Friday, 11 September 2020

Bhishma - the Uberman in Mahabharat

This is a document in progress, as I read the feats of Debabrata aka Bhishma in Mahabharat

Ganga hands over Debabrata to Santanu, Sambhava Parva

Santanu has not met his son for years. One day, while roaming around banks of Ganga, he notices that the river has suddenly become shallow. Bewildered, he inspects and finds a youth who has restricted the majestic course of river by his divine weapons. "Capable of this feat, who are you, son?", Santanu asks. The youth disappears after casting an illusion.


Santanu then calls Ganga and asks her to show her son. Ganga appears and hands over the same youth. Santanu rejoices at his son, and knows that he exceeds his father in capabilities.
Ganga has taken Debabrata and asked the greatest teachers in different realms(heaven, earth, underworld) to teach her son. The education found a worthy student.

Painting/Oleograph - B.P. Banerjee, 1923. Original might have been printed in Germany, but not sure due to ignorance of the technicalities of the printing process.  On lower left corner in the image from British Museum, "Roy, Babajee & Co, 182 Lower Chitpore Road" is mentioned. Chitpore Road is the old aristocracy and cultural hub of Bengal.



Debabrata gives up right to the throne and takes up Brahmacharya, Sambhava Parva

When Satyavati's father hears Debabrata say that he is not going to marry to prevent any conflict between his line and that of Satyavati's children - all the hairs of Satyavati's father stands on its end in glee.

Wednesday, 26 August 2020

Exercises from Theoretical Neuroscience textbook: Ch 2, problem 7

Note: this is an honest attempt at the problem and has not been verified for correctness. Any feedback will be appreciated.

The preferred frequency and phase are:-

Preferred frequency - 2.991993 Hz.

Preferred phase - 20.000000 degrees.

 

The code is as follows. 

Below are the figures generated. Note that the K range is -20:20, which is different than the code provided here.



Saturday, 22 August 2020

Exercises from Theoretical Neuroscience textbook: Ch 2, problem 3

This is a personal attempt at solving problem 3 of chapter 2 in Dayan and Abbott's Theoretical Neuroscience. Any feedback will be appreciated as I haven't found anyone to verify these solutions.

The solution follows the concepts mentioned in the text. The spike-triggered images shows a change in polarity of the central field at τ=1 as mentioned in the problem.

The code is as follows.

The figures generated. Note: the spatial summation images below, uses contourf function. Please replace imagesc usage in the last lines with countourf.







Saturday, 18 April 2020

On Shoulder of Giants

When one begins to think about any human endeavor, one feels a deep reverence for the amount of work, different people have done over their lifetimes. If one takes neurology - Korbinian Broadmann, (while inspired by people before him) classified human brain regions based on their cellular architecture. For people who haven't done microscopy or prepared histological slides - it is hard to describe the amount of labor and careful work over hours, days and months that goes into achieving this kind of feat.

If one takes neuroscientists studying language, their work further rests on neurosurgeons who carefully studied the pre-operative brains of epileptic patients, physicists who studied magnetic resonance, engineers and scientists who developed imaging techniques to study the human brain, "online" and non-invasively.

Neuroscientists who work on functions that are also observed in animals, have spent years studying these animals and training them, hoping to polish earlier knowledge and get a better understanding of brain. (Gratitude to animals who are sacrificed.)

Shifting to a different field - algebra. Though most of the books don't mention any history of mathematical workers - a little bit reflection is enough to know that these theorems and proofs have taken time and effort of many human minds. Elaborate proofs, theorems which build on previous theorems, connections which are brought up between different constructs were not made in a day.

These are the things which inspire a student.

Thursday, 2 April 2020

The literary, metaphysical origins of Mahabharat

This is a speculation and represents my preliminary thought-processes on the matter. This might turn into scholarly work if Lord permits.

As the epic is so complex both in scope of fantasy and range of human condition, this question naturally arises. How did the creative framework and plots arise?

One solution would be that people wanted to write about experience of God. (Arjun's senses getting overpowered by God's vision in Gita, Book of Bhishma.) Those who achieved God vision, wrote a chronological description of their experiences creating a story with life events and other mythological frameworks. (How Vishnu became the Supreme Gdd and history of Vaishnavism from Shatpatha Brahmana is not discussed here.)

