'Rashomon' - A Mathematical Parody

The Original: Japan; Centuries ago; a jungle; a Samurai found killed by a sharp weapon, his wife, who was traveling with him, probably raped; a known bandit arrested from the area. That's about it, as far as the core facts go.

And everyone has different story to tell - the wife, the bandit,... and the dead Samurai's spirit...

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The Parody:
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The core facts: Some time back, an article presenting a conjecture and a proposing a partial resolution thereof was submitted to a popular Mathematical journal. That set in motion a 'process' which has lasted several months ....

A somewhat old version of the article may be seen here:
http://arxiv.org/abs/0812.2241

Here I record what people had to say - A Reviewer for the Journal, the Spirit of the Article (aka the Authors), and three Witnesses, all with substantial academic standing and who are up-to-date with everything that has happened to the article.

The Reviewer:
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1. The authors prove only N=2 of the conjecture. The rest of this long paper has only false starts and incomplete investigations - more than 20 pages worth!
2. The authors write in a choppy style, breaking up the flow with multiple 'observations'; the writing is verbose and uses phrases like 'thought construction', 'proposed proof' etc.. which indicate they are not sure about what they are talking about!
3. There are far too many numerical investigations rather than tight and elegant writing.

Summing up: The article is not suitable at all for publication.

The Spirit (responding to above comments in order):
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1. The reviewer has got even basic facts wrong - apart from the obvious N=2 case, the article contains a complete proof for N=4 with indications of how to generalize it even further. There are a couple of other complete results as well. Yes, we also show how and why some 'standard' approaches to the problem won't work. These are not 'false starts' or whatever but examples which describe the *context* of the problem and show how difficult it is.

2. The numbered 'observations' are not breaks in the flow of some liquid but *steps* building towards the proof. It does not take an Einstein to recognize this, if one has read it with a minimum of sense that is. And if non-standard terminology is so irritating, there are but 2-3 instances and five minutes worth of editing would have cleaned them up.

3. The numerical investigations are there not for the heck of it but to show concrete examples. If they really got his goat for whatever reason, the reviewer could have asked for them to be compressed or deleted. And some seriously analytical thinking will still remain.

Summing up: The reviewer has not bothered to evaluate the main proof we presented (N=4) - indeed the very core of the article has been just ignored - and has gone strictly by peripheral stylistic considerations. His main concerns could have been taken care of with a 2 day rewrite/editing but he has projected these irritants as sufficient grounds to summarily reject our work - without appeal. The fellow has not only made snide remarks on our work but made factually incorrect (indeed we would say, untruthful) observations about the article.

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Witness 1:
It was unfortunate that the article got rejected. The numerical examples seem to have been a major irritant. And maybe the length. I was worried about these factors myself but also quite hopeful that the article would be still accepted, for it really had some serious substance. The reviewer certainly did not do his job properly.

But that said, I would suggest that the authors write the article afresh, get rid of all those numbers and leave out some side-investigations and maybe tighten up the presentation of the N=4 proof... Then it should stand a better chance with some other journal.

A general point: The article appears to use a lot of intuitive, visual arguments. Some rigorous tightening on that front could help.

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Witness 2:
I did not think the article was bad at all. Yes, it was on the longer side, and had a rambling, notes-to-myself feel; but to me, these are not fatal defects. Yes, things were not presented strictly canonically but the journal in question too had said they accept and encourage unconventional/speculative stuff. The reviewer could have commented, rather should have commented on the logical content but he probably had other ideas...

Anyways, I would suggest that the authors take the reviewer's suggestions seriously, tighten up the terminology. And yes, cut the length at least by 60 percent, perhaps by leaving out those numerical examples and submit somewhere else. The full article could of course be kept online as a further reference to those who want the details.

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Witness 3:
I was sure the article would be rejected; and I am not surprised there has been no further review - indeed I think it was an easy decision for the reviewer, in terms of the style as well as the content. Unless one writes Mathematics rigorously, it won't be read. Reviewers do their work as some sort of voluntary service to the community - they are not even paid for it. And the reviewer won't read the article fully unless the writing is rigorous. And it is the writers job to impress him and to keep him interested, else the logic or whatever simply won't be evaluated.

