Wednesday, January 10, 2007

Calculus From Kerala

You were probably told that the discoverer of Calculus was one of these two gentleman --- the Englishman Newton or the German Leibniz (my academic ancestor!). I'm here to tell you that you were lied to. If this BBC radio show is to be believed, the first known Calculus text is the Ganita Yuktibhasa written by Jyesthadeva in AD 1530 in Malayalam ! This was more than a century before Newton and Leibniz appeared on the scene.

There is also this pdf-presentation by S.G.Rajeev of the U of Rochester with more details about the Kerala school and the contents of the Yuktibhasa. Part of the difficulty in translating it into modern mathematical notation is, apparently, that it is written in verse !

A brief history of Indian contribution to Mathematics (gathered from the radio show and the pdf-presentation):

  • Number System: Numerals representing numbers (rather than collections of dots or strokes). The Brahmi numerals (250BC, symbols 1--10 but no zero). The zero is first seen in the 4th century (Bhakshali(?) manuscript). The "placeholder" system of representing numbers spreads from India through the Arabs (as testified by Said Al-Andalus, the historian from 11th century Cordoba). Europeans had a hard time getting used to the zero and the Indian number system, despite the enthusiastic efforts of Fibonacci (who learned it from his childhood in 11th-century Algiers as the son of a diplomat).
  • Aryabhatta (6th century, Patna, Bihar) who wrote the Aryabhattiya. His main original contribution is in summing (finite) series.
  • Bhaskaracharya (12th century) wrote the "Lilavatti" an elementary text. He made contributions in "Pre-Calculus" eg. calculating the movement of planets in smaller and smaller (but not yet infinitesmal) time instants.
  • Madhava and the Kerala School (13th-16th century). Infinite series (with series expansions of pi, sine, cosine and arctangent, building on Aryabhatta's finite series) and integrals (according to Prof.Rajeev's presentation). While Madhava's works don't survive, his students' works do, and they cite him (like all honest scholars should).
I found all of this starting from Robin Varghese's post at (the excellent) 3 Quarks Daily.


Tuesday, November 14, 2006

Cash Cameos

If you like playing name-that-cameo (and can get past the pretentiousness, perhaps) you might like this video. Maybe I'll post the names at some point. Or you can do so in the comments. I'm not sure who the first guy is (who talks about Cash's wearing black).

Thursday, November 09, 2006

San Diego

san diego What did I find in San Diego ?

Sunny skies and palm trees :

san diego This cover of the San Diego Weekly Reader :

SDreaderCover Yes, it's a Sikh man tying his turban. Here's a closeup.

And this pen PenFlash2 that's also a 128MB memory stick. PenFlash1 Did I mention the sun and the palm trees ? san diego And some talks and posters and stuff.

I also learned that 'El' and 'La' are the masculine and feminine versions of the word 'the'. So you have 'El Hombre' (the man) .vs. 'La Mesa' (the table). (Incidentally the hindi/urdu word for table मेज ["Maze"] is also feminine as far as I remember. I suspect Arabic is the link language). 'Los' and 'Las' are the plural counterparts of 'El' and 'La'. I knew about 'San' and 'Santa' being the masculine and feminine versions of 'Saint'. We were wondering about 'Santa Cruz', as Cruz sounds like a man's name. It turns out that 'Cruz' means 'Cross' and, for whatever reason, is feminine. Spanish place and street names make a lot more sense now.


Tuesday, October 31, 2006

Book tag

Thanks for the tag maisnon !

1) One book that changed your life?

I can't think of one that's literally changed my life but a book that resonated with me on a personal level is Arundhati Roy's The God of Small Things. I read it long after it came out and wasn't sure it could measure up to the hype. It described a world that I was really familiar with but had never before seen described in print. And described so accurately on so many levels --- not just the recognizable characters and places and happenings, but also her use of language. Those word-games that she plays, that some might think frivolous, I thought, captured the way Indian kids use the English language. [Ok, I'll stop trying to be M.Kakutani now. Or M.Vij, for that matter]. I was also relieved to finally be able to answer the question "You're Indian, but why is your last name an anglo-saxon first name ?" with "Read this book".

2) One book you have read more than once?

I was going to say that the exciting prose and plot of [insert-textbook-name-here] kept me coming back for more, but realized that there isn't even a textbook that I've read all the way through twice.

3) One book you would want on a desert island?

A Practical Guide to Ship-building ? Yes, another cop-out (with apologies to GK Chesterton).

4) One book that made you cry?

