as given by Vidya.

There are many discussions about the authenticity of the claim to be Vedic sourced mathematics. I saw in one page, it is ascribed to Atharva-veda parishishta. But no specific bibliographic reference is given. Many believe that it was produced by the Swamyji himself, who had through mathematical knowledge and ascribed its authenticity to Vedic source. According to some, still by the fans of the Swamyji, it is adopted for teaching mathematics in some corners to make it popular. The source of the information could not be verified.

Hope this is an attempt of grammatical analysis as proposed. More  could be got, by imagining the possible qualifications with the same words and derive them from following the norms of grammar. I have purposefully omitted the reference to the rules concerned in the Ashtadhyayi text. If anybody feel the necessity, I can provide.

Sorry for the lengthy message.

[lalitaalaalitah]

गोपीभाग्यमधुव्रातशृङ्गशोदधिसंधिग ।

खलजीवितखातावगलहालारसन्धर|  ॥

 

कृष्णपक्षे -

 

गोपीभाग्य = गोपीनां गोपस्त्रीणां भाग्य ।

 

मधुव्रात = मधुदैत्यस्य व्याध नाशक ।

 

शृङ्गशो दधिसन्धिग = शृङ्गेण शृङ्गेण कृतेनाभिषेकेन दधिसन्धिं प्राप्त दधिलिप्त ।

 

अथवा

 

मधुव्रातशृङ्गश = क्षीरसमूहशिखरे शेते इति ।

 

उदधिसन्धिग = समुद्रमन्थनकाले कूर्मात्मनोदधिं प्राप्त ।

 

खलजीवितखात = खलानां जीवितानि खातानि येन , खलजीवितेभ्यः खनित्रमिवेति वा ।

 

गलहालारसन्धर = गले हालारसं यस्य तं सर्पं कालियं धरतीति ।

 

अव = रक्ष ।

 

शिवपक्षे -

 

गोपीभाग्य = गोप्या जगद्रक्षिकाया उमाया भाग्य ।

 

मधुव्रातशृङ्गश = मधु क्षीरं तस्य व्रातस्समूहः तत्सन्निभे धवले शृङ्गे कैलासशिखरे शेते इति मधुव्रातशृङ्गश ।

 

उदधिसन्धिग = समुद्रमन्थनकाले । तत्रैव मोहिन्या मोहितोऽयमभवदिति प्रसिद्धम् ।

 

खलजीवितखात = खलानां जीवितानि खातानि येन , खलजीवितेभ्यः खनित्रमिवेति वा ।

 

गलहालारसन्धर = गले हालारसं धारयतीति गलहालारसन्धर ।

अथवा

गलस्थितविषे रसं स्नेहं धारयतीति । अत एव न तत्त्यक्तमद्यावधि ।

अथवा

गलहालान्सर्पान्रसेन धारयतीति ।

 

अव = रक्ष ।

 

 

 

From: hnbhat B.R.

Sent: Thursday, March 17, 2011 10:52 AM

To: sams...@googlegroups.com

Subject: Re: [Samskrita] Math, Krishna and Shiva

[venetia ansell]

I had seen this same shloka but, while it also gave the value of Pi, it was read as a verse in praise of Krishna and then of Rama.  If I remember correctly this double reading was achieved by reading the shloka first left to right and then right to left. This anuloma/pratiloma technique is I believe a particular kind of citrakavya. 

2011/3/17 lalitaalaalitah <lalitaa...@gmail.com>

[hnbhat B.R.]

It would be helpful if you can please explain in anuloma and pratiloma. It will be interesting too.

Thanks for the suggestion.

2011/3/17 venetia ansell <venetia...@gmail.com>

[श्रीमल्ललितालालितः]

श्रीमल्ललितालालितः
lalitAlAlitaH

2011/3/17 venetia ansell <venetia...@gmail.com>

I had seen this same shloka but, while it also gave the value of Pi, it was read as a verse in praise of Krishna and then of Rama. 

Now, that is difficult.

