Thresholds, Violence and Psychic capital

Both Violence and Memory have thresholds and triggers and can give rise to engulfment psychosis- is there any connection between the two from the perspective of what Kenneth Boulding called Psychic Capital?
A recent paper gives a cogent summary of this notion-
 A collective mental state will be influenced by memories, which can also be collective insofar as they are produced by common experiences. The store of good memories has been called psychic capital, but there will also be bad memories or negative psychic capital. A community can be aided in its survival by a sense of coherence. Psychic capital can be drawn upon in the task of maintaining a sense of coherence and therefore survival.
Put this way, Psychic Capital cashes out as the ex ante Incentive system obtaining at any given point in time. Economic theory suggests that coercion would rely on monetary exactions (fines) rather than physical violence except where agents have no wealth. But, if the proportion of zero wealth agents rises faster than the productivity of Violence,congestion and spatial polarization based multiple equilibria will exist though perhaps eventually converging to a a dominant firm/ competitive fringe type situation.

In this context, the Sociologist Randall Collins stresses the learned aspect of Violence- i.e. a 'know-how ' effect in Boulding's terminology- and we can add a Tardean mimetic hedonics of violence to motivate such learning.

Perhaps the greatest living theorist of Non Violence, Gene Sharpe, takes as his starting point the insight that Power is not monolithic, the People can withdraw their obedience and leave their Masters without Power. However, just as any existing Monopoly has to remain competitive or shore up barriers to entry against potential rivals, Governments too never have more than a notional monopoly of coercion which is in any case  hotly contested at the margin. In this context, 'withdrawal of obedience' imposes a monetary cost on those with wealth- because the State can reciprocally  withdraw protection from crime and delinquency in a discriminatory manner so as to maximize the rent on such Law and Order as remains. This shrinks the economy but it may kill off dissent faster than it enfeebles the State and in any case, by reducing the capitalized value of the returns on Power, turns everybody's focus to short term Machiavellian tactics rather that long term strategic thinking or mechanism design.

 Prof. Sharpe, who has been called the Machiavelli of Non-Violence, highlights what would otherwise seem an oddity in the trajectory of Mahatma Gandhi's Satyagraha such that Civil disobedience did not cease to be non-violent while at the same time dramatically eroding its participants' inner (as opposed to tactical, or hypocritical) commitment to Ahimsa as a principle.

I suppose the take-away point here is that 'Violence' is only perceived as such  when it crosses a certain threshold- in the context of Power, it is the the boundary between delinquency and disobedience.  Similarly, Collective Memory only turns into Psychic Capital when a threshold is shifted- as happened with Ind's recovered memory of sexual abuse at the hands of Evil British people who wore Top Hats and were terribly well spoken and had a real plausible reason for suggesting that they'd lost their mobile phone, and were expecting a real important call, and it was probably hiding in one or other of your orifices and would you mind awfully if I took a look? and it turns out they hadn't lost their mobile phone at all- in fact phones hadn't been invented yet- and OMG having to live with the shame, the humiliation- I mean if that's not a good enough reason to burn your Jermyn St. shirts what is?

Sanskrit translation anybody?

Alas! Adi Shesha, all Samadhi but is klesha- Skandha-mara!

Arise! Ved Vyasa, mount Mount Kailasa- Hari-hara!

Alack! my poison sac, thee, Mohini charms but to excise

So, envenomed against Love, Christ's dove, I, as Suka, revise

(Skandha-mara, or Mara as metaphor for the entirety of conditioned existence)

Inconsistent Finitism & Ontological dysphoria

This is the great mathematician Terry Tao explaining how he spotted the error in Prof. Nelson's proof purporting to show Peano Arithmetic to be inconsistent- thus refuting  'Logic's Lost genius' Gerhard Gentzen 1936 result.

