January 25, 2019

Srinivasa Ramanujan: The 1729 Man

A math column I wrote in December 2012 for Mint, reprised here.


What I've been doing all morning is, I've been trying to come up with some numerically interesting factoid about the number 125. It's what you get when you cube 5 (5 x 5 x 5, or 5^3), but that's kind of ordinary, no? Well, you can write it as the sum of two squares in two different ways:

2 x 2 + 11 x 11 = 4 + 121 = 125
5 x 5 + 10 x 10 = 25 + 100 = 125

Now that's promising. But is 125 the smallest number that can be so expressed? No, because 65 is the sum of the squares of 1 and 8, as well as the squares of 4 and 7.

Hmm. Maybe 125 is the smallest cube that can be written as the sum of two squares in two different ways? It certainly is! Now we're talking!

Yet what exactly are we talking? And why am I pursuing this pointless pastime?

Well, the great mathematician Srinivasa Ramanujan would have been 125 tomorrow, December 22nd. Mathematicians all over India -- and indeed the world -- are celebrating his life. Delhi, for example, hosted a major international Ramanujan conference this week. And I suspect all who attended -- anyone, in fact, who knows something about Ramanujan -- will know the story about him that prompted my quest with 125.

This story: he was in hospital in Putney, England. In walked GH Hardy, his mentor and a fine mathematician in his own right. He told Ramanujan that he had come in a cab whose number, 1729, "seemed to me rather a dull one." (I get the feeling Hardy and Ramanujan rather liked playing around with numbers).

The sick Ramanujan disagreed. "Oh no, not at all!" he said. "It is the smallest number that can be written as the sum of two cubes in two different ways!"

Of course he was right. Here are the two ways:

1^3 + 12^3 = 1 + 1728 = 1729
9^3 + 10^3 = 729 + 1000 = 1729

And 1729 is indeed the smallest such number. And because of this incident, it is now known as the Ramanujan-Hardy number.

What touches me about this story is though Ramanujan was seriously ill that day, he was sharp enough to remember, and tell Hardy, this little nugget about a random number Hardy mentioned. And so, to mark his 125th birthday, I thought it only fitting to search for some nugget like that about 125. (Seeing as I've got other plans for his 1729th birthday).

Though I think I have to admit: 1729 is a more interesting number than 125.

Ramanujan's life-story is too well-known for me to spell it out here. Suffice it to say that when this clerk in Madras sent some of his homespun mathematical research to Hardy in 1913, Hardy saw genius in it and invited Ramanujan to work with him at Cambridge. What followed was an intensely productive five-year collaboration and friendship between these two remarkable men. For me, something of that relationship is captured in a famous tale about how Hardy rated his own and other mathematicians' raw talent for mathematics. On a scale of 0 to 100, Hardy awarded himself 25. And Ramanujan? 100.

But despite Hardy's respect, England took a toll on Ramanujan's health. In 1919, he returned to India. In April 1920, at just 32, he died.

I wouldn't presume to dissect Ramanujan's mathematical work here. The great majority of it ranges far beyond both my understanding and ability to explain. But what I do understand are his efforts to calculate the value of π (pi) that intangible number that tells us the ratio of a circle's circumference to its diameter. Much like Roger Federer used to rack up Grand Slam tennis titles, Ramanujan churned out formulae (the better word is series) to calculate π. One of them turns out to look like this:

1/π = 5/16 + 376/65536 + 19224/268435456 …

Take my word for it: those three terms alone give a value for π accurate enough for most purposes you might imagine. Other Ramanujan formulae have been used to calculate π to millions of digits after the decimal point.

All of which is fascinating and remarkable enough. Yet to a layabout like me, Ramanujan's real appeal lies in that story about 1729. Because in a quiet yet substantial way, it speaks for the way his mind worked. It speaks of his curiosity and passion for numbers and mathematics. It tells me that when you constantly search for and find wonder in the smallest things -- who would have thought, 1729? -- you prime yourself for greater things. And Ramanujan achieved some great things indeed.

That's the lesson I take from the life of this young genius from Kumbakonam.

As of last year, his birthday is observed as National Mathematics Day in India. So celebrate it tomorrow. Celebrate an exceptional mind. And if you stumble on something interesting about 125, please let me know.

February 29, 2016

The watch and the film star

The question I have is, should I blame the film star? I played tennis with him this evening. Good session, apart from two things.

One, I can't get my mind to trust my right knee enough while running, even though I feel no pain in it. Hard to explain or understand, but there it is. So I can't get my footwork right, so I can't get my shots right. So that was frustrating.

