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Katapayadi System (wikipedia.org)
156 points by dedalus on June 25, 2022 | hide | past | favorite | 36 comments

While the article goes into history and detail, here are a couple of analogies that may help explain what this thing is:

• The convention of specifying phone numbers using words, e.g. 1-800-FLOWERS (https://en.wikipedia.org/wiki/Phoneword): this is the mapping

    0 ↔ (space?)
    1 ↔ ??
    2 ↔ abc
    3 ↔ def
    9 ↔ wxyz
Roughly, the Kaṭapayādi system is simply a different mapping between digits and letters.

• So a closer analogy may be, if the conventional English alphabet happened to list vowels (aeiouy, say) and consonants separately, then a mapping something like

    b c d f g h j k l m n p q r s t v w x z
    1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0
(so there are two choices for each digit, e.g. 2 can be represented by either 'c' or 'p'), with the decoding convention that we ignore vowels, and consonants that are immediately followed (in the same word) by another consonant. Then, to specify a sequence of digits like "314159265", we could write down below each digit the two possibilities for it:

    3 1 4 1 5 9 2 6 5
    d b f b g l c h g
    q n r n s x p t s
…and use these letters to make words. So something like "dine rob soul cottage" would stand for DNRBSLCTG = 314159265, as would "dumb funny sex parties" (= DBFNSXPTS = 314159265) or whatever. Then we could write rhyming poems or memorable prose, to memorize the digits (and transmit them accurately in an oral tradition).

With the English alphabet the above mapping would be hard to remember, but the alphabet in Sanskrit happens to be organized in a more orderly way, so it's easier to remember the mapping. (And the name helps: ka ṭa pa ya are simply the beginning (ādi) letters of each chunk mapping to 1234567890, the way our mapping above could be called the "B-N" mapping.)

Something close that there's a (recent) tradition of in English is "pilish": https://en.wikipedia.org/wiki/Pilish where the lengths of the words encode the digits, as in "how I wish I could remember pi" (=3141592). (See "Cadaeic Cadenza" and "Not a Wake": http://cadaeic.net/cadintro.htm )

> the alphabet in Sanskrit happens to be organized in a more orderly way

For the curious, it is consonantaly ordered anatomically in the vocal apparatus, starting from the lowest and furthest back point of articulation, the velum (k and g sounds) and ending with the highest and most forward point: the lips (p and b sounds).

Yes, in particular the main consonants part is arranged like the periodic table: the rows are ordered by place of articulation, and each column a different manner of articulation.


In fact, it is possible that Mendeleev was inspired to arrange his periodic table based on the arrangement of the Sanskrit alphabet (or at least aware of the resemblance). The evidence is thin, but the plausibility argument (quoting from the nice article https://www.americanscientist.org/article/the-grammar-of-the... ) is something like:

• Mendeleev was friends at Saint Petersburg University with Otto von Böhtlingk, a famous Sanskrit scholar and linguist.

• Böhtlingk composed a grammar of "the Siberian language Yakut (also known as Sakha), in which he applied the principles of Sanskrit grammar to extraordinary effect". In particular, he "constructed a periodic system of Yakut speech sounds based on Pāṇinian principles" (that is, he arranged the Yakut sounds in a table like the Sanskrit alphabet).

• Böhtlingk and Mendeleev shared an interest in Siberia (Mendeleev's birthplace) and Arctic languages, and it is likely that Böhtlingk would have told Mendeleev about this.

• Mendeleev when he came up with the periodic table used the unlikely choice of Sanskrit prefixes (eka-boron, dvi-manganese etc) for his predicted elements, rather than Greek/Latin/German/Russian ones. This is likely a homage/result of his friendship with Böhtlingk.

As I said, there is no clinching evidence, but we can only connect the dots. (Anyway, the above article, written by a chemist and a linguist, is an interesting read.)

Thank you very much. Your post should be the first chapter in that Wikipedia article.

As of now, it is the first chapter of that Wikipedia article.

The mnemonic major system is a more approachable technique for number memorization (in english), learnable in several hours: https://en.wikipedia.org/wiki/Mnemonic_major_system

+1 I learned this as a kid and have been using it continually ever since.

This is certainly a cool system from a theoretical perspective, and functions as a great mnemonic device, provided you know how the standard Indian alphabet is structured.

But fear not, there's a sort of mnemonic for that as well:

The first group of consonants are the stops. They are organized first by place of articulation from back to front (there are five of these), and next by the mode of articulation (five of these as well). So the first group (velar) for instance is

K kh g gh ng

In the katapayadi system these would stand for 1, 2, 3, 4 and 5, respectively.

After the stops come the vocalic consonants (y r l v) and then the sibilants (three of them once again back to front in articulation) (mnemonic: 1 thru 7) These are rounded off by 'h', whose placement I must confess I don't fully understand.

Having said all this, the practical implications of the katapayadi system for the actual learning and performance of Carnatic music are essentially none. A lot of the older ragas were retrofitted into the system ('dhee-ra'Shankarabharanam for the equivalent of the standard major scale, Shankarabharanam, with dh = 9, r = 2, flipped to give you 29)

Still cool though!