If I remember correctly this double reading was achieved by reading the shloka first left to right and then right to left. This anuloma/pratiloma technique is I believe a particular kind of citrakavya. 

So, you read some explanation. Try to search and post. It will help all. We have never seen any commentary.

[venetia ansell]

Namaste

 

I will try to find the reference tonight and post tomorrow.

2011/3/17 श्रीमल्ललितालालितः <lalitaa...@gmail.com>

[hnbhat B.R.]

Really it would be helpful.

कृष्णपक्षे गोपीभाग्यस्य मध्व्रातत्वेन निरूपणे तस्य मधुराधिपतेरखिलस्यापि  मधुरत्वमेव निमित्तम्, यथा गीतमष्टाभिः श्लोकैः -

अधरं मधुरं वदनं मधुरं नयनं मधुरं हसितं मधुरम् |. हृदयं मधुरं गमनं मधुरं मधुराधिपतेरखिलं मधुरम् || १||--

इत्यादिभिः।

[Sunder Hattangadi]

Apologies for the careless error in typing the title! Yes, it Tantrasamgraha.   Regards,   sunder --- On Wed, 3/16/11, hnbhat B.R. <hnbh...@gmail.com> wrote:

From: hnbhat B.R. <hnbh...@gmail.com> Subject: Re: [Samskrita] Math, Krishna and Shiva

[lalitaalaalitah]

 

(कृष्णपक्षे गोपीभाग्यस्य मध्व्रातत्वेन निरूपणे तस्य मधुराधिपतेरखिलस्यापि  मधुरत्वमेव निमित्तम्, यथा गीतमष्टाभिः श्लोकैः -

अधरं मधुरं वदनं मधुरं नयनं मधुरं हसितं मधुरम् |. हृदयं मधुरं गमनं मधुरं मधुराधिपतेरखिलं मधुरम् || १||—

 

इत्यादिभिः।

)

 

कर्मोपासनजन्यापूर्वस्य भाग्यपदार्थत्वेन मधुत्वमपि पुण्यगतमेवेति तत्पाकत्वं कृष्णस्य सम्भवत्येव । पुण्यलभ्ये पुण्यत्वोपचारात् । एवमेवोमातपोजनितापूर्वसमूहात्मकत्वं शिवस्य । एवमत्र स्तोत्रसमन्वयाग्रहे हृदयं मधुरं पुण्यात्मकमिति व्याख्यातव्यम् । तच्च नोचितम् ।

 

कृष्णावयवादीनां मधुरत्वं प्रकाशयत्स्तोत्रं तु गोपीभाग्यस्य, तल्लभ्यस्येति तु पूर्ववत् , कृष्णस्य मधुरावयवसमूहत्वं द्योतयति । तथात्वे न समस्तपदं स्यात् । मधुव्रातपदस्यार्थप्रकाशनसामर्थ्याद्गोपीभाग्यपदेन कृष्णवाचकेनाकाङ्क्षाशमनात् । समस्तत्वे त्वपूर्वघटिता पूर्वोक्तैवोचिता व्याख्या ।

 

इति

विज्ञापयति

॥श्रीमल्ललितालालितः॥

 

[hnbhat B.R.]

2011/3/17 lalitaalaalitah <lalitaa...@gmail.com>

गोपीभाग्यत्वेन रूपिते, रूपकान्तरोत्पत्तिर्न पौनरुक्त्यायेत्यालंकारिकनयः। गोपीभाग्यमेव मधुव्रात इति रूपकादेव रूपकान्तरोत्पत्तिः, मधुराधिपतेरुपमानत्वमुभयत्राप्यव्याहतमेवेति नात्र साकाङ्क्षत्वनियमः बाधकः, समस्तत्वे ऽपि इति, "कमले कमलोत्पत्तिर्दृश्यते न श्रूयते" इत्यादिवद् रूपकद्वयप्रयोगः, समस्तासमस्तत्वं न भेदकमस्य विषयस्येति यथामति विज्ञाप्यते। यदि साक्षाद् वाचकत्वं तथापि रूपके बाधाभावं पश्यामः।

शेषे शेषा विद्वांसः प्रमाणम्।

--

[Shreyas P. Munshi]

To: samskrita

Subject: [Samskrita] Re: Math, Krishna and Shiva

Date: Wed, 16 Mar 2011 20:46:56 IST Arvind_Kolhatkar wrote (to Vidya-ji):

"I know that the above may sound sacrilegious to some but I believe, in the modern times it is our right to demand reasoned answers and not
just be invited to rely on श्रद्धा, which is not an acceptable
standard of proof".

