Guru Purnima and Yogic rahasya

It is said that Guru Purnima was the day that saw Shiva become the Adi Guru, or the first Guru. The story goes that over 15,000 years ago, a yogi appeared in the upper regions of the Himalayas. Nobody knew what his origins were. But his presence was extraordinary, and people gathered. However, he exhibited no signs of life, but for the occasional tears of ecstasy that rolled down his face. People began to drift away, but seven men stayed on. When he opened his eyes, they pleaded with him, wanting to experience whatever was happening to him. He dismissed them, but they persevered. Finally, he gave them a simple preparatory step and closed his eyes again. The seven men began to prepare. Days rolled into weeks, weeks into months, months into years, but the yogi’s attention did not fall upon them again.

After 84 years of sadhana, on the summer solstice that marks the advent of Dakshinayana, the earth’s southern run, the yogi looked at them again. They had become shining receptacles, wonderfully receptive. He could not ignore them anymore. On the very next full moon day, the yogi turned south and sat as a guru to these seven men. Shiva, the Adiyogi (the first yogi) thus became the Adi Guru. Adiyogi expounded these mechanics of life for many years. The seven disciples became celebrated as the Saptarishis and took this knowledge across the world.

Guru Purnima is held sacred in the yogic tradition because the Adiyogi opened up the possibility for a human being to evolve consciously. The seven different aspects of yoga that were put in these seven individuals became the foundation for the seven basic forms of yoga, something that has still endured.

Karmayog- Dr. Srinivasa Ramanujan

Ramanujan has been described as a person with a somewhat shy and quiet disposition, a dignified man with pleasant manners.He lived a rather spartan life while at Cambridge. Ramanujan’s first Indian biographers describe him as rigorously orthodox. Ramanujan credited his acumen to his family goddess, Mahalakshmi of Namakkal. He looked to her for inspiration in his work,and claimed to dream of blood drops that symbolised her male consort, Narasimha, after which he would receive visions of scrolls of complex mathematical content unfolding before his eyes. He often said, “An equation for me has no meaning, unless it represents a thought of God.”

Hardy cites Ramanujan as remarking that all religions seemed equally true to him. Hardy further argued that Ramanujan’s religiousness had been romanticized by Westerners and overstated—in reference to his belief, not practice—by Indian biographers. At the same time, he remarked on Ramanujan’s strict observance of vegetarianism.

Srinivasa Ramanujan Iyengar  (22 December 1887 – 26 April 1920) was an Indian mathematician and autodidact. Though he had almost no formal training in pure mathematics, he made extraordinary contributions to mathematical analysis, number theory, infinite series, and continued fractions. Ramanujan initially developed his own mathematical research in isolation; it was quickly recognized by Indian mathematicians.

By age 11, he had exhausted the mathematical knowledge of two college students who were lodgers at his home. He was later lent a book on advanced trigonometry written by S. L. Loney He completely mastered this book by the age of 13 and discovered sophisticated theorems on his own. By 14, he was receiving merit certificates and academic awards which continued throughout his school career and also assisted the school in the logistics of assigning its 1200 students (each with their own needs) to its 35-odd teachers. He completed mathematical exams in half the allotted time, and showed a familiarity with geometry and infinite series. Ramanujan was shown how to solve cubic equations in 1902 and he went on to find his own method to solve the quartic. The following year, not knowing that the quintic could not be solved by radicals, he tried to solve the quintic.

In 1903 when he was 16, Ramanujan obtained from a friend a library-loaned copy of a book by G. S. Carr.The book was titled A Synopsis of Elementary Results in Pure and Applied Mathematics and was a collection of 5000 theorems. Ramanujan reportedly studied the contents of the book in detail.The book is generally acknowledged as a key element in awakening the genius of Ramanujan.The next year, he had independently developed and investigated the Bernoulli numbers and had calculated the Euler–Mascheroni constant up to 15 decimal places.His peers at the time commented that they “rarely understood him” and “stood in respectful awe” of him.

When he graduated from Town Higher Secondary School in 1904, Ramanujan was awarded the K. Ranganatha Rao prize for mathematics by the school’s headmaster, Krishnaswami Iyer. Iyer introduced Ramanujan as an outstanding student who deserved scores higher than the maximum possible marks.He received a scholarship to study at Government Arts College, Kumbakonam, However, Ramanujan was so intent on studying mathematics that he could not focus on any other subjects and failed most of them, losing his scholarship in the process. In August 1905, he ran away from home, heading towards Visakhapatnam and stayed in Rajahmundryfor about a month.He later enrolled at Pachaiyappa’s College in Madras. He again excelled in mathematics but performed poorly in other subjects such as physiology. Ramanujan failed his Fellow of Arts exam in December 1906 and again a year later. Without a degree, he left college and continued to pursue independent research in mathematics. At this point in his life, he lived in extreme poverty and was often on the brink of starvation.

