Short fiction: The train

She stood there next to the doorway on the tube, a stylish Gucci bag slung casually over her shoulder, her formal suit & briefcase indicating that she was employed in a high profile corporate job. “Must be an investment banker”, I mused; as she self-assuredly communicated succinct instructions to some underling on her sleek mobile phone. I watched her, fascinated, impressed by her confidence and poise.

As she spoke, she momentarily removed the cooling glasses obscuring her eyes. I was startled to see a visible ugly gash near her eye marring the otherwise flawless face. A purple wound- still capturing the violence with which she was struck-it was obvious that she had been brutally hit (“by an abusive boyfriend or husband?” I thought to myself). “How can a girl, so obviously accomplished and confident, allow herself to be subject to such callous brutality”, I thought. Her eyes wandered briefly in my direction, and she realized that I had noticed it.

Her face colored, as she felt exposed; her humiliation revealed to a total stranger, privy to her worst demons by nothing more than a passing glance. Her expression was a confused mixture of annoyance & defiance; annoyance at my inadvertent violation- as if by just realizing her predicament, I had transgressed some unspoken boundary between strangers; a facade of defiance- by pursing her lips; the show of emotional strength belied by the pain in her eyes.
She melted, as she realized from my expression by own embarrassment. My silent empathy was wordlessly acknowledged by her, a shared experience of an intensely personal nature, amidst the chaos of a noisy train.

I was confused as to how to react. My hand half-outstretched, unsure whether to offer comfort; and confused if that presumptuous act would break the tenuous bond that we had built. Would I embarrass her by indiscreetly acknowledging the intimacy of our brief encounter? My confusion led inexorably to inaction, as I got down at the next station- the deep & ineffable interaction likely to leave a lasting impression despite its ephemeral nature.

The creaking doors shut slowly, our gazes locked with each other, as she evanesced along with the train, her eyes still mirroring her pain & gratitude.

I never saw her again after that day.

Stuck!

Catastrophe strikes!: No tickets are available from Bhutan to India for next 2 weekends! Wll be stuck here indefinitely, wihtout being able to meet family for close to a month.

Depressed mood leads (as always) to Urdu poetry. Here are snippets of this poignant poem by Faiz Ahmed Faiz, soulfully rendered by Abida Parveen (I've included only the first and last verse which best describe my state of mind!)

Nahin nigaah mein manzil to justujoo hi sahi,
Nahin visaal mayassar to arzoo hi sahi.

Translation:
If the destination eludes sight, let the search be;
If union defies attainment, let the longing be.

Dayaar-e-ghayr mein mehram agar nahin koi,
To Faiz zikr-e-watan apne ru-ba-ru hi sahi.

Translation:
In this abode of strangers, if no confidant exists,
Then Faiz! Let the invocation of homeland, with yourself be.

Pattern-recognition, not data-crunching (or why my mother is as accomplished as Kasparov)

Practically everyone thinks their mother is the best cook in the world. Let me assert that all of them are wrong, because my mother is clearly the best!

The distinctive feature of my mother’s cooking is her inventiveness. She can literally concoct new dishes with a dizzying array of ingredients across different cuisines. Succulent Indian vegetables & spices would add just the right amount of tanginess to a continental dish; a mélange of Mexican ingredients would find themselves in the midst of Indian roti-curry. And these disparate ingredients would all somehow come together to make culinary magic!

Truly good cooking then is not so much about knowing a wide array of recipes; it is really about knowing how ingredients work together. It is an art of being able to work with rules or ‘good moves’. This article (http://www.slate.com/id/2219243/pagenum/all) I read recently also talks about the same- master chefs are not storehouses of a zillion recipes, they are artists who can compose something new by creative application of heuristics that they pick up over the course of time. Cooking is hence, a pattern-recognition and not a data-crunching problem.

I remember reading an article about chess players that pointed to a similar thinking process. Grandmasters and professional chess players are expert pattern recognizers, not people with either elephantine memories or faster computational ability.

2-3 observations indicated this: Chess pros were no better than laymen or amateurs in rearranging chess pieces on a board that they were shown, if the pieces were randomly arranged (making it an ‘illegal’ position in chess). This showed that superior memory is not the cause for the difference in chess ability.

Similarly, self-reporting by chess pros showed that they had not evaluated more moves than amateurs before deciding their move. So it wasn’t even faster data crunching that explained the difference.

The true difference was in the pattern recognition- chess pros evaluated less ‘bad’ moves than amateurs. It is almost as if they had developed (or were born with) a filter that left out bad moves, just as amateurs would not evaluate illegal moves.

