Srinivasa Ramanujam

Srinivasa Ramanujam, the great mathematician passed away on 26th April, 1920.

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Srinivasa Ramanujam

A person who lived for a little over 32 years, Ramanujam was born in Kumbhakonam, the famous temple town in the Cauvery River delta.

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Kumbakonam

Kumbakonam, the rice bowl of Tamil Nadu has been famous for many things, from temples to rice and now for the aromatic Kumbakonam Degree Coffee.

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Kumbakonam Rice Fields

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 Kumbakonam Degree Coffee

But, the greatest son of Kumbakonam is the mathematician, Srinivasa Ramanujam.

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Srinivasa Ramanujam’s house

In his Dreams

Ramanujam attributed the mathematical formulae that he came up with, to Namagiri Thayar, the Goddess of Namakkal temple.

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                         Namakkal Temple                                                               Goddess Namagiri

He often mentioned that it was Goddess Namagiri who came to him in his dreams and gave answers to his mathematical problems.

From Wife

 The wife of Ramanujam, Janakiammal has an interesting input about her husband.

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Janakiammal

Ramanujam used to feverishly do all his basic calculations on a black slate. This was the norm of every student in India then.

She says, “Ramanujam did his calculations on a hand held slate, then transferred the final results to his note books, erasing the slate.”

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Ramanujam did his calculations on a slate

Thus we have few clues as to how he arrived at these equations, and there is no doubt that they are true.

This is expressed by the mathematics historian George Gheverghese Joseph in his book ‘The Crest of the Peacock’, Page 11.

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The Crest of Peacock Book
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George Gheverghese

His work notes and formulae that he arrived at are available in his now famous notebooks.

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Ramanujam’s notebook

Mathematicians till to date are trying to understand and use them.

To Cambridge University

When Ramanujam was working as a Clerk in Madras Port Trust, he sent some of his mathematical workings to Prof. G H Hardy of Cambridge University.

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Prof. G H Hardy

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Cambridge University

Ongoing through the notes, Prof G H Hardy felt that here was an absolute genius at work.

Prof Hardy invited Ramanujam to the Cambridge University.

Ramanujam spent 6 to 7 years in Cambridge. The work that Ramanujam did then along with Hardy has now become a part of the legend of Mathematics.

The mathematical formula that Ramanujam came up has been used as algorithms in modern computer systems.

Unfortunately, due to severe cold weather of England, Ramanujam who was more used to the tropical climate of Kumbhakonam, could not acclimatize and picked up an illness. The illness grew from bad to worse and he sailed back to India.

A sick and sad Ramanujam returned to Madras on April 2nd 1919.  He passed away on 26th April, 1920 at Chetpet in Madras.

Ganitham

Srinivasa Ramanujam belonged to an illustrious lineage of mathematicians that India has offered to the world starting from Boudhayana, Apastambha, Aryabhatta, Varahamihira, Brahma Gupta, Bhaskaracharya, Madhava and a galaxy of others.

All these illustrious people through the ages specialized in this field of Ganitham, the Indian term for mathematics.

The word Ganitham has in it the phrase Gana, meaning weighty, heavy.  The field of mathematics has always been weighty and heavy.

The Lord of Mathematics in Indian tradition is Ganesha, Ganapathy. The term Gana also means numbers.

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Lord Ganesha, the lord of Mathematics

 

An illustrious lineage

India has had an illustrious lineage of people who excelled in Ganitham.

Srinivasa Ramanujam is one among this illustrious lineage.

Today in our midst, we have another illustrious mathematician of Indian origin settled in USA, Prof Srinivasa Vardhan who is an Abel Laureate.

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Prof Srinivasa Vardhan

Abel Laureate

It is to be noted that in mathematics there is no Nobel Prize as Alfred Nobel did not like Maths.

The same Norwegian Academy which confers the Nobel Prize year after year has instituted an award for mathematics, equal to novel prize in the name of their Norweigian mathematician, Niels Henrik Abel.

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Niels Henrik Abel

It would be nice if the Indian government could institute an international award in the name of Srinivasa Ramanujam for the lineage that India has given to world in the field of Ganitham, mathematics.