Respected Arvind-ji,

I admire your insistence on maintaining an objective, unbiased , approach before accepting or rejecting anything. First it was on Macaulay. It virtually woke me up! And now on use of the adjective Vedic...

In full support of the paragraph of your mail which I have quoted above, I may mention that some six years ago,a gentleman (in Mumbai) approached the medical association to teach what he called was Vedic Meditation. Many doctors fell for it but on persistent queries by one unassuming doctor, the fellow could not say why it was called Vedic Meditation by him. When the doctiors kept demanding the answer, he blurted out that meditation is an ancient technique and it was easy to attract participants with the adjective...Vedic!

Well in the above case nothing was lost because basically it was just a modified shavaasan yoga technique. It had to do some good! But the point is that it showed that one's offer becomes more acceptable by using the adjective ...Vedic..for better marketing! (I hasten to mention: No aspertions cast on respected Vidya-ji's post. I am only admiring your insistence on the objective approach).
Submitted...Shreyas

just be invited to rely on श्रद्धा,which is not an acceptable

standard of proof. Please notice the word परिपृच्छतिin the श्लोक

below:

यः प��ति लिखतिपश्यति परिपृच्छतिपण्डितानुपाश्रयति।

तस्य दिवाकरकिरणैर्नलिनीदल��®िवविकास्यते बुद्धिः॥

Arvind Kolhatkar, Toronto, March 16, 2011.

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[श्रीमल्ललितालालितः]

गोपीभाग्यत्वेन रूपिते,

कृष्णे इति शेषः स्यात् । एतत्पृथक्पदमपि । मया तथैवोक्तत्वात् ।

रूपकान्तरोत्पत्तिर्न पौनरुक्त्यायेत्यालंकारिकनयः।

कस्मात्पुनरुक्तिः । न हि मधुव्रातपदमपि तथैव रूपयति तम् ।

गोपीभाग्यमेव मधुव्रात इति रूपकादेव रूपकान्तरोत्पत्तिः,

समानपदे एकस्मिन्नेव रूपके समन्वयोऽभिप्रेतस्याद्भवताम् । तथा चापूर्वपरैव व्याख्योचिता । भाग्यपदस्य तत्रैव प्रसिद्धत्वात् । अपि च भाग्यमिति क्लीबप्रयोगेणापि तथात्वं समर्थितमेव भवता ।

मधुराधिपतेरुपमानत्वमुभयत्राप्यव्याहतमेवेति

तत्र न विवादः । सदोषत्वादावेव सः ।

नात्र साकाङ्क्षत्वनियमः बाधकः,

नायं नियमत्वेनोदाहृतः । व्यस्तपदपक्षे न्यूनतावारणाय तदुक्तेः ।

समस्तत्वे ऽपि इति, "कमले कमलोत्पत्तिर्दृश्यते न श्रूयते" इत्यादिवद् रूपकद्वयप्रयोगः,

पदद्वयमत्र भिन्नार्थकमित्यवधेयम् । प्रकृते तु न तथा । कृष्णमात्रवाचकपदद्वयोक्तेः ।

समस्तासमस्तत्वं न भेदकमस्य विषयस्येति

अस्य विषयस्येति किम् । व्याख्यानस्येति चेत् । कथं नेत्युच्यते । समस्तपक्षे दोषोक्त्यैव व्यस्ततायाः प्रदर्शितत्वात् । 

यथामति विज्ञाप्यते। यदि साक्षाद् वाचकत्वं तथापि रूपके बाधाभावं पश्यामः।

साक्षाद्वाचकत्वं कस्य पदस्य । न हि रूढं तयोरन्यतरदपि पदं कृष्णे ।

इति

श्रीमल्ललितालालितः

lalitAlAlitaH

[hnbhat B.R.]

