Criticisms of a Fractured Republic

I came across a question on Quora  asking rather obtusely – “India: What are some things you hate about India?” and I thought about it long and hard for about 15 minutes and wrote this as an answer there. I repost the answer here (because I find Quora extremely unwieldy and outdated.)

I think hate is a strong word. The question should rather be phrased as things you dislike about India. Either way here is my answer. Please note that the points are not in any order of hierarchy, I think each of these points is extremely important.

1. A heavily patriarchal society
India is one of the most patriarchal societies on the planet. A large contribution to this comes from the primary dominance that this concept holds in the various religions that form core tenets of this country. What are the consequences of the heavily patriarchal mindset?

  • Overall negative mindset towards the female gender : A large portion of the population considers the female gender to be a matter of property. Before she is a woman, she is a daughter, a wife, a sister, a granddaughter. She must be protected to protect the sanctity of the family image primarily, not because as a woman and as a human being she deserves basic human rights like the other sex.
  • Marriage as a legal sale of the female: A shockingly large number of woman are brought up in an environment where they are made to believe that their ultimate goal in life is to get married. I have been in the company of several members of the opposite sex who have been pursuing bachelor degrees for the sole purpose of becoming marriageable in today’s society. And this is a predominantly middle – upper middle class environment. The situation in the vast majority of India is much worse of. Women are considered burden, to be married off as early as possible, since they are not expected to earn money nor are they often allowed to. The Country’s secular law itself has a lower age limit of 18 for the woman to get married compared to the male’s, which stands at 21. Why this disparity? I do not even bring into question the marriage acts via the religious laws which through loop holes can even legalize child marriage.
  • Dowry: As a continuation of the previous sub-point, the female is considered a liability since birth, a lower form of some kind, which means that marriage does not just act as a sale of the woman, the proprietors of the marriage (which is generally arranged) will charge for taking in this liability. Inhuman as this sounds, it is highly rampant in urban as well as rural environments. Defenders of the concept will talk about its original purpose which has been perverted, while I dispute that very argument, it is by itself irrelevant to the fact that dowry is one of the most widespread and perverse evils propagated in this country in the name of tradition.
  • Female Infanticide: India has a pathetic statistic when it comes to female infanticide, a few statistics are provided here. India: What are five things girls hate about being in India?
  • Moral Policing of Girls: The moral brigade is always on the roll, looking for the opportunities to restrict freedoms of the females with arguments that will make the dead turn within their graves. From the assault of innocent girls at nightclubs for doing “morally obscene” things  to making rules that are obstructive in nature. As mentioned in this post. India: What are five things girls hate about being in India?.
  • Eveteasing, Apathy of other females: Eveteasing is extremely rampant, a by product of this patriarchal society. It is acceptable to stare or intrude the privacy of a girl in public. Another troubling issue is the apathy of many girls themselves. I have seen girls advising another girl not to enter a temple because she was on her periods, or to keep her mouth shut about such a “small thing” as being eveteased. More than anything, I feel this trained self axing of ones own feet is amongst the biggest problems in Indian society today.

2. A society divided on Caste.
India constantly bears the brunt of a highly regressive caste system, a discriminatory system that segregates on the basis of birth. While mistakenly considered to be endemic to followers of Hinduism, modern sociological research has repeatedly shown that caste permeates across religions, and created subcastes in different religions. It is also common for denial of caste prejudice among the educated middle classes, which for one directly shows a manifestation of caste based bias.

  • For a decent sensitization to caste based prejudices one can watch

    India Untouched a documentary on caste discrimination. Another great documentary movie is Jai Bheem Comrade by acclaimed documentary makerAnand Patwardhan on the same topic. Ambedkar makes for some good reading on historical caste based oppression but is not quite up with the times of today’s globalized India.

  • Intercaste marriages are as taboo as ever. Often friend circles of most people happens to be of similar caste (this is less prevalent in urban settings where immigration can make this nigh impossible).
  • Jobs are segregated on the basis of caste, as pointed out in the Mandal Committee report and consequently also briefly in the Sachar committee report, that traditionally “brahminical” jobs (that is office bearing jobs) have a statistically abysmal percentage of oppressed minorities of caste and religion. In many places the “dirty jobs” like cleaning drainage canals, collecting garbage, cleaning horrifyingly dirty places are always ending up predominantly belonging to lower caste people with the percentages polarisingly shifted in the reverse for better jobs.
  • Anti Reservation Rhetoric : This is one of the perfect examples of a lack of understanding of not just the basic concepts of what underlies merit, (I provide an introduction here What exactly is Merit?) and a denial of millenia of caste based oppression upon which they themselves rose to the convenient privilege from where they can access Quora unlike over 90% of the country’s population.
  • Political Victim Complex of Fairly affluent lower castes : The sad part is that the representation of the lower castes in the political sphere is often by people from this small minority of professional victims who make pathetic points in defense of reservation without providing actual arguments for the argument of affirmative action, rather engaging in senseless rhetoric about sentiments of the people and similar rhetoric.

3. Intermixing of Politics and Religion and Law
The Indian model of secularism is a very unusual model in the sense that the religion is not separate from politics and law, instead embraced by it. Instead of keeping church and state separate, we have church rules the state, but which church rules you depends on which church you were born under or which church you convert to. I have philosophical problems with said premise, in that the law does not take equal standing for all in such a case, since religions can pass regressive laws which do not require the consent of the people following those laws but rather the people in positions of power. Also such laws are not equal for all “religions”, and further questions of how does one differentiate between a religion and a cult also arise. The entrenchment of religion in political process is also no secret, vote banks are often formed on the basis of religion. The directive principle of the constitution to form a Uniform Civil Court is all but forgotten.

4. Abysmal lack of basic Physical Infrastructure
India for all it’s high growth rate has had abysmal improvement in basic physical infrastructural facilities and accessibility for the same to a large mass of the people. As has rightly been termed by Amartya Sen in his latest book, India is looking more and more like Islands of California entrenched in the endemic drought of the Sub-Saharan countries. In  terms of all major social indicators other than the Gross Domestic Product, India lags behind even its South Asian neighbors by a long way, (infact it is second worse better only to Pakistan).

  • Abysmal primary education system that contributes a massive dropout percentage.
  • A Public distribution system in a state of despair.
  • Lack of basic health care facilities.
  • Lack of connectivity to border states.
  • Absence of a stable electricity supply to approximately half of the country.
  • Bad state of water accessibility – a majority of the country depends on groundwater for access to a basic resource.

