Monday 22 July 2013

Katapayadi Sankhya

गोपीभाग्यमधुव्रात-शृङ्गिशोदधिसन्धिग । 
खलजीवितखाताव गलहालारसंधर ॥

Gopibhagya madhuvrata srngisodadhisandhiga|
Khalajivitakhatava galahalarasandhara||

Oh Krishna, the fortune of the Gopis, the detoryer of the demon Madhu,
protector of cattle, the one who ventured the ocean-depths, destroyer of evildoers,
one with plough on the shoulder and the bearer of nectar, may (you) protect (us)!

The shloka above, seems to be one of the many written in praise of one of the most enigmatic and divine Lords of Hinduism, Krishna. The shloka, like many others, praises certain attributes of Krishna and requests him to protect the devotee.
So, what is so special about this shloka, that out of all the shlokas dedicated to Krishna, this particular one turned out to be the starting point of this post?

Simple enough, the shloka demonstrates one of the strongest and most intelligent examples of extreme knowledge and wisdom of our ancient men.

Grahacāraṇibandhana based in the year 683 CE and Laghubhāskariyavivarana based in the year 869 CE speak of a certain numerical notation which goes by the name of Katapayadi Sankhya.
Under this system, a number is ascribed to each and every alphabet of the script, a concept highly similar to the ASCII system in computers. The image below would better explain the relation between the alphabets and the numbers

So, based on the above method, if the letters in the shloka are replaced by the corresponding numbers, i.e. 'go' by 3, 'pi' by 1,  'bha' by 4, 'ya by 1' and so on, the following result is obtained:
The number, as obvious, is the decimal representation of pi upto 32 decimal places.
Who could have thought encrypting a mathematical concept in a devotional Shloka dedicated to Krishna?

So, what do they gain out of it by performing such extraordinary feat? The answer is two-fold.
Firstly, they used methodologies like this to check the correct usage and pronunciation of the verses, where every variation from the correct mantra or shloka would result in an incorrect rendition of the pi number(or any other system which they would have encoded)
Secondly, they used concepts like above to perform encryption and decryption so that the message would reach the intended receiver and no one would be able to catch the real meaning of the message.

Karanapaddhati: Written in the year 1733 CE by mathematician Puthumana Somayaji, the book consists of 10 chapters in total. Our  interest, however is in the 6th chapter.
In the 6th chapter, is given a shloka in Malayalam,

ssmāhatāścakra kalāvibhaktoḥ
vyāsastadarddhaṃ tribhamaurvika syāt

Not exactly Katapayadi system at play here, this is similar to encrypting formulae or constants in shlokas.
The above shloka, when translated simply means
"The circumference of a circle of diameter anūnanūnnānananunnanityai(10,000,000,000) is caṇḍāṃśucandrādhamakuṃbhipālair(31415926536), which, in turn, gives the value of pi till 10 decimal places.

Representation of dates:

palahāre pālu nallū, pularnnālo kalak kilāṃ
illā pālennu gopālan - āṃgḷamā sadinaṃ kramāl

Conceptualized in modern day India, based on Katapayadi Sankhya, the above shloka, which is in Malayalam, when translated, means that "Milk is best for breakfast, when it is morning, it should be stirred. But Gopālan says there is no milk - the number of days of English months in order"
True to its meaning, when the pairs of letters are substituted in accordance with Katapayadi system, yields
31 28 31 30 31 30 31 31 30 31 30 31

 The Vatsyayan Cipher:
Interestingly, the first written example of encryption in the entire history is found in the most unexpected source. The method, not that strong in that sense, is still used by army and security forces in a much more complex and stronger form.
As per Vatsyayan in his book Kamasutra, a girl needs to have certain attributes and learn certain arts and tricks, including how to cook, how to read and write, and how to send her lover secret messages which no one else would be able to decipher. Vatsyayan even goes on to give an example of such a cipher in the book.
The method is based on substitution cipher. Each alphabest would represent a certain another alphabet. The image below would explain the substitution cipher better:
So, the substitution cipher was invented in ancient India.

Validating the Shlokas:
Almost every major deity of Hinduism has a certain "Shata-Namavaali", or a list of 108 names dedicated to that deity. Shiva and Vishnu  have a list of 108 names dedicated to them. 
Venkateswara Ahtottara Shatanamavali is a list of 108 names dedicated to Lord Venkatesha.
Needless to say, if any of the name is forgotten by a devotee, the hymn would never be complete. 
It is always easier to remember a certain list of they are in a certain order.
For the same reason, and for validating the occurrence of all the 108 names in the order in which they are written in the text, a certain Anustup Chanda was composed, which consists of 4 shlokas, which are made up of the first letters of all the 108 names, in that order, thus validating the 108 names.

अनुष्टुप्छन्दसि चत्वारः पादाः भवन्ति प्रत्येकपादे च अष्ट अक्षराणि।श्लोके षष्ठं गुरु ज्ञेयं सर्वत्र लघु पञ्चमम्।
द्विचतुष्पादयोर्ह्रस्वं सप्तमं दीर्घमन्ययोः॥
अस्य छन्दसः षष्ठम् अक्षरं गुरु पञ्चमम् च लघु। सप्तमम् अक्षरं प्रथमे तृतीये च पादे गुरु, द्विचतुष्पदयोः सप्तमम् अक्षरं लघु भवति। सप्तमम् अक्षरं यथाक्रमम् परिवर्तते, प्रथमपादे गुरु द्वितीयपादे लघु तृतियपादे गुरु चतुष्पादे लघु।

Encryption or Miracle?
The most interesting part of this entire post, Sri-Raghava-Yadaveeyam deserves a distinct status altogether. Not exactly a work of the ancient Vedic men, this short text of 30 verses, which was compiled in the 17th century, actually deserves a separate blog post altogether. 
The name of the text itself, is quite curious. While the first part of the name of the text denotes Lord Rama, the latter, Yadava, denotes Krishna.

