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October 31, 2005
Thousands lakhs and crores oh my!
Those outsiders who follow the Indian press may occasionally come across statistics cited using the Indian system of numeracy. Rather than proceed in thousands, millions and billions, the Indian system of enumeration proceeds with thousands, lakhs and crores. Western systems of enumeration group digits by threes. The number 1048576 would be split up as 1 048 576 (one million, forty eight thousand five hundred and seventy six). The Indian system splits a large number into groups of two, except for the rightmost group, which contains three digits. A thousand ones make up a thousand (duh!), but a hundred thousand is a lakh and a hundred lakhs is a crore. 1048576 would thus be split as 10 48 576 (10 lakhs, forty eight thousand five hundred seventy six). Hindi newscasts frequently use the word arab (most likely unrelated to the ethnicity) to refer to one hundred crores. Other than that, modern Indian numeracy stops at the crore and anything higher is expressed just in terms of crores, e.g. one billion would be expressed as 10,000 crores.
The origins of lakhs and crores lie, as with so many other cultural artifacts, in Sanskritic antiquity. Lakh and crore are the modern day descendants of Sanskrit's laksha and koti. The ancients definitely knew what they were doing with the Sanskrit system of numeracy. There are named points for each power of 10 in the decimal system, all the way from 100 to 1018. The names are as follows| Number | Sanskrit | English equivalent |
|---|---|---|
| 1 | ekam | one |
| 10 | dasham | ten |
| 100 | shatam | hundred |
| 1 000 | sahasra | thousand |
| 10 000 | dasha-sahasra | ten thousand |
| 100 000 | laksha | hundred thousand |
| 1 000 000 | dasha-laksha | million |
| 10 000 000 | koti | ten million |
| 100 000 000 | dasha-koti | hundred million |
| 1 000 000 000 | abja | billion |
| 10 000 000 000 | kharva | ten billion |
| 100 000 000 000 | nikharva | hundred billion |
| 1 000 000 000 000 | padma | trillion |
| 10 000 000 000 000 | mahapadma | ten trillion |
| 100 000 000 000 000 | shankhu | hundred trillion |
| 1 000 000 000 000 000 | jaladhi | quadrillion |
| 10 000 000 000 000 000 | antya | ten quadrillion |
| 100 000 000 000 000 000 | madhya | hundred quadrillion |
| 1 000 000 000 000 000 000 | parardha | quintillion |
By naming every power of ten, the ancient Indian system tried to combat number numbness, a term coined by the venerable but excessively-in-love-with-his-own-ideas academician, Douglas Hofstadter (it's hard to allot this guy a field, such as computer science, neuroscience, philosophy or psychology). The human brain can easily comprehend numbers under ten or even a hundred. Anything over that and you'll see eyes beginning to glaze over. I'd be willing to wager that this is somehow related to the magical rule of 150 that governs human social interactions.
It's well worth considering that the progress of human mathematics has usually happened as and when necessity dictated it. For example, zero was most likely invented in a business context, to indicate a perfect balance of credit and debit. The ancient societies of the Sanskritic era most likely didn't have 1018 of anything, but they definitely would have been perfectly at home with the concept of an exabyte (1018 bytes), which is a unit that modern storage technology is approaching only now. Heck, they'd probably even be comfortable with the magnitude of Avogadro's number: 1023. I don't know what drove the ancient Indians to come up with such a sophisticated system of numeracy when they probably had nothing to apply it to (perhaps the closest viable prospect is cosmogony -- the ancient Indians came up with the best estimate of the earth's 4.5bn year age before the advent of modern radiocarbon dating techniques: an eerily close 4.32bn). Viewed from another perspective though, it shouldn't come as a surprise, given the ancient Indian's passion for enumerating interesting things of all kinds.
Posted by Vishy at October 31, 2005 12:14 AM