Tuesday, February 07, 2012

Balram talks of Primes

Balram was relaxing on his long chair in the balcony, poring over the newspaper and a cup of hot coffee by his side. It was his favourite way to pass a Sunday morning. He was engrossed in the political affairs section when the doorbell rang. With a tinge of irritation, he ignored it. After a minute, the bell rang again. This time it was a long one. There was irritation on the other side of the door too. Balram put aside his newspaper, got up from his chair, stretched his back and ambled towards the door. There was a third restless ring. He opened the door and saw an irritated Suyodhana staring at him.
"What took you so long? I've been standing here for the last 10 minutes!" he said as he walked past him and entered the house.
"Yes. You can come in." said Balram closing the door.
"I think you're becoming deaf. If you hadn't opened the door now, I swear I would have banged on the door."
"Did it occur to you, that it was quite possible, that I wouldn't be at home? It's a Sunday and people have weekend plans."
"You want me to think that, don't you? You have a problem with me barging in like this?"
"Now I don't have a choice, do I?"
"Yeah. You don't. Is that coffee you're drinking? Can I have it?"
"No. I'll make another cup of coffee for you."
"Thank you. Make it a bit strong. And don't be stingy with sugar."
"I see. So what makes you so impatient today?" asked Balram as he went into his kitchen.
"Ah! Don't ask!" said Suyodhana following him.
"I already did. And I have a feeling you want to talk about something."
"Rishi was at home this morning. The kid wanted me to teach him mathematics. GCD, LCM and what not! I just spent more than an hour trying to put some sense into that boy. But the boy! Oh boy! Nothing gets into his head! It's such a simple thing -- Greatest Common Divisor, Least Common Multiple. It's not like only the greatest can understand it. He doesn't put the least effort in understanding it either. Keeps confusing between the two. And if I scold him, he talks back! Oh the boy has some guts, I tell you! He asks me what use it is to learn such stuff! Can you imagine how difficult it is to deal with such kids?!" said the exasperated Suyodhana.
"I can only imagine." said Balram with a hint of a smirk passing his face. "So were you successful in teaching him?"
"I was able to help him solve his homework. But that boy is dumb. He'll forget it before his exams."
"So you weren't successful?"
"Bah! Who cares!"
"Why did you agree to teaching him mathematics? That too so early on a Sunday? It's quite strange."
said Balram, as he handed the strong coffee with extra sugar to Suyodhana. They started walking back towards the balcony.
"His mom asked my mom. I couldn't refuse."
"Interesting."
"Why is that?"
"Doesn't Rishi have an elder sister? She is your age isn't she?"
Suyodhana blushed for a second before changing his expression, "Oh! How sly of you! You think I'd do anything like that just to get in the good books of his sister?!"
"Wouldn't you?"
"Would you?"
"This is about you, not me." said Balram looking at Suyodhana with a raised eyebrow and a mocking smile. Suyodhana kept silent and sipped the coffee. "So, were you able to tell Rishi about the practical uses of GCD & LCM?" he asked.
"I told him some things I got off the Internet."
"What are they?"
"Oh, you don't know either? You want me to teach them to you too?!"
"Yes. Please do."
"OK! I give up. I don't want to make a fool of myself in front of you. I seriously can't understand the real uses of these things. These and even Prime Numbers. God! Why do people make so much noise out of it, is beyond me!"
"I think a story needs to be created to make this interesting. A hypothetical situation."
"I'm all ears." said Suyodhana, getting comfortable and leaning back in his chair. "Why else do you think I'm here?!"
"Alright. Do you see Giridhar leaving his home there? He has taken money from some Chaturvedi and hasn't repaid him. Chaturvedi doesn't know where Giridhar lives, but they go to work from the same bus stop. Now here is the hypothetical problem.
1. Chaturvedi (C) and Giridhar (G) leave their home only once a day. We'll assume it's the same time of day too.
2. If C meets G, G has to pay whatever money he has. Or he runs the chance of being humiliated in front of others; or worse being beaten up.
3. Both can't stay at home for very long. G works as a researcher who does most of his work from home and doesn't have to go to office regularly. C is a writer who goes out occassionally to meet people.