2011/3/17 श्रीमल्ललितालालितः <lalitaa...@gmail.com>

ऒमिति ब्रूमः।

परस्परतपःसम्पत्फलायितपरस्परौ।

प्रपञ्चमातापितरौ जायापती स्तुमः॥

[श्रीमल्ललितालालितः]

श्रीमल्ललितालालितः
lalitAlAlitaH

ऒमिति ब्रूमः।

The time to stop talking is when the other person nods his head affirmatively but says nothing.
-- Henry S. Haskins

So, stopping.
 

परस्परतपःसम्पत्फलायितपरस्परौ।

प्रपञ्चमातापितरौ जायापती स्तुमः॥

 

सुन्दरमेतत् ।  किन्तु प्राञ्चौ जायापतीति पठनीयम् ।

[hnbhat B.R.]

2011/3/17 श्रीमल्ललितालालितः <lalitaa...@gmail.com>

-- 

क्षमा याचे लेखनप्रमादाय+  

--

[hnbhat B.R.]

2011/3/17 hnbhat B.R. <hnbh...@gmail.com>

2011/3/17 श्रीमल्ललितालालितः <lalitaa...@gmail.com>

श्रीमल्ललितालालितः
lalitAlAlitaH

ऒमिति ब्रूमः।

The time to stop talking is when the other person nods his head affirmatively but says nothing.
-- Henry S. Haskins

So, stopping.
 

परस्परतपःसम्पत्फलायितपरस्परौ।

प्रपञ्चमातापितरौ जायापती स्तुमः॥

 

सुन्दरमेतत् ।  किन्तु प्राञ्चौ जायापतीति पठनीयम् ।

-- 

क्षन्तव्यो मे ऽपराधः शिव शिव शिव भोः श्रीमहादेव शम्भो॥

[श्रीमल्ललितालालितः]

Did you find that ?

श्रीमल्ललितालालितः
lalitAlAlitaH

[S. L. Abhyankar]

नमो नमः !
कृपया किञ्चित् परिष्करणं ग्राह्यं भवतु ।
क्षः = शून्यम् ।
वर्णानां मूल्यानि
कादि नव टादि नव पादि पञ्चक याद्यष्टक क्षः शून्यम् ।
एतस्मिन् सूत्रे निबद्धानि ।
सस्नेहम् ,
अभ्यंकरकुलोत्पन्नः श्रीपादः |
"श्रीपतेः पदयुगं स्मरणीयम् ।"

Arvind Kolhatkar, March 16, 2011.

[Sunder Hattangadi]

There is a composition Raghava Yadaviyam by Venkatadhvari, which may be the one being referred to (?):

 

http://sanskritdocuments.org/all_pdf/raaghavayaadaviya.pdf

 

http://sanskritdocuments.org/all_txt/raaghavayaadaviya.txt

 

 

 

Regards,

 

sunder

 

 

 

 

 

 

 

From: श्रीमल्ललितालालितः <lalitaa...@gmail.com>
To: sams...@googlegroups.com
Sent: Tuesday, April 19, 2011 3:37 AM
Subject: Re: [Samskrita] Math, Krishna and Shiva

[venetia ansell]

Namaste sarvebhyaH

vilambaH kSamyatAm - I had said that I would post the verse I thought I remembered seeing in which a shloka that gives the value of Pi also reads as a verse in praise of Krishna one way and Rama the other way.  I am afraid I have either got two things mixed up or have misplaced the book in question.  There is certainly a verse about Krishna and Rama which can be read anuloma and pratiloma but it may not also contain the value of Pi.