Actually, Nelson's proof was relatively easy to understand, in part because he took the trouble to write out a short outline which make clear the general strategy of proof while omitting most of the technical details (though it was ambiguous at one very crucial juncture), and also because I had already previously thought about the surprise examination (or unexpected hanging) paradox and the Kritchman-Raz argument (see the last section of http://terrytao.wordpress.com/2011/05/19/epistemic-logic-temporal-epistemic-logic-and-the-blue-eyed-islander-puzzle-lower-bound/ ).From the outline one could already see that the main idea was to adapt the Kritchman-Raz argument to the theory Q_0^*, which "almost" proved its own consistency in that it contained a hierarchy of theories Q_1, Q_2, Q_3, ..., each of which could prove the consistency of its predecessor. 
Now, I did not at the time fully understand the definition of Q_0^*, nor was I fully aware of the Hilbert-Ackermann result which guaranteed this chain of consistency results, but I was willing to accept the existence of such a hierarchy of theories. (I've since read up a bit on these topics, though.) The question was then, given such an abstract hierarchy, whether one could use the arguments of Chaitin and Kritchman-Raz to establish the inconsistency of at least one of these theories. 
These arguments were simple enough (they were basically formalisations of the Berry paradox and surprise examination paradox respectively) that I could then try to do that directly, without any further assistance from the outline. And, indeed, when I attempted to do this, I did at first seem to obtain a contradiction (much as paradoxes such as the Berry or surprise examination paradoxes also lead to absurdity if one reasons somewhat carelessly using informal naive argument). So I could see where Nelson was coming from; but then I spent some time trying to expand out my arguments in detail to find the error. The key, as I found out, was to specify exactly what proof verifier would be used for the Chaitin portion of the argument (this was an issue that was left ambiguous in Nelson's outline), and in particular whether it would accept proofs of unbounded complexity or not. Since Nelson wanted to keep all proofs at bounded complexity, I used a proof verifier that enforced such a bound, and eventually worked out that this could not be done while keeping the length of the Chaitin machine constant; this was the objection that I raised in my first few comments. However, after Nelson responded, it became clear that he was using an unrestricted proof verifier, and this led to a different problem, namely that the proofs produced by Chaitin's argument were of unbounded complexity. So there was not a single "flaw" in the argument, but rather there were two separate flaws, one of which was relevant to one interpretation of the argument, and the other of which was relevant to an alternate interpretation of the argument. 
Aside from this one ambiguity, though, the outline was quite clear. Certainly there have been other manuscripts claiming major results that were much more difficult to adjudicate because they were written so badly that there were multiple ambiguities or inaccuracies in the exposition, and any high-level perspective on the argument was obscured.

Nelson's quickness to recant after examining Tao's objection has been commented on in a post titled 'why do Mathematicians always agree'?
In response, Catarina Dutilh Novaes, writes-

In my current research project on deduction, I am working on the idea of a dialogical reconceptualization of deduction. One of the upshots would be that the mathematical method itself is able to counter our tendency towards confirmation bias, in virtue of what I call the 'built-in opponent' feature. When formulating a mathematical proof, proponent has to ensure that there are no counterexamples to any of her inferential steps, as if anticipating possible objections by an opponent. In this way, she is 'forced' to adopt the position both of someone who is convinced of the cogency of the claim and of someone who is not.

My response, from the socioproctological perspective is-
In this specific case, all the mathematicians involved relied for their work on a specific highly developed theory-  call it a module- and none was prepared to bear the cognitive cost of re-writing the entire module which is why there could be a quick resolution. Surely this happens all the time in other disciplines as well? Indeed the less 'rational' or alethic the subject area the lower the cognitive pay-off for rewriting entire modules so we might find even faster resolution, without even the pause for critical thought. Prof. Nelson was quick to see his error precisely because he is one of the brightest people in his discipline. A lesser mind, even if capable of formulating Nelson's thesis, would  have taken much longer to concede the disputed  point. 

Still, suppose there was a big cognitive pay-off, currently available, for entirely rewriting the Chaitin/ Kolmogorov 'module' re. complexity, then it may be that some one or other of those involved in this dispute  might have taken that tack.

Surely an 'in-built opponent' is a feature of all social communication? It weighs down most heavily where the cognitive cost of re-writing modules are high or the reward is miniscule? I suppose statements about fashion or syntax or what is considered politically correct, have this feature and thus in most social sub-sets there is going to be very quick recantation simply because the cost greatly outweighs any possible benefit.

At this point, I'd like to introduce a notion of ontologically dysphoria- the feeling of being in the wrong Universe, the intuition that the Cartesian duality of mind and body points to something more troubling, bizarre or tragic. It may be that there is a sort of genotypal canalisation towards a widespread feeling of this sort- perhaps, rather than a malaise attributable to the weltgeist, ontological dysphoria is the driver for the necessary-but-not-too-much preference diversity needed to drive trade, but also communication and the elaboration of Knowledge systems.

