Monday, 9 November 2009

Game Theory and the Gita

Noether's theorem tells us that (for a non dissipative system) evidence of a symmetry is proof of a conservation law or conserved property.
The Mahabharata displays two systems of symmetries in a remarkably systematic and well thought out manner. People like Buitenen and Lal had noticed the 'two trees' motif- the duality- the fact that everything happens twice, each character has a dual, every episode ties up with or reflects some other episode- it is as though the bards were continually employed in a type of double entry book-keeping.
Nothing is accidental, or a matter of chance, in the Mbh.
The two conserved principles, so to speak, in Mbh are karma and dharma. Karma, operating across life-spans, gives coherence and meaning to everything that is experienced. Dharma- operating across the social space- makes social life meaningful and socially defined entitlements and obligations a proper subject of study.

How does this relate to game theory? Well, we notice that Yudhishtra, to become a just King, must learn probability and tactics. He comes to see that virtue and morality is actually a vector, not a scalar. We are getting to a notion similar to the notion of Evolutionary Stable Strategies- i.e. a range of ethical choices all equally valid. Balaram is not condemned as a drunkard for refusing to fight. Krishna is not condemned as being partial to Arjuna for assisting him.
Yet the outcome of Mbh is not perfectly symmetrical. Though the Pandavas win, it is a tragic outcome.
The symbiotic nature of the Kaurava Pandava dichotomy had been pointed out early on by Sanathkumara who employed an ecological analogy- 'without the forest, the tiger dies. Without the tigers, the forest disappears. Your sons (Kauravas) and the Pandavas are like the forest and the tigers.'
Yuddhishtra can understand this. Dhritarshtra can't. When Yuddhishtra offers to fight Dhritrashtra himself he recognizes that the Kaurava principle of Power politics had as much validity- indeed, it is the starting point for-  his own. The optimal solution lay in a meta-game.

The relationship of the Gita to game-theory arises from the fact that 'meaning is being gamed'. This fulfills the condition of apoorvata such that on each reading, or each hearing, there is something new and therefore the condition for Gita to be considered Shruti is fulfilled. This is nothing to do with rituals. Gita can be heard in any language where the author was properly inspired rather than just a translator.
In what manner is 'meaning being gamed'? Well, Krishna is arguing for a purpose not just showing off. Initially it looks like the Lord- out of love for his friend- has made a mistake. To spur on Arjun's martial spirit- while at the same time showing him the need to be cautious and plan things out- Krishna straight away takes him to see the two chiranjivis (immortal, unvanquishables) on the other side. This should stir up Arjun as well get him to think carefully. But, Arjun (unlike Dhrtrashtra) is so confident he starts thinking his foes are already dead! (Alternatively, we may note that a Gandharva had gifted Arjuna with cakshushi vidya- a sort of second sight. This parallels Krishna's own  gift- mentioned in Chandogya. However, notice that whereas the Gandharva's caksuci yields only Vishada (depression) Krishna's gift is of another order.)
Arjuna blames himself- how could he have killed his own Guru and his beloved Grandsire- not to mention so many cousins and friends! Of course, there is a simple answer. Fight so well, that the other side loses morale and sues for peace! But, we know that those assembled, having forgotten they were desecrating a holy spot, were ripe for a vishodhana- a ritual type of cleansing. In any case, Sociologically speaking,  the feudal code was untenable and the aristocracy had to die.
From the theistic point of view, if the Lord is depicted as twisting and turning to help his friend (that is devotee) there is a noble purpose here- viz. to illumine the psychological truth that at every moment, taking on every form- (rupam rupam pratirupo babhoova etc)- the Lord is struggling to come to us and to win us away from anxiety and depression.
However, we notice that Krishna's every philosophical excursion ends in aporia- more notably, from the point of view of ordinary people (for whom the work was intended) these philosophies are immediately shown to be false because they lead to social injustice. I don't need to know Philosophy to know that any Philosophy is wrong which arrives at the conclusion that I should be the slave of its practitioners.
From Theism's point of view, it is important that even Krishna should not be able to show any philosophical system or approach to be other than silly. It's like Douglas Adams's story about the philosopher who provides a valid proof of God's existence. Even God is impressed. But, the philosopher points out, there is no longer any need for Faith. But there is no God without Faith. God is convinced and immediately ceases to exist.
Still, the Gita is quoted as supporting misogyny, casteism, the morality of slaughtering millions of people coz you're miffed that your cousins get to rule rather than you- and so on and so forth.
The point is that though ad captum vulgi arguments can be adduced for all of the above- they, nevertheless are complete shit. The Gita does have a message- it's the same as Buddhism, Jainism... urm common sense actually which is that we are all radically interdependent. Mutually supportive co-existence must be the rule. Pluralism is necessary for Life is about Symbiosis not Extermination. As Jefferson said, in matters of Religion, divided we stand, united we fall. There are delicious ironies in the casteist and misogynistic portions of the Gita. The whole thing is like one of those sit coms where, if at the beginning of a scene, an actor states some principle, then he or she will be shown to behave in the opposite way by the end.  Thus, there is nothing casteist about a work which shows the destruction of the fucking aristocrats- no matter how splendid their attributes and achievements.
The reason that the Mbh exhibits a lot of mathematical structure is that, if not its conception, then certainly its transmission depended on heuristics. But heuristics- including rules of thumb- are just special cases of a more general law. Since Mbh is trying to show karma and dharma as being logically consistent, there is obviously going to be a lot of symmetry.
Thus if the question is raised 'what did this guy do this at this time?' we can reconstruct it by figuring out who his dual is and what episode elsewhere is the dual of this episode and so on. Of course, this method of comparison also gives a lot of scope for clarifying matters. It is like you have two parallel cases to which the same rule applies in which the decision was different.
If Krishna has one way of discharging his duty as a charioteer, Shalya has another.  Actually, Shalya's is pretty effective. Insults get a guys dander up. He fights harder.
On the other hand, we say the parallelism here is imperfect. Krishna is a pal and relative of Arjuna. Shalya is a relative of the Ashvins (he is their maternal uncle). BUT, if Karna revealed his true birth to Shalya the latter would have been obliged to inform his nephews (so as to prevent them from falling into the sin of filial impiety) in which case the Kauravas get a walkover! Thus the symmetry here is- Krishna reveals his true form to Arjuna, Karna conceals his true birth from his charioteer. This is subtle, not mechanistic.
No wonder people write crap about Mbh.