As for the content, an article has to have at least a couple of solid results; just a conjecture is not really good enough, since there are hundreds of conjectures all over the place. And even using the word 'conjecture' is shaky here; what has been presented is more of an interesting problem than a proper conjecture - indeed, there does not appear to be enough intuition in the work to really float a serious conjecture.

Anyways, I shall try to read the article and give some specific inputs as to how the writing could be improved....
(continuing after a week)
The article is absolutely unreadable; no mathematician will read it and no serious journal publish it. This may sound harsh but that is the fact of the matter.
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And here is what another Witness had to say the other day:
"I saw the article about 2 months back and read the initial few pages, maybe 2 or 3 pages.... yes, I had an impression then ... rather, I remember forming a general impression then, that the article was a piece of bad writing. I can't recollect anything more!"

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And I sign off with a quote, the source of which I won't reveal: "The pressure for conformity is enormous. I have experienced it in editors’ rejection of submitted papers, based on venomous criticism of anonymous referees. The replacement of impartial reviewing by idiotic censorship will be the death of science."

Two Quotes

Yesterday TOI published an interview of N.R. Narayana Murthy. The title "Rein in Ego, Greed". Excerpts:

"Actually, India is a nation of entrepreneurs. You go to villages, small towns you have all these kirana shops, they are taking risks. However, when the Mughals and British came - the past 1000 years - the focus shifted to keeping us law-abiding and tax-paying citizens. When the government becomes stronger, automatically the chances of corrption and patronage become higher. In such a society, you wont see entrepreneurship, which is all about using personal initiative, dreams and optimism to create wealth and jobs...

(We are still ambivalent about strong Leaders) ... again due to foreign rule. Between 1000 and 2000 AD, we were free of foreign rule only for 53 years. When you are subjugated for 947 years, what do you have leaders for? We had leaders who curried favor with kings and rulers but by and large were not for the people. I used to ask my father - an honest, good man - "Why did you not fight the British?". He had no answer. How many of our ICS officers said "This is not fair, we cannot be ruled by foreigners" How many people spoke up? How can leaders develop in such an environment?...we had a wonderful generation of leaders post-Independence. "

Comment: Must say Murthy is propagating a hyper-simplistic view of our history, especially our medieval history - as if Indians as a whole were Free before 1000AD when they were abruptly enslaved. Indeed, that year only marks the establishment of a Muslim sultanate over the far North-west and Ghazni's attacks on Somnath and NOT Muslim dominance being switched on over the whole country. It took over half a millennium since Ghazni for the so-called 'Muslim power' to work its way down and across the rest of India. And crucially, at no point during this so-called Muslim period, was Indian Islam a centralized, overpowering monolith (Aurangzeb tried to forge something of that sort and failed spectacularly) - for instance, during Akbar's time, there were several Sultanates all over, coexisting with several Hindu kingdoms not too different in essence from themselves. And the 'foreignness' (cultural or ideological) of most of these Sultanates was ... well, very dubious.

Further, during the period immediately preceding 1947, fighting the British was not the sole hallmark of a genuine leader - Ambedkar, for instance, was not much of a 'freedom fighter', but certainly he was an outstanding leader - one who cared and achieved much. As for our wonderful post-independence leaders (one cannot include Patel and Ambedkar (and even Nehru) among them since they lived only the last few years of their lives in free India), I doubt if they will stand serious comparison to those who developed a couple of generations earlier.

Ironically, Murthy's analysis is a rehash of the picture of Indian History worked out by the British Colonial Masters - a history neatly divided into fundamentally different Hindu, Muslim and British periods. Detail: the latter two have been merged into 'foreign' in the new model.

Aside 1: Napoleon is said to have referred to England as "a nation of shopkeepers". It is rather unlikely that he was paying tribute to English entrepreneurship.

Aside 2: The mix: Nationalism + an extra-strong emphasis on 'strong leaders' has a real potential to brew into Fascism proper.

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On another note, here is another quote:

"I love this city,.. it gives me so much. ... the sheer joy of just going out on to the streets and the malls and meeting and talking to people; all those little conversations... they fill my loneliness.... And, it is great fun to catch hold of some chaps and thrust sharp metal hooks down their throats and hang them up nicely..."

Well, did that sound rabidly homicidal - or worse? But then, it is but a parody of this original:

"It is this river that made me a lover of Nature, a writer... you know, as a child I used to sit here everyday for hours on end, fishing. The only company were the fishes, and I would just talk and talk to them - the 'pallattis', 'kooris',..."