It is this knowledge of heuristics that distinguishes good chess players- they probably would be thinking stuff like “never sacrifice a pawn after castling if you’ve lost a knight”, “use a rook to check, with a knight threatening the opponent’s queen” and so on, just as a great cook must be thinking “Use cardamom with sautéed vegetables only if either tofu or mushroom is part of the salad” etc.

In fact, this would likely be the case with all art- it is the application of a wide range of ‘rules’ in varied permutations. We probably would not be able to identify all the rules, neither would a true artist be able to articulate them. But subconsciously, they are working with patterns, and therein lies their wizardry

The new feminist agenda: Eat rice, not rotis!

My time in Bhutan has left me with time to blog once again. After a 2 year hiatus (after heroically managing to put up all of 4 posts), I hope to blog regularly this time.

In the tradition of ‘Freakonomics’, my latest musing is a wacky hypothesis on the reason for south Indian women being more socially empowered than those from the north.

Marxist methodology always seeks to explain social behavior and phenomena (the ‘superstructure’) in terms of underlying ownership of economic resources (the ‘base’)

With that thought- here’s the wacky hypothesis: South Indian women are more empowered since the South is (predominantly) rice growing, while the North is largely wheat growing.

The cultivation and harvesting of rice is something that women can (and do) participate in, since it requires deft work to remove the paddy from the fields, unlike wheat, whose harvesting requires heavy labor.

Women are thus part of the wealth-generating, productive employment in the south, which would lead to greater power and say even on social issues.

Secondly, the consumption of rice as compared to wheat also favors greater female empowerment.

Cooking rice has huge economies of scale (in terms of time invested) - cooking for 8-10 people (the typical size of a joint family) does not take much more effort than cooking for 2-3 people. It is possible for a woman to cook the rice and have her meal with the rest of the family

With wheat (as in roti, chapatti etc.) however, the cooking process does not have any economies of scale. Cooking 20 chapattis requires nearly 20 times the effort of cooking a single one. This coupled with the fact that Indians like to have their food hot, means that women have to spend their time slaving away cooking one roti after another for the family, and will end up having their own food only after everyone else is done.

The effect of this on a male child in the house too, is that he sees his mother as subservient to the male members of the family, hence retarding the rate of change & female empowerment

Bhutan itself is largely rice growing (over 60% of the population here grows rice). Unsurprisingly, women in Bhutan are highly empowered, owning most of the land & running most of the businesses. Even socially, they have an equal status with the men.

It will be interesting to see if women are noticeably more empowered in other rice-growing countries in the world (Vietnam, Philippines etc.)

Blink before you think!

We human beings like to think of ourselves as rational beings. It gives us the comforting feeling that there is a method to our madness. Most of our decisions are however based on ‘gut-feel’; the elaborate arguments that we give for them are mostly convenient explanations that we think of after we make up our mind. (To sound intellectual and philosophical, let’s give it the technical name: ex-post facto justification).

I read the book “Blink: The Power of Thinking Without Thinking”, by Malcolm Gladwell recently, where the author takes over 200 pages to establish that spontaneous decisions are often as good as - or even better than - carefully planned and considered ones!

So Man is not ill-served by the ‘trust instinct-to-hell-with-logic’ approach, we can all happily continue making random decisions and pretend that we followed a step-by-step logical approach, this process works perfectly well!

Hmmm, but a thought…is it that since we know that this is the process that we follow ( viz of arbitrarily making a decision and then justifying it) we have just found a convenient explanation to establish that that’s actually ok!
Is it just an ex-post facto justification of… well, ex-post facto justification!

I found this uproariously funny, and this is what probably passes off for humour among philosophers ( can’t you just imagine a bunch of white haired men with no fashion sense rolling on the floor laughing while talking of ‘ex-post facto justifications’ and the ‘ad-hominem’ fallacy!).

Which is the sort of reason why philosophers never get laid!

Orders of rationality?

One of the fascinating problems of Game Theory is the Traveler’s Dilemma, a variant of the classical Prisoner’s Dilemma situation -where rational actions by individuals to maximize individual welfare leads to sub-optimal outcomes for each of them.

