In order to avoid war and resulting loss of man and material, Rama asked Ravana, “O king of Asuras, return me my legally wedded wife, and there will be no war”. Ravana replied, “Not even at the cost of everything. No force can stop me from doing what I want. I will never, come what may”.

For the same reasons as those of Rama, Krishna went to the palace of Duryodhan and asked for just five villages for Pandavas instead of half of the Kingdom. Duryodhan replied, “Forget five villages, I won’t give land as much as amounting to the tip of a needle, come what may”…

Both Ravan and Duryodhan met a dreadful end.

Our current generation who use phrases like “No Force can do it…..” “At any cost…”, “Come what may..” should read the scriptures like Ramayana and Mahabharata. May they escape the fate of Ravana and Duryodhana.

Ego Hurts………..

Chitrakoot: Sphatik Shila

Literally translated, Sphatik Shila is Sanskrit for ‘crystal rock’. It is essentially a flat boulder, where Lord Rama was believed to have once rested upon, with his wife Sita, and admired the scenic beauty of Chitrakoot. The boulder gets its name from the fact that it has a glass like or crystalline finish, which still contains the footprints of the lord, his knee print, Sita’s footprints and Lakshman’s foot prints.
To see the footprints one has to make a climb up the boulder. The priest here will tell you about a particular incident in Ramayana that took place in this very place.

Rama is exiled to the forest with Sita and brother Lakshmana. A fatigued Rama was sleeping in the lap of Sita, when a crow attacked her. The crow pecks at her twice on her feet. Rama is awakened by the stirrings and recognizes the crow whose claws were dripping in blood as the son of Indra. An enraged Rama, at the behest of Sita, unleashes the divine weapon Brahmastra on the crow, who flees in fear. The crow flies across the universe, but the weapon follows. Turned back by Indra, the gods and rishis, the crow takes refuge in Rama and surrenders to him. He requests pardon, but Rama says that the Brahmastra cannot be withdrawn. So, the son of Indra asks it to hit the crow’s right eye, and he is left half-blind.

It is also believed that while Sita was injured, Lord Rama took care of her, which is why Sphatik Shila also represents the love between Lord Rama and Sita. This makes it a prime destination for all the pilgrims visiting Chitrakoot.

Located on the banks of the sparkling Mandakini river which harbours an array of pretty little colourful fishes, and surrounded by lush greenery, the tranquility and the picturesque beauty of this place makes it a must see.

In an article for the Freer | Sackler Galleries at the Smithsonian Institute, Sanskrit scholar James Mallinson provides a very interesting commentary on a number of paintings and historical records depicting sannyasis and ascetics from the 11th to 16th Centuries. A famous battle that broke out amongst the sadhus during the reign of Emperor Akbar. These battle scenes are given special focus by Mallinson in his article because they depict the various types of sadhus involved, identifiable by their dress, hair, ornament, etc.

During his brutal reign of destruction of Vaisnava temples and deities, and about a year before the massacre of nearly 40,000 civilians and Rajputs at Chittor, Akbar and his men went to Thaneswar in Haryana. It was there that the great saffron battle took place.

It happened that at the time, a congregation of sadhus had gathered at a tank in the village. Among all the ascetics gathered to take holy bath, a fight broke out between the two predominant groups over who should get to bathe first, and at the best spot.

The fight between the sadhus became violent, and the Mughals gathered to watch. Akbar himself came, and ordered his soldiers to intervene on the side of one of the groups. The logic apparently was that as long as one group of infidels killed members of the other group, the total number of infidels would be reduced, thereby making the presence of Islam even greater.

Akbar’s soldiers stepped into the middle of the unfortunate sadhus fighting at the tank that day, and began cutting them down with swords, axes, and arrows.

Surprisingly enough, the events at Thaneswar were recorded by four different historians from Akbar’s court: Nizamuddin Ahmad, Badauni, Abu’l Fazl, and another anonymous writer. The accounts provided by the latter two were embellished with lavish illustrations of the sannyasis, dressed in various types of attire, engaged in combat with one another and with the Mughals.

While there are some discrepancies between the four accounts, for the most part the writers were in agreement about the main facts:

* that Akbar’s entourage had encountered two bands of Hindu ascetics at Thaneswar;

* the location of the event was a large body or ‘tank’ of water, to which people from throughout north India flocked to take holy bath and make offerings;

* each group claimed to have the right to occupy the most auspicious location at the shrine that day;

* each group of sadhus was armed;

* after some discussion, Akbar granted permission for the ascetics to take up an armed contest to settle the issue;

* as the contest escalated, Akbar ordered some of his soldiers to enter the fight, assisting the smaller group; and

* after considerable violence and bloodshed, the smaller group of sadhus prevailed.