It may make a sort of collocational sense for us to agree that Math represents a limit case of one sort and philosophy, with its distinctions without differences, as the limit case of its opposite.

Godel and Von Neumann, both Theists on their death beds, who agreed on so much in the way of mathematics yet had ontological dysphorias of opposite tropism. It may be that the latter type of 'madness'- or stark solipsistic discontinuity- is as important a driver for breakthroughs in Maths as the great powers of 'reason' both possessed which enabled  Von Neumann to grasp Godel's ultimate result, perhaps, more thoroughly and more quickly than the latter had done himself.

Barzakh & the Avestan Ram Yasht

Salman H.Bashier has suggested that the Quranic 'barzakh'- that isthmus between two bodies of water, one salt, one sweet- derives ultimately from the Persian 'purdah'. The importance of the 'rending of the veil- or apocalypse'- in Christianity makes this poetically interesting. However, I still couldn't see any really fundamental connection between barzakh and purdah till I read the Ram Yasht- the 15th chapter of the Avesta- i.e. the Zoroastrian Scripture-

42.

I will sacrifice to the Waters and to Him who divides them....
To this Vayu do we sacrifice, this Vayu do we invoke....
We sacrifice to that Vayu that belongs to the Good Spirit, the bright and glorious Vayu.

It has been suggested that the parting of the Red Sea by Moses is related to a still observable phenomenon somewhere in that region whereby the wind, from time to time, rises up to divide the freshwater of the Marshes from the salt water of the sea and maybe this was confused with the isthmus at Lake Mareotis or something of that sort.

For the Indians, the equivalent of 'barzakh' is 'antarabhava' which is associated with the Gandharvas whose Iranian form is highly suggestive-

aom jaidhyat,
avat âyaptem dazdi-mê
vayush ýô uparô-kairyô
ýat kaêna nijasâni
azem brâthrô urvâxshaya
ýat janâni hitâspem
raithe paiti vazaidhyâi,
uiti asti gafyô âhûirish uiti aêvô gafyô paitish uiti gañdarewô upâpô.

26.

I will sacrifice to the Waters and to Him who divides them....
To this Vayu do we sacrifice, this Vayu do we invoke....

27.

To him did the manly-hearted Keresaspa offer up a sacrifice by the Gudha, a channel of the Rangha, made by Mazda, upon a golden throne, under golden beams and a golden canopy, with bundles of baresma and offerings of full-boiling [milk].

28.

He begged of him a boon, saying: 'Grant me this, O Vayu! who dost work highly, that I may succeed in avenging my brother Urvakhshaya, that I may smite Hitaspa and yoke him to my chariot.'
The Gandarewa, who lives beneath the waters, is the son of Ahura in the deep, he is the only master of the deep.

29.

Vayu, who works highly, granted him that boon, as the Maker, Ahura Mazda, did pursue it.
We sacrifice to the holy Vayu....
For his brightness and glory, I will offer unto him a sacrifice worth being heard....

In Ram Yasht 7.28- asuiti asti gafyô âhûirish uiti aêvô gafyô paitish uiti gañdarewô upâpô- the Gandharva is described as the son of Ahura and master of the deep- nevertheless the hero is able to avenge his brother's death on it.

However, a brother is also a double, like a reflection in water. Without playing up a Rene Girardian notion of 'mimetic desire' and the sacrifice of the twin (Gemini obviously relates to King Jam- i.e. Yama though, actually, it is the Ashwins who are more profitably invoked in this context) it is enough to mention 'Adi Vigyan' (the original science- of casting off illness or blemish onto one's reflection) to realize that it is the esoteric aspect of a ritual, rather than a clear cut mythology, which underlies this.

Buddhist 'bardo' (unlike its Vedantic equivalent which just concentrates on erotic 'karmic residues' impelling to further re-birth) is as richly suggestive as Sufi barzakh.

Interestingly, the Zoraostrian 'Ilm e Khushnoom' school synthesizes Sufism and Zorastrian ideas in a suggestive manner.

Indeed, there are plenty of Sufi Buddhists of Iranian origin and, perhaps, Central Asian culture can only be understood from this perspective.