The game design is as follows: (Reference: Traveler’s Dilemma by Kaushik Basu, Scientific American:
link: http://www.sciam.com/print_version.cfm?articleID=7750A576-E7F2-99DF-3824E0B1C2540D47)

Lucy and Pete, returning from a remote Pacific island, find that the airline has damaged the identical antiques that each had purchased. An airline manager says that he is happy to compensate them but is handicapped by being clueless about the value of these strange objects. Simply asking the travelers for the price is hopeless, he figures, for they will inflate it.
Instead he devises a more complicated scheme. He asks each of them to write down the price of the antique as any dollar integer between 2 and 100 without conferring together. If both write the same number, he will take that to be the true price, and he will pay each of them that amount. But if they write different numbers, he will assume that the lower one is the actual price and that the person writing the higher number is cheating. In that case, he will pay both of them the lower number along with a bonus and a penalty--the person who wrote the lower number will get $2 more as a reward for honesty and the one who wrote the higher number will get $2 less as a punishment. For instance, if Lucy writes 46 and Pete writes 100, Lucy will get $48 and Pete will get $44.
What numbers will Lucy and Pete write? What number would you write?

The solution to the problem is that each would choose $2 as the value of the antique-hence getting only $2 each! Also, this is a dominant solution (i.e. it is the strategy to be adopted, not just one of the strategies)

Note: For the detailed proof visit the link given above

Now if $2 sounds ludicrously low….you’re right! When the Traveler’s Dilemma game was administered on actual players most players chose $100 or a number close to that rather than $2 though, by the tenets of Game Theory they ought to have chosen to play $2. And by deviating from the rational choice, they were better off!

Other fascinating aspects include how strategies changed with the change in reward/penalty, and on repeated play.

Why would people deviate from expected rational behaviour. Three possible explanations have been offered: irrationality, rational altruism and meta-rationality (Usage:mine).

The first explanation, that players were simply ignorant or unable to deduce the ‘correct’ strategy might be true in some cases but was dismissed as a general explanation since even Game theorists who arrived at the dominant (2,2) solution, chose to play a number close to 100.

The second explanation is based on the premise that in the real world people do not want to ‘cheat’ their partners to make an extra buck-, that some degree of “altruism” and a sense of “fairness” is hardwired in all of us.
As an insight, it is extremely useful, but the implications are simple to factor in, it wil involve just tinkering with the utility function ( a function that maps actual winnings to the ‘utility’ that players assign to them). Right now, the utility function is a simplistic f(x)=x, i.e. if I earn $50 it is ‘worth’ $50 to me, now we will have to design utlity functions which are a function of not just our earnings but possibly that of the other’s earnings ( “altruism”) and/or of the difference between earnings ( “fairness”). Constructing such utility functions by analyzing actual moves by players could be a very interesting empirical research study. However, is this explanation correct? Even if we control for this effect, is it possible that players will still opt to play an ‘unexpected’ strategy.

Which brings me to my favourite explanation- the second one, wherein lies the most fascinating insight (its fascinating for me- I came up with it! ),that of ‘orders of rationality’

‘Orders of’ something, is the level at which it loops back at itself. If that seems complex, think of the Friends episode where Rachel and Phoebe discover that Monica and Chandler are involved, and want to ‘play’ a prank on them. Set 1( Monica and Chandler) have first order knowledge- they know they are involved and have no idea what Phoebe and Rachel ( Set 2) know, whereas Set 2 has second-order knowledge since they know, AND they know that Set 1 doesn’t know that they know. ( Note: This brings out the distinction between not knowing that the other set knows and knowing that the other set definitely doesn’t know; absence of evidence is not evidence of absence).
As the episode goes along, successively the orders of knowledge possessed by each Set increases ( Chandler and Monica find out that Phoebe and Rachel know( which Phoebe and Rachel don’t know!) and decide to play a prank themselves ( in the words of Chandler : “The messers become the messees!!”) and this continues).

In a Game Theory situation, knowing the rules of the game would be first order knowledge, knowing that the other player knows the rules of the game is second order knowledge, knowing that the other person has second order knowledge is third order knowledge ( or more generally- knowing that the other person has nth order knowledge is (n+1)th order knowledge). If this process continues ad infinitum(if you are not Joey, you can conceive of this!), the players are said to have “common knowledge”. Most games ( even the simple ones like the Prisoner’s Dilemma) have a premise of common knowledge. Common knowledge, is hence, an infinite stack of the orders of knowledge.

Can we then conceive even of rational behavior- a basic premise of game theory, and indeed of economics in general, as a stack of decisions rather than as a one-shot one.

To make it more clear, consider this: we human beings have the ability to think about our thinking ( We do it all the time “ I was not thinking straight when I said that”; “ When I think about incidents, I find I index them by date”; “ I think about sequences more easily than I do of individual entities” etc). This thinking about thinking (or meta-thinking to put it more elegantly) is very interesting- we can ‘step-out’ of a mode to look at our own thought processes at a higher level of abstraction. This leads us to the next insight, that, similarly, we could also be deciding sequentially. (I can meta-think to about 4 levels, after that my head starts to hurt!).

