JOST A MON

The idle ramblings of a Jack of some trades, Master of none

It turns out that the strong oral tradition of communicating knowledge in India resulted in various mnemonic tricks to keep track of large numbers in multiple ways. In Kim Plofker's Mathematics in India: 500 BCE-1800 CE is a discussion of Bhūtasaṃkhyā, a method of representing a number by an object that 'exist[s] in that number'. And so one could communicate mathematics in verse form, as Madhava of the Kerala School is said to have done:
Gods, eyes, elephants, serpents, fires, three, qualities, Vedas, nakshatras, elephants, arms: the wise have said that this is the measure of the circumference when the diameter of the circle is nine nikharvas.
There are 32 33 gods in the standard pantheon; two eyes and arms; four Vedas, eight elephants and serpents; three kinds of ritual fires; three gunas (or qualities) in the world; twenty-seven nakshatras (or constellations like the Zodiac); a nikharva is 1011; and the numbers are all indicated in increasing order of place-value.

So we can compute:



which is good to 11 decimal places.

Reference:

1. H.S.White, "Review of Kim Plofker, Mathematics in India", The Mathematical Intelligencer, Volume 32, Number 2, 2010.

8 comments:

km said...

Impressive. (I actually had to google for "nikharva"...how did that word not come up in my middle school Sanskrit lessons?)

BTW, how is 32 the "standard pantheon"?

Fëanor said...

Sorry, that should have been 33. I've corrected. I'm not sure what kind of 'standard pantheon' it is - more accurately the Vedic pantheon, I guess. But check this out: eight Vasus, eleven Rudras, twelve Adityas, Indra and Prajapati Brahma.

milieu said...

Just shows the importance of religion in all aspects of indian life!

You might also be interested in this article about the school of mathematics founded by madhava.

http://www.icm2010.org.in/wp-content/icmfiles/uploads/CIRCLE.pdf

Fëanor said...

Thanks for that. Is that the Plofker presentation? I knew she was speaking at the ICM, but didn't realise the presentation was available online. That site is horribly slow, I find.

milieu said...

Hi,

No, this seems to be the work by P.P. Divakaran, who appears to be a visitor at IUCAA. http://www.iucaa.ernet.in:8080/iucaa/jsp/Visitors.jsp

I don't have much more info but I found the paper quite interesting.
Also related,
http://www.iias.nl/nl/44/IIAS_NL44_46.pdf

Fëanor said...

Thanks for the links and references, Milieu. I'll check 'em out.

shreevatsa said...

You (or Plofker) forgot to say why this is a mnemonic, better than memorizing the digits themselves: the verse is actually in perfect metre, appropriate for chanting and remembering. Most Sanskrit works, even technical and scientific works, were composed in metrical verse and meant to be memorized, as they were transmitted orally. (This is why they would be terse ("sutras"), with separate prose commentaries explaining what the verses you had memorized meant.)

Fëanor said...

shreevatsa: thanks a ton for that. I can't speak for Plofker, but I didn't forget - I actually didn't know.

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