5. Superstition
India is called the country of the spiritual plane. To each his own I guess, but if the name of movies need an extra K or released on a date whose digits add up to 3, for people not starting businesses or surrendering their lives to the concepts of vaastu and astrology, something is seriously wrong. India currently officially allows for undergraduate and graduate courses in Astrology (as allowed by the University Grants Commission). A nice article by Jayant Narlikar on Astrology in India An Indian Test of Indian AstrologyIndia also has a blasphemy law that is so badly framed it is easily prone to misuse as has happened in the recent case with Sanal Edamaruku who was slammed with a blasphemy case for debunking a superstitious myth. 

When people in positions of power, and respect in the spheres of politics, entertainment, education and perhaps almost every other sphere engage in such a cognitive dissonance they lay the platform for a superstitious state. This spirit is directly contrary to the constitutions directive for us in Article 51A(h) in the constitution to develop the scientific temper, humanism and spirit of inquiry and reform.

6. Bureaucratic Roadblocks and Repeated Circlejerks
It takes an amazing number of permits in India to start up the smallest of businesses. I feel India has a large problem of too many checkpoints. The problem of India is not the corruption as is always harped about in the media. Its the number of avenues provided for corruption. Each new person one goes to to get another paper signed is another probably money greaser, reduce the number of roadblocks and you reduce the inefficiency as well as avenue for corruption in one stroke. Too many cooks spoil the broth goes the saying, India has the case of too many cooks trying to make the spoilt broth palatable. It is not working.

7. Apathetic Media 
The Indian media is extremely apathetic to the voices of the poor and under privileged. What product they produce is (perhaps due to the very nature of their flawed business model) simply to whet the appetite of the Indian Middle Class and upper Middle Class populace. There is almost next to no coverage of events affecting the poor, and village dwelling majority of the country’s population. Investigative journalism is practically non existent, with most leaks coming either from the government or enemies of the political party in power themselves. News is openly paid for (in the TOI marketing style) and quality journalism is practically non existent.

8. Alienation of Tribals and demonisation of the poor.

This is the so called Tribal belt in India.

This is an image of the power plants in India.

As can be seen in the image, there is a high density of power plants in this tribal region. Large tracts of tribal lands have been taken from them because of the non implementation of the 9th schedule of the constitution, to make way for Coal mining, power plants and other such land grabbing initiatives that only benefit the urban populations in the cities at the cost of the only available resource to a vast majority of tribal societies in this country – Land. The tribals, for whom there has been little effort to integrate into the mainstream political scenario, whose only protection stated in the constitution in the form of the 9th schedule has not been correctly enacted upon, and who are effectively out of the caste system and the affirmative action process to raise their consciousness in the society, have consequently been demonized and carefully put out of the public eye.

Combined with this the middle class and especially rich peoples’ prejudices on the inability of the poor to vote cleverly, while only voting on the basis of caste, religion or gender (often putting the blame on their illiteracy), while engaging in exactly the same kind of biases despite being “educated” puts into question this very notion of blaming the poor.

9. Blaming the Government in power for everything.
People in this country love to play the blame game especially without introspecting at all. They are also prone to mass influencing, especially by the television media which sadly is the trend setter in the nation. In a sense the media has a symbiotic relationship with its viewers, in feeding what the viewers find “entertaining”. Among these past times of the people is blaming the government for everything.

There is regular blame on the government in power regarding inflation, but little effort on the part of the criticizer to find out what is causing this inflation. Enormous amounts of import of nonsensical items like jewelry in the form of gold and high demand of energy resources like Coal in a GDP obsessed country which applauds the entry of large scale MNCs to come and practically legally usurp our dwindling coal resources are amongst the reasons for a high inflationary rate.

(This answer is an answer in progress.)

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What exactly is Merit?

With the advent (and passing) of the recent examination season and the accompanying results, it comes as no surprise that social networking sites are abuzz with the regular outcries of “injustice meted out” on the regular citizens who do not get the benefits of affirmative action. Regardless of what my own personal views might be on the matter, I think the first and most important thing to understand is what the word merit means? Why do we take it for face value in society? What are the issues that a system of merit aim to tackle and does it succeed in achieving them? What is its scope?

What is merit?

The dictionary defines merit to be

merit (plural merits)

  1. Something deserving positive recognition.
    His reward for his merit was a check for $50.
  2. Something worthy of a high rating.
  3. A claim to commendation or reward.
  4. The quality of deserving reward.

Merit, to put it reasonably, is the idea that there exists some particular class of ideas/objects/people/occupations that are more valuable than others of the same category of comparison. The concept of merit thus creates a hierarchical differentiation in society by setting an agenda of what is desirable, towards which the societal inertia gravitates.

What is a meritocratic system?

A meritocratic system (or a meritocracy) is a society which values the concept of merit and that influential and/or powerful positions of interest for the society should be vested into the hands of members who are deemed meritorious in the sense described above.  Meritocracies tend to exalt the philosophy of merit as the optimal method to create a workforce of the most efficient members.

How does one define what characteristics are meritorious?

Probably the biggest sources of confusion regarding this issue, is the question of what categorizes as meritorious and what does not? Merit in someways has its roots in the human desire to endorse exceptionalism. However, modern definitions of what constitutes merit can be quite obfuscating and in many cases myopic. Traditionally today, the concept of merit is conceptualized in terms of testing “competency” and ability, often through standardized tests such as an IQ test, standard equivalency tests, entrance or eligibility tests.

Why such a definition of merit?

In today’s industrial age societies, the primary aim of a majority of the citizenry (due to various socio-economic conditions)  is to obtain a well earning/satisfactory job (the two are often equivocated). Considering how we live in a global world dominated by money,that the aim of obtaining money becomes a central dogma in the life of people does not come a a surprise. However, with the rush among people for such a path of least resistance the competition increases over the board. Given a supply much larger than demand, the authorities choose to take in the “best” into the fold. This concept of “best” is where merit comes in.

