Wednesday, October 11, 2006

long article on indian mathematics

oct 11th, 2006

i heard about the kerala school of mathematics about two years ago when i attended a conference on indian mathematics in baton rouge, louisiana. amazing -- the calculus and infinite series were probably invented in kerala, not in europe.

also, i reiterate my claim that panini's grammar was pure genius -- it was the greatest invention of a single human mind in history. he invented the Grand Unified Theory of Language -- the audacity of which still boggles the mind 2600 years later!

someone sent me this paper, without a URL. i have met and interviewed k v sharma, a manuscriptologist, who edited the critical edition of the aryabhatiya. according to him, there is a tremendous amount of untapped mathematical knowledge in obscure palm-leaf manuscripts. these are rotting away, while the human resources minister invents ever newer ways of destroying indian education.

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History of Mathematics in India
In all early civilizations, the first expression of mathematical understanding appears in the form of counting systems. Numbers in very early societies were typically represented by groups of lines, though later different numbers came to be assigned specific numeral names and symbols (as in India) or were designated by alphabetic letters (such as in Rome). Although today, we take our decimal system for granted, not all ancient civilizations based their numbers on a ten-base system. In ancient Babylon, a sexagesimal (base 60) system was in use...

deleted

thanks to drisya for the URL, which is:

http://members.tripod.com/~INDIA_RESOURCE/mathematics.htm

6 comments:

drisyadrisya said...

Rajeev

I think this is the URL

http://members.tripod.com/~INDIA_RESOURCE/mathematics.htm

Madhwa said...

There is an error, hopefully typo, while mentioning Backus-Naur form. It is not Backus-Normal!

Shahryar said...

Excerpt from Backus–Naur form

(From Wikipedia, the free encyclopedia)

The Backus–Naur form (also known as BNF, the Backus–Naur formalism, Backus normal form, or Panini–Backus Form) is a metasyntax used to express context-free grammars: that is, a formal way to describe formal languages.

abhiha marathe said...

Rajeev,

This is indeed a fine well researched
article. Thanks for posting it on your blog.

There are a few Indians based in the US who write good ojective articles on Indian achievements, past and present. You are one of them. My request is to start writing a column in mainstream media, like Time / Newsweek magazine, or appear on popular programs like NPR or Bob Edwards' show on radio, or TV. This could help correct the biased Western perceptions about India. Any thoughts? Regardless, pl keep writing and keeping us all informed.

Thank you. ... Abhiha

virat0 said...

Rajeev,
I haven't dared yet to read panini's grammer, but one thing is certain. These things were known widely. SOme of these are known still today, from first principles. The idea is that, there exists a relation between the word and its meaning, the random meaning is not sole importannce as in modern times. So while for common uses, aham can be locally translated as mein, or words with m, these wouldn't have been gramatically perfect. Further I would have been different than mein. As I said, I don't get all of these, inspite of a lot of effort. There is a subtle difference between death and eternity according these ideas, while it is difficult to know the life.

It is a different matter, and best ignored inspite of their controll of JNUs that, the linguists spend all their time in finding the idiotic aryan movement or tourism ( TM- this blog), which essentially is one relation, X moves to Y. If I find your adress somewhere, I can mail you a little book on numbers(in Hindi)- Bit confusing to me, I didn;t understand much- But it has changed my perspective, and I have hundreds more qustions on a subject on which I thought there couldn't be any queries.

Cacoethes said...

OT Mobile phones help Kerala fishermen
In Kerala, Cell Phones Go Fishing
The English translation is provided by Truthout, http://www.truthout.org/issues_06/101106LB.shtml
or [Printer version]: http://www.truthout.org/issues_06/printer_101106LB.shtml
“ In Kerala, Cell Phones Go Fishing
By Esther Duflo
Libération | Monday 02 October 2006

The images that come to mind when one thinks of the role of modern technologies in development are those of Bangalore computer companies or Bombay call centers where young women dubbed "Sally" or "Barbara" handle credit card problems in English with a carefully trained American accent. But in spite of the impressive growth of these sectors, they employ only a minute fraction of the population, and their impact on the majority of the population remains very limited. Some think that communication technologies could have a more profound impact on the population of poor countries. The initiatives to overcome the digital divide (the inequality of access to information technologies) abound. Thus, southern India's land tax registers have been wholly digitalized, which allows for the immediate issuance of property titles, facilitating land transfers. The Massachusetts Institute of Technology (MIT) media lab is trying to develop a 100 dollar portable computer, supposed to revolutionize education in developing countries and help them to "catch up with a good four decades of development." After popularizing micro credit, Mohammed Yunus, founder of Bangladesh's Grameen Bank, founded Grameen Phone, a mobile phone company. The bank's poor clients can take out a loan to equip themselves with a mobile phone, the services of which they rent out to the residents of their villages.

Others (including Bill Gates!) are more pessimistic. They believe that developing countries must first resolve their essential problems (water, hygiene infrastructure, basic health care, roads, electricity) before investing in digital technology. Information technologies are luxury technologies for countries that are already more advanced. The enthusiasts retort that it's precisely in developing countries, where infrastructures are of poor quality, and villages are often very isolated, that communication technologies are a fundamental tool, capable of bringing doctors together with their patients or peasants together with their consumers. In Bangladesh, the hope is that the Grameen telephone ladies, as they are called, can exercise a profitable activity even as they help peasants find the best prices for their products. The introduction of the mobile telephone in Kerala, a coastal region of southern India, furnishes a perfect example of how this could work.

Fishing is an essential industry in Kerala. Sardine fishermen put to sea very early and bring their catch back to the wholesale markets that are held on the beaches between 5 and 8 a.m. Before the introduction of mobile phones, they had to decide beforehand at which beach they should disembark. Changing beaches if the demand was not very strong one morning or if the competition was too intense was not possible (the beaches are roughly 15 kilometers apart, but the fishermen have no transportation apart from their craft).

And since fish cannot be stored, if they didn't find buyers, they'd have to throw their merchandise away. Conversely, if too few fish were for sale, the buyers would leave empty-handed. From one beach to another, conditions could vary enormously the same day: fisherman selling at a discount or throwing their fish away at one beach, while prices soared or buyers left empty-handed ten kilometers away. Between 1997 and 2001, telephone transmission towers were progressively installed in Kerala. Most are close to the sea and transmission is still good at the 25 kilometer band of sea within which the sardine fishermen work. Consequently, the fishermen can use the telephone to sell their catch to potential buyers before unloading. They can set the price before they come in and chose with the buyer where the merchandise must be delivered. All sellers now have access to all buyers, and vice versa. That allows them to coordinate, avoiding situations where supply is excessive in one market and inadequate at another. Harvard economist Robert Jensen interviewed fishermen before and after the introduction of the transmission towers in fifteen Kerala sardine markets. He shows that, as soon as a tower is introduced into a region, the variability of prices from one market to another is considerably reduced and that waste (5 to 6% of the catch previously) disappears. He concludes that the introduction of the telephone led to an 8% increase in fishermen's profits and a 4% reduction in prices, which also increases consumer well-being. An example as remarkable as unexpected of the power of technology!

Esther Duflo is a professor at the Massachusetts Institute of Technology and the Ecole d'économie de Paris.
Translation: t r u t h o u t French language correspondent Leslie Thatcher.”