Tuesday, 7 March 2017

Zero-knowledge proofs and the Gita's Indecision theory

This post is a response to a paper by H.J Wiese entitled 'A Decision Theorist's Bhagvad Gita' which seeks to show that the 'Rational Shortlist method' is consistent with the 'svadharmic' (deontic) message of the Gita.
There is some literature (e.g. here) seeking to apply a rational-choice hermeneutic to ancient or medieval texts. In general, these attempts fail. They show rational choice theory to be foolish and its practitioners to be philistines.
Wiese says ' Árjuna asks Krishna for help in his decision of whether to fight or not. Broadly speaking, Árjuna prefers consequentialist arguments while Krishna stresses the warrior’s svadharma.' In other words, Arjuna does not want to fight because the outcome will cause him grief. Krishna replies that he will suffer grief through loss of reputation as a warrior if he does not fight and the woeful outcome will happen anyway. Thus, since Arjuna can't get his preferred option- viz. no big slaughter- he should content himself with maintaining his martial reputation and developing equanimity regarding the inevitable bloodbath and the intense guilt and psychic distress it will cause him.

If Wiese is right, Hinduism is an evil religion. Its teaching is- you may as well pretend to believe you have a duty to do bad things because God exists and the bad things will happen anyway because God wants bad things to happen. By pretending to believe you had to do those bad things you will get a good reputation of a certain sort and moreover be considered a God fearing man. This rule applies even if, or indeed applies more strongly if, God does not exist.

Compare this to Pascal's wager- 'You may as well believe (not pretend to believe) in God, absent any direct proof, because if you do so you may attain Heaven whereas if you don't believe in God you may be condemned to Hell.'

This is a cynical argument but at least it involves a genuine belief, the struggle to maintain which may nurture the seed of Faith which, in turn, by itself may change your inward ethos. In other words the struggle to believe may have some positive 'spiritual' value.

Another approach which arrives at the same conclusion is that of Evidential as opposed to Causal Decision Theory. Suppose we have evidence that only supports the conclusion that there is a gene which both causes people to smoke and which also causes cancer. Causal Decision Theory says you may as well smoke, if that is what you want to do, since whether you get cancer or not has already been decided. Evidential Decision Theory says you should stop smoking because then you will believe you won't get cancer- a better outcome. Now it may be that there really is a link between smoking and cancer which we are not able to establish. In this case, Evidential Decision Theory is better. The problem is that it could turn into a program of 'managing the news'- i.e. being selective in what new information we incorporate into Decision making. We may end up evaluating new information on the basis of 'auspiciousness' -i.e. the feeling there is a higher power able to assure us we are on the right track- rather than on the basis of 'agency' - i.e. increasing our own power to change things in the world by understanding causal processes. Individually, it may be rational to 'manage the news' and seek only for 'auspicious' signals rather than research causal connections. Collectively, it is irrational to do so. Society would be governed by the utterances of Oracles and Prophets rather than by the causal connections posited by Scientists and established by Statisticians.

One way round this problem is to limit the scope of any oracular utterance or other auspicious or supernatural event to some specific aspect of an individual's dilemma. In other words, it would be a purely private matter and have no wider implications. Interestingly, the Just King, Yuddhishtra, has to learn Statistical Game Theory to overcome his 'vishada' whereas Arjuna, who is an agent, not a principal, gains a 'zero knowledge proof' that he is on the regret minimizing path.

In economic interactions we often trust the other party if our loss will be small and this is socially helpful. However, if the loss could be large, we may equally desist from trusting the other. Suppose the other genuinely means to stick to the terms of the agreement but can't afford to prove this without incurring risk of substantial loss. Then a 'zero knowledge proof'- i.e. one such that neither side gets any strategic information but is able to verify that the transaction is likely to be completed satisfactorily- is useful.
It is sufficient to know that there is some mechanism which can elicit the truth from all agents such that the coordination problem common to them has an optimal solution, for Economics to go ahead on a scientific and rational basis in a manner which increases Trust and Cooperation and therefore Peace and Prosperity. This, at any rate, is why the 'Revelation Principle' is fundamental to the theory of Mechanism Design.

