The Lone Footballer

Saturday, August 13, 2011

math in madness

The cult of Andaz Apna Apna continues to impress and I have done my bit towards its continuing popularity. So I was watching it for the umpteenth time yesterday when I discovered a hidden mathematical message in the movie. It was almost like figuring out the mathematical references in Alice in wonderland.

The scene I am referring to is where Amar while recounting the fictitious Mohan Bagan football match shuffles the poisoned glass of juice (sharbat e jannat :D) with the non-poisoned glasses and gives all of them back to everyone. As it happens, in the end either Bhalla or Robert have the poisoned juice while the others evidently having drunk the non poisoned ones. At this point Bhalla swaps his drink with Robert.

Now this is a variant of the Monty Hall problem. With a twist. Bhalla’s decision to swap the glass turned out to be wrong, reinforcing my opinion.

Friday, August 20, 2010

Enough with the diaries already (go stream of consciousness way)

Have’nt written in a long time, not like I haven’t got any ideas to put down on paper. I guess it’s visiting the whole perishibility of ideas concept again. Gotta make the most of a single idea. Makes me wonder, when is the right time to pick a unified philosophy of life (assuming of course the need to have one). This is not unlike the question one would face in a hypothetical social setup where you only get to choose your life partner once in a lifetime. It’s another matter, the situation described is not so hypothetical either in practical life or in the realm of a purely imaginary construct (‘life partner once in a lifetime’, get it?).

Have’nt written in a long time, not like I haven’t got any ideas to put down on paper. I guess it’s revisiting the whole perishibility of ideas concept again. Like it’s déjà vu all over again. Like you build redundancies and then one fine day get confused which version is which and in a rage delete everything. Memory loss is an over-psyched fear. I on the other hand almost find it a romantic idea. A clean slate, tabula rasa, no emotional baggage, no worrying about the baggage retrieval system they’ve got at Heathrow.

PS: Cultural references are italicized.
PPS: Discovered yesterday, I share the habit of ending a ‘letter’ with a post script with the great Marx (of the Groucho variety).

Thursday, May 27, 2010

Tales from Gzbd - Vol III

There was a time during early nineties when I used to watch all international cricket matches, including those of India. I used to admire the West Indies team the most. I was familiar with the bowling style of all the bowlers and could mimic them all including the likes of Paul Adams. You see, it was the nineties and I don’t know about others but I found cricket interesting mostly because of bowlers #.

Hero cup changed it all; the pure love for the game was tinged by nationalism. Not only would I root for the Indian team fanatically but gradually stopped watching neutral matches. This was not all, because the prime motive for watching cricket was to see India win the match, I would promptly switch off the TV as soon as I was reasonably convinced the match was beyond India (the strategy worked perfectly well for me except for the India -Pakistan quarter finals in 96). This for all practical purposes meant switching off the TV whenever Tendulkar got out.

The naive sense of patriotism was shattered in 2000 when Azharuddin and Co. were implicated in the match fixing scandal and I more or less stopped taking any interest in the sport. A year later I moved out of home and the next 6 years were spent without much exposure to the box.

IPL revived my interest to a great extent. I guess part of the reason was the flexibility it afforded, I could cheer Rajasthan (home team)/Delhi (home team)/ Bangalore (home team)/ Mumbai (Tendulkar). Modigate and the apparent match fixing in the 2010 season final have tainted the game but I don’t mind. I don’t find match fixing repulsive; in fact I have already accepted it as an integral part of the game – as long as the matches are close and hard fought. So much so that I secretly wish there would two different groups of match fixers in every match, bribing their respective sides. That would be a real test of losership, not to mention acting skills as well.

# And Tendulkar. I find it annoying that no one calls him Tendulkar anymore.

Some more on cricket and childhood memories.

Although I wasn’t a big fan of Prabhakar and in fact hated his bowling action (I still maintain he used to chuck) I secretly thanked him every time I used his example to refute the alleged cricket rule that one can’t open the batting as well as bowling in a match.