Advantages of the concept of Merit

The concept of merit  is in pervasive use in today’s world (although in a obfuscate sense)  because in principal the concept has certain advantages in application:

  • The concept of a standardized test is among the most cost efficient, least labor intensive method to select a subset of the competitive subscribers and offers an easy solution to the question “who is best suited for the job?”
  • It superficially provides an illusory outlook of legitimacy to the successful candidates because of the “fair and just methodology” of selection employed.
  • It sets clear goals for the competitors, who translate their long term and often uncertain goals such as having a successful and meaningful life into short term concrete agendas such as successfully passing the standardized test for example.
  • It offers authorities an efficient method to obtain a large number of reasonably good to excellent workforce from the population competing in one stroke, while claiming to indulge in no selection bias at any stage.
  • With the commendation of merit often linked (not necessarily correctly) with desirable virtues like dedication, hard work, intelligence and the like, it provides for a good motivation for competitors to work harder and better themselves, thereby increasing the overall sample from which the meritorious are chosen and consequently the implication (unverified?) that the quality of selected candidates is optimal.

Does the meritocracy achieve its goals?

As a political system or social architecture the idea of a meritocracy has several short comings. While it does provide an easy mechanism to create a pool of legitimately qualified personnel out of a much larger pool, it’s claims pertaining to being a methodology to find the most appropriate people for the task at hand are largely unsubstantiated and only superficial.

  • The superficial layer of equality of opportunity in a meritocracy is anything but equal. Probably one can say it’s equal in the Orwellian “Animal Farm”  sense. A meritocratic system over several generations creates an elite class of people who are “more equal than the others.” The biggest illusion of equality in merit comes from the fact that the conditions of the selection process are identical and there is a lack of personal bias while judging the credibility of a competitor. However the biggest ingrained fallacy that remains hidden is the very concept of merit is the unequal distribution of opportunity to prepare the required skill sets which are highly skewed in favor of various socio-economic factors like the monthly income, location, exposure, language of instruction, race, gender, class, caste and minoritarial statuses.
  • Often while the selection procedure is philosophically the means to an end (merit), the procedure becomes an end in itself. Where the competing population prepares to develop skills not to succeed in the interested job but in the qualifier (the skills of the two often not being the same set).
  • The equivocation with success in a meritorious criteria with success in life is an equally fallacious one. The criteria for being meritorious in today’s world is often a very narrow one in scope and does not in any way measure life skills other than ability to succeed with the traditional goals of an industrial age.
  • The Peter Principle.
  • The question of how one defines merit is also very susceptible to criticism, particularly since the lack of a concrete definition leads to a personal bias among different people leading to different ideas about what merit really is? This translates to another conundrum – Which merit is the best merit? And the argument for merit is itself hopelessly derailed by this point.
  • A common egalitarian argument against meritocracy is that the system only aims to preserve status quo. Since the people by construction who are most like to have an upper hand are privileged sections of society by the sheer consequence of their privilege. Moreover merit tries to disguise this by equating a failure at the selection procedure, whose consequence is often a nontrivial factor of uncertain uncontrollable events and sociological phenomenon, with the lack of ability, thus also spreading the obtuse notion that privileged backgrounds are some how having better abilities and the like. (A kind of semi-caste system politic).
  • Other concerns for the validity of a merit-based system have arisen from studies in psychology, sociology, and neuroscience. Given the proposition that a person’s life prospects should not be decided by factors outside of one’s control or, for which a person cannot claim personal credit (i.e., social status, inherited wealth, race, and other accidents of birth) a meritocracy proposes a system where people are rewarded based on their efforts, and if everyone can start on equal footing with the same opportunity to advance, then the results are just. However, some studies have shown that even our motivation, work ethic, and conscientious drive is, in fact, outside of our control and can be affected by such arbitrary factors as birth order. For example, children who are first in birth order tend to aim at goals that reference their own past level of mastery, while second born tend to aim at goals based on other-referenced expectations and competence standards. Therefore, a system which rewards effort in this way is not completely just, because effort and hard work is not something we can claim complete credit for. For a reference, go here.

 

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The Unethical Graduation Ceremony

The graduation ceremony at the end of a gruelling undergraduate degree is amongst the highlights of one’s life. Every year thousands of students graduate, many more dream of graduating in coming years and when the moment comes, it is meant to be a moment of reminiscence, of enjoying the last moments in the place where one has spent the last so many years of her life, made lifelong friends, has had good times and bad.

It then comes out as an extremely shocking, rude and exploitative behavior on the part of a certain college which is planning to monetize the graduation ceremony of its graduating students this year. I declare upfront that I am unaware about this monetizing behavior happening in the previous similar ceremonies, but it certainly seems to be happening this time around.

To put in context why I find this exploitative, I would like to point out that the “entry fees” for this particular graduation ceremony amounts to approximately a third of the annual fee that the said college charges for its educational services. Not just is this an exorbitant amount in itself, there are many issues at hand here that I would like to address.

  • Firstly, this is clear underhanded exploitation due to the very monopolising nature of the graduation ceremony. An official graduation ceremony cannot be held without the college’s permission and the college is free to over charge and squeeze out cash as much as possible. The college also has plausible deniability, in that it doesn’t enforce compulsion on its students to pay up and attend. However this conveniently ignores the social compulsion the college has engineered to produced in the process, one has to pay a huge sum to avail his degree in an environment where all of his friends and peers would, one has to face social pressure from her peers who would not mind paying upfront. Obviously the college did not “force” the student.
  • This economic barrier to attend one’s graduation ceremony is elitist and totally does not beget a college that supposedly prides itself for its valuation of social justice issues. The age old proverb practice what you preach applies here, it’s fine to call Arundhati Roy and Binayak Sen to talk about injustice against the poor people by exploiting rich capitalists, but it would be instructive to look a little closer home. A nontrivial population comprising of graduate students in this college find it difficult to meet ends meet, and even pay the subsidised fees that the college asks for annually, and this economical barrier in effect just pushes them out of the ceremony. It just gives a signal of if you can’t afford it, you are not wanted.

I am sure that most people end of the day wouldn’t care about it. A large subsection of the graduates probably spends that much for a dinner at a moderately decent restaurant in Mumbai and don’t find it to be that big a deal. But I do. I think this kind of unethical behavior must not be tolerated and certainly not encouraged. It is a clear isolation and cornering of economically weaker students.

Until they make paying this exorbitant fee optional for an optional add on ceremony and allow everyone to enter the pedestal to collect their graduation degrees without emptying their pockets I boycott this graduation ceremony.

NOTE: In case you are looking to file a lawsuit, please allow me to make it clear that this  is a work of fiction and any resemblance, passing or exact to reality is entirely coincidental and unintended.