In Theology, too, we may wish to stipulate that there is a sort of Divine knowledge beyond mortal ken whose existence can nevertheless be verified without humans gaining any access to 'forbidden knowledge' or god-like powers. Theism, as opposed to a Soteriology based on Theosis, requires this. In general this is a good thing because Religion does offer some benefits to Society provided random nutjobs don't get to claim Divine or Prophetic powers.

A Political Science which is based on the notion of Checks and Balances, too, might wish to stipulate that Judicial deliberative processes follow a different logic and observe different protocols from those used by the Legislative or Executive branch such that though results are verifiable, they can't be systematically predicted, reverse engineered or otherwise gamed.
Hermeneutics itself, as Blaise Pascal pointed out, requires some similar informationally parsimonious verification protocols because 'Languages are ciphers in which letters are not changed into letters, but words into words, so that an unknown language can be deciphered.'
In all these cases, it is sufficient to affirm the findings of Computational Complexity theory and to use things like zero-knowledge proofs so as to, on the one hand affirm the univocity of information, while, on the other, guarding the integrity of plural autopoietic systems which nevertheless can interact in a regret minimizing way.

One alternative, for deontology, is to consider the meaning of an imperative statement as arising out of its conceptual tie to action. Alan Gibbard may be cited as an example of this sort of 'semantic normativity'. But this approach soon slides into Dialethia or ontological mystagogy.

For Christianity, sincere belief in a Credo is necessary and perhaps this makes 'semantic normativity' salient. For Hinduism, however, whereas Faith (shradda or eusebia) may matter, Belief (as opposed to legal or ritualistic knowledge) does not. Why? Perhaps it is because Hinduism has no historical origin and was not seen as something one needed to convert to.
Purva Mimamsa ritualism made no requirement re. the beliefs of the officiants because to do so would be detrimental to public confidence in Vedic rituals. Similarly, the Christian Church has a complex metaphysical reason why an ordained Priest who has lost his faith can still discharge ritual functions in a proper manner. However, the faithless Priest's soul would still be in danger. In Hinduism, by contrast, though improper Belief might have indirect karmic consequence, only intentional actions had salience.

Thus, apropos of Wiese's analysis of the Gita, Arjuna would have attained the same final state had he only pretended to believe that God had given him a particular, unpleasant, duty. Indeed, since God's activities are themselves described as 'lila' - i.e. a play- pretence could be a mark of superior ontological status.
True, Krishna gives Arjuna a direct proof of the existence of God so there is no need for any pretence. Yet, Arjuna could have chosen to witness a 'virtual' theophany indistinguishable from the real thing. Why does he not do so? The answer is that he loves Krishna as his Lord and Saviour but loves him in a humble way. He wants only what Krishna wants for him.

This is not H.J. Wiese's view. For him, the Gita is about a 'hard-choice' situation- one where, even if one has complete preferences, it is difficult to decide how to act. It is because preferences are inadequate to motivate actions that Krishna produces 'reasons' to persuade Arjuna to fulfil his supposed Warrior 'svadharma'.
Isaac Levi, who introduced this notion of 'hard choice' moral dilemmas, had previously attempted to recast scientific enquiry itself in terms of a certain sort of axiomatic decision theory. However, he had not considered that formally determinate Bayesian probability functions can be defined in terms of complexity classes such that Newcombe type problems or one's involving Turing type Oracles become ubiquitous. In other words, the practical problem we face is that there is a big gap- even in mathematics- between things we can prove and things we have good reason to believe are true but which can't yet be proved because we are not advanced enough. Thus it is not irrational if, at least individually, we are guided by purely subjective intuitionist, aesthetic, or 'auspicious' considerations.

Still, it is worthwhile to observe that Levi, in line with the Pragmatic tradition, sees categorical reason as informing ampliative induction such that actions undertaken under conditions of moral uncertainty escape suspicion of akrasia. After all, as Krishna points out, not acting too is an action.

The problem with this view is that it assumes categorical reasons can have low Kolmogorov complexity while consistently verifying specific actions as correct in a noisy, uncertain, or impredicative environment. Such a view is naive. Now it may be that P really equals NP or that some Quantum computer oracle has an easily implementable inference engine analogue. But we don't know this will ever be the case and certainly it would be foolish it to assume any such thing now.