"Now, if C & G met daily, G would have to pay every day and he wouldn't save anything for himself. So, he decides to go out once in 2 days. C realises he meets G on alternate days & he changes his schedule too. G changes his schedule to 3 days now. When will C & G meet now?"
"Umm. Every 6th day? Ah. I see that's the LCM of 2 and 3!" said Suyodhana.
"Yes. Now, G doesn't have enough money to give every 6th day either and he has to change his plans. If he goes out every 4 days, he'll run in to C every time he went out. Same goes with every 6 days and so on. You understand why it is so?"
"Because 2 is a prime and those numbers are its multiples?"
"Precisely. So our researcher G decides to go out only on prime number intervals. C keeps altering his schedule too to grab hold of G. If G came out every 7 days & C came out every 5 days, G gets 35 days to collect sufficient money for the month. G tries to increase his gaps and not finding him often, C reduces his gap. G can't be at home for long periods; he has to go out to get work and money. C can reduce his gap to every day, but he gets frustrated at not finding G often. The question that arises is 'What is the optimal gap for each of them?'"
"I get it! C has to choose a small prime number - a greatest common divisor. While G has to choose a reasonably high prime number so that their least common multiple is big enough for him to have enough money for him." said Suyodhana with a tinge of delight in his voice.
"Yes. That's correct." said Balram who was glad that Suyodhana understood the problem.
"Wow! That's cool!"
"The problem is a type of Predator-Prey model. And this particular solution is called Predator Satiation. It is often seen among cicadas. They appear once in 11 or 13 years in large numbers. It's a type of evolutionary adaptation process that allows them to survive assaults from their predators. There are many other uses of Prime numbers, but very few like these can be spotted in nature. You can see uses of Primes in encryption algorithms like RSA. There are many other applications of primes too, but I'd rather have you discover them."
"No, no. That's ok. This is sufficient. Now, if only I could make that kid understand all of this!"
"Or, from what I have gathered, more importantly, you should attempt to tell him that with his sister around."

Tuesday, January 24, 2012

8 years have passed

January 24, 2012. It is 8 years since I moved to Chennai. It doesn't seem like it was too long ago. I was a young, 21-year old, bursting with energy, brimming with ideas and ready to take on the World. I look at that person and the 8 years do seem to belong to a different decade. My internal clock has a conflict. Some time back, I wrote these lines:
Smells bring back memories. I just smelled few years in the past. We had just moved to Chennai. Furniture from Mumbai lay scattered in my bedroom. Misplaced remnants of an earlier life transported across cities. They looked so different now. A medicine bottle broke and the room reeked of it. The stench lingered for a few weeks. I would walk into the room and it would be there. I used to crinkle my nose and think, "This is how it is going to be from here on. Life will stink."
Nation's Glory  That pessimist still lies within me. But I have consciously attempted to become more open minded while forming opinions. I will not try to talk about my life in this city. I've been doing that for 8 years on this blog. This post will be about the city. The lines I wrote earlier might throw poor light on Chennai, but I know better now. A city cannot be defined by pre-conceived notions. Your life in it cannot be judged by those biases you still carry from your earlier life. You are too insignificant to change the city the way you like it. It is a bustling organism representative of the millions that breathe life into it every day. You are just a tiny cell.

 A friend of mine was lamenting about missing Mumbai after he shifted to Bangalore. I used to do that. Looking back has helped me realise where I was wrong. Where most people go wrong when they begin to compare cities. The weather, the history, the money, the power, the night life, the gardens and the rest are only some facets that attract or repel each person's sensitivity. A new city is like a new friend. He is different from your other friends. He has some peculiarities. He has different views, different ideas and a whole new perspective your other friends could never reveal your mind towards. You are cautious with your friendship at first. But then you begin to find it interesting. The horizons have broadened. Your mind is more receptive to newer ideas.
MGR Samadhi  Why did you like your earlier friends? You knew them very well, like your old city. Each time you took a guest for a tour, you had some story to say about every corner in that city. It is all about the stories. My stories from my school, your stories from your college, your parents' stories from all the places they have relatives, the relatives' story about how the city used to be in their grandparents' time, your friends' stories about favourite hangouts, her stories and histories. Your old city was like a book full of stories and the new book is blank. It isn't daunting. It is a story that is waiting to be told.