(Arundhati Roy in a Malayalam weekly, reminiscing about her childhood spent on the banks of the Meenachil river).

And here is British academician Simon Schama on an encounter with a herd of British Bison: “Oh, the bison, they were such happy animals. God, were they happy animals! They are in a little social community, like bison always used to be... and their meat, it’s staggeringly wonderful. I cooked it on a cast-iron grill last night. It’s like beef with a tang, the best beef you ever had, like superbeef, with a delicate richness to it..."

A Note To Myself

This post is 'addressed' to a young lad of a generation ago who evolved into what I am today. I wish I had then got to meet someone like what I now am or at least got to read something like *this*.... If that had happened, this post would never have been written! I grew up in Kerala, among popular science books idolizing Albert Einstein. The 'Sastra Sahitya Parishad', a Mallu organization I have mentioned in some earlier posts, had built up a virtual cult around the Master - indeed if I were to say he was a grand-fatherly figure for self and a whole host of Mallu schoolers of my generation, I would not be exaggerating one bit. Projecting Einstein as the one Scientist who really counted, 'Parishad' fed us verbalized and romanticized - and indeed, dumbed-down - interpretations of Relativity theory thru half a dozen books on the life of Einsten (one of these hagiographies began: "Dear children, each one of you would want to be a scientist, not just a scientist but a very big scientist, right? Here is the life-story of the greatest scientist of them all; try to be like him!") and countless articles which kept appearing in their Students' Magazines. To give an example of the impact all this had, I could confidently make statements like "gravity is the curvature of the space-time-continuum" at the age of 10 - and I was nowhere near being a child prodigy! Although I developed grand dreams of becoming a Theoretical Physicist, I was never quite comfortable with Mathematics - and was clearly less than sharp at manipulating algebraic expressions. A fear slowly grew witin - what if I am fail to do lengthy calculations - to fill page after page with all those messy equations, how will I do Einstein-class work?... Then, towards the end of junior college, I read 'The Physicists' by C.P.Snow. And the following bit (I quote from memory) sank deep: "The reader may wonder if to be a top-flight physicist, one also has to be great with Mathematics. Well, not necessarily! Indeed, more than facility with Mathematics, a profound physical intuition is what marks out an outstanding physicist. Of course, Dirac could have been any type of Mathematician, of the highest level. Feynman, Pauli and Dyson were also formidably gifted in Mathematics. But Einstein, who was bored with Mathematics, had to pick up on the way whatever Mathematics was needed in his theoretical work..." Wow, the great Einstein (the greatest of them all!) was no great shakes with Math - and did not like it much either! Ergo, I too had a chance, if could really hone my 'physical intuition' to the required sharpness. And when, a few weeks later, I had to choose my future career, I confidently declared to Pop: "I am going to study pure Physics!". I remember using the English word 'sublime' somewhere there. Several years passed and despite all efforts (sometimes optimistic, sometimes desperate), my Physics Research petered out; and the love affair with the subject had ended long before a certain eminent (and loud) theoretical physicist made a public declaration which went: "Our Institute has many good students. But there are also a few mediocrities and one or two deficient guys. And finally, of course, there is a certain Nandakumar!" Utterly disillusioned, I switched to hacking software to earn a living. Over the next few years, thanks to a fairly rigorous study of computer programming - and the internet - I discovered Mathematics (yes, I am not saying 'rediscovered' because I never really knew it before!) and noted with considerable surprise that I was actually *liking* it! And I found out C.P.Snow was plain wrong (perhaps I am being uncharitable here, but I even suspect he lied) - Einstein might have been no great Mathematician but he certainly greatly loved Mathematics (and he was definitely not BORED with it!). And Mathematics is a subject that returns love with the deepest fulfillment; and without connecting - viscerally - with this fulfillment, one simply cannot do anything worthwhile with any Mathematical Science, Physics included - and viewing Math as a necessary evil, as I used to, is to put it mildly, bad tactics! My discoveries also had a reassuring element: to relate to Math at gut level, one does not need to be a Math Wiz; even I could do it! Snow and the 'Parishad' books had not only missed this vital point about the quintessential nature of Math but had hopelessly - and unpardonably - obscured it. I want to emphasize that it is simply not necessary to be 'gifted' or even terribly well-trained to make a nontrivial contribution to Mathematics. Indeed, one could say this is one crucial difference between it and Physics: the days when an energetic amateur could hope to do ground-breaking work in Physics are almost certainly over; but with Math, the scene, even now, is: "there (still) are theorems .... which have never been proved and which any fool could have guessed." From personal experience, I am very much in agreement with this quote by G.H.Hardy, although I can't share his snobbery - perhaps Hardy, having been a genius, could afford to be a bit snobbish. Mathematics is one subject where the quality of teaching is vitally important (I can only think of Music as an area where the teacher has a comparably critical role to play) and in our country, Math remains a very poorly taught subject, including at the highest levels. One other serious problem with the way Math is introduced in our system is the element of competition it always and essentially involves. There are some who are naturally sharp and skilful and there are some who are naturally competitive. And I belong to neither category. Moreover, Geometry, an area of Math which I found (quite late in life) I could relate to much more naturally than, say, Analysis, is nowadays much neglected - for example, IIT-JEE, allegedly, the ultimate Desi test of *real* mathematical ability, usually has zero questions on pure geometry. David Hilbert once remarked: "Mathematics is often confused with juggling numbers". One could rephrase it, in the context of modern Indian academia: "Mathematics is almost always confused with juggling equations - at speed!". And computer programming is a very useful means to get to love Math, especially for those who are less than facile with equations. Indeed, programming and geometry were what enabled me to get to the heart of Math - or better, Mathematics entered my heart via programming and geometry. I sign off with a very reassuring and more to the point, true statement (at least a hell of a lot truer than the stuff I got to read in more innocent times) on Mathematics that I heard from one of our leading experts: "It is not that Mathematicians find the subject easy. Trust me, that is just not the case. They don't find the subject easy at all. Indeed, the whole idea is not to do Math with ease or to do it better than everybody else, but to love it and to enjoy doing it!"