Returning to classical Buddhist understanding of the Gandharva, it might be worth our while to look again at the strange role they play in the Mahabharata.

The Kuru war only happened because a Gandharva resented the rightful heir possessing the same name as himself. Apparently, Gandharvas have to change their name if defeated in battle. This happens when Arjuna defeats a Gandharva. The upshot is that Arjuna gains 'caksuchi vidya'- the ability to see anything he wants in the form he desires, this is a type of omniscience but one that only grants you the knowledge you actually desire. The Bhagvad Gita gains poignancy because Arjuna has this gift. He can see that he will prevail even over his 'chiranjeevi' (unkillable) foes but can't see that his enemy is his eldest brother (because Karna does not want him to see this and Arjuna, after all, is a good younger brother who wants to obey his eldest brother).

As everybody knows, the Gita ends with a theophany and the proclamation of a pure Occassionalist metaphysics (like that of Ghazzali and the Sufis). However, both the Sufis and the Buddhists have a doctrine of momentariness such that Occassionalism is empty. Vedanta too embraces 'Mayavadi' doctrine such that all that exists is a Gandharva dream- much music and drama and superb poetry and powerful incense but it is all a shadow play, that is all.

I may mention that Jainism, thanks to Umaswati (who started off as a Mathematician) becomes 'observationally indistinguishable' from Nagarjuna's Buddhism or Sankara's Vedanta because of a subtle property of the sort of maths used in 'matching problems'- essentially this links to entropy.

'Karmic-obstructors' (i.e the matching problem for the writer of an Epic- or indeed a Kabbalistic interpretation of Scripture) run out of steam because though the sort of Maths used in Combinatorics soon yields very very big numbers, still those numbers are infinitely small relative to the decimal expansion of the vast majority of 'real' numbers.  

The sort of 'discrete maths' used by ancient tax gatherers and Monastery bursars meant that 'state space explosion' was as familiar to the literati back then as it is to us now. What was aberrant was the brief period when calculus flourished and intellectuals believed in a Laplacian universe.

The koranic term barzakh, of Persian provenance (presumably from *burz-axw "high existence"), was also used in the Islamic tradition in a similar sense. The term has not survived in extant Persian sources (cf. also Bölken, pp. 57 ff.). 

I mention all this because, it seems to me, something new comes into the poetic reception of the Ramayana- that is Riti type poetry- at about the time when Akbar, or perhaps his mother, ordered the translation of the Ramayana into Persian.

Abu Fazl tells us that the Emperor wanted to end the hatred between Hindu and Muslim by dispelling their mutual ignorance but, it seems, the barzakh between them was one that Vayu had made to go through and overtake both.

As to Ayodhya's Apocalypse, for us contemporary poets, what is it if not this?

Evolutionary Justice and the Price of anarchy

This is a link to a very readable paper on Evolutionary Theories of Justice which raised a possibly naive and foolish question in my mind- we have a notion that correlated equilibria in animals must be genetically canalised because they don't have reflexivity and we also have a notion that something like reflexivity is a general module which does some sort of, collocation method, correlated equilibria computation- but does this mean that talk of Justice is really a sort of arbitrage of anarchy?
One of the main tools in the study of selfish behavior is the price of anarchy [14, 20], a measure that compares the worst case performance Nash equilibrium to that of the optimal allocation. Naturally, the concept of the price of anarchy extends to correlated equilibria.
If we know only that the players play at some equilibrium, the price of anarchy bounds the deterioration of system performance due to selfish behavior. On the other hand, there is the optimistic point of view in which the players are guided to play at the best Nash equilibrium.
Especially with correlated equilibria, the latter makes much more sense: The mediator who selects the probability distribution, the correlated equilibrium, and presents it to the players, can select the correlated equilibrium with minimum system cost. In other words, one can view correlated equilibria as a mechanism for enforcing good behavior on selfish users. The optimistic price of anarchy of the best equilibrium is also called price of stability  (Click here for the whole paper)

Deontology's Royal Road to Beenakker's boundary

This is a link to an interesting paper suggesting that any deontology can be collapsed into a Consequentialism by an appropriate weighting of Utilities but not vice versa  thus generating an asymmetry in favour of the latter.
An obvious rejoinder is that you can have a Deontology specified thus
1) first compute all possible Consequentialist solutions be they rule, act or whatever.
2) find something better than any of them.
However, there is one sort of Consequentialism, which I've just this moment invented, which goes something like 'discontinuously assign very high Utility to particular ordinal Utilities which have interesting mathematical properties, like Pi or e, such that what is maximized relates to something to do with  doing the Consequentialist calculus itself. In this case the deontology suggested above fails because something at step 1 encounters a halting problem.