Two, I served only double-faults. I'm not proud.

Session done, I walked back to the apartment. Looked at the time and noticed that my watch had a small film of water droplets inside the glass. Which sometimes happens if I have been sweating a lot. I usually put it under a table lamp for five or ten minutes and it clears. Trouble is, no table lamp in this apartment.

I looked for alternatives. Found a lamp on the wall that would do the job, except nowhere to place the watch near enough to it. So I hit on possibly the most brilliant idea I've had in my entire life to date: let's wrap the watch around the bulb.

Which I did, and went off to have a shower.

When I emerged, there was a slight but definite burning smell. I couldn't place it, so I put it down to my hyperactive imagination.

But then I remembered. Ran over to the lamp. Strap totally melted, some of it is still stuck firmly to the bulb. Watch partially melted and badly warped -- or in a word, destroyed. Stuck forever at 732. My favourite watch too, a bright blue face with a single big "2" on it. 

Hard to comprehend just how stupid I was, doing this. But there you are. Watchless for the next couple of weeks. Brainless, always. And no, I can't blame him.

June 23, 2015

John and the phone scam

My university buddy John wrote recently from the States. He has found an intriguing way to ... well, perhaps I'll just let him explain. Here is his mail, verbatim.


Hi Dilip,

There is a phone scam that has been going around in the US for a number of years. Someone calls (always from an Indian call center with a lot of noise in the background) saying they are from Microsoft, and they noticed that your PC is spewing out packets and harming the performance of the Internet. They then ask you to walk through a sequence of steps that if done would give someone the ability to completely control your Windows machine remotely and install all sorts of malware and what not.

The first time they called me I had been taking a nap, so I naively  asked which of my machines was causing the problem, and told them I have Mac computers so it could not be me. After I hung up, I Googled to see what the exact scam entailed and it made sense.

Since then, I've had great fun toying with these guys, and there is a connection to you.

I pretend that I am following their commands, and they ask me to bring a command line prompt and tell them what I see. Then they ask me to type stuff and tell them what I see. At a certain point, I tell them "the screen says B H E N C H O D.... What does that mean?" They are astonished and asked me to read it back three or four times. Then they get really angry. I've been called a "bloody bastard" and more.

The connection is that you taught me this word and its meaning more than 30 years ago, and said that it is quite powerful. You were right!!! :-)

This just happened again on Friday. The caller denied knowing what the phrase meant, even though he was clearly rattled. I told him I would Google it "to see what this error message stood for". I then said "it says you are a sister f******". He then insisted that the "you" in the Google result referred to me and not him. I could barely contain myself, and pretended to Google it again, and said "no, it is saying that it refers to you" and he got even more upset.

This is a really sinister thing they are doing, so I don't mind wasting their time.

Thanks for teaching me that phrase! :-)


June 19, 2015

What if they gave a triple-century and noone came?

The new issue of Wisden's quarterly of cricket essays and long-form writing, The Nightwatchman, is out. I have an essay in it, about watching the Ranji Trophy final at the Wankhede Stadium in Bombay last March.

Sadly, the issue is only available in print or e-book versions. You can buy it at their website, which I urge you to do. But I'm hoping you'd like to read my essay -- it is appended below.

Comments welcome!

 What if they gave a triple-century and noone came?
The Ranji final in a time of the World Cup

When Karun Nair got to 300, late on the third day, I looked around and counted as best I could. It wasn’t hard. The great majority of cheering spectators was in the Sunil Gavaskar Stand alongside me, but a small, disproportionately vociferous lot was to our left in the Divecha Stand – between us and the pavilion, where the cricketers emerged from and disappeared into. But don’t be fooled by that phrase “great majority”: in a stadium that can seat something like 35,000, those present here numbered about… 125.

If Nair had scored two runs for each man – the audience was mostly male – who watched him reach his triple ton, he would not have reached it. Luckily he didn’t approach his task quite like that. But that count might just have summed up this match.

There were other ways the lack of interest in the 2015 Ranji Trophy final hit me. The first morning (8 March), for example, I arrived at the Wankhede Stadium at 9.15am – 15 minutes before the start. The gate was locked and a guard in a smart dark-blue uniform asked why I was there. “For the Ranji match,” I said. “Ah, but then you might as well go have some tea and take a nap,” he replied. “The match won’t start till about 10.30 or 11.” When I told him the scheduled start was 9.30, he looked disbelieving, but reluctantly opened the gate for me. I was the first fan in the Gavaskar Stand, though Divecha had an already voluble handful, waving green and gold flags.

