What are some mind blowing facts about Sanskrit?


Answer by Anirudh Acharya:

Encrypting the value of pi in a shloka.

There is a numbering system in Sanskrit called the Katapayadi system. This system ascribes a number to every letter or alphabet in the script, something similar to the ASCII system in computer science. When the letter in the following shloka is replaced with their corresponding number from the Katapayadi Sankhya, we get the value of pi accurate to 31 digits.

गोपीभाग्यमधुव्रात-शृङ्गिशोदधिसन्धिग ।
खलजीवितखाताव गलहालारसंधर ॥
OR

Gopibhagya madhuvrata srngisodadhisandhiga|
Khalajivitakhatava galahalarasandhara||

(The shloka extolls Krishna and his achivements.)

I have verified the above for the first few numbers from the wiki article of the Katapayadi Sankhya, and I thought it was a very cool bit of encryption.

Edit from the comments section( thanks to R. Shreevatsa):

For an idea of what’s involved here, note that the Kaṭapayādi system dictates that:
* As the first digit is 3, the first consonant must be one of ga, ḍa, ba, la
* As the second digit is 1, the second consonant must be one of ka, ṭa, pa, ya
* For the third digit to be 4, the third consonant must be one of gha, ḍha, bha, va…

So to fit 3.141592653589793…, the list of consonants in the verse must satisfy the regex
{g,ḍ,b,l}{k,ṭ,p,y}{gh,ḍh,bh,v}{k,ṭ,p,y}{ṅ,ṇ,m,ś}{jh,dh}{kh,ṭh,ph,r}{c,t,ṣ}{ṅ,ṇ,m,ś}{g,ḍ,b,l}{ṅ,ṇ,m,ś}{j,d,h}{jh,dh}{ch,th,s}{jh,dh}{g,ḍ,b,l}…
(where the choices actually made I’ve marked in bold), with vowels and half-consonants added as desired:
gopībhāgyamadhuvrāta-śṛṅgiśodadhisandhiga…

The “mind-blowing fact about Sanskrit” here is that its rich vocabulary and syntax permits choosing and filling in letters to make something meaningful, while satisfying the metrical constraints.

Note BTW, that this one is a modern verse (first published in the 1960s by Swami Bharati Krishna Tirthaji in his “Vedic Mathematics”). The traditional Indian way of writing numerals was actually little-endian, as you can see in the examples of other pi-digit verses at Katapayadi system (i.e. instead of 314… they are written like ..413; one of the examples ends with “bhūpagī”). Also of course, π wasn’t known to so many places until recent centuries. (Though there are similar verses with fewer digits, e.g. 11 and 17 digits in works from the 15th century and 1819 respectively.)

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