On 14 July 1909, Ramanujan was married to a ten-year-old bride, Srimathia Janki (Janakiammal) (21 March 1899 – 13 April 1994).She came from Rajendram, a village close to Marudur (Karur district) Railway Station. Ramanujan’s father did not participate in the marriage ceremony.

After the marriage, Ramanujan developed a hydrocele testis, an abnormal swelling of the tunica vaginalis, an internal membrane in the testicle.The condition could be treated with a routine surgical operation that would release the blocked fluid in the scrotal sac. His family did not have the money for the operation, but in January 1910, a doctor volunteered to do the surgery for free.

After his successful surgery, Ramanujan searched for a job. He stayed at friends’ houses while he went door to door around the city of Madras (now Chennai) looking for a clerical position. To make some money, he tutored some students at Presidency College who were preparing for their F.A. exam.

In late 1910, Ramanujan was sick again, possibly as a result of the surgery earlier in the year. He feared for his health, and even told his friend, R. Radakrishna Iyer, to “hand these [Ramanujan’s mathematical notebooks] over to Professor Singaravelu Mudaliar [the mathematics professor at Pachaiyappa’s College] or to the British professor Edward B. Ross, of the Madras Christian College.” After Ramanujan recovered and retrieved his notebooks from Iyer, he took a northbound train from Kumbakonam to Villupuram, a coastal city under French control.

In early 1912, he got a temporary job in the Madras Accountant General’s office, with a salary of 20 rupees per month. He lasted for only a few weeks.Toward the end of that assignment he applied for a position under the Chief Accountant of the Madras Port Trust. In a letter dated 9 February 1912, Ramanujan wrote:

Sir,
I understand there is a clerkship vacant in your office, and I beg to apply for the same. I have passed the Matriculation Examination and studied up to the F.A. but was prevented from pursuing my studies further owing to several untoward circumstances. I have, however, been devoting all my time to Mathematics and developing the subject. I can say I am quite confident I can do justice to my work if I am appointed to the post. I therefore beg to request that you will be good enough to confer the appointment on me.

The number 1729 is known as the Hardy–Ramanujan number after a famous anecdote of the British mathematician G. H. Hardy regarding a visit to the hospital to see Ramanujan. In Hardy’s words:

I remember once going to see him when he was ill at Putney. I had ridden in taxi cab number 1729 and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavorable omen. ‘No’, he replied, ‘it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways.’

The two different ways are

1729 = 13 + 123 = 93 + 103.

Generalizations of this idea have created the notion of “taxicab numbers”. Coincidentally, 1729 is also a Carmichael number.

Samba : Son of Krishna married to a daughter of Duryodhana

Jambavati is one of the Ashtabharya, the eight principal queen-consorts of Hindu god Krishna. She was the only daughter of the bear-kingJambavan. Krishna married her, when he defeated Jambavan to retrieve the stolen Syamantaka jewel.

The Mahabharata and the Devi Bhagavata Purana narrate a story of the birth of Samba, Jambavati’s chief son. Jambavati was unhappy when she realized that only she had not borne any children to Krishna while all other wives were blessed with many children. She approached Krishna to find a solution and to be blessed with a son like the handsome Pradyumna, Krishna’s first-born son from his chief wife Rukmini. Then Krishna went to the hermitage of the sage Upamanyu in the Himalayas and as advised by the sage, he started to pray to the god Shiva. He did penance for six months in various postures; once holding a skull and a rod, then standing on one leg only in the next month and surviving on water only, during the third month he did penance standing on his toes and living on air only. Pleased with the austerities, Shiva finally appeared before Krishna as Samba, (Ardhanarishvara) the half-female, half-male form of the god, asked him to ask a boon. Krishna then sought a son from Jambavati, which was granted. A son was born soon thereafter who was named as Samba, the form Shiva had appeared before Krishna.

Samba grew up to be a nuisance to the Yadavas, Krishna’s clan. His marriage to Lakshmana, the daughter of Duryodhana (the head of the Kauravas) ended up in his capture by Duryodhana. He was finally rescued by Krishna and his brother Balarama. Samba once pretended to be a pregnant woman and his friends asked some sages that who will the child. Offended by the mischief, the sages cursed that an iron pestle will be born to Samba and will destroy the Yadavas. The curse came true leading to the death of Krishna and his clan.