 

At any rate here is what I have found in the book 'Pride of India' produced by Samskrita Bharati (which by the way is full of interesting facts):

 

gopIbhAgya madhuvrAta shRNgIshodadhisandigha

khalajIvita khAtAva galahAlAharasandhara

 

the translation given is "Oh (Krishna), the fortune of the gopis, the destroyer of the demon Madhu, protector of cattle, the one who ventured the ocean depths, the destroyer of evil-doers, the one with a plough on his shoulder and the bearer of nectar, may you protect us'

 

But I find this translation hard to follow - for instance how does 'vrAta' mean 'destroyer' and how does 'khala-jIvita' mean 'the destroyer of worthless men' rather than 'the life-force of worthless men'. I am also not familiar with the word khAtAva - perhaps the pada-ccheda given above is wrong.

 

Using the katapayaadi sankhya system you get the value of Pi: 3.1415926535897932384626433832792

 

Apologies is this is a repetition of the earlier discussion. If I am able to find the other palindrome verse I will post it.

 

ShubharAtriH

 

Venetia

2011/4/20 venetia ansell <venetia...@gmail.com>

Namaste Mahodaya,

bhavatA smAraNaM dattaM dhanyavAdaH.  dRSTvA ahaM e-patraM preSayAmi.

vilambaH kSamitavyaH.

Venetia

2011/4/20 श्रीमल्ललितालालितः <lalitaa...@gmail.com>

---------- Forwarded message ----------
From: श्रीमल्ललितालालितः <lalitaa...@gmail.com>
Date: 2011/4/19
Subject: Re: [Samskrita] Math, Krishna and Shiva

[श्रीमल्ललितालालितः]

2011/4/20 venetia ansell <venetia...@gmail.com>

Namaste sarvebhyaH

vilambaH kSamyatAm - I had said that I would post the verse I thought I remembered seeing in which a shloka that gives the value of Pi also reads as a verse in praise of Krishna one way and Rama the other way.  I am afraid I have either got two things mixed up or have misplaced the book in question.

Relief for me. Thank you.

[संस्कृत संवादः]

The below part is omitted in the website but available on scribd.

https://www.scribd.com/document/194521026/Vedic-Mathematics-and-Spiritual-Dimensions

सोमवार, 2 सितंबर 2024 को 1:04:07 pm UTC+5:30 बजे संस्कृत संवादः ने लिखा:

Based on below extract, I guess it has only one interpretation, that of krishna.

https://www.sanskritimagazine.com/vedic-mathematics-spiritual-dimension/

Tirtha Maharaja states, “In order to help the pupil to memorize the material studied and assimilated, they made it a general rule of practice to write even the most technical and abstruse textbooks in sutras or in verse (which is so much easier-even for the children-to memorize). And this is why we find not only theological, philosophical, medical, astronomical, and other such treatises, but even huge dictionaries in Sanskrit verse! So from this standpoint, they used verse, sutras and codes for lightening the burden and facilitating the work (by versifying scientific and even mathematical material in a readily assimilable form)!” [8] The code used is as follows:

The Sanskrit consonants

ka, ta, pa, and ya all denote 1;

kha, tha, pha, and ra all represent 2;

ga, da, ba, and la all stand for 3;

Gha, dha, bha, and va all represent 4;

gna, na, ma, and sa all represent 5;

ca, ta, and sa all stand for 6;

cha, tha, and sa all denote 7;

ja, da, and ha all represent 8;

jha and dha stand for 9; and

ka means zero.

Vowels make no difference and it is left to the author to select a particular consonant or vowel at each step. This great latitude allows one to bring about additional meanings of his own choice. For example kapa, tapa, papa, and yapa all mean 11. By a particular choice of consonants and vowels one can compose a poetic hymn with double or triple meanings. Here is an actual sutra of spiritual content, as well as secular mathematical significance.

gopi bhagya madhuvrata

srngiso dadhi sandhiga

khala jivita khatava

gala hala rasandara

While this verse is a type of petition to Krishna, when learning it one can also learn the value of pi/10 (i.e. the ratio of the circumference of a circle to its diameter divided by 10) to 32 decimal places. It has a self-contained master-key for extending the evaluation to any number of decimal places.

The translation is as follows:

O Lord anointed with the yogurt of the milkmaids’ worship (Krishna), O savior of the fallen, O master of Shiva, please protect me.