6 comments:

  1. This all sounds a bit like Jug Suraiyya's latest piece in Times of India.
    What exactly is the basic dilemma in Gita? Surely it is- if Arjun fights he kills his kinfolk, if he does not fight his brothers die though their cause is just. Notice that Arjuna's decision is not affected by what any other party does. There is neither a question of optimization- i.e. a one person game- nor a dynamic non co-operative game such that Arjuna's payoff matrix depends on what other players do. Hence GAme theory is irrelevant to Gita.
    This is not to say that military tactics are not discussed in Mbh, or that dilemmas do not occur- e.g. the yaksha's question.
    However, Gita is not Game theoretic. It is purely about Arjuna's ignorance of the true nature of Reality- one where payoff matrices don't matter because simply doing your duty is always the optimal choice. No Game theory here at all. No tactics, no strategy, no 'consequentialism' (judging actions by results) etc.
    I don't see how you can say 'meaning is gamed'. This is nonsense. All words in Gita mean what they do in common use. Krishna is not saying duty means something totally different from what is commonly called duty.
    The gunas mean what the gunas have always been held to mean. God is shown to be God as all people's understand the concept. There is no 'apoorvata' in the hermeneutics. We may find more and more in Gita because it is a great poem depicting awe inspiring events.
    I don't understand what you are talking about.