Two days later, I arrived at the stadium ten minutes before the start. How many in the stadium, you think? Not just in my stand, but in the whole complete stadium. Including me, the count was – get this – one. Have you ever been the sole spectator in a massive stadium? It’s breathtaking. I urge you to try it. Maybe at next year’s Ranji final.

This dearth of fans has persisted at Ranji games despite tickets being free, which by itself says something about the state of long-form cricket in India. The Ranji final is effectively the Super Bowl of domestic cricket, but those who run Indian cricket know they cannot ask would-be attendees to cough up even a nominal amount – there’d be no attendees at all then. So it’s free, but the administrators are stingy about where they allow us freeloaders to sit: only in the east (Gavaskar) stand, subject to the fierce afternoon sun, and side-on to the pitch so there’s no way to get a sense of bowlers’ spin or swing.

Imagine the Wankhede as the face of a watch, with the pavilion at 9 o’clock. Throughout this match, the arc from 9 clockwise to 6 had absolutely nobody in it. The arc from 6 (where I sat) clockwise back to 9 had – at its most crowded – 150 spectators.

Thus did Karnataka and Tamil Nadu do battle for the Ranji Trophy. Which itself brought on one last niggle about those who run Indian cricket: why did they schedule this match at, of all places, a neutral venue like the Wankhede? Why not in Bangalore or Chennai, where home-team enthusiasm, if nothing else, might have swelled the crowd to – dream big, son! – 200?


It’s now commonplace to bemoan the steady sidelining of the Ranji Trophy. How is this sedate form of the game to compete with the razzmatazz of the IPL? (No free entry to IPL games, in case you were wondering.) Or with the World Cup, going on at the time in Australia and New Zealand?

The short answer has got to be: there really is no competition. I found that out for myself the night before the game started. A friend was over for dinner and I mentioned my cricket-watching plans. “Oh, so you’ll see all those cheerleaders, then?” she asked. (Let’s leave aside her cricket illiteracy on several counts.) When I explained there would be no cheerleaders, she wrinkled her nose and looked bewildered: “Why are you going, then?”

Was this a commentary on cricket: without cheerleaders, this match could hardly be much of a spectacle? Or was this a commentary on me: she could not believe I would make the effort to attend an event free of cheerleaders?

Either way, the point was made: the Ranji tournament – even the final – interests few. This is a difficult pill to swallow when I wallow, as I often do, in the nostalgia of too many days of my youth spent listening to cricket on the radio. All long-form then, of course. My Rajasthan college campus came to a standstill, I remember, for a few days in the mid-1970s when Delhi hosted Bombay in a Ranji final. I no longer recall who scored and who picked up wickets. I do remember several stellar names in both teams: Gavaskar, the Mankad brothers, Solkar, Gidwani, Bedi, the Amarnath brothers, Madan Lal. Bombay won a gripping, seesawing match in front of a full house whose baying we could hear, on our tinny medium-wave sets, all the way in Rajasthan. The match divided the campus right down the middle: the guy in the room behind me was a Delhi fanatic who yelled good-natured abuse at me in the middle of the night through the little grille that separated our rooms. Staunch Bombay fan that I was, I went one-up – I flung eggs through the same grille. Ah, the passions the Ranji Trophy aroused. Once.

Though both have impressive Ranji résumés, neither Bombay nor Delhi made it to the final in 2015. Karnataka and Tamil Nadu, fierce southern rivals, did. Both teams were also stacked with stellar names: Murali Vijay, Abhinav Mukund, L Balaji, Vinay Kumar, Abhimanyu Mithun, KL Rahul, Karun Nair, Robin Uthappa. If this had been the mid-1970s all over again, they’d have played in front of another baying full house. But when you have 150 or fewer, the baying is rather muted.


The elephant in the room – or at the Wankhede – was that the Ranji final happened smack in the middle of the World Cup. So the stands were empty not only because cricket fans have lost interest in the Ranji Trophy, but also because they were following goings-on – 50 overs at a time – in faraway Australia and New Zealand. So it was a wonder by itself that, during the World Cup, as many as 150 people turned up to watch a Ranji game. That wonder was what pulled me to the Wankhede.

Most of the much-anticipated league matches of the Cup – India–Pakistan, Australia–New Zealand, Australia–England – were done by the time the Ranji final came around. But there were still games every day, including an India game (against Ireland) on the third. I travelled to the Wankhede each morning feeling slightly sorry for these Karnataka and Tamil Nadu cricketers – some of whom had probably hoped to be playing for India, all of whom probably wanted to watch Cup games on TV. How were they going to focus instead on this match?