Religious Identities And 'Communal Violations'

'Gurusagaram' ('An Infinity of Grace' in English translation) is a novel by O V Vijayan. Let me quote an episode from distant memory.

The protagonist Kunhunni is a journalist covering the Bangladesh Uprising and the aftermath of its successful conclusion (helped by Indian military intervention). While walking the streets of a war-ravaged city in the newly liberated country, a desperately poor woman tries to seduce Kunhunni. "Take me, I am Salma, I promise you...". Kunhunni gives her a tight slap, grabs her by the throat and asks: "No, you are not Salma, tell me your real name!".

"I am Kamala" she stammers. "Then why...?" before he could finish the question, she says: "You are Indian, so you must be Hindu; I thought if I had promised you an opportunity to violate a Muslim woman, that would have been an extra incentive.. get me some food!"

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N S Madhavan is a well-known Malayalam author. His famous short story 'Higuita' is an episode from the life of Geevarghese, a Mallu soccer player turned Christian priest.

Father Geevarghese runs an orphanage in Delhi. Jabbar, a local pimp/hoodlum, has designs on one of his wards, a Christian Tribal girl named Lucy. In the climax of the story, the Father confronts Jabbar in a violent showdown.

A certain old acquaintance of mine once remarked: "Did the villain need to have such an emphatically Muslim name? The place being Delhi, it makes better 'statistical sense' to for him to have a Hindu name like 'Kishan'. At least the name could have been a religion-neutral name like Roshan or Aman!"

Note: Here are some 'corrections' to the above recollections from 'Higuita' from a reader's comment (see below for the full comment): "Fr. Geevarghese is not running an orphanage. He is a parish priest and Lucy, the tribal girl is a parishioner, from Bihar. Jabbar, her tormentor, is a pathan from Bihar. In tribal areas of bihar (Jharkhand) moneylenders are mostly Kabulis".

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The Hindi movie 'Bombay' deals with the Hindu-Muslim riots which rocked Bombay in 1992-3 and their impact on an inter-religious marriage. Bollywood had earlier hardly dared to show Hindu-Muslim marriages; boys and girls of the 'opposite' religions were always brother and sister (let me note here that 'Malluwood', on the other hand has been exploring Hindu-Muslim dynamics and tensions (and marriages too) for several decades; that of course DOES NOT mean that the inter-faith relations in Kerala are more harmonious or enlightened than in the North).