The 30 shlokas in the text, describe glimpses of Rama's life and works. Sample a verse from the text:

वंदेSहं देवं तं श्रीतं रन्तारं कालं भासा य:।
रामो रामाधीराप्यागो लीलामारायोध्ये वासे॥

The above text translates to
I pay my obeisance to Lord Sri Rama, who with his heart pining for Sita, travelled across the Sahyadri, returned to Ayodhya after killing Ravana, and sported with his consort, Sita, in Ayodhya for a long time.

The translation justifies the term "Sri-Raghava" in the name of the text. But, why the reference to Lord Krishna, as in the name of the text?

Now, the above text is read exactly in the reversed order:

सेवायेध्यो रामालाली गोप्याराधी मारामोरा:।
यस्साभालंकारं तारं तं श्रीतं वन्दे अहं देवं॥1

Interestingly, the above translation means:
I bow to Lord Sri Krishna, whose chest is the sporting resort of Sri Lakshmi who is fit to be contemplated through penance and sacrifice, who fondles Rukmani and his other consorts, who is worshipped by the Gopikas, and who is decked with jewels radiating splendor.

Astonishing, isnt it? The 30 shlokas when read in the order which they are composed in, describe the story of Rama, while when they are read in reverse order, describe the story of Krishna. Needless to say, the strong computational attributes of Sanskrit are at play here. And though I have been able to take up only one such Shloka here, the entire composition is an astounding work in itself. 
The text projects the strong computational, and hence encryption prowess of Sanskrit and also how smartly Sanskrit could be played with to create magnificent compositions

With that, I wish to bring an end to my post. The purpose of this post was to bring forward the same familiar concept, that not only were our ancestors religious, but all the concepts around religion and their lifestyle, overall was highly scientific and analytic in nature. Encryption was already in use and in place very smartly, the reason why most of the ancient texts is still considered unsolvable by our neo-modern intellectuals. What people claim to have invented or solved only lately, has been in place in this country since ages.

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Bidding Adieu for now.



  1. that was amazing can you please make a post of that Sri-Raghava-Yadaveeyam please.. all 30 shlokas..

    1. Namaste,
      Definitely, its in offing, and I do plan to write one on the topic as soon as I can

  2. how to decipher "ksha" "tra" "gya" ??

    1. Namaste,
      A very nice question, and my first reaction was "Honestly, I dont have an idea".
      But when I think about it, maybe they made up Ksha as a Sandhi of Ka and Sha, Tra as Ta+Ra and Gya as Ga+Ya.
      Aur maybe they avoided using the three letters in their encryptions, knowing that may confuse them.
      Or maybe, we only have half the knowledge, the alphabetical order in Devnagri was actually much more vast and versatile.
      Maybe time will tell. Thanks for putting this up, though

    2. क्ष = क् + ष
      त्र = त् + र
      ज्ञ = ज् + ञ

      So these are not anything new, just that in Hindi alphabet people have got used to them as separate letters.
      So they do not cause any issues with the kaTapayAdi scheme. :)

  3. Replies
    1. Namaste
      Vande Mataram.
      Do keep following the blog

  4. Namaste ,

    Great post Excellent , am very happy by reading this blog.

    1. Namaste Kiran
      Thanks a lot for the appreciation. Do keep reading the blogs

  5. Namaste Sapan Saxena

    Great post , Excellent , am very happy to read this blog and waiting for your 30 shlokas....

    1. Namaste Kiran
      Thanks a lot for the appreciation. Do keep reading the blogs
      Will try to write the blog as soon as I can

  6. Namaste Sapan,

    Great info. Happy to see you posting such interesting blog.

    Keep writing and keep sharing!!!


    1. Namaste Satish,
      Thanks a lot for your kind words

  7. The numeral system enlightened the so called technology bearer western countries and super power China and Russia only after they got the knowledge of ZERO from Arabians , the traders who had contact with Hindu civilisation. So all world now try to be Hindu . Not by means of religion but by adopting the ancient remedies. We , the Indians , slowly try to forget our culture.

  8. Some really great nuggets of inspiration. It's more than 2 years since you posted it, but believe me, it's an ever-green post, an eye-opener for any new audience. (so just don't delete this blog, even if it remains not-maintained).

    This year (during August-Sept) I was searching for some Sanskrit Wonders on the web, and stumbled upon your article. It's really inspiring. The "Shri-Raghav-Yadaviyam" intrigued me so much, that i made an app (on web, android and windows phone) that lets anyone interactively browse the whole poem. here is the link:

    Thank You very much.

    1. Thank you sir ...for the app
      It made it a lot easier to learn about it ... without having the book...thank you really

  9. Dear editor, I had a plan to write a research paper on Hindu Mythology and modern Computer Science. Finally I found this. Will you have any problem if I refer your blog for that? Please mail me

    1. Sure, please go ahead and use it. Just put up a reference list as that adds credibility to the work

    2. Thank you sir. Will let you know it that is published .