Bhaskaracharya the celebrated Indian mathematician, astronomer, and astrologer who lived 800-900 years ago was born in Bijapur, Karnataka and then is believed to have settled in Maharashtra. He is also known to have headed (for some time) the Astronomical Observatory Center at Ujjain, the leading mathematical center of medieval India.
His works and treatises on Arithmetic, Algebra, the pythagorean proof, Calculus, planetary movement etc. predate (by several 100 years) those of modern western Mathematicians, but that is not the focus of this post.
This post is about the inexorable nature of “Time” and “Destiny“. “What is destined shall come to pass…”
Bhaskaracharya’s daughter Lilavati was very dear to him. However, when he drew up her horoscope he realized that his dear daughter was destined to become a widow soon after her marriage. He re-worked on his calculations and arrived at a specific time when the planetary positions would be so favourable that they would ensure his daughter enjoyed a long married life of conjugal bliss.
Bhaskara set out to defy fate and destiny.
In order to ensure that he conducted the marriage of his daughter at the exact time arrived at through his calculations he used a Water Clock called Ghatika in Sanskrit. The words Gadikara in Kannada, Gadikaram in Tamizh and Ghadi in Hindi are all derived from this Sanskrit root.
This Ghatika was a simple two-vessel set-up – a smaller upper bowl and a larger lower bowl. The lower bowl was calibrated with markings to denote the passage of time. The upper vessel had a small aperture in it. The upper bowl was filled with water which dripped through the aperture into the lower bowl. The lower bowl had 60 markings with the each mark denoting time equivalent to 1/60 of a day.
This unit of time is called Ghatika (Ghati) and is still used in Panchangams and astrological almanacs. One Ghatika is equal to 24 minutes and one hour therefore has two-and-a-half Ghatikas. In Tamizh the Ghatika is referred to as “Nazhigai“. The muhurtha or the auspicious time of a marriage or other such important function is often denoted in Ghatis or Nazhigai’s.
This Ghatika was the precursor of the western sand-clock in which sand replaced water.
Coming back to the story of Bhaskaracharya and Lilavati, Bhaskaracharya set this Ghatika and waited for the precise time to conduct the marriage. As was the custom in those days Lilavati’s marriage was fixed when she was still a child. The child Lilavati while playing came near the Ghatika and a small pearl from her nose-ring accidently fell into the upper bowl and blocked a part of the aperture and reduced the amount of water dripping into the lower bowl.
The marriage was therefore conducted in a “lagna” that was well past the auspicious time that Bhaskaracharya had calculated and Lilavati became a child-widow. It was only much later that a distressed Bhaskaracharya found the real reason but it was too late by then.
This story is not to defend astrology or child marriage etc. It is just to show how inexorable “Destiny” and “Time” are. What is destined to happen shall happen – to fight it is stupidity and focusing only on the present moment is the way to happiness.
Bhaskaracharya’s book on arithmetic titled “Lilavati” was a dedication to his daughter. He also taught her mathematics and made her into a high-ranking mathematician.
The beauty of the book lies in the fact that several of the problems are addressed to Lilavati herself in the most adoring and endearing way – typical of a father to a daughter…
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