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Rebel without a cause!

Thursday, December 14, 2006

Kerala School of Mathematics

We are all parochial at heart. This must be an adaptation or learned behavior to preserve and protect the group to which you belong. According to Amartya Sen, everyone has layers of identity which overlap. I may hate you because you are a Pakistani and I am an indian in one situation but in another situation, here in US, we might grow to like each other because from the point of view of Americans we are both South Asians.

It is really absurd how much parochial we can be and the group to which we show parochial tendency depends usually on the external environment.

So let me indulge in a little bit of parochialism here and glorify the achievements of my ancestors. And I feel I really am justified because they worked some of the most beautiful and complicated theorems in mathematics and yet they are largely unrecognized except in the rarefied atmosphere of high academicians.

I am talking about the Kerala School of Mathematics founded by Madhava of Sangamagrama. They had developed mathematics which was at the highest point reached by anyone in the middle ages.

It was an achievement which should be popularized more atleast back home in India.

Addendum: Found this more informative link on this subject.
http://www.pas.rochester.edu/~rajeev/canisiustalks.pdf


9 comments:

Manjunatha said...

Do you think secular mathematics(not catering to Astrology and only dealing with Astronomy) could have popularized it within the population or would have helped in practical applications? That's what some people believe.

Sreekumar said...

That is certainly a valid reason for the decline but then we are comparing it with the growth of science and scientific spirit in the west. I believe comparisons are a bit difficult because ancient Indians had much less use of mathematics and science than the west had. Ancient India was content because it had a trade surplus and it did not need to go to other countries because it had lot of natural resources at home. It is the need of science and technology in navigation etc which drove the continued development of sciences in west. That drive was much less severe in India and other oriental countries.
Thats the way I see it.

Manjunatha said...

That drive was much less severe in India and other oriental countries.
Why? Is it in our genetic make up?

If you read East Asian history or Chinese history in particular, till 15th century their scientific and technological achievements in navigation and in warfare were much advanced for that time. In fact, some believe Chinese were ahead of the West during that period. Later what happenend is entirely political or cultural misjudgement. China became a closed country. In a way they closed the "necessity" for innovation. Probably, more appropriately(as Jared Diamond would put it in his 'guns, germs and steel'), an opportunity to generate necessities for inventors(who would anyway invent for the sake of it) was lost.

Ancient India was content because it had a trade surplus and it did not need to go to other countries because it had lot of natural resources at home.

Isn't it "content Indian" and "greedy European" stereotype? Even otherwise, don't you think your words conveniently forget social structure of India? How a trade surplus would benefit non-landlord, non artisan/trader population?

Again, trade involves navigation. Why our ships did not become highly sophisticated after so many centuries of trade(anyway, during Chola period we had good enough ships to invade South East Asian countries). Mathematics would be of some use in this. So, probably, division of labour was a wrong cultural step. But worse I believe complete physical segragation of people assigned with different vocations as this completely cut off knowledge flow between skilled person and literate person.

Anyway, it is a bit strange that content people made a law that person who crosses the sea would lose his caste.

Sreekumar said...

Why? Is it in our genetic make up?

I don't think that different populations of humans are genetically so different that their behaviour can be explained on the basis of genetics.
The drive was less because physical conditions in India were much more conducive than Europe. We had lot of agricultural land and did not have freezing winters.

Jared Diamond also makes the same case that the reason why different civilization are at different social and economic level had a lot to do with serendepity. The people who are well off now, had lot of good luck but then they also made us of that luck.

Isn't it "content Indian" and "greedy European" stereotype? Even otherwise, don't you think your words conveniently forget social structure of India?

They are definitely stereotypes but then there must be some truth in the stereotypes. I think that the stereotypes are just averages and their will be greedy Indians and content european outliers but then the average is definitely closer to the stereotype.



So, probably, division of labour was a wrong cultural step. But worse I believe complete physical segragation of people assigned with different vocations as this completely cut off knowledge flow between skilled person and literate person.

I agree with you entirely here. However, I think the division of labor was something similar to communism. It was an idea which was good in theory but did not work most efficiently in practice. Division of labour or communism for that matter is not a wrong thing in isolation. It is merely wrong because there were more efficient ways of organizing a society.
And you are right, the cutting off of knowledge flow induced by this system was the greatest tragedy and responsible for such heroic ancient figures like eklavya.


Anyway, it is a bit strange that content people made a law that person who crosses the sea would lose his caste.

It doesnt seem strange to me. They were content in the sense that they were comfortable with the status quo. They sensed danger if people started going outside and brought new customs and way of thinking as this might topple the existing hierarchy.

Thanks a lot for your comments. They helped me in clarifying my stand even more.

Manjunatha said...