Thursday, January 12, 2012

Balram dispels a paradox

Balram: "You look drowsy for this time of the day. Are you feeling sick?"
Suyodhana: "Nope. I'm OK."
Balram: "Why are you so dull, then?"
Suyodhana: "I'm just feeling very sleepy."
Balram: "Having trouble sleeping in the nights?"
Suyodhana: "Nope. Actually, I've started going for early morning runs the last two days. By the time it's afternoon, I start feeling very sleepy."
Balram: "Early morning?! Wow. That's very interesting to know. How early is this in the day?"
Suyodhana: "I wake up by 5:30 and start running by 6."
Balram: "That's very encouraging. For someone who used to wake up at 9 a.m every day, a 4 hour advance must be a big change for the day's routine."
Suyodhana: "Man! It sure is. By the time I come back from my run, it's just 7:30 and I have two hours at hand with no clue how to utilise them."
Balram: "There is always a lot of things you could do to make good use of that time. Mornings are particularly wonderful when you want to learn something new. The mind is fresh from all the rest it got the previous night and it is more receptive to newer ideas."
Suyodhana: "Argh! C'mon. Now don't start off with your creative pursuits. This running business itself is tough to handle for now."
Balram: (laughing) "I can see that. How are you motivating yourself to do this?"
Suyodhana: "I met this old chap some days back. Fellow claims to have a discipline like he just came out of military or something. Says that he's been logging his runs for the past 3 months. Just think of it. Every day after he runs, he notes down the time he started, the time he stopped, route he ran on. He might even log how much water he drank! He claims to have run 450 kilometres in that time. He kept on nagging me more than an hour about how splendid he felt every day. He made fun of my belly. I mean, look at this, you really think this is fat here I have? Fine, it isn't exactly rock hard abs that I have, but it isn't a big paunch either. But that chap kept going on and on about health, fitness, joy of running, feeling of high and what not? I could have heard and dismissed all of it. Then he started talking down on 'this generation'. You know that type, don't you? They think their generation was the last one where everything good stopped. You know what I'm trying to say?"
Balram: "Despite the English of your generation, yes. I guess that behind my back you talk of me also belonging to that generation?"
Suyodhana: "Of course not! I have huge respect for you! Why would I do anything like that?"
Balram: "Never mind. So what happened afterwards?"
Suyodhana: "I got pissed off with the old chap, what else? I took him up for a challenge. I told him I'd start running from the next day and in less than 3 months, I'd run more than he did."
Balram: (smiling) "And how are you going to do that?"
Suyodhana: "That is what even he asked me. He actually laughed it off. It pissed me even more. I told him I'd do it in 2 months. He accepted the challenge and said that if I won, he would gift me a gaming console. His way of saying that 'this generation' prefers being couch potatoes."
Balram: (laughing) "Oh, he got you there! What if you lost?"
Suyodhana: "That's not going to happen."
Balram: "What did he ask in return if you lost? Must be something as expensive as a gaming console, surely!"
Suyodhana: "He said, he only asked for respect in return. That I needed to respect elders more if I lost. His way of showing me humility."
Balram: "That man sounds interesting! So tell me, how are you planning to go about it?"
Suyodhana: "It's quite simple, you know? The old chap runs 5 kms a day. Nothing less, nothing more. I'll run 10 kms a day and in half the time I will have completed the 450 kms."
Balram: "Interesting. Just out of curiosity, how much have you run in the last 2 days?"
Suyodhana: "I could run just 4 kms yesterday. And only 3 kms today. My legs hurt and my breath gives away."
Balram: "Uh Oh!"
Suyodhana: "It doesn't matter. It's just the beginning. He said I'll get consistent after a week."
Balram: "Oh! He's also tutoring you?!"
Suyodhana: "Old men can't give up an opportunity to give lessons, can they? Yes, he does that after his run. I wait for him to complete. He's much slower than I am."
Balram: "I'm beginning to doubt if you really passed mathematics in school, Suyodhana."
Suyodhana: "I did very well in Maths, for your information. Aced it sometimes! Soon, I'll be running 10 kms a day. And if not in 45 days, I could do it in 60-65 days. It's still faster than the 90 days he took."