But, what solution is provided by Mahabharat, itself? In Adivansavatarana Parva in Book of Beginnings, the initial point is kept as Earth getting exploited by sons of Diti(demons). Sons of Diti were being reborn on Earth, because they were dying in wars against celestials(sons of Aditi) in heaven. Demons created oceans as boundaries and ravaged the environment with their strength and haughtiness. So, Earth requests the Creator Brahma for a solution.

The creator(Brahma/Prajapati) asks different celestials to take the war from heaven to Earth. How? The creator asks the gods to get birth on Earth and seek conflict with demons. Sakra(the king of gods) then goes to Vishnu, and asks him to be born. Vishnu agrees.

Again before the final great war, Vishnu(as Krishn) tells Arjun, that he is born again and again for the benefit of righteous and destruction of non-righteous.

Interestingly in story of Ram(son of Janmagdani, carrier of axe) also kills kshatriyas and makes a lake out of blood of countless kings. The lake(called Samanta panchaka) coincides with the battlefield of Kurukshetra. As if the same place/location/arena is being used again and again for the conflict resolution between good and evil.

Friday, 19 April 2019

Gambling and the tragedy of Kurus

Note: This is a rough work that highlights a portion in the Sabha Parva of Vyasa's Mahabharata. This might get edited in the future on the availability of new resources.

Dhritarashtra reprimanded Duryodhana and Dushashana to stop the act. His daughter-in-law was delivered from the shameful cruelty. But, it was too late. Bhima took a vow of killing all the hundred sons of Dhritarashtra. Gangaputra Bhisma, the pitamah of both Pandavas and Kauravas was seeing the evil that had become a part of his own family. A war was now inevitable.

How did gambling end up with such terrible transactions, acts and vows? I don’t know the history of gambling, why gambling was placed inside the epic and how popular gambling was when the epic was composed. But, I will still try a breakdown of what gambling meant in the context of (Maha)Bharata.

Context

Duryodhana harboured resentment against Pandavas(especially Bhima) from childhood. So prone was Duryodhana to evil that he poisoned Bhima even as a boy. He created many plots such as a lac house for burning Pandavas and Kunti alive. When Duryodhana came to Yudhithira’s Rajsuya Yajna, his head turned completely on witnessing Pandava’s wealth. His envy couldn’t accept this. This Pandavas created a city(Indraprastha) out of a forest(Khandavaprastha) and surpassed Hastinapur’s grandeur in so little time. As his uncle Shakuni knew how to control dices - Duryodhana hatched a plan to take away Pandava’s kingdom through gambling with dices.

Dice and a King

Vyasa writes that a Kshatriya’s dharma is to accept an invitation to gambling. (I don’t know the reason behind existence of such a rule.) Being a virtuous king, Yudhishtira agreed to play with Shakuni(on behalf of Duryodhana). Kaurava brothers made arrangements for the expected entertainment and the game began.

Loss of Kingdom, Brothers, Wife and Clothes

Yudhisthira couldn’t win even a single bet due to Shakuni’s treachery. As the losses mounted, Yudhisthira lost his reasoning and began to bet more aggressively. He slowly bet everything present in his kingdom, including the kingdom itself. He bet himself and lost. He bet his brothers and lost. He bet his wife, Draupadi and lost. He bet Pandava’s clothes and lost. Duryodhana was waiting for it. He ordered Dushashana to take Draupadi’s garment using force. Mysteriously, as if a divine power was overlooking the events - Draupadi’s garment turned out to be endless. Dushashana failed to achieve the entertainment, he hoped for. Dhritarashtra seeing that his sons have crossed the limit - hastened to put an end to the dice game.

The Game of Dice

Some questions can be asked about the rules, contracts and players surrounding the dice game:-
  1. In a gambling match, how bound is a person to losses and gains?
    
In a way, gambling is about the loss of a player and direct gain of the opponent. As Yudhisthira was a king, the only authority that bound him was his word. Being virtuous, he agreed to give whatever he lost(including his kingdom). That was the main goal of Duryodhana - to get the kingdom through indirect means as he was not strong enough to fight Pandavas directly.
     
  2. Was betting humans legal in a dice game?
    
I don’t know for sure. But, it seems to be allowed. Nonetheless, betting humans was disagreeable. Any respectable person(even if he gambles) won’t agree to the bet. But, Duryodhana and brothers were of different mould altogether and seemed jolly at Yudhisthira’s obsessive bets.
     
  3. Was Yudhisthira legally allowed to bet his brothers and wife?

    Technically, no. He has already lost himself in the dice game. Irrespective of his own loss, he doesn’t own his brothers and wife per se. The bet was disagreeable as it was mistaking relations as objects. But again, Duryodhana saw that Yudhisthira continues with the play.
     