In the asking of that question lies the certainty that I’m not – could never have been – a professional cricketer. Cup or no Cup, these 22 men played out an intense match filled with superb batting, bowling and fielding performances, including a spectacular reflex catch at silly point that made me long for an instant replay. One-sided though the match was – a Karnataka victory seeming inevitable as early as the second day – there was verve and vigour on display throughout.

But if that described the players’ approach to the game, the audience cared significantly less. Day one passed with regular updates about the nearly simultaneous Australia–Sri Lanka game, an evidently more attractive proposition than either this match or New Zealand–Afghanistan, also that day. Amid the regular sharing of scores in the stands, a friend sent me a text: “Maxwell going berserk against SL!” My beeping phone caught the attention of a thick-set older man nearby. “What’s the score?” he asked, automatically assuming that if I was getting text messages while watching the cricket, they must be about the World Cup.

If Maxwell was going berserk somewhere in Australia that day, Vinay Kumar and his merry Karnataka men were running roughshod over Tamil Nadu. Wickets fell with depressing regularity. Normally that’s the kind of cricket I like – give me regular wickets any day over batsmen dominating the game. But perhaps my otherwise-dormant Tamil roots made this procession disheartening. Only their captain and opener, Mukund, showed any spunk. A curious inwardly-bent right knee is his initial movement as the ball leaves the bowler’s hand. Surely not what the coaches suggest? But he defended well – and stroked several boundaries too – on his way to 35. He must have been dismayed, though, as he watched teammate after teammate capitulate. Across the aisle from where I was sitting, three Tamil speakers who had travelled from Madras (they used their city’s old name) were reduced to glum automatons after a vocal and cheery start. They shook their heads in silence, despair mounting with each wicket. Tamil Nadu subsided to 134 – a barely adequate score in T20, let alone the five-day game. After this first-innings train-wreck, their hopes of winning the Trophy hung by a fingernail.

But Tamil Nadu perked up within the hour, as did the men who had travelled from Madras. Their fast bowler L Balaji – best known for his feats during India’s tour of Pakistan in 2004 – carved through Karnataka’s top order. It was probably his wide, ready smile that endeared him to our western neighbours: he was the most popular member of that team, “Balaji, Balaji” screamed by full-throated crowds at every Pakistani stadium. He had a reasonably good tour, but hasn’t played much for India since. Today, with his gentle run-up and explosion through the crease, he worked up some serious pace to take three wickets – his pacer partner Parameswaran took one – leaving Karnataka, at an overnight score 49 for 4, pondering the vicissitudes of cricket. One afternoon, you’re walking on cloud nine because you’ve gone through Tamil Nadu like a knife through hot butter. Not long after, Tamil Nadu returns the favour.


The next morning, though, things don’t start well. Not in the stands, not out in the field for Tamil Nadu. I reach the Wankhede as the first over of the day ends, turn to two young men fiddling with smartphones and ask: “Who bowled that over?”

One responds: “Kya maloom, sab toh kale dikhte hain!” (“Who knows, they all look black!”)

When I express some disgust at this, his friend rounds on me: “What, are you from Tamil Nadu? Who do you support?” There’s the implication that, being dark myself, I must back those darkies from TN. Whatever.

In the middle, Karun Nair and Abhimanyu Mithun, the nightwatchman, hold firm. The Tamil Nadu fielders clap each other’s efforts, urging their bowlers on to make inroads into Karnataka beyond 49 for 4. But the score chugs along smoothly, Mithun responsible for most of it.

About half an hour into the day, a large group of boys in school uniform appears behind me. “Who’s playing?” they ask of no one in particular. The skin-obsessives have a swift reply: “It’s India and Pakistan, playing a Test match.” Much backslapping and chortling that they have managed this snappy answer. The schoolboys mill around for a while, then turn and leave.

Soon after, a huge lbw appeal persuades the umpire to raise his finger, slow and studied, and Mithun walks off reluctantly. Replacing him is KL Rahul, who made a smooth century for India against Australia in the recent Test series. With pink highlights on his shoes, blue and pink gloves, and several fluorescent green patches on his bat, he is quite the vision: when Rahul runs, it’s like a small carnival of colour cavorting down the pitch.

And he runs a lot. For Rahul and Nair proceed to bat Tamil Nadu into submission. No more wickets fall that day, which ends with Karnataka at 323 for 5 – nearly 200 runs in front with centuries to both batsmen. It is a skilful display from the Karnataka pair – who never once look in trouble – but for this fan of bowling and wickets, it is a stultifying passage of play.