So does the solution to the Traveler’s Dilemma puzzle lie in the insight that we can rationally decide to act rationally/irrationally! (To put it more vividly, to accurately reflect the sequential process- can we META-rationally decide to act rationally/irrationally). This is consistent with what players said that they knew that rationally they ought to have played 2 but they chose to ignore rationality in making the choice ( citation: Kaushik Basu).

This has far more profound implications for the way we study Game Theory. Unlike the previous explanation, which also challenges a basic premise of Game Theory ( i.e. of selfish rationality) but can easily be made endogenous to current literature merely by changing the functional specification of utility, this would radically alter the way we approach the problem solving in the abstract, and would require an entire supporting theory ( as opposed to mere empirical work) which discusses the orders of rationality and how at meta-rational levels, choices of rationality and irrationality are made.

Truth and provability

Like most people of my generation- my sensibility has been shaped by science more than anything else. I am using ‘science’ in the broadest sense to describe a systematic schema for thinking, which starts of with a small set of axioms (or self evident truths) and by a logical evaluation of data/information posits and proves hypothesis, which can then have predictive power, by mean of inductive inference.

Provability is hence central to the scientific approach- in fact philosophically that marked the deviation of modern science from religion

(In the pre-industrial revolution period ‘faith’ was as valid as ‘reason’ for advancing a theory. Science was accorded primacy (after a long and fierce struggle) only when its explanatory power clearly oustripped that of religion)

It is thus disconcerting if in the province of science, there exist truths that are not provable.Such truths exist- in that most impregnable of fortresses – mathematics! In fact the discovery of the ‘incompleteness’ of mathematics can be extended, by the same reasoning, to show that any formal system is inherently incomplete ( since all formal systems have mathematical analogues).

This was proposed (and proved dare I say!) in a paper titled On Formally Undecidable Propositions in Principia Mathematica and Related Systems I by the Austrian mathematician Kurt Godel in 1931

The proof is vast and rather abstruse- it took a whole book- Godel, Escher, Bach by Douglas Hofstadter for me to grasp it. But what is more fascinating than the proof, or even the insight, are the implications.

Hofstadter himself brilliantly builds on Godel’s Incompleteness theorem to build the best explanation I have read on the classic question of metaphysics- namely, the mind-body problem.

At a more general level the philosophical implications are mind-boggling. It demonstrates that there exist definite truths, that are definitely not provable! Truth and provability, seen as concomitant if not identical, have effectively been delinked!

The reason this is so disconcerting is that we have always had a sense that with science we were inexorably moving towards a situation when everything could be explained and proved ( possibly in infinite time; the relevant fact is not whether it was practically achievable, but that theoretically we were moving towards that).

What the incompleteness theorem demonstrates is that we are consigned to have atleast some knowledge without demonstrable basis. That is, provability is a weaker concept than truth, the known truths will never be circumscribed by provable hypothesis.

But wait a second- doesn’t that sound suspiciously similar to religion- that something is true without it being proved!

That is actually a specious argument; formal systems have not been undermined to the extent that in terms of validity it is on par with religion. It is only that we now have a more modest expectation of the explanatory power of the methodology of logic, which was hitherto over-estimated.

But in a fundamental sense the certainty of formalism has been challenged- we will always know things that we cannot prove- that is inescapable. In the abstract, at least experientially that does parallel a religious experience- where you know something is true but cannot prove it.

For someone who is scientifically inclined, but has turned from atheism to being a believer only recently, its comforting to know that I am not being inconsistent vis a vis my scientific temper, when I know something without being able to prove it!

Hofstadter's Law in action!

I have finally started blogging...a mere two years since I came up with the plan!
Planning is by far my favourite activity. It makes me feel like I am doing something important which will revolutionise my life....while the only concrete thing that I achieve is kill time till I have to come up with the next plan!

S.T. Coleridge put it eloquently ( while referring to Shakespeare's Hamlet) whom he said was mistakenly dubbed 'indecisive' by most critics. The more appropriate description, he wrote, was that Hamlet would

" Continually resolve to do, yet do nothing but resolve" !

Captures the way I spend my time precisely!

The title of the post is an allusion to the droll recursive law proposed by Douglas Hofstadter-

"It always takes longer than you expect, even when you take into account Hofstadter's law" !- in the context of starting this blog, I totally understand what he was talking about!