Thursday 8 November 2012

When Bhaskara tried to cheat destiny

Bhaskaracharya or Bhaskara , the great mathematician and astronomer of the 12th Century was also a well-known astrologer. When his daughter, Leelawathi, was born, he decided to cast her horoscope.
When he was calculating the planetary positions in the horoscope of his daughter, he found to his horror that Leelawathi would become a widow within an year of her marriage.
Bhaskara then decided to groom his daughter in the best possible way. He also wanted to educate her and her brother Lopamudra. Both seem to have taken after Bhaskara as they loved mathematics.
When Leelawathi reached marriageable age, the search for a suitable companion started. Bhaskara had not forgotten the horoscope he had cast of his daughter  and he decided to cheat fate by fixing an auspicious time for the marriage.
Bhaskara, by his precise mathematical calculations, concluded that if the mangalasutra was tied at a particular time, both his favourite child and his son-in-law would live a long and eventful life. He then determined to endure that nothing went wrong and himself determined the exact time when the mangalasutra has to be tied.
All arrangements for the marriage were being made and the marriage party had come to Bhaskara’s house in Ujjaian. Bhaskara was the head of the Ujjain Observatory and he had invited several people to the wedding.
Bhaskara had decided to rely on science to ensure that the mangalasutra was tied at the most auspicious time he had predicted. In this way, he thought he could change the destiny of his daughter.
Bhaskara had kept a simple device in the house to give him the exact mathematical time when the mangalasutra would have to be tied. He took two vessels and placed them one above the other. He filled the upper vessel with water and made a tiny hole in the centre. Water would trickle down to the lower vessel. The time was calculated by estimating the depth of the water that had collected in the lower vessel.
The unit of time was a Nadika. One Nadika was equal to 24 minutes. Thus, this was the water clock that was used in India. It was very accurate. 
Bhaskara had warned Leelawathi not to go near the clock. Curiosity, thy name is woman, says an adage. Leelawathi went near the clock as she was fascinated by the simple mechanism. She bent to look into the vessel. A small pearl set in her nose ring fell into the upper vessel. It sank down and it covered the tiny hole, thus blocking the free floor of water into the lower vessel.
Leelawathi was not aware of the nose ring having fallen into the vessel. Bhaskara too did not know what happened. When he saw that the water flow had stopped, he thought that the auspicious time had arrived.
He got the marriage ceremony performed. This was the very time he had wanted to avoid. Thus all the minute calculations  that Bhaskara had come up with went awry. His daughter was married at the most inappropriate time. Bhaskara realised that something had gone wrong when he went to check the time and found that the water flow had stopped.
However, the marriage had already taken place and nothing could be done to undo the prediction. Leelawathi’s husband died soon after marriage and she came back home.
Feeling cheated by destiny, Bhaskara consoled his daughter saying that he will make her immortal. “I will see you’re your name will live on forever”, he said.
He then began writing his magnum opus, on Mathematics and Astronomy and called it Sidhanta Shiromani.
The first portion of the book was called Leelawathi and it dealt with mathematics. He named it after his daughter.
Leelawathi was good at mathematics and in the book, Bhaskara addresses mathematical and algebraic problems to her. Leelawathi and other portions of Sidhanta Shiromani are in verse form.
Leelawathi has 278 verses and it deals with arithematic, algebra and geometry.
He poses the question to Leelawathi as follows:   
“Partha was determined to slay Karna. Posing his mathematical query, he asks, With half the arrows in his quiver Partha (Arjuna) destroyed those of Karna; with four times the square root of the total, he killed Karna’s horses. Six arrows were needed to kill Karna. With three arrows, Partha cut down Karna’s royal standard, his umbrella and bow, With the last arrow Arjuna killed Karna. Tell me O Leelawathi, how many arrows did Aruna have in his quiver?         
In another verse, he says a peacock which was sitting on a nine foot high pillar saw a snake going towards its anthill at the foot of the pillar. The snake was at a distance of three times the pillar’s height when the peacock swooped down. If both the peacock and snake travelled at the same speed, tell me O Leelawathi how far from the pillar did the peacock peck at the snake?
However, Bhaskara could never forget the incident of the pearl from the nose ring falling into the vessel and ruining Leelawathi’s marriage.
In perhaps the most poignant verse, he says

Whilst making love a necklace broke
A row of pearls mislaid
One sixth fell to the floor
One fifth upon the bed
The young woman saved one third of them
One tenth were caught by her lover
If six pearls remained upon the string
How many (total)  were there in the necklace.
Leelawathi was first translated into Persian by Abdul Faizi on orders of the Mughal Emperor Akbar. The other portions of Sidhanta Shiromani were translated into Persian during the reign of Akbar’s grandson, Emperor Shahajan.
The story of Leelawathi is narrated by Faizi in his Persian narration and other sources. Leelawathi remained the standard mathematical text for centuries till the advent of the British and the adoption of the English mathematical text.
If you have the time and interest, please go through Bhaskara’s Sidhantha. I can assure you that it is not boring as European mathematical texts. Nor is it uninteresting. It is in Sanskrit and it has been translated into almost all languages, including English.

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