ANCIENT INDIAN MATHEMATICS
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Despite developing quite independently of Chinese (and probably also of Babylonian mathematics), some very advanced mathematical discoveries were made at a very early time in India.
Mantras from the early Vedic period (before 1000 BC) invoke powers of ten from a hundred all the way up to a trillion, and provide evidence of the use of arithmetic operations such as addition, subtraction, multiplication, fractions, squares, cubes and roots. A 4th Century AD Sanskrit text reports Buddha enumerating numbers up to 1053, as well as describing six more numbering systems over and above these, leading to a number equivalent to 10421. Given that there are an estimated 1080 atoms in the whole universe, this is as close to infinity as any in the ancient world came. It also describes a series of iterations in decreasing size, in order to demonstrate the size of an atom, which comes remarkably close to the actual size of a carbon atom (about 70 trillionths of a meter).

As early as the 8th Century BC, long before Pythagoras, a text known as the “Sulba Sutras” (or “Sulva Sutras”) listed several simple Pythagorean triples, as well as a statement of the simplified Pythagorean theorem for the sides of a square and for a rectangle (indeed, it seems quite likely that Pythagoras learned his basic geometry from the “Sulba Sutras”). The Sutras also contain geometric solutions of linear and quadratic equations in a single unknown, and give a remarkably accurate figure for the square root of 2, obtained by adding 1 + 1⁄3 + 1⁄(3 x 4) + 1⁄(3 x 4 x 34), which yields a value of 1.4142156, correct to 5 decimal places.

As early as the 3rd or 2nd Century BC, Jain mathematicians recognized five different types of infinities: infinite in one direction, in two directions, in area, infinite everywhere and perpetually infinite. Ancient Buddhist literature also demonstrates a prescient awareness of indeterminate and infinite numbers, with numbers deemed to be of three types: countable, uncountable and infinite.
Like the Chinese, the Indians early discovered the benefits of a decimal place value number system, and were certainly using it before about the 3rd Century AD. They refined and perfected the system, particularly the written representation of the numerals, creating the ancestors of the nine numerals that (thanks to its dissemination by medieval Arabic mathematicans) we use across the world today, sometimes considered one of the greatest intellectual innovations of all time.

The Indians were also responsible for another hugely important development in mathematics. The earliest recorded usage of a circle character for the number zero is usually attributed to a 9th Century engraving in a temple in Gwalior in central India. But the brilliant conceptual leap to include zero as a number in its own right (rather than merely as a placeholder, a blank or empty space within a number, as it had been treated until that time) is usually credited to the 7th Century Indian mathematicians Brahmagupta – or possibly another Indian, Bhaskara I – even though it may well have been in practical use for centuries before that. The use of zero as a number which could be used in calculations and mathematical investigations, would revolutionize mathematics.

Brahmagupta established the basic mathematical rules for dealing with zero: 1 + 0 = 1; 1 – 0 = 1; and 1 x 0 = 0 (the breakthrough which would make sense of the apparently non-sensical operation 1 ÷ 0 would also fall to an Indian, the 12th Century mathematician Bhaskara II). Brahmagupta also established rules for dealing with negative numbers, and pointed out that quadratic equations could in theory have two possible solutions, one of which could be negative. He even attempted to write down these rather abstract concepts, using the initials of the names of colours to represent unknowns in his equations, one of the earliest intimations of what we now know as algebra.

The so-called Golden Age of Indian mathematics can be said to extend from the 5th to 12th Centuries, and many of its mathematical discoveries predated similar discoveries in the West by several centuries, which has led to some claims of plagiarism by later European mathematicians, at least some of whom were probably aware of the earlier Indian work. Certainly, it seems that Indian contributions to mathematics have not been given due acknowledgement until very recently in modern history.

Golden Age Indian mathematicians made fundamental advances in the theory of trigonometry, a method of linking geometry and numbers first developed by the Greeks. They used ideas like the sine, cosine and tangent functions (which relate the angles of a triangle to the relative lengths of its sides) to survey the land around them, navigate the seas and even chart the heavens. For instance, Indian astronomers used trigonometry to calculated the relative distances between the Earth and the Moon and the Earth and the Sun. They realized that, when the Moon is half full and directly opposite the Sun, then the Sun, Moon and Earth form a right angled triangle, and were able to accurately measure the angle as 1⁄7°. Their sine tables gave a ratio for the sides of such a triangle as 400:1, indicating that the Sun is 400 times further away from the Earth than the Moon.

Although the Greeks had been able to calculate the sine function of some angles, the Indian astronomers wanted to be able to calculate the sine function of any given angle. A text called the “Surya Siddhanta”, by unknown authors and dating from around 400 AD, contains the roots of modern trigonometry, including the first real use of sines, cosines, inverse sines, tangents and secants.