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Things to do in India before you Die

So I was talking to this friend of mine about what it really means to be successful in life and ended up talking about dreams and how we should fulfill our dreams. Thinking about these things led me to an oft thought about talking, list of things to do before you die. Since I’ve spent approximately 15 years in this country, I thought let’s do a check of things I have done and could possibly do.

  1. See the Taj Mahal – Check. I have visited the Taj Mahal in Agra, gone inside it, taken tons of pics, only I don’t have them with me. Even bought a Taj Mahal replica made of marble, looks amazing (it’s supposed to be a table lamp of sorts).
  2. Eat at the highway Punjabi dhaba – Check. Absolutely brilliant stuff this. Done this during a roadtrip to New Delhi – Agra. Realy miss the Paratha and Lassi. Really filing and delicious food. I think the dhaba was called Monty’s Punjabi Dhaba.
  3. Watch an Indian movie in the theatre – Done this multiple number of times. Sometimes dragged along as a kid, sometimes unintendedly gone to  watch Indian movies in a movie theatre. It’s a rare thing though nowadays. I’ve seen DDLJ at Maratha Mandir theatre.
  4. Play cricket on the street – Done this all too often as a kid. Don’t really enjoy playing cricket or sports much nowadays. But I have played all kinds of box cricket, played matches bet on money, broken windows by hitting a six, dominated small kids in gali cricket, played a match where I never got out (it was a “test” match :P) and got badly beaten by opponent teams as well.
  5. Put mehndi aka henna on your palms – Well, this is embarrassing. I painted my hands with Henna as a kid at a relative’s engagement ceremony. (Not completely, just a little bit.)
  6. Take a dip in the Ganges at Varanasi – No freaking way. If I do this, it will probably be the last thing I ever do. The river is highly polluted especially at Varanasi.
  7.  Walk through the bazaar of Chandni Chowk, Old Delhi – Done this as a kid when I went to Delhi once. Didn’t really care two cents about it honestly, but I guess it counts?
  8. Go to Pushkar Mela(Fair) – Not done this yet.
  9. Sip tea at a streetside stall – This is one of the common small things that everyone has done. And so have I on many occasions, but I particularly remember a roadside tea I drank in Vadodara, Gujarat. It burnt my tongue.
  10. Watch the cricket match at Eden Gardens Stadium, Calcutta  – I have not been able to accomplish this. But I have done something related to this that is probably far more desirable as a collectible. I saw the World Cup final of 2012(or was it ’11) where India won the world cup live at the wankhede stadium from the reserved Garware Pavillion (for free :)) thanks to a most generous friend.
  11. Visit the city of Palitana, City of Jain temples – Hadn’t even heard of Palitana before this. Must definitely check this thing out.
  12. See the Golden Temple, Amritsar. – I so want to do this!
  13. Spend a week at Osho Ashram, Pune – Have heard quite a bit about Osho, but I’m not really the meditative types. I don’t believe that alienating oneself from humanity leads to growth of intellect or mental well being of the kind i desire.
  14. Sunset with the camels on the sand dunes of Rajasthan – Rajasthan is a place I have been highly unfortunate to not have been able to go to. Some day..
  15. Visit the mystical ruins of Khajuraho – I haven’t even been to Madhya Pradesh.
  16. Tiger Safari at one of the many Tiger Reserves – Haven’t done this either. It’s something I wish to do in the near future.
  17. Visit the Gir Sanctuary, the last refuge for the endangered Asiatic Lions in the world. – Had the opportunity to go to this place twice. Was disallowed by my parents both times. Was not happy with that.
  18. Attend the Durga Puja in Calcutta – Did this quite recently. It was a time well spent. The culture and vibrant attitude of Kolkata shows itself in the pandals.
  19. Fly kites at the annual kite flying festival – I’ve flown kites since I was a kid and I am really pathetic at it. I have always got my kite rope cut, or hurt myself by the sharp nylon threads.
  20. Blind yourself dancing in the monsoon rains – Done this all too often in Mumbai’s torrential rains. I’ve even danced in a hail storm (it was not hailing really badly though), but that was not in India.
  21. Go the southern tip of India, Kanya Kumari.  – So want to visit Kanya Kumari, Andaman Nicobar and Lakshadweep.
  22. Ganesh Visarjan, watch the idol of Ganesh the Hindu God being immersed in the sea. – I have seen this on multiple occasions. The festival of Ganesh Chaturthi is celebrated quite lavishly in Mumbai.
  23. Visit the Tirupati Temple, Tirumala, Meenakshi Temple, Madurai– I am not really interested in visiting these temples.
  24. Stay at the Udaipur Lake Palace Hotel, Udaipur. – Not something that I have done or plan to do in the near future.
  25. Dine at The Taj Hotel, Bombay – Well yes! If you consider having 150 bucks worth of chat as dining that is. Taj is overhyped in my opinion.
  26. Take the Darjeeling Train Journey, Darjeeling. – This is something I want to do.
  27. Volunteer at an Orphanage – I will most definitely do this.
  28. Travel in the train  – I have not only travelled in trains, I have travelled in Mumbai local trains, the most densely packed ones, 6:00pm Dadar trains towards Virar or Karjat,  in the world. It’s honestly something I’d rather avoid, I’m tired of them mad crowds.
  29. Attend the Republic Day Parade, New Delhi  – I might have done this as a child perhaps, if I had the opportunity. I’m not really the patriotic type now.
  30. See the world famous Dabbawallahs (lunch delivery specialists, all of them uneducated) in action in Bombay. (given a six sigma rating for organization and zero wrong deliveries) – Okay I’ve seen them too many times to count. I’ve travelled with them, in the cargo bogie of the local trains when the trains have been too crowded. Their dabba numbering system is quite confusing, but they are ever so efficient at taking out or throwing in those long wooden crates holding about 50 dabbas.
  31. Meet the Real Maharaja staying at one of the heritage hotels. – Budget Constraints. Lots of luck involved in such a possible encounter.
  32. Go to Ladakh the highest plateau in the world – This is something I have missed out on. I so badly wish to go to Ladakh but no one to accompany 😦
  33. Visit the Chapel of St. Francis Xavier in Old Goa. – Done that, twice. Once as a kid, other time as a tourist. Nothing special, overhyped coffin with fake rumors surrounding the place about it’s perceived mystical powers.
  34. Yak Safari in Sikkim – The high North and North Eastern States have repeatedly eluded me. These places are going into my to go list.
  35. Stay in the Shikara or House boat in Dal Lake, Kashmir.  – Should possibly be clubbed with the ones above.
  36. See the Mysore Fort lit up, Mysore. – Have not been to Mysore, the city of palaces. Another to visit place.
  37. Sun Bathe in Goa. – Done this. I’ll add something more. Have fish fry in the frying heat of Goa’s beaches at one of the sandy outhouses. It’s amongst the best sea food I’ve had.
  38. Visit the Gandhi Ashram, Ahmedabad – I did this the only time I went to Gujarat (for a summer project at Vadodara). It was a nice quiet place, ambient and empty (to an illogical extreme I thought), but I liked the concept. The trip was an enjoyable one.
  39. See the Red Fort and Qutub Minar, Delhi.  – Yes I took a tour of these places in a Marathon touring session that even covered Humayan’s tomb, Fatehpur Sikhri amongst others.
  40. Tashi Jong Monastery, a Buddhist Monastery, Himachal Pradesh. – Sounds interesting to check out.
  41. Scuba Diving in Andaman Islands. – Must do. Must do badly.
  42. Ride a motorcycle on the street of India. – Most Indians have done this. Including myself. I despise personal forms of transport on principle though.
  43. Do Kushti i.e. Indian form of wrestling. – I would die…
  44. Get a Gold Facial. Yes, 22 carat gold facial. – Lol? Never even heard of that before, sounds eccentric in the extreme!
  45. Eating Chat, roadside food – Done! Chat and Mumbai go hand in hand.
  46. Have a pani puri (gol gappa/fuchka) spree – The memories of mine regarding these are epic. During the farewell of the batch senior to mine in High School we had a pani puri eating competition (informal) and I had around 70 pani puris! It was incredible, my hoarding capacity in those days, today I can hardly eat more than 20 of them.
  47. Live like a Daily Wage Worker/Manual Labourer – I got this incredible opportunity to live like a Manual Labourer as part of the Social Service League’s (A respected club of St. Xavier’s College, Mumbai) to go for a “Rural Camp”. I had to work on digging, shovelling, and other gruelling forms of manual labour that really changed my perspectives towards these chores. The 20 day camp changed me for the better in some ways.
  48. Travel the Entire Stretch of Marine Drive and Chowpatti Beach – Done this a few times. Love the sunsets on Marine Drive.
  49. Travel every State of India – It’s probably an Impossible to achieve dream, but most certainly is something that I wish to do. At the moment the number of states I have visited are abysmally small.