I myself never saw 'Bombay'. But an acquaintance of mine, who saw it in a theatre, made this observation: "Although the movie tries - superficially - to be 'balanced', it seems to actually deepen the communal divide and connect with certain deep, 'tribal' instincts. For example, the *heroine* being a Muslim was strangely enjoyed by many in the audience. There is one scene where the girl runs frantically towards her beloved and her purdah gets caught in a thorny bush; and she throws off the veil and rushes on. The crowd roard in approval seeing her come out of the purdah - they almost seemed to take a certain vicarious pleasure in 'violating' a woman from the 'other' side!"

Note: This acquaintance does have a point. Indeed, conquering women from the 'other' side - and jealously guarding those of one's - is an obsession with Desi religious zealots of all persuasions. And I know several hyper-educated gentlemen who tend to be quite promiscuous with girls from faiths other than theirs and who also turn very protective - and territorial - about those who belong (even if only 'officially') to their own.

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About 'Chandni Bar', a critically successful movie made a few years ago on the life of a bar dancer, there were questions: "Why is the bar dancer a Muslim?", "Why does the gangster who ultimately saves her from her evil (Muslim) 'guardian' and marries her have a Hindu name?" and so forth. I don't think these questions became major public issues; and I also don't think that is any indication our society is becoming any less hung-up about religious identities than it used to be.

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That brings me to 'Slumdog'. The hero of the original story 'Q and A' had a Bollywood-style, pseudo-interfaith name 'Ram-Muhammad-Thomas' but the diector Danny Boyle rechristened him with the Muslim 'Jamal'. And his love-interest has a Hindu name Latika. Although he and his brother Salim witness, as children, their mother being cut down by a frenzied Hindu mob (during the '92 riots), religion and religious identity sit lightly on Jamal throughout the story. The 'darker' - and far more interesting - Salim gradually veers to crime and, even as he builds an impressive list of gangland murders and other 'achievements', rapes Latika and keeps her as his concubine.

The movie does not show Salim's subjection of Latika as an act with clear communal overtones; but subsequent events in the story make things rather ambiguous. Indeed, towards the climax, Salim experiences a change of heart, kills his gangster-boss and sets Latika free (to join her true love, Jamal). Just before he prepares to carry out his fateful decision, Salim dons the white cap and performs Namaaz; and having taken out his evil boss - in a hopelessly unequal battle - he dies with the Muslim declaration of the Almighty's Greatness (with 'Allah' suitably translated to the more secular 'God'). Such scenes, which emphasize a qualitative change in a acharacter with a strong affirmation of his religion (a heroically uplifting interpretation thereof), appear to insert a communal subtext into Salim's characterization and further, by 'hindsight' into his relations with Latika; and I tend to believe that this insertion was a conscious decision on the part of the director.

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Note: 'Mallu' movies with much more explicit across-the-faith 'violations' (and various types of violations, apart from sexual) have been made. A shocker of a movie on the Malabar Rebellion, titled '1921', comes to mind; mercifully, it did not stir up a storm when it hit the screens (quie successfully) in the mid-eighties, no cable channel seems comfortable with the idea of re-telecasting it in our more deeply divided times. One could also note that in Malluwood, showing violations between Hindus and Christians is considered less offensive, irrespective of the 'direction' of the violation; still more 'favored' are violations between Muslims and Christians. For example, in the novie 'Dadasahib', the cop who abuses the Muslim hero as a 'Pakistani agent' is very conveniently shown as a Christian!

One may also remark that the depictions of cross-faith violations could also be masochistic, with the author's own community graphically shown at the 'receiving end'. The most telling example I could quote is a gruesome communal gang-rape described in the award-winning the Malayalam novel 'Kayar'.

In my opinion, Boyle's Firangi-ness seems to have helped in the making of 'Slumdog'- it would have been much harder for a Desi director to have made the 'unbalanced' sort of movie it is.

Update (June 2012): Divisions in Kerala society are exposed in the media with alarming regularity. There are violations and attempted violations (and counter violations and anti-violations) galore taking place. Some of these acts have been given quite interesting and spanking new labels: 'love jihad', 'moral police'... but the conclusion is the same and old one: ours is a deeply fissured and wounded society.