Yet this is what Harald Wiese is doing in his paper. The conclusion he comes to is that 'Action non contextuality' is defeated by Krishna's theory that actions with the same consequences differ based on the deontic rule applicable to the agent. Since, in Hinduism, no svadharma deontic prescription carries a confessional entailment, the message of the Gita is-  it does not matter whether you believe your Sociologically determined 'duty' is ordained by God or not. All that matters is that you act as if you do have this belief  because what matters is your reputation, or chance of gaining Heaven, not your inward ethos. In other words, according to this view, the Gita, and Hinduism by extension, affirm ethical heteronomy.

It seems this German economist- not a philologist- has found a novel way to carry forward his country's grand tradition of distorting and rendering hateful even the most sublime of Hindu texts!
However, Wiese is merely following in the footsteps of Amartya Sen- so it is not German Indology but an ignorant or obsolete type of Choice theory, linked to Sen, which is to blame.

In what follows, I will argue that Wiese is making the following, explicit or implicit, assumptions which are unwarranted by the text and this vitiates his argument. However, in the process, a new hermeneutic horizon is opened.

I believe Wiese, for the purpose of his paper, implicitly assumes
1) Uncertainty. Minimally it must be the case that at least one future state of the world becomes uncertain because of Arjuna's 'vishada' (mental anguish or abulia which may cause indecision or inaction)
Otherwise, decision theory has no purchase. We are in a pure occassionalist universe and Arjuna and Krishna are like clockwork mechanisms. This is certainly one way the Gita can be interpreted.

Is such an interpretation well founded? Firstly we must recognise that both Arjuna and Krishna have some unusual informational endowments- the latter not just being omniscient but also the final, and perhaps the efficient, cause of all things.
Thanks to a Gandharva's gift of chaksuchi vidya, Arjuna  possesses the boon that whatever he wishes to see will be shown to him in the manner he would choose. However, he never formally accepted the gift, nor ever consciously relied upon it. However, the Gandharva did not take the gift back either. Thus the boon exists as svatva property of an asvamika (lit. without a lord) kind.  When Arjuna develops 'vishada', his mind becomes deranged and his volition is weakened. He is not in possession of himself- i.e. he is asvamika. Thus the Gandharva's boon which continued to exist as asvamika svatva (unvested property) now vests in him by reason of this 'vishada'. It therefore follows that his vision of the devastation caused by the War is alethic. If it wasn't, Krishna could persuade him to fight by pointing out the extreme improbability of the Pandavas prevailing over the Kauravas- two of whose leading warriors could only die by their own wish.

Interestingly, the Gandharva's boon gave Arjuna, while in the grip of vishada and thus not the master of himself, a vision which, despite all appearances to the contrary, is precisely the one he would have, with hindsight, chosen for himself because, in a non deterministic manner, it enables him to gain the beatific vision which however he wished to experience as a pure gift of the Lord.

Notice, if Arjuna wishes to have a dispassionate view of how all things are connected, he can gain this thanks to his supernatural boon. However, in that case, he would know that Karna is his true eldest brother, in which case there would be no occasion for War. However, Karna does not want this outcome and since Arjuna is an obedient younger brother and wishes to remain so, his boon excludes his envisioning this truth.

Normally, when a supernatural boon is given to a hero or a ascetic, there is a karmic price to be paid because of some subsequent act of hubris or hamartia. Even Frodo and Bilbo Baggins, in Tolkein's masterpiece, feel the urge to put on the Ring of Power. However, in the Mahabharata, Arjuna feels no similar temptation to accept or use the Gandharva's gift. This did not mean it disappeared. Rather it remained asvamika svatva- a property not conveyanced for karmic purposes- till Arjuna himself became asvamika and, purely by Grace, gained the beatific vision of his true Swami- Lord Krishna, which, indeed, is the salutary goal of svadharma because all egotistic karma, all will-to-power, is burnt up.

Thus, the story of the Gita begins with 'Vishada Yoga'- the Yoga of mental illness, in which Arjuna sees a horrific vision of the outcome of the battle. This causes him to lose heart. Lord Krishna counsels him till Arjuna recognises that his friend is in reality the one true and eternal Lord. Arjuna then asks Lord Krishna to disclose his cosmic form.
Chapter 11, Verse 1
Arjuna said-' I have heard Your instruction on confidential spiritual matters which You have so kindly delivered unto me, and my illusion is now dispelled.
'O lotus-eyed one, I have heard from You in detail about the appearance and disappearance of every living entity, as realized through Your inexhaustible glories.
'O greatest of all personalities, O supreme form, though I see here before me Your actual position, I yet wish to see how You have entered into this cosmic manifestation. I want to see that form of Yours.
'If You think that I am able to behold Your cosmic form, O my Lord, O master of all mystic power, then kindly show me that universal self.