In ‘The Adventure of the illustrious client’, one of the characters says “….and that the opinion of all of the world is no more to me than the twitter of those birds outside….” What a remarkable anachronic coincidence, describing the opinion of the world in terms of tweets!

Did you ever notice how significantly different a choreographed dance you watch in a movie appears from the video of the exact same dance at the time of shooting. They look quite different; let me assure you that in case you haven’t had the opportunity of watching one of those movie previews where the director mostly only discusses song choreography and the exotic locations where the songs were shot.

Nothing scandalous there, the problem really is as follows. Remember how the enlightened (is that the right description?) Neo all of a sudden could ‘see’ the matrix in its real form – rows and rows of binary digits, that’s exactly how I feel now. Every time I see a touched up dance video in a movie I ‘see’ the crude live shooting of the dance on the sets. Stupid excess knowledge.

When I write my first novel#, I will either keep the last few pages of the book blank or keep a short story at the end of the novel. I wouldn’t like my readers to see the climax coming.

As an aside, there is no sadistic pleasure like the pleasure in reading out aloud the climax of novels others are reading. I like to believe that it’s this sinister temptation and not incompetence which is the reason why Indian reviewers do little more than spew out spoilers.

# No, it will not be a campus or corporate life novel. I guess it is the facebook syndrome – people honestly believe their life is interesting and others will be interested to know about the finer details.

Who would have ever guessed that the corporate department invented to improve employee productivity would evolve into the least productive of all departments? I wonder if there is any research which studies the productivity of hr department. More specifically if someone has enquired whether it’s the right aptitude for the profession which results in a certain personality types going for this career or is it the work and the work ethos of the hr department which moulds the personality of those who choose this career.

The not so recent SachinisGod trending topic set me thinking - I can not revere anyone, let alone worship. If Tendulkar (the doer type) doesn’t play the right shot it’s incompetence and if he does...…well that was the way he should have played it, so what’s the big deal.

Applies as much to the thinker types. If they are wrong (in my assessment, of course) they are idiots and if they say something new and true…well how difficult was that to figure out? In case you are wondering - what if they say something which I don’t understand? Well I ignore them; if they can’t express it in a manner intelligible to me they are not lucid and therefore must be wrong.

I am not a secretive person, in fact I am quite the opposite. However, I do treasure the luxury of dialoguing with myself (not aloud), sometimes even when I am in the company of others. I know its not considered civil, but does it give others the right to ask outrageously personal questions like ‘what are you thinking?’ or insinuate telepathic abilities by uttering axiomatic statements – ‘I know you are thinking about something’.

So last week turned out to be the detective week, reread ‘The casebook of Sherlock Holmes’ and Poe’s August e Dupin stories and started watching ‘Monk’. That’s when the series of coincidences (just coincidences, ‘there are no small coincidences and big coincidences’ ;)) started.

After I watched Monk for the first time, the next two movies I saw were ‘Searching for Bobby Fischer’ and ‘A life less ordinary’ respectively and both of them have cameo appearances by Tony Shalhoub (Guy who plays Monk’s). A few days later I watch ‘The Mom and Pop Store’ (Seinfeld Season 6) where the whole episode revolves around George buying a used car previously owned by Jon Voight (except that its not the actor Jon Voight but some dentist John Voight) and guess what, the next movie I watch is ‘Heat’ starring Jon Voight.

So keeping in mind an extreme version of Rava’s maxim – there are no coincidences, this is my interpretation of the events – the frequency of a person observing an obscure thing (obscurely placed in the later encounters) is inversely proportional to the exponent of time elapsed after the first encounter with the said thing.

Default food preparations

Milk – Hot

Roti – Buttered

Cooked vegetables – With gravy

Sandwich - Has lettuce and onions

Lime water – Sweet

Gol gappe - With sweet chatni

I hate all these preparations. And that’s all I have to say about that.

Thursday, April 15, 2010

Non native mathematician’s problem statements

The first one is inspired from observations; the second is a bit more hypothetical. Needless to add, I think the second one is more difficult to solve and has more profound implications. I should be able to derive the results myself (at least the first one) having read statistics and probability distributions. However, I haven’t quite used that knowledge in more than 3 years now. Hence the title.