The Bhagavata Purana records the wailing of Krishna’s queens and their subsequent leap in Krishna’s funeral pyre immolating themselves (sati). The Mausala Parva of the Hindu epic Mahabharata which describes the death of Krishna and end of his race declares that Jambavati killed herself by burning alive after being attacked by robbers while leaving Dwarka after Krishna’s funeral.

According to Bhagavata Purana, Jambavati was the mother of Samba, Sumitra, Purujit, Shatajit, Sahasrajit, Vijaya, Chitraketu, Vasuman, Dravida and Kratu.The Vishnu Purana says that she has many sons headed by Samba.

VarahaMihir – Author of Hellenistic astronomy (including Greek, Egyptian and Roman elements).

Varahamihira’s wrote the book Pancha-Siddhantika, on the Five Canons (Astronomical Treatise) dated ca. 575 CE gives us information about older Indian texts which are now lost. The work is a treatise on mathematical astronomy and it summarises five earlier astronomical treatises, namely the Surya Siddhanta, Romaka Siddhanta, Paulisa Siddhanta, Vasishtha Siddhanta and Paitamaha Siddhantas. It is a compendium of Vedanga Jyotisha as well as Hellenistic astronomy (including Greek, Egyptian and Roman elements).

He was the first one to mention in his work Pancha Siddhantika that the ayanamsa, or the shifting of the equinox is 50.32 seconds.

The 11th century Iranian scholar Alberuni also described the details of “The Five Astronomical Canons”:

“They [the Indians] have 5 Siddhāntas:

  • Sūrya-Siddhānta, ie. the Siddhānta of the Sun, thought to be composed by Lāṭadeva,but actually composed by Mayasura also known as Mamuni Mayan as stated in the text itself.
  • Vasishtha-siddhānta, so called from one of the stars of the Great Bear, composed by Vishnucandra,
  • Paulisa-siddhānta, so called from Pulisa, the Greek, from the city of Saintra, which is supposed to be Alexandria, composed by Pulisa.
  • Romaka-siddhānta, so called from the Rūm, ie. the subjects of the Roman Empire, composed by Śrīsheṇa.
  • Paitahama-siddhānta.

Varāhamihira called Varaha or Mihir, was an Indian astronomer, mathematician, and astrologer who lived in Ujjain. He was born in Avanti region, roughly corresponding to modern-day Malwa, to Adityadasa, who was himself an astronomer.

According to one of his own works, he was educated at Kapitthaka. He is considered to be one of the nine jewels (Navaratnas) of the court of legendary ruler Yashodharman Vikramaditya of Malwa.

Partridge Birds ate Veda- Black Yajurveda- By Yajnavalkya

The Saṃskṛt name for partridge is “Tittiri”. As the Tittiri (partridge) birds ate this Veda, it is thenceforth called the Taittirīya Yajurveda. It is also known as Kṛṣṇa Yajurveda or Black-Yajurveda on account of it being a vomited substance. The Taittirīya Saṃhitā thus belongs to this Yajurveda.

Yājñavalkya was the son of Devarāta and was the pupil of sage Vaisampayana . Once, Vaisampayana got angry with Yājñavalkya as the latter argued too much to separate some latter additions to Yajurveda in being abler than other students. The angry teacher asked his pupil Yājñavalkya to give back all the knowledge of Yajurveda that he had taught him.

As per the demands of his Guru, Yājñavalkya vomited all the knowledge that he acquired from his teacher in form of digested food. Other disciples of Vaisampayana took the form of partridge birds and consumed the digested knowledge (a metaphor for knowledge in its simplified form without the complexities of the whole but the simplicity of parts) because it was knowledge and they were very eager to receive the same.

Then Yājñavalkya determined not to have any human guru thereafter. Thus he began to propitiate the Sun God, Surya. Yājñavalkya worshipped and extolled the Sun, the master of the Vedas, for the purpose of acquiring the fresh Vedic portions not known to his preceptor, Vaiśampāyana.

