Bhāmatī

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Bhamati is Vachaspati Misra's commentary on Adi Shankara's Brahmasutra Bhashya. Bhamati School of thought in Advaita vedanta originated from this commentary of Vachaspati Misra.The naming of Vachaspati Misra’s commentary on Brahma Sutras has a very interesting story which has become part of Mithila folklore.

Vachaspati's enlightened master asked him to write a commentary on Brahma Sutras. The master also married his daughter Bhamati to him and died soon afterwards. Vachapati started work in the right earnest and soon it became an all encompassing endeavour for him. Time flew. Months turned into years and years into decades. For all these years, he thought about nothing else , saw nothing else and heard nothing else. Finally he finished the great work. Only the title remained to be given. He looked up and saw a lady, lighting a lamp next to him.

Vachaspati asked the woman, "Who are you? And why do you go on serving me like this?"

The lady replied, " Never mind, continue with your work. "

He said , " My work is over, but tell me who are you? "

"I am your wife !" , answered the lady.

Vachaspati was shocked to realize that for 30 years his wife had been serving him dutifully without he even being aware of it. Tears rolled down his cheeks but Bhamati had no complaints. She said she is proud to have a husband like him and has been very blessed to associate with him in letting him finish the great work.

Vachaspati expressed his immense gratitude for his wife and said ,"You are a rare woman". As a tribute to her wife's sacrifices he named his commentary on her, Bhamati. Bhamati also used to make a rangoli on the floor. The geometric patterns used to help him discover a number of formulas.

[edit] Bhamati as a Mathematician's wife

Bhamati is the beautiful and faithful wife Vachaspati Mishra who means a world to him — he has neither seen the world nor his wife. His world is limited to only devising theorems and formulas. His neighbours have never seen him, but the world has heard of him.

"Someone has again created a rangoli on the floor outside my room. Who does it everyday?" Vachaspati says on coming out of his room a morning after spending another sleepless night, writing the penultimate chapter of his book. "These geometric patterns have helped me discover a number of formulas. Tonight, I will find out who makes these," he says.

At night, from his hiding place behind the pillar, Vachaspati watches a woman enter the compound. After making a triangular grid of matchsticks, she is preparing to leave when Vachaspati blocks her way. "Who are you and why do you make these patterns?" he says. "I am your wife and these patterns are to inspire you," she says. "I don’t remember getting married," says the learned man. "It is because you are always absorbed in your work," says the wife. "Prove that you are a mathematician’s wife," says the husband. "How?" says the lady. "The grid that you have made today is beautiful. Can you find out the least number of matches that have to be removed to break all triangles in this size 3 grid of 18 matches?" says the husband.

The wife says, "Three matches are needed to make a single triangle. To break it, you can remove any single match." She colours the small triangles in red and blue alternately, so that, no two adjacent triangles are of the same colour. If the grid is of size ‘n’, she now has n*(n+1)/2 triangles in red and n*(n-1)/2 triangles in blue. All upward-pointing triangles are of one colour and all downward-pointing triangles of another colour. No matchstick is part of two small triangles of the same colour, so, at least n*(n+1)/2 matches have to be removed to make all small triangles disappear. "If I do this by removing a match from each of the n*(n+1)/2 triangles of the same colour, so that all matches that are removed point in the same direction, I have removed all matches in that direction, due to which, no triangle can now be formed. For this size 3 grid, 3(4)/2=6 matches must be removed to make all triangles disappear," she says.

Vachaspati says, "Beautiful indeed! I will use this formula to end my book, which reminds me that I still have to dedicate it to someone." He picks up his pen, finishes his book, and writes on page 1 — "Dedicated to my wife". "What is your name dear?" he says to his wife, "Bhamati," replies the woman. On the title page, Vachaspati writes in bold letters — Bhamati.

[edit] References

Potter, Karl H. Encyclopedia of Indian Philosophies ,Vol 2. The tradition of Nyaya Vaisesika up to Ganesha. P 453-455
Mishra, Umesh. History of Indian Philosophy ,Vol 2.
Prossonno Coomar Tagore( (Trans.) . Vivada Chintamani: A Succinct Commentary on the Hindoo Law Prevalent in Mithila
Mahāmahopadhyāya G. Jha (Trans. ) . The Tattva-Kaumudi. Vāchaspati Misra's Commentary on the Sānkhya-Kārikā
Hajime Nakamura, Trevor Leggett (2004). A History of Early Vedānta Philosophy Vol-2. (p65 -66). Motilal Banarsidass Publication, ISBN 8120806514