However, I think the division of labor was something similar to communism. It was an idea which was good in theory but did not work most efficiently in practice.

I am not a Keralite. So, my understanding of Communism is poor. And Communism was irrelevent in my life in the past and most likely in the present too. So, I am not bothered about it. Please clarify how division of labour is good in theory. How do you justify disallowing a person's right to choose a work of his choice? Of course, division of labour was never a mere identification of your occupation but based opon your birth from Rig Vedic period. You see various Varna's took birth from various parts of Purusha, therefore, the segregation was there from its inception.

Sreekumar said...

I am a Keralite but I am not a communist either :-)
I think that division of labour must not have been rigid at the begining. It started as it started everywhere else. It exists even in western society like Bush Jr. following Bush. The reason is that someone who has seen his father and other family members practicing a profession would naturally have an advantage in doing that better than someone who does not have any prior family experience.
The society couldnt have one fine day decided that from now on those who are priests, their son will be priest etc. It would have been a gradual process.
The reason it is good in theory is that a shoemaker's son would know much more about the nuances involved in the craft from his father and would have a better chance of becoming an expert shoemaker than a priest's son who joins the shoemaker as an apprentice.
But then society began to differentiate between different vocations and a hierarchy rose. Paradoxically one of the most important job, that of cleaning became the lowliest job.

Manjunatha said...

The reason it is good in theory is that a shoemaker's son would know much more about the nuances involved in the craft from his father and would have a better chance of becoming an expert shoemaker than a priest's son who joins the shoemaker as an apprentice.

Indeed. A son may be helped by existing cultural capital at home. In many a cases, he may follow the family tradition. But the fact is every son knows it and it is a common sense for him to follow the tradition of his father to utilize his skills.

And that is the precise reason for not making a rule that a son must follow his father's footstep. You see even without such a rule George Bush followed his father's footsteps. Today, Western society has people with surnames like Smith, Shoemaker etc. without any caste system. Therefore, you can see occupations might have been hereditary generations after generations in old days. And even today eventhough such families might have diversified to other fields they still produces good shoes, good steel products. Don't they?

Therefore, I think thre could be two reasons for such a bad theory.

1. Whoever created this division of labour rule was completely devoid of any imagination. This we are inferring after observing societies that did not have this rule and of course with a common sense approach(In my opinion, a social theory can be bad because it has an innocent wrong logic and not just because it has an evil intention...which of course leads to a bad logic).

2. Whoever created this rule was driven by self interest. A shoemaker's son might have tried his best to become a good priest if the king offers land to priests for every occasion or for every mood.

Sreekumar said...


And that is the precise reason for not making a rule that a son must follow his father's footstep. You see even without such a rule George Bush followed his father's footsteps. Today, Western society has people with surnames like Smith, Shoemaker etc. without any caste system. Therefore, you can see occupations might have been hereditary generations after generations in old days. And even today eventhough such families might have diversified to other fields they still produces good shoes, good steel products. Don't they?

I guess we are going in for some hair splitting here. But lets do that. I think there was a big difference in terms of taking on a new career in old days. They did not have too many institutes etc where you could go and learn the art of good shoemaking. People who got some skills and knowledge in some field guarded it and would rather teach it just to their sons rather than some stranger.
I guess what must have happened (and I am only speculating) the existing practice must have been given the sanction of law by people who get to have most benefit out of it

Whoever created this division of labour rule was completely devoid of any imagination.
I dont have a strong view on this matter.


Whoever created this rule was driven by self interest. A shoemaker's son might have tried his best to become a good priest if the king offers land to priests for every occasion or for every mood.


Thats the point. It was mostly self interest, but my point is that it is only natural. I certainly dont blame someone who was a priest and getting lot of benefits of this profession wanting his sons to inherit it. It is not that person's fault. But what surprised me was that the people who were at disadvantage in this scheme took it fatalistically. It must have required a great deal of brainwashing to make a washerman believe that this is his and his family's fate and occupation.
Thankfully, such people have awakened and such a condition will not arise in the future. I guess that is a positive note to end on!

Mosilager said...

Interestingly one of the most successful Kings of Kerala, Marthanda Varma, appointed people without regard to the occupations their parents followed, i.e. a meritocracy. He was the guy who defeated the Dutch and ended their Indian colonial dreams.

The printing press in the west was what catalysed change in my opinion. More people were able to achieve literacy and this drove innovation. Toppling of the previous elites by the common folk led to the caste lines being blurred and egalitarianism. We did not have this in India or in China.

Some people have speculated that the black death contributed to this by killing off many of the elite and reducing everyone else to abject poverty. But who knows? I think we have to reform our society so that it is a meritocracy and we are ahead in science and technology. I think a scientific mindset among the general population is a necessity for this.