The Sun God, pleased with Yājñavalkya penance, assumed the form of a horse and graced the sage with such fresh portions of the Yajurveda as were not known to any other. This portion of the Yajurveda goes by the name of Śukla Yajurveda or White-Yajurveda on account of it being revealed by Sun. It is also known as Vajasaneya Yajurveda, because it was evolved in great rapidity by Sun who was in the form of a horse through his manes.The rhythm of recital of these vedas is therefore to the rhythm of the horse canter and distinguishes itself from the other forms of veda recitals. In Sanskrit, term “Vaji” means horse. Yājñavalkya divided this Vajasaneya Yajurveda again into fifteen branches, each branch comprising hundreds of Yajus Mantras. Sages like Kanva, Madhyandina and others learnt those and Śukla Yajurveda branched into popular recensions named after them.

It is important to note that within the hierarchy of Brāhmaṇas, certain sects believe in the Kṛṣṇa Yajurveda while others practice from the Śukla Yajurveda.

Yājñavalkya married two wives. One was Maitreyi and the other Katyaayanee. Of the two, Maitreyi was a Brahmavadini (one who is interested in the knowledge of Brahman).The descendant sects of Brahmans are the progeny of the first wife Katyaayanee. When Yājñavalkya wished to divide his property between the two wives, Maitreyi asked whether she could become immortal through wealth. Yājñavalkya replied that there was no hope of immortality through wealth and that she would only become one among the many who were well-to-do on.When she heard this, Maitreyi asked Yājñavalkya to teach her what he considered as the best. Then Yājñavalkya described to her the greatness of the Absolute Self, the nature of its existence, the way of attaining infinite knowledge and immortality, etc. This immortal conversation between Yājñavalkya and Maitreyi is recorded in the Brihadaranyaka Upanishad.

Wisdom of Yājñavalkya is shown in Brhadaranyaka Upanishad where he gives his teachings to his wife Maitreyi and King Janaka. He also participates in a competition arranged by King Janaka about the selecting great Brhama Jnani (knower of Brahman). His intellectual dialogues with Gargi (a learned scholar of the times) form a beautiful chapter filled with lot of philosophical and mystical question-answers in Brhadaranyaka Upanishad. He was then praised as the greatest Brahmajnyani by all the sages at the function organised by king Janaka. In the end, Yājñavalkya took Vidvat Sanyasa (renunciation after the attainment of the knowledge of Brahman) and retired to the forest.

Maitreyi was a Vedic philosopher from ancient India. She was the second wife of famous sage and philosopher, Yajnavalkya, the first being Katyaayanee.

Maitreyi was well-versed in Vedas and associated scriptures and was called brahmavadini or “an expounder of the Veda” by people of her time. About ten hymns in Rig Veda are accredited to Maitreyi.

According to legend, Maitreyi really did not want to marry Yajnavalkya, but she wanted to live with him as his disciple and a spiritual companion to do sadhana or spiritual development. She went to Yajnavalkya’s wife, Katyaayanee and expressed her desire to live with her husband, and with Katyaayanee’s consent, she became his companion.

Learning of Life- Nachiketa and Yama

Vājashrava, desiring a gift from the gods, started an offering to donate all his possessions. But Nachiketa noticed that he was donating only the cows that were old, barren, blind, or lame; not such as might buy the worshiper a place in Heaven. Nachiketa wanting the best for his father’s rite, asked: “I too am yours, to which god will you offer me?”. After being pestered thus, Vājashrava answered in a fit of anger, “I give you to Death (Yama)”.

So Nachiket went to Death’s home, but the god was out, and he waited three days. When Yama returned, he was sorry to see that a Brahman guest had been waiting so long. He told Nachiketa, “You have waited in my house for three days without hospitality, therefore ask three boons of me”. Nachiket first asked for peace for his father and himself. Yama agreed. Next, Nachiketa wished to learn the sacred fire sacrifice, which also Yama elaborated. For his third boon, Nachiketa asked to learn the mystery of what comes after death.

Yama was reluctant on this question; he said that this had been a mystery even to the gods. He asked Nachiketa to ask for some other boon, and offered many material gains.

But Nachiketa replied that material things will last only till the morrow. He who has encountered Death personally, how can he desire wealth? No other boon would do. Yama was secretly pleased with this disciple, and elaborated on the nature of the true Self, which persists beyond death. The key of the realization is that this Self (within each person) is inseparable from Brahman, the supreme spirit, the vital force in the universe. Yama’s explanation is a succinct explication of Hindu metaphysics, and focuses on the following points:

  • The sound Om! is the syllable of the supreme Brahman
  • The Self, whose symbol is Om is the same as the omnipresent Brahman. Smaller than the smallest and larger than the largest, the Self is formless and all-pervading.
  • The goal of the wise is to know this Self.
  • The Self is like a rider; the horses are the senses, which he guides through the maze of desires.
  • After death, it is the Self that remains; the Self is immortal.
  • Mere reading of the scriptures or intellectual learning cannot realize Self.
  • One must discriminate the self from the body, which is the seat of desire.
  • Inability to realize Brahman results in one being enmeshed in the cycle of rebirths. Understanding the Self leads to moksha

Thus having learnt the wisdom of the Brahman from Yama, Nachiketa was freed from the cycle of births.