The Lord does fulfil his devotees request- clearly Arjuna's boon means he can physically witness the cosmic vision without suffering any ill effect.
The Blessed Lord said: 'My dear Arjuna, O son of Prtha, behold now My opulences, hundreds of thousands of varied divine forms, multicolored like the sea.O best of the Bharatas, see here the different manifestations of Adityas, Rudras, and all the demigods. Behold the many things which no one has ever seen or heard before.Whatever you wish to see can be seen all at once in this body. This universal form can show you all that you now desire, as well as whatever you may desire in the future. Everything is here completely.'
Then the Lord realises that Arjuna isn't seeing anything at all because, in accordance with the Gandharva's boon, he can only see what he wishes to see. As a true Bhakti Yogi, Arjuna seeks the vision of Yogishvaram- the God of Yoga- only if it purely the Lord's gift and not the result of any sort of merit or endowment natural or acquired.
Thus Lord Krishna says-'But you cannot see Me with your present eyes. Therefore I give to you divine eyes by which you can behold My mystic opulence. (yogam aishvaram) '

The outcome of this theophany was that Arjuna accepted his part in the Divine plan without knowing that it involved his own slaying of his true eldest brother. The actual content of that vision did not give him any knowledge he didn't already have. It merely confirmed that Krishna had offered a coherent and alethic argument such that Arjuna's doubts were removed and he decided to fight.

I think it is worthwhile to reiterate the importance of the Gandharva's boon from the Game Theoretic point of view. Thanks to the 'asvamika svatva' nature of the Gandharva's boon, Arjuna's preferences constrain his information set in two different ways. Firstly (I believe) he can't see that Karna is his eldest brother because Karna doesn't want him to know this and he himself wishes to obey his eldest brother (even if it is Karna).
Secondly, he does not want a theophany he is otherwise physically fitted to receive- like the Sage Utanka who gains this vision without Krishna having to give him 'divine eyes' because he already possesses sufficient 'ascetic merit' or supernatural power- because, as a pure Theist, he only wants it as a pure, unqualified, act of Grace on the part of the Lord.

Clearly Arjuna's information set depends on his preferences- not as they actually exist- but from the perspective of backward induction. In other words, with hindsight, these are the preferences he'd have wanted to constrain his information set.

Suppose this were not the case. Suppose the Hindus believed Arjuna had no special supernatural gift which could operate when his volition was weakened by 'vishada'. In that case, the Gita only provides evidence that no argument based on Spiritual Science or Revelation can overcome indecision. Only Theophany- i.e. something miraculous- can counter the 'Agrippa's trilemma' Pyrhho learned in Punjab. If Hindus held this view, why would they consider the Gita an orthodox text?

I believe, in accordance with the terms of the Gandharva's boon, Arjuna, if he chose, could 'see' every single episode of the Gita even if it did not actually come to pass. He could gain the vision of Krishna's theophany ('vishvarupa') by his wish alone. However, since he is a sincere devotee of the Lord, his wish is that Krishna should only reveal himself by his own uncoerced or otherwise solicited wish & volition. This type of impredicativity requires increased indeterminacy in its I-Thou dialogic.  It is also a feature of highly wrought romantic poetry of a baroque or 'riti' type. The intensely passionate devotional love poetry which is feature of Vaishnavite Bhakti Religion owes its sublimity to a self-abnegation in Love which never ceases to act in accordance with the wishes of the occluded Deity. Since this is also a feature of the higher, self sacrificing, types of Love which enrich our personal lives and our most significant nurturing relationships, the message of the Gita is, in fact, univocal. It does not matter if we are seeking to do the best thing for a child or a parent or a friend without imposing upon them in any way, or if we are seeking to serve the Lord of Creation for no higher reward than that of performing that service in a selfless manner.