I shall update more as I think about them. But out of 49 listed I’ve done 24 of them which is definitely not bad!

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Geometric Inequalities – Algebraic bounds due to geometric conditions

So it’s been about two weeks since I have made my abode here at hyderabad for my Indian Academy of Sciences project. The first week was more or less spent on getting used to the jargon and basic notions of topological dynamical systems, cellular automata, julia sets, the ordinal numbers and mobius groups.

In the course of that week, my guide pointed to me a question he came across: a standard high school problem during a demonstration :

Given a triangle with sides a, b and c constrained by the condition that the perimeter p=a+b+c is fixed, what relationship between a, b and c would lead to a triangle with maximal area?

The interesting thing about this rather simple problem are the multitudinous ways in which the solution can be found. I would not wish to delve into the solution, but a few ways in which this can be done, include calculus, a simple application of the AM-GM inequality, etc.

The result states that the triangle must be equilateral for it to have maximal area meaning that a=b=c=p/3.
Now this is nice, but this immediately puts an excellent inequality in place amongst 3 numbers a, b and c.
Since a, b and c are sides of a triangle they must satisfy the triangle inequality, and the above mentioned question translates into an algebraic inequality for general real numbers satisfying certain conditions.

If a<b+c; b< a+c; and c<a+b then let a+b+c = p and let s = p/2.
Using Heron’s formula for the area of a triangle given the sides a, b and c,

\sqrt{s\left ( s-a \right )\left ( s-b \right )\left ( s-c \right )}\leq \frac{\sqrt{3}}{4}\frac{p}{9}^{2} with equality occurring if and only if a = b = c = p/3

This is a pure algebraic inequality on a, b and c satisfying the three triangle inequalities mentioned above and proving it directly without resort to geometry seems to be a non trivial task to say the least. This is just one out of many such possible examples of what are called geometric inequalities.

The next stage of the question is to try and find out possible such geometric inequalities using similar questions of maximisation and minimisation of geometric functions like area over perimeter, etc.

For example, the next generalisation for the above question could be

For a given quadrilateral a, b, c and d constrained to a fixed perimeter p = a + b + c + d, what is the condition on the four sides such that the area of the quadrilateral thus formed is maximal?

Another interesting question to look at would be,

For a given set of triangles with fixed area, what is the minimal possible perimeter?

It could be an interesting way forward, to try to attempt a direct proof of them same, though I am sure one can use the above (semi)derived geometric inequality to give an easy proof of the problem. Proving that the two problems are equivalent is another very nice problem.

While one avenue is to try and create more geometrical inequalities, the final goal might be to reach the pinnacle of geometric inequalities for any simple closed curve. Something I might write about next time.

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The Quest for Knowledge 2 – How does the Indian society perceive Education?

In the previous post, I tried to describe what I think the aims of an ideal education should be. In this one my attempt will be to discuss how the Indian society perceives education, what are the aims of an arbitrary person inhabiting any cultural space in this society and perhaps try to figure out what broadly drives such a view.

We are increasingly becoming a civilization that is inherently knowledge based, that is knowledge and expertise of a certain kind are tied to some value in society – be it economical, social or otherwise. In such a scenario it is but obvious that education as is conventionally understood is a primary process that every new member of society is put through to become “successful” in this society.

The first steps of a child’s education begin via their parents. So let me begin by wondering what exactly does a parent understand by education and learning? What according to them is the value of knowledge?
As far as I have observed ( I do not have any empirical data to support this observation), the idea most parents have  of education is return based. It is just a process a child must be forced/coerced (too strong a word?) through so that in the future their child would be guaranteed a successful life, it is a systematically designed path which must be followed according to a set system of procedures and adhered to till the very end.

To quote a friend on this matter:

This is what parents want, they think they are the best decision makers for their kids as they might be vulnerable and shit, the socio-economic factors do make them to think so, but nonetheless its their aim to control every move children wanna make, making each and every decision for their kids which would directly/indirectly decide the course of his/her life.