  4. Was the dice game, legal?

    Regardless of technical details, the dice game was flawed because Shakuni could control the dices. That makes the game illegal. But only Shakuni and Kaurava brothers knew about the dices. Yudhisthira continued to think that he was losing a game based on chance. He couldn’t stop his obsessive betting.
     
  5. Why was Yudhisthira so obsessed about betting?

    I don’t know the psychological pressures and passions that a game of dice entails. Perhaps, as losses began to mount - Yudhisthira thought that the next throw of dice will reverse his fortune. He expected that the dices will take his side at least once.

Meta context

One of the treatises that comprise (Maha)Bharata is Gita, told by Krishna to Arjuna before the war. As Arjuna went through compunction, Krishna told him to control his emotions and fulfil his duty as a warrior. Control of emotions - both negative and positive - is a requisite to become a complete person. If he doesn’t, then the emotions become his master rather than the other way round.

If one tries to see the placement of Gita in the epic, one may see how well it tries to connect the past events with the upcoming war for Dharma. Duryodhana out of his evil heart couldn’t keep his resentment aside. Shakuni refused to forget his humiliation as Gandhari married Dhritarashtra and worked crafty ways to destroy the very kingdom, Bhishma wanted to protect. Negative emotions were controlling both the characters.

As cruelty, dishonour and evil shows the weakness of a person, both Duryodhana and Shakuni may be considered as having weak minds. Duryodhana should have accepted that his younger brother, Bhima is stronger. Shakuni should have fought Bhishma in a direct manner rather than creating dishonourable plots and using dice as a weapon. There are other characters in the epic whose emotions went astray and eventually concluded their fate.

In sharp contrast, stand Pandavas and Gandhari. Pandavas, though they had the caliber, didn’t attack the Kauravas during humiliation of Draupadi because they were the losing parties. Gandhari accepted Pandavas as her caretaker after the war, without cursing or complaining about the death of her sons. They were virtuous because they accepted the justice of fate with heavy-handed control over their emotions.

Mysteriously though, Gandhari couldn’t teach her virtue to her sons. No one knows why some parents get evil children and some parents end up with virtuous ones.


Further Discussion
Interestingly, there is a trace of above questions in Adivansavatarana Parva. Vaisampayana finishes his brief summary of the events, after the snake-sacrifice ends midway. Janmajeya expresses his dissatisfaction at the length of the summary and asks Vaisampayana to further elaborate on each and every detail of the history.

Janmajeya elaborates on the reasons behind his dissatisfaction:-
  1. That could never have been a trifling cause for which the virtuous ones could slay those whom they should not have slain, and for which they are yet applauded by men. 
  2. Why also did those tigers among men, innocent and capable of avenging themselves upon their enemies, calmly suffer the persecution of the wicked Kurus? 
  3. Why also, did Bhima of mighty arms and of the strength of ten thousand elephants, control his anger, though wronged? 
  4. Why also did the chaste Krishna[Draupadi], the daughter of Drupada, wronged by those wretches and able to burn them, not burn the sons of Dhritarashtra with her wrathful eyes? 
  5. Why also did the two other sons of Pritha (Bhima and Arjuna) and the two sons of Madri (Nakula and Sahadeva), themselves injured by the wretched Kurus, follow Yudhishthira who was greatly addicted to the evil habit of gambling? 
  6. Why also did Yudhishthira, that foremost of all virtuous men, the son of Dharma himself, fully acquainted with all duties, suffer that excess of affliction? 
  7. Why also did the Pandava Dhananjaya, having Krishna for his charioteer, who by his arrows sent to the other world that dauntless host of fighting men (suffer such persecution)?
 This only highlights how honestly attentive were the people who were involved in giving Mahabharat, a concrete form in writing. One gets a mental picture of the Sanskrit scholars of those days and their motivations in answering questions presented by their psyche.

Saturday, 30 March 2019

Drona - a tragic summary

The depth of Mahabharata not only comes from the length but also the apparent contradictions and life journeys of characters which concluded with the Kurukshetra war. One prominent character is Drona, son of Bharadwaj. Much is seen when one looks back to the chronological events which brought him to the war.

Poverty was prominent in his life. When Bharadwaj was teaching Prince Drupad in his Gurukul, Drona became his friend. He also sought out a promise from the future king. The innocent promise said that Drupad will give half of his kingdom to Drona on wearing the crown. As it was a promise between children, Drona forgot about it initially.