Balram: "I still wonder how you cleared your Mathematics exams."
Suyodhana: "Why is that?"
Balram: "Have you forgotten that your 'old chap', whatever his name is, is also running every day? He is running 5 kms every day. Even if you ran 450 kms in 60 days, he would have run 300 kms more. That's 750 kms. In 60 days, you'd only be where he is now, not where he will be 60 days from now."
Suyodhana: "Oh! Darn! I didn't think of that?! I'd have to run more in that case? How much more?! 15 kms a day? 20kms? A whole marathon every day?! How much?"
Balram: "That 'old chap' must be a genius. There's no way you can catch up with him, you know? It's an ancient problem, this one. They even call it a paradox, of sorts."
Suyodhana: (panicking) "You've got to be joking! What are you talking about?! I don't understand anything?! How can that be?!"
Balram: "You know that you can run more than him every day. So you think you can out-run him eventually. It seems quite obvious to you. But he has got a headstart and you will always play catch up. In 60 days, if you get to 450 kms, he would be at 750 kms. You will take 30 days more to get to 750 kms. In those 30 days, he would have run 150 kms and would be at 900 kms. You get where I am going? Keep breaking it into smaller intervals. You both keep running and you might make up ground by reducing the gap between you two, but by the time you've run as much as he has, he has run just a bit more. You can get as close to his total as possible, but you will never be able to run more than he has run."
Suyodhana: "But... but... that doesn't make sense?"
Balram: "Have you read about Geometric series in those Mathematics classes that you claim to have aced?"
Suyodhana: "Of course I have."
Balram: "Can't you see this is a geometric series? Every time the interval (the time you take to run as much as the 'old chap' did earlier. 60, 30, 15, 8...) keeps reducing into half of the original. 1/2 + 1/4 + 1/8 + 1/16 + 1/32 and so on. If you add them up it comes very close to 1, but is never equal to 1."
Suyodhana: (Scribbles on a paper with some confusion. Scratches his head and looks at Balram in bewilderment) "That's... surprisingly right. Darn!"
Balram: "So what are you going to do about it? The man has fooled you, no doubt. You had lost the challenge even before it started."
Suyodhana: (frustrated) "I hate that man!"
Balram: "But all he asked in return was for respect, wasn't it? Maybe you can give him that. He managed to fool you for 2 days straight."
Suyodhana: (resigned) "Yeah. I guess so. I'll speak to him tomorrow. Very respectfully, I'll add."
Balram: "So you've given up?"
Suyodhana: "Yeah. I have. Like I have a choice. Don't rub it in now."
Balram: "Well, then let me tell you that I was only pulling your leg. Run the equations again. And going by the geometric series logic I confronted you with, in 130 days, you might actually start running more than him, if you ran 10 kms every day."
Suyodhana: "I knew you were tricking me!"
Balram: "And yet you gave up so easily. All because I tried to confuse you with representing the problem in such a manner that it became difficult for you to think clearly. You could have confronted me and asked me to explain the paradox. It's actually called Zeno's paradox, named after Zeno's philosophical problem after Achilles and the tortoise. Look it up.
People will always try to confuse you, either to make a fool of you or to delay your judgement for their selfish needs. Never get bogged down by complexity. If you feel there is something wrong in the problems in front of you, take a moment and try to simplify it. If you can't get rid of the confusion in your head and achieve clarity, people will succeed in creating further confusion."
Suyodhana: "Wow. That's some lesson I have learnt! I'll try to remember that."
Balram: (smiling) "I hope you have understood what I was trying to convey."
Suyodhana: "Oh! Definitely! I won't get let people confuse me like that anymore."
Balram: "Then can we revisit the Mathematics again?"
Suyodhana: "What do you mean?"
Balram: "Your old chap runs 5 kms a day. He's already run 450 kms. If you run 10 kms a day, in how many days will you run as much as he has?"
Suyodhana: "That's how it is to simplified?"
Balram: "Yes. If 'x' is the no of days, your equation becomes:
450 + 5 * x = 10 * x
Solving it, shows that x is 90 days. In 90 days, you can outrun him."
Suyodhana: "Wow!"
Balram: "And if you still want to beat him in 60 days, like you challenged him, you need to run 12.5 kms a day. Now go ahead and get that gaming console."