The control freak type nature of many parents regarding their children is not a very rare phenomenon in this country, where a large number of important decisions that would guide the outcome of a person’s life are made totally devoid of the child’s wishes. While I agree that many times children may not be capable of rational judgement, but a control freakish behavior is not exactly rational either.

Here is another quote on this matter:

They want their kids to excel in all the fields they think their kids should apply to, regardless of the kid’s own choice, even though their kids don’t even have the slightest idea as to what they are doing. When i was in 4th standard or just got into 5th standard I was asked in an assignment to write a bit about my hobby and I went to my dad asking him what a hobby was and showed him that assignment.
Then he told me what hobby was and asked me to write mine to be philately, I was confused coz in the first place i didn’t knew what the heck it was and why should I write it coz I loved watching cartoons and playing. But he just insisted me to, rather compelled me to write against what i wanted to, because my dad wanted me to project myself as an intellectual ass

And here is a stimulating angry rant about parents obsession for their children’s success which makes me wonder whether they even do it out of altruistic feelings towards their children or for their own benefit?

They will send their kids to FIITJEE, CAREER POINT AND OTHER SUCH “INSTITUTES” spending tons of money because they want their fucking kids to be in top class institutes like IIT K, and if they don’t get what’s being taught in class then they will be shouted at and rebuked “Is this why i spent all this money on you? you are a leech……etc etc…”

They will send their kids to reality shows so that they can show the society what a fine lad they’ve got and in turn what are those kids becoming? what about their ideas, their passion?

These incidents are by no means rare,and I suspect that a majority of both urban and rural youth of India will find this similar to what happens in their neighborhood or perhaps their own homes. Education to most parents is simply a tool to make their kids successful and has no consequence in of itself. This crisis of modern parenting is a crux in the reason for the deteriorating educational condition of Indian school and college graduates and post graduates.

Well that is parents. But how do kinds and learners themselves understand education? (It is safe to assume in India that a learner is not an adult unless in very rare cases, because as mentioned before the practice of considering education as a temporary bitter medicine for success is very prevalent in India.)Most learners fail to appreciate the need of education, nor are they ever introduced to the notion that education can be a means in itself to achieve a better and more enriching life, rather the notion of education being a horribly boring chore is imbed into the learners, perhaps by intuitively considering their parents’ approach to the idea.

A Physics M.Sc student’s views on the same:

“Well, they (kids) are indoctrinated into altruism (Gandhi being their national father, even though they’ve already got one), nationalism and India is great. But then, they want better jobs than the rest of the batch mates (preferably U.S) or an esteemed high profile position at an MNC, they care only about marks and as most of the entrances are MCQ based they just want to have a brief amount of information on every topic/sub-field. What they instead wanna learn are shortcut techniques and formulas so that they can fetch more marks.

That is what education has turned out to be in India. If you are not in an IIT/NIT/BITS in case of engineering or AIIMS, et al for medical then you’re a faggot.

And mainstream courses like physics, chemistry, mathematics and biology are meant for numbskulls. This is sadly what Indian education system has turned out to be.”

The main point echoed is the fact that everyone has become goal oriented, with the goals being more or less shallow in nature. There is no ambition other than to have a secure lifestyle, have high status and a good bank balance. Perhaps the esteem of being in a restrictive club is one of them. The surprising fact that I observe is the unidirectional goal that almost the entire population of learners have. If an extremely high percentage of individuals proceed towards a particular kind of education over all others regardless of supply demand scenarios and irrespective of location is a matter of concern. Even from a purely economical perspective, such a system makes neither sense nor is it sustainable.

In all this hullabaloo the true aim of an education is lost and it ends up a means to grapple at some pseudo-sensible dream that in most probability isn’t even the learner’s to begin with but has been reinforced within them  over time.  The sad part is eventually even educators have fallen prey to this and lost confidence in their own abilities. This turn for a dystopic end of education in India is honestly very saddening, but there is hope, but the hope as always lies in small pockets of islands of excellence, but can this hope permeate to the general populace? I doubt highly.
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Quest for Knowledge 1 – What should education be?

Education is a burdened word. Heavily rooted within the word is the general distaste of one`s own personal experiences as well as several inbuilt assumptions regarding what education is. It is a societal phenomenon, driven primarily by what society requires at that point of time and what society finds valuable or worthwhile teaching to its following generation for it`s (perceived) benefit to societal strata as a whole.

Under such a heavily polarised topic as the right kind of education, what do I think is the right way to go about accumulating knowledge? Is accumulating knowledge the right thing to do? What is the purpose of education at a personal level? These are a few of the questions that I want to tackle based on my own experiences as a learner as well as a peer of several people who are attempting their own personal approaches at trying to learn something.

The first question that comes to my mind is what education in principle means to me?

To me, education is the means by which I accumulate data, learn abilities to manipulate the accumulated data and develop the creativity required to come up with my own abilities to use the data in novel, efficient and useful ways that gives me self satisfaction. Now a crucial part of any learning process is truly understanding the core of the material whose study is being undertaken, and in such is one of the most important and widely applicable abilities to use raw data.

But education is also more than that. It`s the desire to fulfill the innate curiosity that has come to define us as a species, the intrinsic nature of us humans to want to know more, to have answers to every question and to question everything. It is the desire to obsessively master something before moving onto another,it is a desire of doing as much as possible yet realising that you can never really know everything and most importantly it is the development of humility that the more one knows the more one realises that they know so less.

Learning is that human prerogative that enables us to engage in such a educative worldview. It requires us to question, to seek answers, to look for more questions, to work hard, to toil, to be creative. It needs us to be earnest with ourselves, to be motivated to know more, to be self aware of the need to be educated and educate oneself. It is a search for the inner self, a roadmap to our dreams. Knowledge is the driving force behind ambition and ambition is the driver of progress, be it economical, social, cultural, scientific or any other field.

I feel education should be a wholesome growth of a person, engage our critical reasoning and thinking skills, develop and hone questioning capabilities and strive towards the zeal and commitment of a vibrant and stimulating atmosphere for a free exchange of ideas. It should promote an interest in mutitudinal disciplines and not singularly isolate a particular kind of knowledge as a primary skill while ignoring all other facets of learning.

 

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Summer Fellowship under Indian Academy of Sciences

This summer I got  the opportunity to work on a 2 month long summer research project in mathematics at the Central University of Hyderabad, under Prof. Kannan, a resident faculty at the same institute. This is just the first week of the project term, but I must admit that I am already learning quite a lot of new things here.