Mathematics – Crest of Peacock

Mathematics among the sciences is given a high place, like the crest of a peacock among its colored plum, in its ancient treatises. Vedanta Jyothisa, an ancient treatise on mathematics and astronomy mentions this.

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The Man who saw Infinity

In the last decade or so, there has been a spurt of interest on Srinivasa Ramanujam. Books are being written and films are being made on this great man who saw infinity.

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The Man who knew Infinity, Book

We need to sustain this interest to encourage more Indians to take up pure mathematics.

Election System in Ancient India

Election season is on. Indians will soon be making a choice on who should lead them. From when did the people of this country get the right to vote and choose their leaders?

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The constituent assembly framed the constitution of India to be republic. Being a republic entails voting by every person – Universal Adult Franchise. All adults above the age of 21 were eligible to vote.

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Jawaharlal Nehru moving the resolution for an independent sovereign republic in the Constituent Assembly

  It is interesting to note that India gave equal voting rights to women in 1951 itself, whereas countries like Switzerland gave voting rights to women only in 1972.

When doubts were raised about whether the illiterate people were capable of voting, Dr. Rajendra Prasad, a member of constituent Assembly, who later became the first President of India gave a fitting reply in the constituent assembly.

His observation is pertinent even to this day, 65 years after his speech.

 The relevant extract being,

“Some people have doubted the wisdom of adult franchise. Personally, although I look upon it as an experiment the result of which no one will be able to forecast today, I am not dismayed by it. I am a man of the village and although I have had to live in cities for a pretty long time, on account of my. work, my roots are still there. I, therefore, know the village people who will constitute the bulk of this vast electorate. In my opinion, our people possess intelligence and commonsense. They also have a culture which the sophisticated people of today may not appreciate, but which is solid. They are not literate and do not possess the mechanical skill of reading and writing. But, I have no doubt in my mind that they are able to take measure of their own interest and also of the interests of the country at large if things are explained to them. In fact, in some respects, I consider them to be even more intelligent than many a worker in a factory, who loses his individuality and becomes more or less a part of the machine Which he has to work. I have, therefore, no doubt in my mind that if things are explained to them, they will not only be able to pick up the technique of election, but will be able to cast their votes in an intelligent manner and I have, therefore, no misgivings about the future, on their account. I cannot say the same thing about the other people who may try to influence them by slogans and by placing before them beautiful pictures of impracticable programmes. Nevertheless, I think their sturdy commonsense will enable them to see things in the right perspective. We can, therefore, reasonably hope that we shall have legislatures composed of members who shall have their feet on the ground and who will take a realistic view of things.”

Did elections in India come in vogue only when the constitution was framed in 1950?

Elections in ancient India have been recorded in the different stories and texts of the land.

In different parts of India right from the Mahabharata period, there have been many Janapada, republics. The very word, ‘Janapada’ means “People’s Republic, where people come together to choose their leader.”

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Some of the Mahajanapada of Ancient India

These are some of the Janapada, republics of yore that the historians have been able to list. Like this other parts of India also have had their republics. Similarly, to the west of Sindhu River in the west of Afghanistan comprising of present day Pakistan, there were a few such Janapada, republics.

 Among these, one of the mentioned example is Uttaramerur.While the exact election mode in Janapada then is not available, the Uttaramerur inscription is a classic example, of eligible and disqualifiable candidates.

Uttaramerur Inscriptions

One of the early inscriptions specifically relating to elections in villages is available at the Srinivasa Temple in Uttaramerur village. Uttaramerur is a small prosperous town, 100 kilometres to the south of Chennai. These inscriptions are now popularly known as Uttaramerur inscriptions.

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Uttaramerur Inscriptions at Srinivasa Perumal Temple

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D K Hari at the inscription site

The Election System was then established by Royal Order under the Chola King, Parantaka Deva Parkesari Varman who ruled between 907 and 955 CE.

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Chola King Parantaka Deva

As per these inscriptions we learn that, the village assembly, panchayat was formed in Uttaramerur Chaturvedi Mangalam, consisting of 30 wards. The period of the assembly was for one year. The area of operation of the village assembly, panchayat, included Village SabhaGrama Sabha, Garden Sabha – Thotam Sabha and Tank Sabha – Eri Sabha.

The inscriptions throw light on the mode of election to Village Assemblies, Panchayat in those days.