Wednesday, December 28, 2011

2011 in Retrospect

The year ends. It is the time for people to put up lists and for more people to read those lists and disagree with what is put on them. I decide to put a list of my own. List all the good things that happened to me in the year 2011. I think hard. But I am listless. That is how I have been all year -- pessimistic. I read some research paper that said that our brains are possibly wired for optimism. In situations where outcomes of events can't be guessed logically, the mind always imagines that something positive will happen. Strangely, that optimism shows up only when I am playing Texas Hold 'Em Poker on Facebook.

When I decided to write this post, I couldn't recollect any good things to write about. That's how much I like to be miserable. Joy is a fleeting moment that needs to be compressed into a 140-character tweet and forgotten. That's how I dilute that emotion. But I decided to request the misery to placate its place for an hour so I could look at the good things that 2011 had to offer.

Fantastic! Thank you very much! This is the upbeat side of me taking over. Let's not waste time and get this list going, shall we?!

Good Books: Salman Rushdie's "Midnight's Children" was read. Awe inspiring. Made me realise how much knowledge, intelligence and immense patience is required to write a novel that can grip a reader. I'll do that some day; next year; or the one after that perhaps. That was followed by the unbelievably hilarious "Hitchiker's Guide To The Galaxy". Suddenly, Life, Universe & Everything were flung into sunshine from the edge of space. All thanks to the consumption of the Pan Galactic Gargle Blaster at the Restaurant at the End of the Galaxy. Life was too serious, it made me realise, to take it more seriously. The seriousness was amplified by finally getting around to read "2001: A Space Odyssey". In short, I'm buying books. Lots of books. I hope to read them soon.

New Hairstyle: I can't recollect what went through my head when I decided to go bald in the Summer. Oh yes, I remember now. It was a razor. The sense of lightness that it left behind has made me dislike growing hair longer than a couple of inches.

Ganga Aarti
Travel & Photography: A wide angle lens was purchased. Frankly, I haven't taken a liking to the lens so far, which presents a bit of distorted perspective of things. But a different perspective always presents a new viewpoint. I didn't travel much. A bit of a disastrous trip to Varanasi in the height of summer that almost gave me a sunstroke makes it to the northernmost point of the country I've ever been to. Chidambaram and Auroville gave good photographs and Bangalore provided much entertainment. An external flash was purchased but hardly put to use. I've blown away a lot of money this year and none of it went in to the Europe trip I'd announced on my blog.


Music: I decided to deviate from the genre of music that I kept listening to over and over again. I've been led to some good musicians and inspiring music in the bargain. Must thank my friend, @jnarin, for providing so many recommendations. I've found respect for Steven Wilson for the enormous work he's put in in numerous bands including Porcupine Tree. Opeth's album, Damnation, evoked something very deep; deep enough for me to cherish that album for years to come. Then there was the Metallica concert. I was hesitant to attend it but bought tickets, never the less. The fiasco at Gurgaon, the maddening crowds at Bangalore, the rain, the jostling for space and the dirt made me question my decision. And then Metallica took over from there; they took over me. I didn't think I had it in me to attend such a high energy concert and enjoy it like the 20 year old version of me would have done. After all, it was his dream that I was living. But he made an appearance. I was surprised to see the world through his heart again. He knew the words of the songs that were played. He jumped; he howled; he punched his fists and went mad. It felt like he had been confined in a dungeon against his wishes and asked to behave all these years and that moment was his moment of freedom. He exploded. What was left behind for me was pain. Pain in every part, every inch of my body. Also, soiled pants and footwear.

Rahul Dravid: I saw a few games of IPL at the stadium this year. Also saw my first cricket match at a World Cup. The Indian team won the World Cup and I enjoyed it. But none of it could match the new found respect I found for this man, Rahul Dravid. Indian team suffered a humiliating 4-0 defeat in England and yet Dravid stood out like a knight among pawns. He certainly battled like one. The greatest victory is not to defeat your opponent, but to win him over. And he won the hearts of the Englishmen. That at a time when his career was said to be over. That was followed by the speech he made at the Bradman Oration. I never knew that the man possessed such a keen insight into the functioning of the game. In a game dominated by commentators making cliched observations, Rahul Dravid's words whipped up reality which seemed forgotten in the pile of rubbish that was doled out by self professed experts of the game. He shared anecdotes that gripped you; some made you smile. And then he went on to talk about his passion for the game. He started talking of how sometimes he'd stand in the slips or at the non-striker's end and get into this zone of solitude. The crowd, their expectations, the money, the fame, the immense pressure and everything else would die out and he'd just stand there enjoying the moment just because he was able to play the game he loved. Such a description of a meditative trance put goosebumps all over my skin. I don't think any other cricketer could elicit such a reaction. Dravid is the paragon when it comes to justifying the adage that hardwork pays. He has immense patience and a relentless urge to achieve perfection. Put him against odds and he will wear his knight's armour and prepare for a long, arduous battle. He relishes such situations. I now give him the same respect I have for Arsene Wenger.