Taittirīya Saṃhitā – Black-Yajurveda on account of it being a vomited substance

Yājñavalkya was the son of Devarāta and was the pupil of sage Vaisampayana .Once, Vaisampayana got angry with Yājñavalkya as the latter argued too much to separate some latter additions to Yajurveda in being abler than other students. The angry teacher asked his pupil Yājñavalkya to give back all the knowledge of Yajurveda that he had taught him.

As per the demands of his Guru, Yājñavalkya vomited all the knowledge that he acquired from his teacher in form of digested food. Other disciples of Vaisampayana took the form of partridge birds and consumed the digested knowledge (a metaphor for knowledge in its simplified form without the complexities of the whole but the simplicity of parts) because it was knowledge and they were very eager to receive the same.It is believed that Yājñavalkya underwent this process at midday and became ignorant. Consequently, descendents of Yājñavalkya are not considered brahmins at mid-day.

The Saṃskṛt name for partridge is “Tittiri”. As the Tittiri (partridge) birds ate this Veda, it is thenceforth called the Taittirīya Yajurveda. It is also known as Kṛṣṇa Yajurveda or Black-Yajurveda on account of it being a vomited substance. The Taittirīya Saṃhitā thus belongs to this Yajurveda.

Then Yājñavalkya determined not to have any human guru thereafter. Thus he began to propitiate the Sun God, Surya. Yājñavalkya worshipped and extolled the Sun, the master of the Vedas, for the purpose of acquiring the fresh Vedic portions not known to his preceptor, Vaiśampāyana.

The Sun God, pleased with Yājñavalkya penance, assumed the form of a horse and graced the sage with such fresh portions of the Yajurveda as were not known to any other. This portion of the Yajurveda goes by the name of Śukla Yajurveda or White-Yajurveda on account of it being revealed by Sun. It is also known as Vajasaneya Yajurveda, because it was evolved in great rapidity by Sun who was in the form of a horse through his manes.The rhythm of recital of these vedas is therefore to the rhythm of the horse canter and distinguishes itself from the other forms of veda recitals. In Sanskrit, term “Vaji” means horse. Yājñavalkya divided this Vajasaneya Yajurveda again into fifteen branches, each branch comprising hundreds of Yajus Mantras. Sages like Kanva, Madhyandina and others learnt those and Śukla Yajurveda branched into popular recensions named after them.

It is important to note that within the hierarchy of Brāhmaṇas, certain sects believe in the Kṛṣṇa Yajurveda while others practice from the Śukla Yajurveda.

Yājñavalkya married two wives. One was Maitreyi and the other Katyaayanee. Of the two, Maitreyi was a Brahmavadini (one who is interested in the knowledge of Brahman).The descendant sects of Brahmans are the progeny of the first wife Katyaayanee. When Yājñavalkya wished to divide his property between the two wives, Maitreyi asked whether she could become immortal through wealth. Yājñavalkya replied that there was no hope of immortality through wealth and that she would only become one among the many who were well-to-do on. When she heard this, Maitreyi asked Yājñavalkya to teach her what he considered as the best. Then Yājñavalkya described to her the greatness of the Absolute Self, the nature of its existence, the way of attaining infinite knowledge and immortality, etc. This immortal conversation between Yājñavalkya and Maitreyi is recorded in the Brihadaranyaka Upanishad.

Wisdom of Yājñavalkya is shown in Brhadaranyaka Upanishad where he gives his teachings to his wife Maitreyi and King Janaka.He also participates in a competition arranged by King Janaka about the selecting great Brhama Jnani (knower of Brahman). His intellectual dialogues with Gargi (a learned scholar of the times) form a beautiful chapter filled with lot of philosophical and mystical question-answers in Brhadaranyaka Upanishad. He was then praised as the greatest Brahmajnyani by all the sages at the function organised by king Janaka.In the end, Yājñavalkya took Vidvat Sanyasa (renunciation after the attainment of the knowledge of Brahman) and retired to the forest.