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English translation of the Uttaramerur inscription

Election Pot

There was an election ballot, a pot, in which the electors polled candidates of their choice with names written on palm leaves. Each person’s preference vote was inscribed on a palm leaf and was dropped into the ballot pot.

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There were also qualifications and disqualifications for contesting an election.

Qualifications for contesting an election

  1. Own more than ¼ th veli of tax paying land

  2. Live in own house

  3. Age 35-70 years

  4. Must know Mantrabrahmana, be well read enough in general knowledge, to teach others

  5. If he owns 1/8th of veli, he must have learnt atleast 1 Veda, Marai, and 1 of the 4 bhasya, i.e. explanation, its Porul, its Artham

  6. Should be conversant with business

  7. Should not have been on any other committee for the last 3 years

Disqualifications for contesting an election

  1. One who has been on any of the committees but has not submitted his accounts.

  2. Following relations of a contestant are also disqualified

  3. The sons of the younger and elder sisters of his mother

  4. The sons of his paternal aunt and maternal uncle

  5. The uterine brother of his mother

  6. The uterine brother of his father

  7. His uterine brother

  8. His father-in-law

  9. The uterine brother of his wife

  10. The husband of his uterine sister

  11. The sons of his uterine sister

  12. The son-in-law who has married his daughter

  13. His father, his son

  1. One against whom incest (agamyagamana) or first four of the five great sins are recorded.

  2. One who is foolhardy

  3. One who has stolen the property of another

  4. One who has committed sins and has become pure by performing expiatory ceremonies

  5. One who is guilty of incest and has become pure by performing expiatory ceremonies

All these persons thus specified, shall not to the end of their lives, have their names written on the pot-ticket, to be put into the pot for any of the committees.

The Contrast

It will be interesting to know that in today’s scenario almost all the politicians who have got ticket to fight in election would be automatically disqualified by this traditional, local law of the land.

Such was the high level of accountability, transparency, morality and ethics in local governance.

It is no wonder that the people were well governed by themselves, by their laws and consequently were prosperous as a civilization which had sustained itself for over 1000 years.

World Earth Day

World Earth Day is celebrated annually on April 22nd every year, whereby various events are held the world over to express solidarity towards environment protection, the protection of Mother Earth.

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Time to come together to protect Mother Earth

Earth is called Prthvi which means ‘wide, heavy’. It is also called Dharti-‘that which bears’. In the Indian tradition, our planet is revered verily as a Divinity, Bhu Devi.

 The earth as Mother, Dharti may innately bear everything, but there’s a limit to which we can expect her to bear the brunt of man’s destructive actions.

 The observations of Chief Seattle in 1964 is apt here on the relationship between man and earth.

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Chief Seattle

“The earth does not belong to man, man belongs to the earth. All things are connected like the blood which unites one family. Whatever befalls the earth befalls the sons of the earth. Man did not weave the web of life; he is merely a strand in it. Whatever he does to the web, he does to himself.”

The themes for this year’s World Earth Day are “Green Cities” and “Water”.

Greenery and Water are inter related. The water bodies ensure an increase in the greenery cover all around them.

But, it is poignant to note that buildings are replacing trees in most of our major cities today, the so called hub of prosperity. Water bodies are also disappearing, making way for residential centres and shopping malls.

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Huge buildings have replaced greenery

In ancient India, the decentralized system was followed. Instead of a centralized hub like the cities where all people migrate to, there were many decentralized villages everywhere where the local community lived. The communities in these villages were smaller, and thus there was more greenery. Moreover, each village had its own water bodies called the Pushakarni, which contributed to the greenery of that area.

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Pushkarni surrounded by greenery

In ancient India, the villages supported the cities. Agriculture happened in villages. Decentralized manufacturing of products such as steel, zinc, copper, also happened in the villages. The cities were just a trading hub. The ecological footprint was thus spread out.

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 The Indian ethos and practice of sustainability emanated from the Bhumi Sukta of Rig Veda and has flowed through the civilization therefrom. Bhumi Sukta speaks of the need to appreciate the life giving qualities of earth and hence need to keep it sustainable for generations to come.

This Earth Day, let us resolve to revive these sustainable practices by becoming aware of them and putting them to right use and protect our planet.