Das Bus problem

There is a route along which buses ply. There is a pickup and a drop point as well as a bus stop just around a kilometer from the pickup point. The fraction of passengers boarding from the bus stop is smaller. The commuters arrive at the bus stop individually or in groups, in any case the drivers don’t know where they come from or what their traveling habits are. The frequency of buses plying on the route is uncertain, also there is a likelihood of the coming bus at the bus stop to be fully occupied as it may have already picked up enough commuters from the pickup point. The passengers are not allowed to board fully occupied buses. Commuters want to minimize the wait time at the bus stop, there being no other quality criterion.

Some of the bus drivers decide one fine day to start plying between the middle of the route bus stop and the drop point. A week down the line they are all flustered. They face a peculiar problem. Since there are no bus stops on their route they have to make sure that they pick all their passengers from the bus stop. The commuters however, are not willing to wait for the bus to be fully occupied. They find it better to wait for the incoming bus and hop into it. But some of the bus drivers are of the opinion that if the passengers decide to board the parked bus the wait time will in fact be shorter – just that the commuters don’t want to take that chance and therefore end up waiting longer for an incoming bus with vacant seats.

Who is right? Who is wrong? And what is the outlook for the bus drivers? #

Strings of failure

A category of events (Let’s call these financial defaults by companies) is preceded by one or more of ‘n’ separate and identifiable events (Let’s call these as the causes). For the sake of simplicity, assume that all the causes are endogenous. Therefore the characteristics of each of the causes can be expressed as a set of performance indicators. Further assume that the performance indicators can be expressed in the form of cardinal numbers. Further, threshold values can be assigned to the performance indicators such that a fall in their value below the threshold value is occurrence of the cause.

The hypothesis is that there are strings of causes in every financial default and there is a certain degree of chronological order in the strings.

# If the first thing that comes to your mind is “please specify the data” you have missed the point altogether.

Sunday, March 21, 2010

Economic Myopia

One of the first articles I read as part of the Marketing Management course curriculum at IIMB was ‘Marketing Myopia’ an HBS article written in 1960 by Theodore Levitt. An influential article in its time it suitably impressed the novice me as well. The theme of the article is that companies should look beyond the obvious (their existing narrowly defined markets) and look for more opportunities by looking ahead in future and defining the markets as broadly as possible.

Being a student of Austrian Economics I was amused that the idea of looking beyond the obvious while readily accepted by the Marketing profession was shunned by the entire economist community (aren’t we all Keynesians) when in fact the idea was conceived much earlier in the field of economics (,_and_That_Which_Is_Not_Seen)

Almost all the post mortem analyses of boom and bust cycles are focused on the asset class where the bubble burst, despite the fact that in each boom and burst situation it was a different asset class which tanked. There is no problem with such analysis, if and only if it is seen as a starting point. But without exception most of the economic commentators stop short at understanding the reasons why the particular asset class suffered (CDOs/Tech Stocks/Emerging Market Bonds/Oil etc) or even worse why a particular financial institution sank #.

Such concretization is not very useful as there are thousands of asset classes (and new financial instruments keep emerging) and if the economists keep their understanding limited to what went wrong with a particular asset class at a particular point of time in history the realisation that had it not been mortgages, the cheap money would have found its way to create some other asset bubble would never dawn upon them.

What is the solution to this economic myopia? The traditional and boring one is to think in terms of abstracts, which I think is a bit difficult because “theory is not really tangible and concrete”. I am tempted to add how much I hate such proud platitudes as “economics is all gas; you need to look at the real data” and why concretized thinking is the core problem in economics, but I will not.

A more colorful solution and this comes from a person who himself doesn’t believe much in economic theory but despite his ignorance of economic theory he is still to an extent immune to economic myopia because of his habit of visualizing ‘alternative histories’, the habit of not looking at a ‘realized outcome’ without reference to the ‘unrealized outcomes’.