At the same time, by application of the consonant code given above, this verse directly yields the decimal equivalent of pi divided by 10: pi/10 = 0.31415926535897932384626433832792. Thus, while offering mantric praise to Godhead in devotion, by this method one can also add to memory significant secular truths.

बुधवार, 20 अप्रैल 2011 को 10:35:56 pm UTC+5:30 बजे श्रीमल्ललितालालितः ने लिखा:

[T.K Gopalan]

संस्Tकृतसंवादः said:

he Sanskrit consonants

ka, ta, pa, and ya all denote 1;

kha, tha, pha, and ra all represent 2;

ga, da, ba, and la all stand for 3;

Gha, dha, bha, and va all represent 4;

gna, na, ma, and sa all represent 5;

ca, ta, and sa all stand for 6;

cha, tha, and sa all denote 7;

ja, da, and ha all represent 8;

jha and dha stand for 9; and

ka means zero.

Vowels make no difference and it is left to the author to select a particular consonant or vowel at each step. This great latitude allows one to bring about additional meanings of his own choice. For example kapa, tapa, papa, and yapa all mean 11. By a particular choice of consonants and vowels one can compose a poetic hymn with double or triple meanings. Here is an actual sutra of spiritual content, as well as secular mathematical significance.

gopi bhagya madhuvrata

srngiso dadhi sandhiga

khala jivita khatava

gala hala rasandara

Applyingthis formula, I get, not 3141592653, but 3143159421 for pix10:

ग प भ ग य म ध व र त 

3 1 4 3 1 5 9 4 2 1, not

3 1 4 1 5 9 2 6 5 3

What am I doing wrong?

***

On Mon, 2 Sep 2024 at 1:04 PM, संस्कृत संवादः <samskrit...@gmail.com> wrote:

Based on below extract, I guess it has only one interpretation, that of krishna.

https://www.sanskritimagazine.com/vedic-mathematics-spiritual-dimension/

Tirtha Maharaja states, “In order to help the pupil to memorize the material studied and assimilated, they made it a general rule of practice to write even the most technical and abstruse textbooks in sutras or in verse (which is so much easier-even for the children-to memorize). And this is why we find not only theological, philosophical, medical, astronomical, and other such treatises, but even huge dictionaries in Sanskrit verse! So from this standpoint, they used verse, sutras and codes for lightening the burden and facilitating the work (by versifying scientific and even mathematical material in a readily assimilable form)!” [8] The code used is as follows:

The Sanskrit consonants

ka, ta, pa, and ya all denote 1;

kha, tha, pha, and ra all represent 2;

ga, da, ba, and la all stand for 3;

Gha, dha, bha, and va all represent 4;

gna, na, ma, and sa all represent 5;

ca, ta, and sa all stand for 6;

cha, tha, and sa all denote 7;

ja, da, and ha all represent 8;

jha and dha stand for 9; and

ka means zero.

Vowels make no difference and it is left to the author to select a particular consonant or vowel at each step. This great latitude allows one to bring about additional meanings of his own choice. For example kapa, tapa, papa, and yapa all mean 11. By a particular choice of consonants and vowels one can compose a poetic hymn with double or triple meanings. Here is an actual sutra of spiritual content, as well as secular mathematical significance.

gopi bhagya madhuvrata

srngiso dadhi sandhiga

khala jivita khatava

gala hala rasandara

While this verse is a type of petition to Krishna, when learning it one can also learn the value of pi/10 (i.e. the ratio of the circumference of a circle to its diameter divided by 10) to 32 decimal places. It has a self-contained master-key for extending the evaluation to any number of decimal places.

The translation is as follows:

O Lord anointed with the yogurt of the milkmaids’ worship (Krishna), O savior of the fallen, O master of Shiva, please protect me.

At the same time, by application of the consonant code given above, this verse directly yields the decimal equivalent of pi divided by 10: pi/10 = 0.31415926535897932384626433832792. Thus, while offering mantric praise to Godhead in devotion, by this method one can also add to memory significant secular truths.