The dramatic tension in the Gita arises from the cognitive dissonance we experience when seeking to picture Krishna as impassable or dispassionate in himself and thus unswayed by the desire to satisfy even his most beloved devotee's desire. Yet, when we act out of self-less love to another, some similar impassability or dispassion is required of us. Thus a mother may have to send her child away from herself to save its life and, afterwards, may have to dissimulate her true feelings for the child, appearing to perform some other sort of duty, in order to continue to protect it.

In the Gita, Krishna has taken on a particular duty- viz. that of the 'Suta' (charioteer or bard), which incidentally is the caste duty of Karna (because he has not admitted his true Kshatriya birth as the eldest of the Pandavas)- and is bound to do this duty to the best of his ability. Since part of the Suta's job is to keep up the fighting spirit of the warrior mounted upon the battle car, Krishna- it seems- is obliged to do his best- using hilariously self-defeating arguments (which, however, like Socrates's arguments for immortality in the Phaedo, may be viewed as an Ariadne's thread supplied by a Divine intelligence) - to overcome Arjuna's vishada, till finally, in desperation, he has to disclose his 'Cosmic form' so as to achieve his aim by 'shock & awe'.

A common trope in folk tales is that of the supernatural being who has taken on the appearance of a mortal. The hero may be able to trick such a being into revealing its true form with beneficial results or, conversely, may do so by some inadvertent action with tragic consequences. In this case, Arjuna's true 'svadharma' is that of the devotee of the Lord. He wishes for what the Lord wishes and, because Philosophy turns out to be worthless- at least to those with a supernatural boon who can gain substantive knowledge of all things- the Lord voluntarily vouchsafes that highest good- viz. the beatific vision- which the devotee could not ask for himself by reason of wishing to be nothing more than a devotee.

What I want to draw attention to is the scandal that arises where a superior being is tricked, or accidentally 'hacked', into disclosing secret information. For Brahmanism, there was the nightmare that an improper disposal of all the materials of the sacred Yagnya sacrifice, or else the unsuspected existence of some crevice or hole into which sacred information could escape or be concealed, would result in the rebirth of officiants as 'Brahmarakshasas' (Brahmin demons). Such Brahmins- from whom, as if to disprove Lamarck's theory, I am descended, required a 'zero knowledge proof' that they had escaped this fate. The Gita supplies this proof. God himself states that, by means beyond mortal ken, He has taken on the karmic burden of any inadvertent sin in any intentional action. Thus a priest can continue to perform his ancestral duties. He is not required to attain omniscience- for example, by following one of the heterodox sects- in order to be sure that no inadvertent damage occurred when he officiated at a ceremony.

It is not the case that the Gita reveals an algorithmic, or even non deterministic method by which God can be tricked, or 'brute force hacked', into revealing what is beyond mortal ken. This is because, under the appearance of natural language 'dialogue' what is actually happening is an internal 'dialogic' between Krishna and the Veda. This 'dialogic' is very subtle- for dharma is subtle- and, fortunately, since my own svadharma is that of a drunken helot, I need only concern myself with it for the purpose of exciting ridicule and contempt on the part of savants & the unco guid.

In order to baffle predators and parasites, all autopoeitic systems, Biological or Economic, have a tropism towards 'zero knowledge' protocols which impose a cost but are regret minimizing. This relates the subject to problems in Decision theory involving

2) Action noncontexuality (i.e. if two actions produce the same outcome, they should be treated as identical) and Outcome Separability (viz. the notion that the contribution that an outcome in one state of the world makes towards the overall value of an option is independent of what other outcomes the option might result in).

Here 'regret minimizing' behaviour is clearly 'rational' yet yields paradoxes. Theologically, the door is opened to either Stoic ataraxia and belief in 'natural law' which undermines social cohesion and collective thymos- more particularly for military or chrematistic civic purposes- or else we may have fatalistic occasionalism and mystagogy of the 'Oriental' sort.

Hiese's account of the Gita implicitly assumes that problems like Uncertainty, Action Noncontexuality and Outcome Separability obtain- which is why a suitably constrained Decision Theory has purchase. However, in that case, the message of the Gita is that some decisions should not be made- more particularly ones involving violence- absent a miraculous event or directive of a supernatural sort. This however is at variance with how the Gita has been understood and interpreted for thousands of years.