But again, colorful as it may seem his is not the best way to prevent economic myopia. Precisely because there is no enquiry into the underlying factors which lead to the one ‘realised outcome’, the fact that he doesn’t proceed any further, choosing rather to label the ‘generator’ unfathomable. I guess the reason is his nihilistic approach to acquisition of new knowledge, his popperian view of the world.

# I however do concede that such specific enquiries into the causes of busts have a certain value, the same value that reading history has. Barnett Hart’s thesis on the failure of CDOs is the most coherent historical account of the 2007 depression that I have come across so far -

Sunday, March 07, 2010

The Elevator Thumb Rule

I have been witness to an interesting social experiment for the last 6 months. It has made me realize that we are living in a society full of idiots who are surviving only because the world around us doesn't require them to think for survival.

The setting:
I stay in a multi-storey building, so you have a lift in it. Now as usual there are two buttons – one pointing up or inverted V shaped (I’ll call it UP) and the other below it pointing downwards or V shaped (I’ll call it DOWN). There is no written instruction about which one to press for going up or down. The location of the lift can be seen in the display.

For a person operating the lift for the first time there are two possible ways of going up from the ground floor – you either press UP - ‘I want to go up’ or you press DOWN - ‘I am calling the lift down’.

The elevator is indeed programmed to operate as per the first rule and not the second. However, because the lift can not read your mind it will open up in front of you no matter which button you press.

So even if a person on 5th floor presses the UP button when he wants to go to ground floor the lift will nevertheless come to 5th floor if the lift is at a lower floor and is stationary or going up. It may then continue to move upwards if it was already moving in that direction (Even if the person on the 5th floor instructs it to go down to the ground floor, quite logically) or wait for the 5th floor person’s instructions.

The observed data:
I have made close to 500 observations so far of more than 100 different people operating the lift and in more than 80% of the cases the buttons were pressed incorrectly. That is:
  1. When on the ground floor, people always press the DOWN button to go up and
  2. When on their respective floors, people always press the UP button to go to the ground floor (when the lift is on a floor below them)
The data as provided is completely objective with if any only a minor error of estimation.

My reactions:
At first I was plain disgusted at this stupid behavior. But later I realized that probably they are operating the lift for the first time and so haven’t yet figured out the right way to do it. But even after a few months the behavior wasn’t changed a bit, if only the incorrect behavior became more prevalent over time. Now I was perplexed – How can all the people be fooled all the time when there is no one to fool them?

From the little knowledge I have gained* about the use of heuristics by acting men, I think people form thumb rules and work according to those till the established norms are challenged by an ‘adverse event’. An equivalent of the ‘adverse event’ in a purely logical process would be – a contradiction. However, as opposed to a contradiction which may be trivial yet by its very existence sufficient to falsify a hypothesis, the ‘adverse event’# has to be significant enough to force a rethinking of the thumb rule.

So I kept condoning these little illogical acts witnessed everyday assuming that even if people operated the lift incorrectly it did not affect their lives in a significant manner. That bounded rationality saves them from overusing their brains. That their brains are hardwired to tolerate minor inconsistencies in the otherwise extremely regular workings of a lift (an artificial thing) as their forefathers had no regularity of events in their lives (except for the dawn and dusk and seasonality in climate).

But then one fine morning as I entered the lift to go down from the 9th floor to the ground floor the other occupants of the lift, a 5 yearish boy and his mother looked quite agitated. The mother addressing me complains, “As it is we are getting late, why then did the lift have to come up instead of going down!” And then it hit me, if this wasn’t an adverse event what would be? The same evening while going up from the ground floor the lift stopped on one of the floors and after the gentleman entered in, the elevator’s upward journey visibly shook him. Not to mention the realization did not dawn on him.

So after all, the ‘adverse event’ did not result in a change of heuristic. Why? After much thought I realized that it is possibly because people are not aware they are using a heuristic. The analogy in the logical/scientific process would be this – a hypothesis can only be tested using evidence if the hypothesis is identified as contingent – contingent on its validity (or invalidity/falsification). If the assumption is not recognized as an assumption and is taken to be axiomatic there is no way for the reasoning to be tested in light of a contradiction.