As early as the 6th Century AD, the great Indian mathematician and astronomer Aryabhata produced categorical definitions of sine, cosine, versine and inverse sine, and specified complete sine and versine tables, in 3.75° intervals from 0° to 90°, to an accuracy of 4 decimal places. Aryabhata also demonstrated solutions to simultaneous quadratic equations, and produced an approximation for the value of π equivalent to 3.1416, correct to four decimal places. He used this to estimate the circumference of the Earth, arriving at a figure of 24,835 miles, only 70 miles off its true value. But, perhaps even more astonishing, he seems to have been aware that π is an irrational number, and that any calculation can only ever be an approximation, something not proved in Europe until 1761.

Bhaskara II, who lived in the 12th Century, was one of the most accomplished of all India’s great mathematicians. He is credited with explaining the previously misunderstood operation of division by zero. He noticed that dividing one into two pieces yields a half, so 1 ÷ 1⁄2 = 2. Similarly, 1 ÷ 1⁄3 = 3. So, dividing 1 by smaller and smaller factions yields a larger and larger number of pieces. Ultimately, therefore, dividing one into pieces of zero size would yield infinitely many pieces, indicating that 1 ÷ 0 = ∞ (the symbol for infinity).
However, Bhaskara II also made important contributions to many different areas of mathematics from solutions of quadratic, cubic and quartic equations (including negative and irrational solutions) to solutions of Diophantine equations of the second order to preliminary concepts of infinitesimal calculus and mathematical analysis to spherical trigonometry and other aspects of trigonometry. Some of his findings predate similar discoveries in Europe by several centuries, and he made important contributions in terms of the systemization of (then) current knowledge and improved methods for known solutions.

The Kerala School of Astronomy and Mathematics was founded in the late 14th Century by Madhava of Sangamagrama, sometimes called the greatest mathematician-astronomer of medieval India.
He developed infinite series approximations for a range of trigonometric functions, including π, sine, etc. Some of his contributions to geometry and algebra and his early forms of differentiation and integration for simple functions may have been transmitted to Europe via Jesuit missionaries, and it is possible that the later European development of calculus was influenced by his work to some extent.

Shankha-kshetra:

In describing Jagannath Puri Dham as Shankha-kshetra, a conch-like area comprised of 115 transcendental tirthas, teerthams and shrines, we have begun to describe the seven concentric folds within which all these holy spots are contained. The first, innermost fold is home to the Jagannath Deities Themselves, in the sanctum of Their 12th century shrine. The second fold, a hexagonal shape adjacent to the inner fold, is home to four Devis and contains two tirthas, two sacred trees, and two tanks.

The third fold of Shankha-kshetra comprises the central part of its lotus-like structure, which has eight petals, each petal being the abode of Lord Shiva and a Devi.

The eight forms of Shiva residing here are Agneswar, Bateswar, Khetrapaleswar, Chakreswar, Baikuntheswar, Pataleswar, Isaneswar, and Lokeswar. The eight goddesses are Dwarabasini, Mahabajreswari, Swanabhairabi, Bhadrakali, Bhubaneswari, Mahakaliaghorea, Sitala, and Jagnyeswari.

All of the Deities in the second and third folds are engaged in guarding and serving the Supreme Lord at the center of the temple complex.

The primary entrance into the third fold is through the Lion’s Gate, in the East, known as Singhadwara. On either side of the gate are two massive lions, in a crouching position and wearing crowns. Next to Lord Jagannatha and the Puri Temple itself, the lion sentinals are perhaps the most famous symbols of Puri Dham.

When entering through the Lion’s Gate, one first passes by the Aruna Stamba, also known as the Sun Pillar. This beautiful 13th c. pillar used to stand before the Sun Temple at Konark, until it was moved here to Jagannath Puri by the Marathas. Made of chlorite, Aruna Stamba has sixteen sides and is 25 feet tall. It stands upon a beautifully carved pedestal, and at the top is a platform with an image of Aruna, the charioteer of Lord Surya, the Sun God. Aruna is kneeling down, offering obeisances.

After passing Aruna Stamba, pilgrims enter the Fumuta, where Lord Jagannath resides as Patitapavana, on the north side. Here, the Lord is visible to all devotees, including those who are not permitted to enter the inner temple premises. A small murti of Garuda sits before Patitapavana. Residing in carved niches in the wall are Sri Sri Radha-Krsna, Lord Nrsimhadeva, and Hanuman.

Next one enters an inner enclosure, which is reached by navigating a flight of 22 steps known as Baisipahacha. The steps vary in size, and are carved of feldspar and khondolite. Installed along the southern side of the Baisipahacha are Deities of Lord Ramacandra, Lord Nrsimha, Kasivisvanath (Shiva), and Ganesh.

To the left is Kasivisvanath Temple, which is the equivalent of Kasi itself. The Chaitanya Narsimha temple is also here, and a small Ramacandra temple, along with Ganesh.