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  2. The dilemma in Gita has nothing to do with Arjuna. It is Krishna who faces a dilemma. He is employed as a charioteer. His job is to keep up the valor of his passenger. One way to do it is by stressing 'Manyu' (dark anger) which has a hymn in Rg Veda. But, being God, he can't go on saying 'those bastards tried to strip your wife, those others stood by idly, most of these shitheads are only here coz Dhrtrashtra paid them big bucks. Human rights violations are occurring. Weapons of Mass Destruction are bristling in Ashvathama's quiver. In any case Drona tried to favor him over you. Kill the bastards!"
    Another way to go- that used by Shalya with Karna, is to taunt the warrior- it's like when the coach says 'you are all a bunch of pussies! Go out and give the other side a good kicking. I don't care if it's your time of the month!". Actually, Shalya's approach wasn't so good because Karna responded in like terms- thus further alienating him.
    Actually, Krishna could have taken a different tack- the straightforward course would have been to say 'What makes you think you will prevail? Drona and Bhishma have the boon of giving up life at their own choosing. You literally can't kill them unless they wish. While they live they can certainly stop you from killing anyone they choose. Why not just fight as well as you can until the other side gets demoralized. They start to desert and go home. Dhrtrashtra feels a complete fool. He is forced to compromise. Later on, make an alliance with him or placate him in some other way. Bury the hatchet after showing your martial skills. All this weeping for warriors who aren't yet slain is premature. Gird up your loins and fight.'
    Why can't the Lord say this?
    The answer is he knows things Arjun does not know. For a start, though warriors slain at Kurukshetra, by the ancestor's boon, gain heaven- they do so only for a space of time. After that they get Hell as well. Karma and Dharma are subtle.
    However the Lord himself has such infinite power, his perspective is different.
    Humans use theology and philosophy and ethics to get closer to understanding the Lord. His position is the reverse. It is like God's statement to Job in Bible. How can the Lord use our human means of comprehending him to influence us for a purely secular end?
    Answer, he has to use different strategies and tactics. Meaning is gamed, here, not by philological dexterity or hermeneutical sleight of hand. Rather, it is a question of psychology- including depth psychology- as well as ethics- including meta ethics.
    The Lord in addressing Arjuna is not just talking to his special pal. He has different sort of truth constraints. He is not committed to a particular philosophy or sociology or culture or race. Such things are human inventions. They don't constrain the Lord. However he can't show doubt about what he knows is foreordained in the same way we humans can. Well, maybe the Lord can do so! But then you don't have a poem. It is like the convention- Superman can't lie, even to Lex Luthor.
    A big problem with current Game theory is that while very good for analyzing things like optimal set up of auctions for bandwith or other situations where all players are highly rational- it does not have a theory of emotions, or a way of integrating meta-preferences and meta-games into its operating procedure. This may come in time. Gita and Mbh can show the way here.

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  3. I'm sorry, I'm not convinced. According to scholars, the Mahabharata evolved over time. The Gita is a later interpolation during a time when the caste system was becoming ossified. The Krishna of the Gita is combating non-violent religions like Buddhism and Jainism. God is depicted as wanting the warrior class to fight. This was because of the invasions of the Huns and other barbarian tribes.
    Your mistake is you naively assume what has to be proved- viz. that the Gita is actually the word of God rather than the invention of a priestly cabal who were bigoted upholders of the caste system.
    Gita is straight forward war propaganda. Because the Brahmins feared the working class, they wanted only the aristocrats to go off and fight the Huns. The kshatriyas would be decimated making the priests even stronger. Lacking weapons and martial arts training the workers and peasants would have to accept Brahmin oppression.
    The typical Brahmin trick is to engage in mystification by invoking some abstract and highly cerebral type of argument. The fact that such abstract types of thinking- like astrological mumbo jumbo- are not fit for purpose is never acknowledged.
    Since Maths and Game Theory enjoy prestige you say Gita is Game theoretic. Previously people like you said 'actually it shows India possessed Television, missiles, nuclear weapons etc. ten thousand years ago!"
    I mean no hurt to your religious convictions. If you are sincere devotee, you don't have to bring in extraneous ideas to prop up your faith.
    Read Gita by all means as act of piety.
    However, no good purpose is served by talking nonsense.