So what is happening here in this bizarre building is people have formed an extremely sticky heuristic which no amount of confusing behavior by the lift is able to change. Because people are not conscious of their reliance on heuristics.

Nice, neat and clean conclusion. But wait a second! What explains the high incidence of use of the incorrect heuristic?

If people are relying on heuristics which have no basis, shouldn't there be an equal incidence of correct and incorrect behavior? Why this bizarre tilt towards incorrect behavior? I had to grapple with this paradox for a few days till the eureka moment** came to me a yesterday. The high incidence is linked to the gradual increase in prevalence of incorrect behavior mentioned earlier - People were pressing the wrong button simply because others were too !! The heuristic has remained stikcy because everyone is following it at the same time notwithstanding the sporadic occourances of 'adverse events'.

So people are in fact aware of the use of heuristic ('Calling the lift'), they are either unable or unwilling to recognize the 'adverse events' as contradictions - I don't know which one!

*I have no formal knowledge of heuristics; all of it is just refined first hand observation.
# I have another term for the ‘adverse event’ – the ‘tongue burning experience’, I think this term is easier to visualize and connect.
** Personally I prefer to call moments of such revelation 'aqaba moments'. Remember the scene in Lawrence of Arabia when T.E. Lawrence spends the entire night cogitating till early morning when the crossing of Nefud desert occors to him.

Saturday, January 30, 2010

Three Mood Cycles

A little known fact about myself revealed to me very recently is that I am a man of dual emotions. Two emotions that’s it. No fewer no more, contrary to the commonly held notion among friends that I know only one emotion – laughter!

The two emotions are extreme happiness and mild sadness and as a corollary there are three moods one can find me in - extremely happy, mildly sad (it doesn’t show) and busy. Yes, there is no typo in the last sentence the third mood is busy. The mood cycle again flows pretty er cyclically. The mildly sad mood lingers for some time before I make myself busy and then once I am exhausted the extreme happiness mood takes over.

The more I think about it, the three mood framework seems applicable in increasingly more kinds of situations. Or may be it is similar to the tendency to detect symptoms when one suspects to be suffering from a disease, a force fitting tendency that is. Assuming that there is no force fitting bias at play, another interesting observation comes out – the three mood cycle has meta-versions as well.

It’s the existence of meta-versions which probably establishes the validity of three mood cycle hypothesis, because they are observed over a longer time period and therefore are free of local stochasticity#

Since the above mentioned revelation, I have tried reviewing my life events to understand this unique psychological hardwiring. With little success. The main reason being as far back I can remember (all the way back to when I was three years old) is that the duality of emotions has been pretty much there. No evolution/life changing event whatsoever! Perhaps the following additional facts hold the key:

  1. Both the mildly sad and busy states are marked by extreme inertia*
  2. Mildly sad state is characterized by outward calmness but a high degree of internal unrest
  3. All Ideation happens during the early phase of busy mood
  4. Busy mood begins on its own and is not assisted by any inspiration acquired in the mildly sad period
  5. The transition from extremely happy to mildly sad mood is quite sudden and yet the change is almost unnoticeable
  6. The intensity and more importantly the time period of busy stage determines the time duration of mildly sad period. Much like the excesses of the Government during boom time determining the intensity and duration of recession.

Every once in a while one of my friends would ping me to inform he/she read some of my blogs (for the first time) and that he/she thinks I am different person when I write, especially only the serious kinds. The humorous ones are fine with them they concede. The three mood cycles therefore may shock those who know me well. To be honest I was also shocked a bit. But I think it’s a good discovery, it’s interesting to know there are so many things I don’t know myself about!

#One such meta cycle fitting neatly with the hypothesis has been observed in the wake up moods for the last couple of years with the second cycle starting some time in January last year. The mildly sad mood has continued for more than a year now and it seems to be making way for the busy mood, hope this state continues for a long time – in the previous cycle it lasted for only 4 months or so.

*For those who are puzzled – a body is in a state of inertia if it’s resting or moving at a constant speed