The poverty eventually took Drona to Parshurama. He had heard that the warrior-sage was giving away his wealth. But on reaching Parshurama, he found that his entire wealth was already donated. Instead, Parshurama offered Drona his weapons and the knowledge to use them. Drona happily accepted Parshurama as a teacher. But, the question of poverty remained.

Meanwhile, Drona started severe penance to Shiva in order to get a son that matches the mighty God’s valour. (I still don’t understand why Drona only asked for valour - he could have asked for more qualities like intellect, strength and warfare skills). The boon was granted and Ashwatthama was born. But as the little boy grew, the question of poverty became more important. One day, Drona saw his son drinking crushed rice with water as a substitute for cow’s milk. Drona couldn’t accept his poverty longer and remembered the promise given by Drupad.

Drona went to meet Drupad. Drupad said that children’s promises carry no weight. Drona asked for atleast one cow. Drupad refused. Humiliated, Drona returned from Drupad’s kingdom. In the way, he remembered that Hastinapur had young princes coming to age for Gurukul. Parshurama had no wealth to donate, but the knowledge and weapons given by him will now become wealth for Drona.

The hundred-and-five Kuru princes were unable to retrieve their playing ball from a deep well. Drona took some broken sticks and threw them one after another at the ball. The sticks ended up being a thin rod protruding from the ball. And, Drona pulled the ball from the well after the rod reached the well's height. The princes were awed by the skill shown by an unknown Brahmin. Drona asked the boys to take him to their pitamah, Bhishma. Bhisma also studied from Parshurama once, and thus accepted Drona as a teacher for the princes. Overnight, the fortunes of Drona and his family changed. Ashwatthama now had proper food to eat.

In the course of education, Drona promised to make Arjuna the greatest archer ever. A tribal boy, Eklavya was following Drona's instruction from hiding. When Drona found that even Eklavya had talent and worth comparable to Arjuna, he demanded Eklavya's right thumb as Gurudakshina. With a missing right thumb, Eklavya couldn't become the greatest archer as Drona has already promised that position to Arjuna. It was a painful experience for Drona to exploit his rights as a teacher and sacrifice a great student. Nonetheless, Arjuna never reached the supreme archer position with Drona, Bhishma and Karna living. Drona couldn't keep his promise and Drupad couldn't keep his, in different settings.

One wonders what would have happened if Drona forgot about the humiliation at Drupad’s kingdom. When the Kuru princes finished their education - Drona asked them to bring Drupad to him as Gurudakshina. The Kuru princes overwhelmed Drupad’s forces and defeated him. Drupad was brought to Drona. Drona reminded Drupad of his past humiliation and told him that even his students are superior to a King who doesn’t keep his promise. Defeated and full of resentment, Drupad returned to his kingdom.

Just as Drona asked for a son once, Drupad now began an yajna to gain a son. He explicitly wanted a son who can kill Drona. Out of the yajna’s fire, came a man with shining armour and holding a curved sword. Gods proclaimed the man as Dhristadhyumna and told that he will kill Drona.

Years later in the Kurukshetra war, Drona killed Drupad. As Drona was not getting defeated, he was lied to about the death of his son, Ashwatthama. Heartbroken, Drona left his weapons in the middle of the battlefield and started meditating. Without waiting, Dhristadhyumna sprinted and beheaded the old man with a single stroke of his sword. The age-worn face of Drona rolled on the ground. Dhristadhyumna fulfilled the reason for his birth and took revenge on Drona for his father’s humiliation and death.

Now was the turn for Ashwatthama to start on the path of revenge. He was fighting on other part of the Kurukshetra when details of his father’s death came to him. At the end of the war, Ashwatthama was inspired by a huge owl killing a crow’s younglings in the middle of night. Inspired, he went to Pandava’s camp in total darkness. On the gates, he found Shiva standing as a guard. To gain access, Ashwatthama jumped into fire and Shiva left his guarding position. Shiva’s own boon of valour was working for Ashwatthama. Ashwatthama furiously chopped everyone sleeping in the camp, in the process killing Dhristadhyumna and the five sons of Draupadi(Drupad’s daughter).

Drupad and Drona mutually annihilated each other’s families by never looking behind their personal resentment. Ashwatthama was cursed that he will never meet death. Drupad never found the satisfaction of seeing Drona’s death. Drona never knew what happened to his son.

This is the tragedy of two childhood friends. Who was the culprit? Poverty, Drupad, Parshurama or Drona?