More on sustainable practices of ancient India is available in our work, “Sustainable Ethos of India.”

Indian New Year and Spring Equinox

In the month of March-April we ring in the New Year as per Indian calendars. We use the word “calendars” because India has a variety of calendars, some are lunar based, some are based on the Sun, some are luni-solar and some are Jovian i.e. Jupiter based.

The calendars in India follow both the Sun and moon. They are essentially Luni Solar and use the Zodiac as the months. Some parts of India use the Sun and Stars of the Zodiac as the marker, i.e. Sauramanam, while some other parts use the moon and the Zodiac as the marker and the months start based on the phase of the moon and the Zodiac being transited by the Sun i.e. Chandramanam.

States such as Karnataka, Andhra, Maharashtra and few others, which follow the Chandramana calendar celebrate – Ugadi and Gudi Padava, as their New Year respectively, based on the day after the New Moon.

While others who follow the Sauramana calendar, i.e states such as Tamil Nadu – Puduvarsham, Kerala – Vishu, Punjab- Baisaki, Assam – Bohali Bihu, Sri Lanka etc. celebrate the New Year typically on April 14th / 15th as the day when Sun transits into Aries Zodiac.

60 YEAR CALENDAR CYCLE – MANAVA YUGA

In any case, most of India also follows an overall Jovian system or Jupiter based system wherein years are counted in cycles of 60 years. i.e. 60 years have different names and once 60 years have passed, the 61st year gets the same name as the first year in the 60 year cycle.

This 60 year cycle is called a Manava Yuga.

Why a 60 year calendar?

While the Earth revolves the Sun in one year, Jupiter revolves around the Sun in 12 years and Saturn revolves around the Sun in 30 years. The lowest common denominator, i.e. the earliest time when both Jupiter and Saturn can meet at the same position, with respect to the Sun, Moon and Earth, is 60 years. Hence this 60 year cycle.  The sixty year calendar cycle repeats itself and each of these years has a name, which is said to denote some qualitative aspect of the year.

The 60 year cycle is also called as Manava Yuga, because a person’s prime life is considered to be 60 years. It is called Yuga, because, it is an alignment. An alignment of man on Earth, the Earth, the Moon, the Sun, Jupiter and Saturn. As we have seen before, Yuga, comes from Jug or Yog which means union as in Yoga which is a union of body and mind.

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60 Year Alignment Cycle

YUGADI

Yug means an alignment of the astral bodies; which in turn denotes a period of time and Adi is the beginning. Thus Yugadi, also popularly spelt as Ugadi, is the start of a period of time or Yuga. Yuga or alignment here is the yearly alignment of the Earth’s equator with the Sun, the Moon and the Zodiac of Chaitra. This is why this New Year festival is called a Yugadi.

VISHU

In the Sauramana calendar, the movement of the sun is used as the base. The equinox is when the Sun is exactly over the equator. After this day the Sun moves towards the northern hemisphere.

This point has therefore been used as the starting point for a year by those who used the Sun as the basis for the calendar.

The Indian word for equator is Visvadrutta Rekha meaning that which splits the world into 2 halves. The word Vishu thus denotes equal and the New Year festival in Kerala is called Vishu, when the sun is at the equal position in its annual transit.

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A few thousand years ago, when this type of calendrical system was probably formed, we had the occurrence of equinox on April 14th. Today the equinox occurs on March 21st. Here there is a difference of 21 days between March 21st and April 14th.

This difference is due to the precision of equinox, where we must adjust 1 day in every 72 years. Such adjustments were done until 1500 years ago or more during the period of Varahamihira in 530 CE, post which it was not paid attention to, due to which this  gap has occurred.

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Varahamihira, 530 CE

 

Calendar Reform

When India attained its independence, a Calendar Reform Committee was constituted with the renowned Astrophysicist, Dr. Meghanand Saha as its Head. This committee studied all these calendars, understood the nature-based aspect of these calendars of India and suggested that the Indian calendar should start on March 21st  keeping in mind the precession of equinox factor that has occurred since the last calibration of the calendar. This calendar, with the year starting from March 21st has now been accepted and used for all official, government records.

Celebrate with knowledge

This knowledge of calendrical system should help us realize the wholistic, scientific and nature-based concepts behind calendars of India and the festival of New Year.