Bhaskaracharya and the inexorable nature of “Time” and “Destiny”

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.

ghatika yantra
Ghatika Yantra*

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…


*Image source and disclaimer: http://vipasana-vidushika.blogspot.in/2014/08/sages-from-hindu-scriptures_24.html. Last accessed: May 6, 2017. Copyright belongs to the original creator and the image is not used for any commercial purpose

The Vedas and their grand concept of TIME – Yugas, Kalpas, Manvantaras, and Brahma

The sheer grandeur with which the concept of “TIME” in its macro sense is discussed in the Vedas boggles the mind. Often, modern interpreters make the mistake of trying to look at similarities between these calculations and those arrived at by modern science as if validation by modern science is the only way the Vedas could be redeemed.

The more important point according to me is to soak in the grandeur and conceptual brilliance of the minds that could think at such a grand cosmic level and come up with numbers that run into Trillions without the help of modern telescopes, satellites and all the other paraphernalia of modern astronomy and science. That their numbers are so close to what modern science says is testimony to the greatness of those seers and vedantins.

In the Srimad Bhagavata (Skandha-III; Chapter-11; Verses 21-23) it is said:

For the Brahmaloka and the realms outside the Universe, a day of Brahma is equal to the 4 yugas multiplied by a 1,000. His night is of equal duration. Creation starts at Brahma’s waking and continues for the entire duration of his day. When he approaches his (Brahma’s) night, he stops all activities, dissolves everything in himself and sleeps…

A short summary of the concept of macro-time as envisaged in the Vedas and explained in the Bhagavata is given below:

  1. There are 4 yugas and each yuga consists of a fixed number of years. {Note that the number of years in each Yuga is in the descending ratio of 4, 3, 2, 1}

    • Satya Yuga: 17,28,000 years (1.728 million years)
    • Treta Yuga: 12,96,000 years (1.296 million years)
    • Dvapara Yuga: 8,64,000 years (0.864 million years)
    • Kali Yuga: 4,32,000 years (0.432 million years)
  2. The 4 Yugas together constitute 1 Maha Yuga (Chatur Yuga) =  43,20,000 years (4.32 million years)

  3. 1,000 such Maha Yugas (i.e 4.32 million years X 1,000) = 43,20,000,000 years (4.32 billion years) makes 1 KALPA or “1 day of Brahma”

  4. Each Kalpa is divided into 14 Manvantaras with each Manvantara headed by a Manu. In other words each Manvantara consists of 71.4 Chatur Yugas. 14 such Manvantara cycles adds up to 1 Kalpa. We are believed to be in the reign of the 7th Manu – Vaivasvata (which is what we say in the Sankalpa mantra “Vaivasvata Manvantare“) and within this Vaivasvata Manvantara we are in the 28th Chaturyuga (again we say this in the Sankalpa mantra “Ashta-vim-shatatitame“)

  5. A similar 4.32 billion years constitutes the “night of Brahma” adding up to a total of 8.64 billion years (which is very close to the modern scientific belief that the earth will not be inhabitable when it reaches the age of 7.5 to 8 billion years and is also the accepted period spanning creation through dissolution)

  6. From now the numbers  are so mind boggling they take one’s breath away: As we have seen 8.64 billion years is the one full day of Brahma. 365 such days constitute 1 year of Brahma! and on this basis his lifespan is a 100 years!! 311 to 315.36 Trillion years!!!

The image below is perhaps easier to comprehend:

vedic timeImage Source: mcremo (Image is not used for any commercial purpose. Copyright belongs to original creator)