Hyderabad as a city, I have not seen much of it yet, but atleast the parts that I did see appear to be much cleaner than Mumbai. The people much less formal, and as such in general appear to be fairly helpful in nature.

The campus of HCU is vast and fairly untouched. But is marred in many places by a political poster war that plagues most of the occupied campus. The place is huge and it takes a lot of time to go from one part of the campus to another without a means of personal vehicular transportation.

AS far as the research experience, I think I am getting a really good idea of how contemporary mathematics is done. Mathematics is rarely done on your own, but mostly through discussions and a continuous series of questions and cross questions until one arrives at a somewhat interesting result.

Uptil now I have been listening to various student seminars from IM.Sc and Ph.D students at HCU about their areas of interest under myguide’s team. It has been an interesting experience so far, and I am looking forward to doing some cool mathematics during these two months.

The main areas of interest here seem to be what are called Discrete dynamical systems, on some particularly interesting topological sets. A lot of this has to do with finding properties of what are called fixed points and periodic points of the dynamical system. The space over which these questions are being asked are highly varied and interesting in themselves, from Cellular Automata and Julia sets to the order topology on the set of Ordinal numbers to a dynamical system on an arbitrary formal language.

At present I am thoroughly enjoying my time under this project.

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TIFR CAM – Bangalore Interview for Integrated Ph.D. in Mathematics

This is a record of my interview which took place at TIFR Center for Applicable Mathematics – Bangalore for the integrated M.Sc. – Ph.D. program in mathematics for the year 2013. The short selection of prospective students was through a common entrance examination GS-2013 for both TIFR Bombay and TIFR CAM.

The interviews were all quite relatively short compared to that at the Mumbai counterpart where my interview lasted for about an hour while here the interview only lasted for about 25 minutes.

My expectations from this interview was that the level of difficulty would be markedly less than that at TIFR Bombay due to this program being targetted towards Undergraduate graduates unlike the other program and before the interview I was relatively confident about myself.

My interview was in front of a panel of 5 professors, all of whom were male, and relatively young. They were very friendly and made a conscious effort to diffuse any tension in me prior to the interview. The following is a transcript of the interview as I remember it, while it might not be exactly what happened, its certainly a good representative of what did. I stands for Interviewers, and A stands for myself in the sequel.

I: Goodmorning. Where are you from?
A: Goodmorning. I am from St. Xavier’s College, Mumbai.
I: Oh nice. (One of the interviewers was an alumnus of the same institution).
I: Do you visit Metro cinema?
A: Yes… (Some other random talk about Mumbai followed.)
I: Okay, so what are your interests in Mathematics?
A: I am particularly interested in Topology.
I: Topology? Do you know what Topology is? Why don’t you explain it to us what topology is?
A: I have studied elementary Point set topology from Munkres and from Klaus Janich – Topology. And as far as I have seen, it deals with the study of properties that are ascribed to a set when a particular subset of the power set of the set is taken to satisfy basic assumptions on unions, intersections. It also deals a lot with properties that are left invariant under “continuous maps”.
I: Okay. So can you give me an example of a topology that surprises you?
A: The Set of Real numbers under the co-finite topology is a very non-intuitive topology. Considering how the sequence of natural numbers (for example) converge to every real number.
I: Would you call that a nice topology? (Laughs)
A: Not for the purposes of Analysis, but as an example that is non-intuitive it is a very nice topology.
I: Okay, tell us how do you visualize open sets in a topology?
A: I visualize them as open balls or cartesian boxes. (Basis elements in the RxR product topology.)
I: Indeed, we visualize open sets as open balls.
I: Are you comfortable with analysis?
A: Yes.
I: Okay go to the board. (pause) Now consider this sequence x_{n+1}=\frac{x_{n}+\frac{1}{x_{n}}}{2}.
Is it convergent? What is its limit? X1 > 1.
A: (Proves it is convergent and terms are always positive and hence its limit is 1).
I: Are you comfortable with group theory?
A: Yes.
I: Give an Example of a group of order 9.
A: Any group of order 9 has to be abelian since the order is of the form of p^2 where p is prime. Thus by the structure theorem of abelian groups, upto isomorphism the only groups of order 9 possible are \mathbb{Z}_{3}\times \mathbb{Z}_{3}\: \: \: or\: \: \: \mathbb{Z}_{9}
I: Good. Now some linear algebra. Consider a linear transformation, and two eigenvectors of that transformation. Take a convex combination of the two eigenvectors. Is it still an eigenvector?
A: Shows that it need not be.
I: So when can it be an eigenvector?
A: If they correspond to the same eigenvalue.
I: Okay, now are you comfortable with continuity, differentiability? Do you know Uniform continuity?
A: Yes sir.
I: Okay, consider the function f(x)= \sqrt{x}\cdot log(x)\: \: \: when\: \: \: x> 0 and 0 when x = 0.
Is this function continuous?
A: (Proves it is continuous)
I: Is it uniformly continuous?
A: Uses Meanvalue theorem as an estimate and comes to the conclusion that the derivative is unbounded at x = 0.
I: (Gives a hint) separate the domain into two parts.
A: (Solves the problem).
I: Okay good. You can now leave.

I think post interview that I had a relatively easy interview. Was it because of my preference for topology or was I just (un)lucky? I cannot say, but the interview did feel like it went really well. Fingers crossed over this one. I am still to secure an admission to some place yet and it would be nice if I got that for once.
results for the interview will be updated as and when I receive them.

 

UPDATE: I have been selected for the Integrated Phd Program in Mathematics at TIFR CAM. I do not plan to pursue my education here though.

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TIFR Bombay – Ph.D. Mathematics Interview

Post the qualifying entrance exam stage for the Ph.D. program in Mathematics at TIFR Bombay, I decided to note down my experiences at the interview that was to follow.

Pre interview stage – I have readied myself for the fate that my chances of getting accepted to this program are minuscule at best and none for the most part at this current stage. Considering the competitive nature of admissions for a Ph.D. at TIFR Bombay, I think this is a pretty accurate view.

I reach on time for the interview, the institute intimidates me a bit with its extremely long passageways and silence which I thought would be an amazing place to do research. I think that TIFR is an amazingly well furnished and well designed place with a small but serene campus with a beach to boot.

I am the first person to be interviewed for the day, my interview panel consisting of five professors: 4 male, 1 female; 2 relatively young and 3 older. I describe the conversation that follows as per my memory. I stands for interviewer; A stands for me.