Football: Now that Arsene Wenger has been mentioned, the talk has to drift to my favourite sport -- Football -- and my favourite team -- Arsenal. The summer was heart breaking. Cesc Fabregas left Arsenal for Barcelona. I could have cried every time a rumour was raised of his departure. By the time, the rumour became reality I had resigned. A new hero was to be found. And the new hero was found. There can be only one person, mention of whose name lifts my heart. They call him Van The Man; they call him Captain Vantastic; he is all of that and more. He is Robin Van Persie! Fabregas left a void behind that got deepened by poor games by the team when the season started. Van Persie filled that void. He has struck staggering form this year. 34 goals in a calendar year. That's as high as Arsenal legend Thierry Henry. He takes up the responsibility of a leader with such ease and excels at it. Some of the goals he's scored have been jaw dropping and they are good enough to wipe off all the frustration that comes from jibes that are thrown at Arsenal supporters. This year shall be remembered for Robin Van Persie.

That wraps up a really long post. Before I let the miserable side of me take over, I wish you all a Happy 2012.

2011 was atrocious; 2012 will be the same. I'll explain why... *log off*

Tuesday, December 13, 2011

Blogpost No. 300

It has been a long, exhaustive, overdue and an utterly boring wait to get here. But we are here. Or at least I am here and by some means I've coaxed you to join me. We are celebrating a milestone. This is post no. 300. And this is not Sparta.
As is the case with most such milestones, it makes me look back. This time I looked back to find out when I had written post no. 200 and post no. 100. Searching for them made me realise how little I've been sharing in the last 4 years. Post no. 100 - A century of pakofying makes me cringe a bit at the way I have written it. I was clearly attempting to please a certain set of audience. Not to mention how I used it as an opportunity to plug so many posts. Post no. 200 - #200: The path of least resistance was reasonably better. I can see how I had moved away from playing to the gallery and entered into a stage where I lived within my own trying to understand myself. I seem to like that change of direction. It made me move into areas of fascinating unknowns. Marveling at them has been quite delightful. Good enough to revisit those writings once in a while. I read those posts and realise how I used to be buzzing with ideas in my head.

And now I am faced with doing a certain justice to this post. When the 40-year old Sudhamshu attempts to write the 400th post, I need to ensure that he comes to the conclusion that I was getting better at doing this. So much pressure to please these old people. (Sorry boss!)

This post is going to be about Honesty; honesty in writing; honesty in thoughts. That is where the drift seems to be going from older posts to the newer ones. I used to attempt to please. I possibly succeeded at that time. It comes at an expense. That of exaggerations and hyped up expectations. Some thoughts weren't even mine to begin with. I entertained them because I was passionate back then and those ideas seemed to fire me up from within. I loved that feeling. Writing about it seemed to give me a purpose. Hindsight shows me the futility of it. Contradictions in your own thoughts have a way of avoiding each other, for a while. Eventually, when there is no one else left to fool or justify, you have to face them. One of the contradicting ideas has to be discarded. It is not easy to admit your own mistakes. Specially when you know that nobody will be praising you for doing so. This introspection comes at a cost. It tends to kill the passion; that catalyst which ignited the spark into an idea, without worrying about the contradictions.
And that is how I have begun moving towards neutrality. It is a difficult process that cannot live with an ego and demands modesty and humility. The fiery passion has no place in neutrality. Only thing that drives you further is an honest attempt in unearthing what is truthful. Or at least something that doesn't have a friction with your conscience. It is a process where you tend to hear all sides of a subject without taking sides. It is a process where facts matter more than emotions. It is an arduous process demanding patience. It is an excruciatingly boring process. What it eventually achieves is a strong opinion that cannot be shaken.

That sets the tone of things to come. What is a milestone without a little thanksgiving, eh? There's just one person that comes to mind when I ask, "Who on Earth would be jobless enough to read each and every one of my blog posts?" and the answer is -- Nandan Hodavdekar. I always appreciate the encouragement he gives and no blogpost is complete without his comment. He sets high standards for the literature he reads and I feel humbled to have a dedicated reader in him. Thank you, Nandan. I hope you're still around here when the 40-year old Sudhamshu continues to spread the Pakau stuff.

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