Saturday, February 28, 2009

Snakes and Ladders

A Board game (board with a grid of 10x10) that we play with dice and token, if token land on the lower-numbered end of the squares with a "ladder", then player can move their token up to the higher-numbered square and if the token land on the higher-numbered square of a pair with a "snake" (or chute), then player must move their token down to the lower-numbered square.... Yes here I am talking about 'Snakes and Ladder'.

It's a game almost all of us have played. It's a game which is related to the childhood memories of all of us.
But do we ever think that who invented this game? What is the significance of this game?

Yes, Snakes and Ladders is an original Indian game.

The board game, today called Snakes and Ladders, originated in ancient India, where it was known with the name Mokshapat or Moksha Patamu.It is not actually known when or who invented it, though it's believed the game was played at a time as early as 2nd century BC. According to some historians, the game was invented by Saint Gyandev in the 13th century AD.

Originally, the game was used as a part of moral instruction to children. The squares in which ladders start were each supposed to stand for a virtue, and those housing the head of a snake were supposed to stand for an evil. 

In Moksha-Patamu, the squares of virtue are faith (12), reliability (51), generosity (57), knowledge (76), asceticism (78), while the squares of evil are disobedience (41), vanity (44), vulgarity (49), theft (52), lying (58), drunkenness (62), debt (69), murder (73), rage (84), greed (92), pride (95) and lust (99). The last square (100) represents Nirvana.The snakes outnumbered the ladders in the original Hindu game as a reminder that treading the path of good is very difficult compared to committing sins. Presumably the number "100" represented Moksha (Salvation).

Once the player reaches the second last square, he has to have the patience to wait for the right number to fall so that he can finally reach home.

The game was transported to England by the colonial rulers in the latter part of the 19th century, with somemodifications. The modified game was named Snakes and Ladders and stripped of its moral and religious aspects and the number of ladders and snakes were equalized. In 1943, the game was introduced in the US under the name Chutes and Ladders. 

Through its several modifications over the decades, however, the meaning of the game has remained the same -- 'that good deeds will take people to heaven (Moksha) while evil deeds will lead to a cycle of rebirths in lower form of life (Patamu).

Thursday, February 26, 2009

Takshila: World's first University

India has a long and venerable history in the field of higher education. In ancient times, the country was known to have been home to the oldest formal universities in the world.

The world's first University was established in Takshila or Taxila or Takshashila (now in Pakistan) in 700BC. This centre of learning was situated about 50 km west of Rawalpindi in Pakistan. It was an important Vedic/Hindu and Buddhist center of learning. It was not a well organized university like Nalanda.

There is some disagreement about whether Takshashila can be considered a university. While some consider Taxila to be an early university or centre of higher education, others do not consider it a university in the modern sense.

More than 10,500 students from all over the world studied here. The campus accommodated students who came from as far as Babylonia, Greece, Arabia and China and offered over sixty different courses in various field such as science, mathematics, medicine, politics, warfare , astrology, astronomy, music, religion, and philosophy. Generally, a student entered Takshashila at the age of sixteen. Students would come to Takshila and take up education in their chosen subject with their teacher directly.
They were supposed to pay for their expenses. However, if a student was unable to pay then he could work for his teacher. The Vedas and the Eighteen Arts, which included skills such as archery, hunting, and elephant lore, were taught, in addition to its law school, medical school, and school of military science.

Takshila was specialized in the study of medicine.

Panini, the famous Sanskrit grammarian, Kautilya (Chanakya) and Charaka, the famous physician of ancient India, and Chandragupta Maurya were the products of this university. It gained its importance again during the reign of Kanishka. It was probably, the earliest of the ancient seats of higher education. Takshashila is perhaps best known because of its association with Chanakya. The famous treatise Arthashastra (Sanskrit for The knowledge of Economics) by Chanakya, is said to have been composed in Takshashila itself.

Taxila has been listed by the UNESCO as one of the World Heritage Sites.

Monday, February 23, 2009

Aryabhatta and origin of zero

Aryabhatta (476-550 A.D.), one of the world’s greatest mathematician-astronomer, was born in Patliputra in Magadha, modern Patna in Bihar. Many are of the view that he was born in the south of India especially Kerala and lived in Magadha at the time of the Gupta rulers. However, there exists no documentation to ascertain his exact birthplace. Whatever this origin, it cannot be argued that he lived in Patliputra where he wrote his famous treatise the "Aryabhatta-siddhanta" but more famously the "Aryabhatiya", the only work to have survived.

The mathematical part of the Aryabhatiya covers arithmetic, algebra, plane trigonometry and spherical trigonometry. It also contains continued fractions, quadratic equations, sums of power series and a table of sines. This work is the first we are aware of which examines integer solutions to equations of the form by = ax + c and by = ax - c, where a, b, c are integers. Aryabhatta was an author of at least three astronomical texts and wrote some free stanzas as well.

He wrote that if 4 is added to 100 and then multiplied by 8 then added to 62,000 then divided by 20,000 the answer will be equal to the circumference of a circle of diameter twenty thousand. This calculates to 3.1416 close to the actual value Pi (3.14159).

But his greatest contribution has to be ZERO, for which he became immortal. He certainly did not use the symbol, but the French mathematician Georges Ifrah argues that knowledge of zero was implicit in Aryabhata's place-value system as a place holder for the powers of ten with null coefficients. The supposition is based on the following two facts: first, the invention of his alphabetical counting system would have been impossible without zero or the place-value system; secondly, he carries out calculations on square and cubic roots which are impossible if the numbers in question are not written according to the place-value system and zero.

He already knew that the earth spins on its axis, the earth moves round the sun and the moon rotates round the earth. He talks about the position of the planets in relation to its movement around the sun. He refers to the light of the planets and the moon as reflection from the sun. Aryabhatta gives the radius of the planetary orbits in terms of the radius of the Earth/Sun orbit as essentially their periods of rotation around the Sun. He believes that the Moon and planets shine by reflected sunlight, incredibly he believes that the orbits of the planets are ellipses. He correctly explains the causes of eclipses of the Sun and the Moon.

This remarkable man was a genius and continues to baffle many mathematicians of today. His works was then later adopted by the Greeks and then the Arabs.

Bhaskara I who wrote a commentary on the Aryabhatiya about 100 years later wrote of Aryabhatta:-
"Aryabhatta is the master who, after reaching the furthest shores and plumbing the inmost depths of the sea of ultimate knowledge of mathematics, kinematics and spherics, handed over the three sciences to the learned world."

To read more about him:
Related Posts Plugin for WordPress, Blogger...