I:  Good morning. You are doing B.Sc.(III)?
A: Good morning. Yes sir, I am, from St. Xavier`s College, Mumbai.
I: Why did you apply to TIFR?
A: Since I have been in college, I have been hearing about TIFR being one of the best institutes to study mathematics at the graduate level in India. That is why I applied.
I: Why not apply after an M.Sc.?
A: I was under the impression that I could do M.Sc. coursework in TIFR under the Ph.D. program..(?)
I: (Laughs) Many students who come for interviews have these misconceptions, they do not realize that we do not provide an Integrated Ph.D. but rather a direct Ph.D. program.
(Pause) Don`t worry, many students from your college have ended up doing a Ph.D. here after B.Sc.
I: What are you primary interests?
A: Linear Algebra, Metric Spaces, Topology.
I: What topic are you comfortable with?
A: I have no particular preference sir. (conscious of being scrutinized )
I: Okay then, what in Topology have you done?
A: Metric Spaces,  point set topology.
I: Which book have you referred to?
A: I am following Munkres – Topology and Klaus Janich – Topology.

I: Okay, Give me an example of a nonmetrizable topology?
A: The set of Real Numbers under co-finite topology is non metrizable. (A sequence 1/n converges to every real number in the cofinite topology, which no metric on R would allow.)
I: Are R^{2} and R^{3} homeomorphic?
A: (Pause) No.. For suppose there existed a homeomorphism then consider a line in R^{2} and its preimage in R^{3}. Delete both these sets then one will be disconnected while the other will still be connected.
I: What if the preimage of the line is a plane? (Space filling Curve?)
A: Sir, that would not be possible since it is a homeomorphism, the homeomorphic image of a line would be a bijective path. The space filling curve is not injective. But in general to prove that the set would still be connected after removing the preimage..
I: (Waits) (Says to the other professor – perhaps he hasn`t done it yet?) Have you studied the fundamental group? Your intuition is correct, but this method of proof can be quite difficult to prove.
A: No sir, I have not studied algebraic topology yet.
I: Okay, if you take a point from 2-d euclidean plane and take a circle around it, you cannot shrink it to a point, but you can do so in 3-d plane.
I: Give an example of a continuous bijection whose inverse is not continuous?
A: Consider F:R(discrete) to R  identity map.
I: Can you provide the topological conditions on the domain and range such that a continuous bijection will always be a homeomorphism?
A: If the domain is compact and the Range is Hausdorff.
I: Prove it on the board.
A: (Prove it on the blackboard)
I: Is every compact metric space complete?
A: Yes. (Use sequential compactness as an equivalent condition)
I: Prove sequential compactness then.
A: (Chokes)(Proves with hint).
I: Is it possible to induce a metric topology on (0,1) which is complete?
A: Yes. Completeness is not a topological property..
I: Provide an example.
A: (thinking)
I: Is (0,1) homeomorphic to R?
A: (Oh!) Yes! (Writes down the homeomorphism on the board.)
I: Okay, now how would you answer the previous question?
A: Let F be the homeomorphism from (0,1) to R. Consider the metric on (0,1) : D(x,y) = |F(x)-F(y)|.
I: Good.
I: Is every complete metric space compact?
A: No. Consider R under usual or discrete metric.
I: Okay some analysis now. Let F_n be a sequence of functions C[0,1] converge point wise to F in C[0,1]. Does \int_{0}^{1}f_{n}(x)\rightarrow \int_{0}^{1}f(x) ?
A:(Could not answer)
I: Okay you can think about it later. A continuous function on R has the set of rationals in its zero set. What can you say about the function?
A: The function is the zero function (because of sequential continuity).
I: Describe a function that is continuous only on the Irrationals.
A:  (thinks) Consider the function which is zero on all the irrational numbers and on the rational numbers it takes the value f(p/q) = 1/q where gcd (p,q) = 1. Thissequence converges only on the irrational numbers.
I: (Nodding) What about 0?
A: 0 can be considered as 0/1, I can assign the value 1 according to my definition, in principle any nonzero value would do.
I: Have you studied Measure theory?
A: No.
I: Fourier Analysis?
A: Very basic Cesaro sum converges to function, weirstrass approximation theorem.
I: So no big convergence theorems.
A: No.
I: A linear transformation which is an Isometry on R3 and orientation preserving is rotation about an axis passing through the origin. Can you prove this?
A: (thinks)
I: Do you know what an isometry is? An isometry means a distance preserving map.
A: Since the transformation is on R3, its characteristic polynomial is of degree 3 and has atleast one real root. Since the map is an isometry it is bijective and hence has a trivial kernel. Thus the real eigenvalue cannot be 0. This would mean that there is a nontrivial invariant line. Consider the plane perpendicular to that line passing through the origin. consider orthonormal basis of that plane it will be a rotation in the plane due it the map being an isometry on the restriction and being orientation preserving while fixing the origin. Thus it is rotation about an axis passing through the origin.

I: Good.
I: What do you know about cardinality? Okay try this question for five minutes. I don`t think you will get it.
Consider V1 and V2 two vector spaces, let f: V1–>V2 be an onto linear map and
g: V2–>V1 be another onto linear map. Does there exist a linear isomorphism from V1 to V2?
A: (Proves for finite dimensional case that dimensions are equal which immediately leads to the result)
I: What about the infinite dimensional situation?
A: (Thinks for a couple of minutes.) I cannot say anything, it could be possible that both the vector spaces are uncountable of same cardinality while one has a countable basis.
I: Do you think two vector spaces with same cardinal numbers have bases of different cardinal numbers?
A: (?..)
I: Okay next question. List the sylow 2 subgroups of S3.
A: (Does so).
I: What can you say about groups of order 9?
A: Its a group of order p*p which is abelian, Hence by structure theorem the only possible groups of order 9 upto isomorphism are Z3xZ3 and Z9.
I: (Nods) Okay. So what is the madhava competition. You have got prize in it? How many people give the exam? Who organises it?
A: (Answers those questions)
I: Okay you may go now.
(Pick my bag and leave.)

After the interview I felt like I have done very little in the last three years.. I do not expect to get into TIFR Mumbai on the basis of this performance, fingers crossed though. I felt good that I could answer questions from topics I have studied.

UPDATE: Well the TIFR Ph.D. Selection for Mathematics is out. And surprisingly I have got in! I am pleasantly surprised by the outcome 😀 It will be a hard choice for me between Ecole Polytechnique and TIFR.

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