Indeed, if informational asymmetry between Human and the Divine had not been abolished by a specific supernatural boon given only for this very dramatic purpose, the Gita could not 'mean what it says'.  If the Hindus had a Church which declared itself 'the bride of Krishna' and declared its pontiff the sole arbiter on what Krishna desired his devotees to do, then- yes- the Gita could have a certain sort of prescriptive force, in resolving doubts as to one's true duty, but only for votaries of that particular Church. Yet, in modern times we find great Scientists and Mathematicians- like Andrei Weil who took a life-endangering decision under its influence- displaying a fascination with the Gita.

The Gita is a Theistic text. Yet, it has a Universal character and has prompted ethical reflection of a sublime nature amongst people with no reason to like or admire the Hindus.

Taken at face value, it is a 'self-defeating' philosophy propping up some essentially evil elite cultus which flourished at a remote time in a currently very backward part of the world. This, certainly, is Amartya Sen's view and it would be a reasonable one but for the fact that it ignores an important plot twist- one which endows the Gita with dramatic, not dogmatic, content.

Arjuna's 'chakshuchi vidya' had begun to operate due to his volitional deficit of 'vishada', abulia, such that no Uncertainty obtained and only his own preferences and intentions had salience. If he can foresee the outcome of the War, what else can he not envision? Why should he not choose to learn the hidden connection between all things so as to make and implement a Plan which is optimal for himself? The answer is that he genuinely wants to obey his eldest brother. He just does not know that it is Karna and that Karna wants to meet him in battle. Krishna has a Plan based on his omniscience but it is one we humans find terrible. Which Hindu has not wept at the death of the valiant Ghatotkacha- grandsire of Barbarik? If this is Cosmic Justice let the Gods keep it for themselves. If such is the ultimate Reality- let us confess, we humans can't bear too much of it.

Since Krishna's 'vishvarupa'- his theophany- being a revelation of his true greatness, is also an act of 'Social suicide' as the Mahabharata later discloses- i.e. Arjuna's theistic Newcomb problem turns out to be Divinity's Kavka toxin!- it follows that it is a 'costly signal' establishing a separating equilibrium. Notice that Arjuna, if he wishes, could get the vishvarupa without Krishna having to disclose it- i.e. there was a potential pooling equilibrium, but Arjuna's own preferences or autonomously determined 'nature' (this is the true meaning of 'svadharma') prevented its fruition.

 However, a co-operative game should be parsimonious of costly signals which is why Screening mechanisms have salience.  But this raises the puzzle as to why more rather than less indeterminacy can be a good Decision theoretic outcome. Surely, some sort of constrained optimisation, or even a satisfying heuristic is better? One reason that occurs to me is that induced indeterminacy rules out a rational choice militating for arbitrage between coordination and discoordination games - i.e. 'moral' or other privileged 'market makers' are known to be a priori pathological.

 No doubt, the Gita contains plenty of 'cheap talk', which is fine if there is an alethic Aumann signaller and a Muth rational, Hannan consistent, correlated equilibrium- e.g if there is a 'Smriti' text which is common knowledge and which prescribes duties and defines entitlements in a robust and incentive compatible way. However, the Gita itself undermines any such notion through high comedy. Thus a hopelessly miscegenated Pandav is lectured about 'purity of the race'! Moreover, the family tradition of the entire clan was for the legitimate heir to cede the crown to one with a lower claim to it. One can multiply such instances endlessly - indeed the sublimity of the Gita arises only out of the fractal ironies and corresponding hermeneutic 'apoorva' ever renewed novelties and enchantments embedded in its every shloka.

There certainly is Decision theory in the Mahabharata- the Just King has to learn Statistical Game Theory to overcome his 'vishada' because he is a Principal (though, only by delegation) not an Agent- but the Gita, being concerned with Agents not Principals, has an 'indecision' theory- a bracketing or epoche- such that an indeterminate costly signal is elicited and a separating equilibrium is established on the basis of a 'zero knowledge proof'.

If restated Decision Theoretically, the Gita would yield only impossibility results which are themselves meaningful only in terms of the theory of Computational Complexity.