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  4. Superman comics have evolved over time. Some Superman story lines have been accepted as part of the core mythology, others have fallen by the wayside. People who look after the franchise have developed ideas about what is or is not constitutive of the Superman mythos. Yes, you can have 'alternative histories' or time delimited special editions which contradict the mythos. However, though there have been many authors and editors and great fluctuations in fashion, any comic book enthusiast can tell what is canonical Superman and 'alternative history' Superman.
    In the case of MbH anyone can at any time add or redact from the vernacular version. However, there are certain rules which enable the Mbh mythos to remain consistent. It is a sort of double entry book-keeping. My feeling is figures like Ghatotkacha & Chitrangada are going to get more attention. Those versions which don't observe karma/dharma symmetries will be seen as alternative history while some, perhaps nameless, redactor who knits the story line seamlessly into the core will have broadened the text- WITHOUT REALLY BEING GUILTY OF INTERPOLATION. A tapestry which is seamlessly mended decade after decade, century after century, is still the same tapestry. The colours are different and no single thread remains the same. To repair fire damage, it may be some decorations are changed. Or, if other pieces of tapestry, assumed to be from the same period, are found they may also be attached in some way to the main piece.
    Just as Hampton Court or Windsor Castle remains itself though some outbuildings are pulled down and others erected, so too with Mbh.
    Your view of the Gita is a crude 'just-so' story. You believe some small group of Brahmins somehow had such magical powers they could fool the whole country and gain enormous power.
    I'm sorry I don't share your faith in the magic powers of Brahmins. Or perhaps you have discovered the Brahmin equivalent of the Protocols of the Elders of Zion? You have the proof, in your hands, that not only was Queen Victoria actually a fat Pundit from Mathura, but so was Karl Marx, Nadir Shah, Marilyn Monroe and the hunter who shot Bambi's mother.
    The core belief of Madhavacharya school of Vaishnavism is that all appearances are special plenary grace of the Lord to us as individuals. I'm not saying Gita is god's word and Quran is not. Nor am I saying appearances must be accepted at face value. No, one has to think, why should a caring God have sent this appearance before me. To what gentle purpose?
    The scientist considers every datum that comes before him as having potential to advance his knowledge. Similarly, nothing wrong in thinking all appearance has potential to convert your heart.
    If Gita has no connection with Math could you please explain to me why Andre Weil and Grothendieck were so fascinated with it? Was it Brahmin conspiracy?
    No, no. Must have been an interpolation.
    At present, in India, talking of caste conspiracies is not just nonsense it also dangerous, divisive, nonsense.
    Decasteing, decommunalising, our common heritage is positive. This should not be done on the basis of falsifying history- i.e. no good saying British created Caste system, Hindu Muslim problem, etc- but proper aesthetics and hermeneutics.
    Why should Hindu not read Ghalib or Muslim not read Gita? No danger to morality or religion arises if it is done in the right spirit.

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  5. Thank you for your prompt reply- what do you do, sleep beside your computer?- but, I'm afraid you have not really changed my opinion. Your playing the communal harmony card is just a cheap tactic. No need to bring up Game theory and Gita as a way of creating communal harmony. Good governance and transparency will do that. Gita and Ghalib (why Ghalib- because his name begins with G?) have nothing to do with it.
    Gita is an interpolation. It is not a mending of the tapestry. It is a whole chapter that has been inserted. It bears no relation with any other chapter. It serves no special purpose in the narrative.
    I am not an expert in Superman comics- which, clearly, you are. However, it may be that the Bhagvad Gita is a different type of literature and so your erudition in that respect is less relevant than the opinions of trained historians.
    I'm sorry. I will withdraw from this dispute. I wish you luck- but you are barking up the wrong tree.

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  6. Okay you have a historicist hermeneutics. In that case who wrote when, for whom, and with what political consequences is what must be focussed on.
    However, historicism is a piss poor ideology fit only for demagogues and technocrats incapable of creative thought or aesthetic response outside their narrow field.
    My original post had apoorvata- there were ideas in it found no where else. Your comment lacks apoorvata. It adds nothing. It is just a knee jerk reaction.
    There is a hadith that 'who makes a judgement and is wrong gets one reward. Who makes a judgement and is correct gets double reward.'
    But judgement is not the same as knee jerk reaction. It has to have some apoorvata to it. Judgement is a higher cognitive faculty. It differs from mere discrimination because it follows independent reason. Proof of independence in reasoning (rather than blind following of a rule) is shown by apoorvata in the way the judgement is worded.
    This is what your comments lacks.
    You are not thinking, you are not discussing, you are not judging- you are merely heckling and shouting slogans.
    You have not withdrawn from this dispute. You were never in it. I too wish you luck- you are barking at the tree you have just pissed upon- but carry on, continue to express your nature.

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