Soon after lunch the following day, as India battles Ireland over in Australia – amid more score-sharing – Tamil Nadu has their first wicket in over seven hours: they stop Rahul in full flow at 188. But by then Karnataka has 470 on the board, Nair has swept past 200, and there’s no doubt where the Trophy is going this year. Time to declare, surely? Yet much like an Energizer bunny, Karnataka just motors on and on and on. Even the few folks in attendance are baffled. One or two actually shout out loud: why are they batting on? The milestones drift past: Karnataka’s 500, 600, Nair’s 300. Time to declare? No. Nair is out for 328 the next morning. Now? No. Karnataka reaches 700, captain Vinay Kumar gets a century. Maybe now? No.

Tamil Nadu finally bowls Karnataka out for 762 – 628 runs in front. What was the point of piling on such a huge lead, except to keep Tamil Nadu toiling in the oppressive heat? Who really cares that – over the remaining day and a half – Tamil Nadu slashes their way to 411 and still loses by an innings and plenty?

Not too many in the thin audience, that’s for sure. A man, his wife and a kid — all in orange, oddly — walk past me and down to the bottom row. Their backs to the cricketing action, they take a number of selfies. In the middle of it all, she takes a call, nodding her head furiously, the other two looking impatient. Then they’re gone. Ah, the passions the Ranji Trophy arouses.

April 23, 2014

Your vote tomorrow

A note I sent out to my friends in Bombay today, April 23 2014.


Dear friend and fellow-citizen of this vast fascinating maddening incredible city:

Tomorrow is the day we'll all vote. May I count on our years of friendship to be bold enough to say a few things about that?

1. First and above all, please vote.

2. You probably know my thoughts on this, but nevertheless: Yes, I hope you will not vote for a candidate whose victory will help Narendra Modi become our Prime Minister. At this late stage, I'm not going to burden you with reading material. Instead, just three points:

- 2a. This is a man who, in 2007, appointed a murderer (Maya Kodnani) as his Minister for Women's Development and Child Welfare. I realize Modi is speaking an inclusive, near-faultless language these days. But he's aiming for the nation's highest elected office: he knows better than us all the need to come across as inclusive, thus to speak this language. Therefore I judge him not on today's rhetoric, but on his record. Among much else in that record is his Kodnani appointment. There is no explanation for this that makes Modi look good.

- 2b. I realize we all see what we want to see in Gujarat. But that alone should tell us that the story of a state far better than every other in every respect has holes in it.

- 2c. What worries me most about a Modi government is not Modi himself, but the loose cannons his ascent will give legitimacy and voice to. We've already seen examples like Giriraj Singh, Praveen Togadia and Ramdas Kadam. When a major politician announces that (for example) those who oppose him must be sent to Pakistan -- well, that kind of attitude simply worries me.

3. Finally, I also realize that I may have stepped on a few toes with this mail. Still, I trust that whatever our different views of politics, we can and will remain friends. That's also my faith in democracy, that we have different views that we are unafraid to express. This country has seen too much that divides us. I believe you will go to vote with the same hopes for a better tomorrow as I do. If you finally choose a different route to that better place than I do, that's your prerogative and mine. But if we let that choice itself interfere in our relationships, we let the divides win. I don't plan to let that happen.

All good wishes tomorrow.

Your friend,

(Comments intentionally disabled until after the vote).

February 22, 2014

Raptor Red

Does it say something that my favourite book of 2013 is one I read for the second time? (The first? When it was released, in 1996). "Raptor Red" is a delightful novel -- but for me, not so much because it is an engrossing story, which it is, or beautifully written, which it isn't. Nor even because its dinosaur protagonists are so engaging.

What makes this book memorable is what it says about an unsung virtue of science: how scientists build edifices of reason from the tiniest scraps of evidence. After all, dinosaurs went extinct 65 million years ago, and all we know about them comes from the fossil record. Yet palaeontologist Robert Bakker wrote this book to support his thesis that they were "warm-blooded, active and social animals."

It positively warms the cockles of my heart that a scientist proposes this, and plausibly, after poring over rocks buried for aeons. Then he writes a beguiling novel. Wow.

Raptor Red by Robert T Bakker
Bantam Books, 1995

January 19, 2013

How Rahul Gandhi blew it

My column in the Daily Beast is about the Gandhi family's reaction to the Delhi gangrape. Please do take a look: How Rahul Gandhi Blew the Indian Rape Crisis

Comments welcome, as always.