Now as a matter of fact, not theory, it is the case that talk about Consequentialism vs Deontology is only interesting in so far as it drives maths or provides a concrete model for cool axiom systems arising from other fields.

The author of the paper linked to above writes-
 A consequentialiser who cannot account for the difference between act and rule consequentialism has not succeeded to deliver a theory that deserves the label ‘consequentialism’. However,only cardinal consequentialism can account for this distinction. Rule consequentialism presupposes that one is able to calculate averages (or at least sum up the utility of different consequences into a sum total) and this requires that we measure utility on a cardinal scale.
Is it the case that Rule Consequentialism (R.C) is constrained in the manner specified? Who is to say that, so long as R.C. doesn't throw away information, that single valued averages are necessary? Suppose a fractal captures the information rather than an average. It would have been news to many, prior to the Seventies, that fractals were in fact rankable on a cardinal scale on the basis of dimensionality. How do we know that the same thing is not true of other, currently exotic or unknown, mathematical objects which capture information?

I suppose this is just a sort of slapdash prelude to the realization that here as elsewhere what appears to be a Philosophical problem dissolves at Beenakker's boundary.

Sorabji on Gandhi & the Stoics

Prof. Richard Sorabji's very readable book on Gandhi & the Stoics is now available in hardback and should soon be downloadable for Kindle.

The question for me, in considering Gandhi from the viewpoint of Greek philosophy, is to what extent his praxis (which Sorabji insists was purely philosophical) operated within Pyrrhonian epoche- a skepticism re. current claims made by Science, Technology and various 'expert' crafts such as that of the Diplomat or Statesman which, nevertheless, in some non trivial manner, also produced a more than mortal serenity or ataraxia- as opposed to a type of Stoic apatheia- which conferred extraordinary powers in terms not only of discovering the Truth but also bringing about seemingly very difficult Social or Political outcomes- for e.g. eliminating the grounds and possibility of class or race or creedal conflict, in a manner mysterious and suggestive of a sort of communal theosis by which different shards or splinters of the Logos are reunited and made whole. In connection with that last, I may mention, Prof. Sorabji's offers a novel interpretation of Gandhi's reception of the Jain anekaantavada epistemology which may interest Divinity students.

I have commented elsewhere on the tenability of Sorabji's central premise- viz that Gandhi was primarily a Philosopher, not a Politician and Social Worker- but I still think it worthwhile to dwell, in this context, on the disjunction between the Ciceronian Stoic, for whom individuated Duty was defined in relation to the Timocratic Cursus Honorum, and the Hellenic slave whose compass of action was much more circumscribed. It is the latter of which the Hegelian dialectic of the gaze might be predicated whereas of the former, in connection with Liberty, what after all can be said- other than that it is at best a pastoral, at worst a patristic, diminuendo addendum to the glorious gloaming of Iron Age Thymos?

Libertas is a Goddess most honored when

Her altar is demolished so an exile return

& Cicero to thy fons et origo Men

Red tho' Tiber roil & darkly burn.

It scarcely needs mentioning that Gandhi's generation turned their backs on both the Hegelian struggle for Recognition as well as the Ciceronian Cursus Honorum. Yet the Ashram or the Jail Cell were, by the very pietas of the chicane sign-boarding them Liberty's temples, rendered altars to, not Stoic Philosophy but Cynical Politics.

My own intuition, for what it's worth, is that the Indians had a 'field theory' (if as Emerson said, Boscovich discovered that things never touch, then perhaps that Jesuit learnt it from the Vimalakirti, just as Leibniz is supposed to have got his Relationist Monadology out of the Avatamsakasutra) or, at least, a discrete maths tradition, and, as such, were free from sorites type mereological problems which, after Euclid, bedeviled the Greeks.
 If this is indeed the case, though the instrumental value of Prof.Sorabji's book is diminished, it may yet serve a purpose as illustrating a certain mind-set which, to us now, appears as archaic as that of Thales and Anaximander and, I increasingly feel, all the better for it.