Because of the implicit assumptions, unwarranted by the text, which I have listed above, Wiese is obliged to end his paper by endorsing Sen's view of the Gita's message, viz. “one must take responsibility for the consequences of one’s actions and choices, and that this responsibility cannot be obliterated by any pointer to a consequence-independent duty or obligation.”

The problem here is that we may have good reasons to impose a 'zero knowledge proof' on a separating equilibrium. Thus if 'responsibility' continues to exist (i.e. it describes a relation than can be subject to Szpilrajn extension) even after we have cut ourselves off from anything more than bare verification, deliberation is vitiated. On one horn of the dilemma, in order to make 'responsibility' effable and deliberative, we have to adopt dialethia- e.g. by adopting P=NP as an axiom- or else 'responsibility' is ineffable and inaccessible to deliberative processes.

The Gita shows that if zero-knowledge proofs are desirable or necessary, then 'indecision' widens the space, till it is larger than the world, between the two horns of this dilemma.

What does this mean in practice? Well, in my view, this means tolerance of separate 'Dialogics'- more particularly those with the appearance of a Red Queen race- as opposed to the demand for a transparent univocity so as to stride quickly to 'optimal' substantive solutions.

To take an example, let us suppose we have an independent Judiciary which follows its own 'artificial reason' based on stare decisis. At the same time, let us suppose we have a free Market system continually adapting to new Technology, new Social configurations, new trading opportunities etc. It would be natural for entrepreneurs to fear that the Law is not adapting quickly enough. The people could be mobilised against the Judges- because legal language and Jurisprudential considerations are difficult to understand- and so the independence of the Judiciary could be endangered. One solution is 'transparency' and more 'oversight' etc. However, there is a risk that if the Judiciary lays bare every detail of its working- it would make it more easy for it to be 'gamed'. In other words, opacity too has an advantage.

In practice, Judges have found a way to signal an understanding of rapidly evolving market conditions but have done so couched in their own specialised terminology. This means that Economists are no longer crude Benthamites. They are respectful of the separate 'artificial reason' or 'dialogic' of the Judiciary. This, of course, involves no 'zero knowledge proofs' at all and perhaps I would be well advised to drop the comparison. Still, it seems to me, that Indian Economists have repented their Benthamite, or Marxist, demand for a 'committed Judiciary' because 'indecision' in this respect has proved to have advantages. The Judge should do his duty and the Legislator his duty. It is not the case that we are required to impose an immediate univocity between them. There is an advantage in being aware of a problem but not acting decisively.

Currently, there is some Institutional panic about zero-knowledge proofs in digital communications, E commerce etc. I personally, by reason of my advanced age and declining mental powers, may be inclined to endorse this panic. After all, when I was young, the assumption we made in Economics was that all relevant information could be aggregated in a substantive manner. Every Enterprise had books which we could seize and examine. How can we be sure our fundamental theorems in Welfare Economics will still have salience where an increasing amount of relevant information is completely private? There is a result from Chichilnisky & Heard which induces optimism in this regard. However, it is the Gita which can give us the moral courage to resist panicked reactions on the part of political leaders who want to appear 'decisive.'


  1. 'When Arjuna develops 'vishada', his mind becomes deranged and his volition is weakened. He is not in possession of himself- i.e. he is asvamika. Thus the Gandharva's boon which continued to exist as asvamika svatva (unvested property) now vests in him by reason of this 'vishada'.'

    I am not familiar with any such argument. Svatva-rahasya considers svatva and svamitva as the same category. Arjuna is not asvamika by reason of vishada because mental illness does not make a person 'ownerless property' whom anyone can take as a slave.

    What is the authority for your claim that Arjuna gained this boon?

  2. You are quoting a Navya-Nyaya view. The Mimamsika doctrine is that svatva is a samskar. Furthermore, it is the popular view which determines what is legal. Since I am a stupid person and the Mahabharata was written for me- not some smarty pants savant- it follows that my view prevails.
    Once Arjun's vishada opens him to the Gandharva's boon his own chariot can be destroyed. The sacrifice is complete. Nothing is left over. What has been achieved is a song, not an ear-worm- except of course for savants who deserve nothing better.

    1. I am not quoting any view. I am just asking a simple question. What is your authority for claiming that Arjuna used boon of chakshushi vidya? You say it is the popular view. If so at least one person beside yourself would hold it.

    2. Do you hold this view? If not, why not?