बुधवार, 20 अप्रैल 2011 को 10:35:56 pm UTC+5:30 बजे श्रीमल्ललितालालितः ने लिखा:

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[संस्कृत संवादः]

ग् and व् shouldn't be counted as it's not accompanied by a svara. Try this tool.

https://sanskrit.iitk.ac.in/jnanasangraha/sankhya/katapayaadi/decode/sa/

सोमवार, 2 सितंबर 2024 को 3:17:28 pm UTC+5:30 बजे T.K Gopalan ने लिखा:

[संस्कृत संवादः]

I had deleted my message and sent a clarification message but it's not delivered. I don't know if it's intentional as many times it happens. The original book also hints at 3 interpretations.

https://archive.org/details/vedic-mathematics-bharati-krishna-tirth-ji-maharaj/page/348/mode/1up

सोमवार, 2 सितंबर 2024 को 1:31:26 pm UTC+5:30 बजे संस्कृत संवादः ने लिखा:

[T.K Gopalan]

Kindly explain where one can find ‘a self-contained master key to determine pi to any number of decimal places’.

***

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[संस्कृत संवादः]

I don't know.

मंगलवार, 3 सितंबर 2024 को 11:03:49 am UTC+5:30 बजे T.K Gopalan ने लिखा:

[T.K Gopalan]

Yes. There appears to be no such master key here that I can see either.

Thepoem गोपीभाग्यमधुव्रात … does not appear to be a formula for evaluating pi to 32 decimal places. Rather, it encodes the value of pi to 32 decimal places using the कटपयादि system. The poem is a mnemonic, and not a formula.

 It is important to note this distinction.

***

To view this discussion on the web visit https://groups.google.com/d/msgid/samskrita/101feefa-5d08-44bc-8ad5-280ff34e3d2en%40googlegroups.com.

[अभ्यंकरकुलोत्पन्नः श्रीपादः | श्रीपतेः पदयुगं स्मरणीयम् ।]

You may like to see my blogpost <https://slabhyankar.wordpress.com/2015/01/03/learning-sanskrit-by-fresh-approach-lesson-no-120/> 

Also my YouTube video <https://youtu.be/QTG0Tw4mkuk?si=_kiSYPGiUqrrZfhG>

[संस्कृत संवादः]

I had checked it earlier. Writing is good but it lacks organisation. It should have clear outline and better organisation. Collapsible sections can be very helpful. 

Regards,

संस्कृत संवादः

linktr.ee/samvadah

शुक्र, 13 सित॰ 2024, 10:44 को अभ्यंकरकुलोत्पन्नः श्रीपादः | श्रीपतेः पदयुगं स्मरणीयम् । <sl.abh...@gmail.com> ने लिखा:

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[S. L. Abhyankar]

स्वमते स्वतंत्रो भवान् !

Cordially, S. L. Abhyankar
सस्नेहमिदम् अभ्यंकरकुलोत्पन्नस्य श्रीपादस्य |

"श्रीपतेः पदयुगं स्मरणीयम् ।"

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[T.K Gopalan]

Dear संस्कृत संवादः

I am unable to understand what you mean. Could you explain?

Do you agree with my view or not, that the poem merely encodes pi and is not a formula for evaluating pi and that there is here no formula for evaluating pi to any number of decimal places?

Thanks.

T K Gopalan

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[T.K Gopalan]

I am having difficulty figuring out his मत।

Cordially,

T K Gopalan

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[S. L. Abhyankar]

केनापि पृष्टम् अस्मिन् श्लोके किं सूत्रम् ? 

सूत्रम् तु "कादि नव टादि नव पादि पञ्च क्षः शून्यम्" इति मन्यते |

तत्सूत्रं तु श्लोके नास्ति इति सत्यम् | 

श्लोकपठने तु कृष्णशिवयोः स्तोत्रम् गम्यते | तथापि अनेन सूत्राधारेण अस्मिन् श्लोके परिघ-व्यासयोः गुणोत्तरम् सिध्यति एतदपि सत्यमेव | 

Cordially, S. L. Abhyankar
सस्नेहमिदम् अभ्यंकरकुलोत्पन्नस्य श्रीपादस्य |

"श्रीपतेः पदयुगं स्मरणीयम् ।"

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[S. L. Abhyankar]

तस्य मते सः स्वतन्त्रः | तत्र संवादेन किम् ? 