Hmmm. The only one that comes to mind is "What's So Amazing About Grace" by Philip Yancey. My younger, less cynical, less skeptical, self was easily moved by stories of selflessness and grace. Later when I heard the song "Grace" on U2's ATYCLB I was convinced that Bono had also read the book [and according to the internets, I might be right].

5) One book that made you laugh?

Only one ? There's Them: Adventures with Extremists by Jon Ronson which describes some interesting characters that Ronson spent a lot of time with. In my mind Ronson, Sedaris and Dave Eggers form the TAL posse of really funny writers (because TAL is where I first heard them). Ronson, like Sedaris, also has a hilarious voice (literally). When I read his stuff, I hear his voice reading it to me in my head, and it's even funnier.

6) One book you wish had been written?

How to have your cake and eat it perhaps?

7) One book you wish had never been written?

I hate to be a downer here, but ... The Left Behind series ? I do not need to have read a sentence of that tripe to wish it had never been written. When a piece of fiction forces a literalist nineteenth-century interpretation on an allegorical first-century text, bad things happens. What bad things you ask ? Otherwise mild-mannered, (presumably) well-meaning people start cheering for ethnic cleansing, the destruction of the environment and nuclear war.

8) One book you are reading currently?

White Teeth by Zadie Smith. I've been reading it in tiny bites for several weeks now and I hope to finish it during the 8+ hrs that I'll be spending in aircraft this week.

9) One book you have been meaning to read?

I've been meaning to get through the second half of Life of Pi after I abandoned it halfway and was told that there was a payoff at the end. My friend's copy has been lying unopened on my shelf for several months now.

It's hard to choose who to tag from my vast readership. Perhaps I'll go with the 'B's'. So badmash, bdeshini and brimful --- you're all tagged (whenever you get around to reading this post, that is).


Thursday, October 05, 2006

Goodman on Colbert

Irony will meet its opposite when Amy Goodman is on the Colbert Report tonight. I expect it to be a good interview as the best Colbert interviews are when his guests play it completely straight and leave all the humour-generation to Stephen. Also, being in character means Colbert doesn't need to suck up to his guests (hint, hint JS).

Note to Comedy-Central: Please fix your slow, clunky, site with its often undependable video-streaming. Perhaps you can learn from MSNBC; whose site we have no complaints about (well, except that it doesn't like Firefox). The cheapskates and freeloaders of the world demand it !


Thursday, September 21, 2006

Hugo's book club

I was watching my daily dose of over-the-internet news bulletins (MSNBC,CNN) and thought I saw footage of Hugo Chavez holding up a book by Chomsky during a UN speech. The reporters didn't mention it and were more focused on his "Diablo" line, and so I figured that it was old footage. But today I find out on Democracy Now, that he did in fact do what I thought he did.

And then from Google News/CBC I read the following. "Hugo's book club? Chavez speech sparks sales for Chomsky"

Author Noam Chomsky got an unexpected boost in sales after Venezuelan President Hugo Chavez cited one of his books in a speech to the UN General Assembly.
At the start of his talk Wednesday, Chavez held up a book by Chomsky, Hegemony or Survival: America's Quest for Global Dominance, and recommended it to everyone in the General Assembly, as well as to the American people.

"The people of the United States should read this ... instead of … watching Superman movies," the long-time critic of U.S. foreign policy later told reporters.

The unexpected promotion had a surprising effect on online bestseller lists.

Hegemony or Survival, originally published in 2003, had jumped into the top 10 of Amazon and Barnes & as of Thursday afternoon.

A deeper look at the Amazon results shows an even more profound impact. The online bookseller also charts what it calls "Movers & Shakers," books that have seen a sudden rise in popularity in the last 24 hours.

At the moment the two versions of the book are ranked #2 and #19. This reminds me of the report of the Iraqi prime-minister also being a Chomsky fan (atleast according to Tim Russert).


Tuesday, September 05, 2006


A post is long overdue, so here's a link my friend sent me today.

It's a collection of talks from TED. I'd never heard of this conference before. TED stands for "Technology Entertainment Design". Ignoring the fanciful name, it's a collection of 20-min talks (video and audio) from an interesting group of people --- from A.Gore to Z.Frank.

I haven't seen them yet, but they come highly recommended, so I look forward to doing so soon. The speakers include this smart,funny lady, and this excellent teacher/presenter whose class I've had the pleasure of being in.

Interestingly, the organizer Chris Anderson is a missionary-kid from South Asia who says that he "went to a wonderful (American) school in the Himalayan mountains". I'm pretty sure he means this one.