Probably something no one here wants to hear, but astrology is a big thing in India -- serious astrology, which is highly mathematical and historically goes hand-in-hand with advances in astronomy, not "sun sign astrology." I'm guessing that's not entirely irrelevant to there being this mnemonic system, though I don't know enough about India to support that suggestion.

As far I went down the ancient sanskrit traditions, I also think this numbering system has deep ties to numerology, astrology and derived spiritual disciplines like raga (classical carnatic music, hindustani) and classical dances like Kathak, all of which are studied through numbers, patterns and thus math. Though I'm sure I'm missing something.

I’m curious why you think no one here would want to hear it?

I've been on HN a long time. I know how it usually goes to say anything at all about astrology.

Not today as 5 planets are moving into a rare alignment this week :-)

That's called astronomy, not astrology. It's fine to be fascinated with the sun, moon and stars and go outside to look at them before dawn.

It's not okay to think they influence events here on earth (like tides, winds, moods) through "invisible forces" (like gravity).

It was a mild joke as planetary alignment does play a part in Vedic Astrology.

Astrology indeed had a high place in ancient India and significantly influenced the development of mathematics and astronomy. 5th/6th century mathematician Aryabhatta was also an astronomer as well as an astrologer. He even devised his own numerical encoding, which is far more compact than the Katyapadi system but not as amenable to writing numbers poetically.

You don't believe in astrology but u believe it's ""3 PM"" ?!?!?

Why is it not ok? And who decided that? Or is it just your opinion?

That's not my opinion. That's the general sentiment of HN as judged by the negative reactions I've gotten over the years as someone who once studied astrology in earnest and dares to occasionally comment on it.

Is Indian astrology falsifiable?

Katapayadi is heavily employed in the nomenclature of melakarta ragas in carnatic (south Indian classical) music. One of the most fascinating mnemonic schemes ever.

That's really interesting, because the first thing that came to mind was the rhythmic syllables used in carnatic music, and borrowed from there for western use in takadimi. I don't know if mnemonic devices like this are more common in Indian culture or not.

Oooh. This article taught me that in India of 1400 someone figured out how to calculate pi more accurately than had ever been done before and it took until 1600 in Europe that these methods were independently rediscovered.

It's such a beauty to see this and so many sophisticated systems from India showing up. Unfortunately the white history always wiped out the parts of math, history, and culture that have influenced so many things that are part of normal world today.

Btw, i recently also learned that Mathematics, Medical Science, and Economics have always been part of the Hindu Religious texts. No doubt such intelligence could be produced in the country.

wasn't this the one where they had very accurate value of PI in a poem about lord krishna.

Found it, it's mentioned in the Wiki Page

This verse encrypts the value of pi (π) up to 31 decimal places.

गोपीभाग्यमधुव्रात-शृङ्गिशोदधिसन्धिग॥ खलजीवितखाताव गलहालारसंधर॥

... <Malyalam shloka/poem> This verse directly yields the decimal equivalent of pi divided by 10: pi/10 = 0.31415926535897932384626433832792

This link goes into more details of this one shloka/poem


Not anything about Krishna. The Sadratnamala:


And it was intentional.

Yes, indeed. It is mentioned in the wikipedia link ("गोपीभाग्यमधुव्रात..."). I first read it in the "Vedic Mathematics" book by HH Bharati Krishna Tirtha Swamiji. Since he didn't give any attribution, I suppose he was the first one to reveal it.

Yes that’s right. This is the verse-

गोपीभाग्यमधुव्रात-शृङ्गिशोदधिसन्धिग॥ खलजीवितखाताव गलहालारसंधर॥


This is cool + reminds me of [Konnakol](https://en.wikipedia.org/wiki/Konnakol) , which is a similar system for time signatures in music. [Here](https://www.youtube.com/watch?v=h2LzlLMbqpM) is a good intro.

Katapayadi system has also been used to construct tables of related entries whereby the position of an entry in the table (its row and column) completely determines its properties. See, for example, the paragraphs on 'Carnatic Music' in the wikipedia entry for the katapayadi system. This Carnatic Music arrangement dates to the 17th century.

This table pertains to the 72 main raga's (melodies/modes) of south Indian music. Each raga gets a number which completely determines its scale (of notes). The number is derived from a two syllable mnemonic for the raga using the katapayadi system.

My go-to for memorizing numbers is Goroawase (0 = ma, 1 = i/hi, 2 = ni/fu/tsu etc.). It is less flexible in comparison (you can't choose the vowels freely) but uses less phonemes, so I think it's more intuitive for an English speaker to learn (e. g. you don't have to know the difference between ka and kha).

Phonetic number systems like this are commonly used by memory athletes, like the Major System[1]

The usable range can be expanded further using color, smell, taste, and so on.


Here is an interesting video on this https://youtu.be/QxTjaK8suMo

Is this related to the ta ka di mi mnemonic for rhythms?

Telephones and credit card numbers are coming any millennium; you can never be prepared too far in advance!

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