सर्वे मताः न स्खलनीयाः 

Cordially, S. L. Abhyankar
सस्नेहमिदम् अभ्यंकरकुलोत्पन्नस्य श्रीपादस्य |
"श्रीपतेः पदयुगं स्मरणीयम् ।"

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[T.K Gopalan]

Namaste.

With the greatest respect to all, I maintain that using the कटपयादि coding, with a good knowledge of Sanskrit meter one can transform a given number into a coded poem which, when read using the कटपयादि , can render back the number.

I maintain that the value of pi to 32 decimal places can be encoded into a poem (nay, several alternative poems) by a Sanskrit pandita without any knowledge of pi. He just has to encode 32 numbers in their order. Thats all.

Can it be shown how कटपयादि sutra computes the value of pi? to say 50 decimal places. Most certainly not. Not even to two decimal places.

I shall be happy to be proved wrong.

Cordially,

T K Gopalan

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[T.K Gopalan]

This is not his मत। We Indians have a lot that is marvellous in our culture. Astadhyayi is such an undisputed ‘monument to human intelligence.’

But we must be wary of floating false claims that will lower our credibility. 

This is a question of fact, not अभिप्राय।

Cordially,

T K Gopalan

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[संस्कृत संवादः]

> This is a question of fact

Correct, There's no conflict between us. I too believe the author should have given more clear information on that shloka without which any conclusion is meaningless.

This doesn't mean mathematics was any less developed in ancient India. Take this for example.

चतुरधिकं शतमष्टगुणं द्वाषष्टिस्तथा सहस्राणाम्।
अयुतद्वयविष्कम्भस्यासन्नो वृत्तपरिणाहः॥

विषकम्भः = Diameter  
परिणाहः = Perimeter (circumference)  

ये भी कोई पूजा का मंत्र ही लगता है, परन्तु ये किसी गोले के व्यास और परिधि का अनुपात है। वृत्त की परिधि और व्यास के अनुपात का, यानी कि, π के निकटतम मान का संशोधक आद्य गणितज्ञ आर्यभट हैं। जब पाश्चात्य जगत से ये आया, तो संक्षिप्त रूप लेकर आया ऐसा π जिसे २२/७ के रूप में डिकोड किया जाता है। आर्यभटीय में भूमि के अक्षभ्रमण की अवधि २३ घंटे, ५६ निमेष और ४.१ क्षण बताई गई है।  

उक्त श्लोक को अंकों में डिकोड करेंगे तो कुछ इस तरह होगा- 
{(१०० + ४) × ८ + ६२०००}/२०००० = ३.१४१६  

Regards, 

संस्कृत संवादः

शुक्र, 13 सित॰ 2024, 12:53 को T.K Gopalan <tkgo...@gmail.com> ने लिखा:

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[अभ्यंकरकुलोत्पन्नः श्रीपादः | श्रीपतेः पदयुगं स्मरणीयम् ।]

Curious, who claimed that the Shloka gives the formula or method to determine the value of Pi ?

It gives the value of Pi to 32 digits. Period

What is the false claim ?

[T.K Gopalan]

This is the false claim:

“

It has a self-contained master-key for extending the evaluation to any number of decimal places.”

Evaluation implies a formula for determining the value. If the sentence above said “for extending the ENCODING the value of pi” there is no false claim.

 Trust I am clear.

Regards,

T K Gopalan

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[S. L. Abhyankar]

It is that author's personal opinion. 

He should explain how the value can be extended to say just one more digit, to 33 digits. 

Actually the 32nd digit itself as per the श्लोकः is 2, whereas the value available on the internet shows that the 32nd digit should be 5. 

Cordially, S. L. Abhyankar

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