So I just finished David Quammen’s __The Song of the Dodo__. An intricate, fascinating, sweeping book on many different levels that I highly recommend. My mother wrote a review of it years ago, and I made a mental note then to read it. Only, it’s been on my shelf the last 20+ years and I finally yanked it off only last month and read it.

There’s plenty in the book that resonated, particularly the long sections about Madagascar which brought back so many memories of the months I spent travelling there. But I wanted to share with you one sentence from the book. It’s in Indonesian (Bahasa), a language Quammen only knows bits and pieces of.

He visits a remote Indonesian island chain called Aru in search of a bird of paradise. Now there are many species of this bird, but the one he is in search of here is *Paradisaea apoda*, the greater bird of paradise, the lovely creature in the picture above.

There’s a whole story to be told about why he searches, and why Aru — all that, I’ll save for another time (better, please read the book). But it takes him, early one morning, across a stretch of mangroves and up a muddy slope to reach a particular tree.

And as he gets close to the tree, he hears a “chorus of squawking” like “a truckload of hysterical geese”. Even his otherwise cynical and laconic Indonesian guide Jimmy, writes Quammen, “seems thrilled” by the sound.

Jimmy says: “*Suda, suara cenderawasih*.”

“Already, the song of the *cenderawasih*.”

If you read the book and absorb all that Quammen discusses, you might agree with me that it is a deeply moving, hopeful, profound thing that Jimmy says. Not least because of where it appears in the book. (Yes, you should read it).

But for now, I wanted to share the delight that a special someone pointed me to in the line. For which, I need to tell you that “*cenderawasih*” is pronounced more or less as written except that the “*c*” is said “*ch*”, and that it is the Bahasa name for these utterly beautiful birds.

Knowing that much, look again at the line and its translation. What can you tell about those words? (OK, it helps to know a little Hindi).

## September 26, 2020

### Song of the Dodo, Resident of the Moon

## May 24, 2020

### Peculiar events in a lockdown

Allow me to list here a few of the more peculiar events of the last several days. I mean, there have been many, and don’t get the idea that these are the most peculiar. I picked them out at random.

* A woman is desperate to get to her home in a distant corner of India. She has her father with her. She chooses her only option: to cycle home. 1200 km, with him riding pillion. You don’t need me to tell you that this is just one more wrenching story from this migrant tragedy that we have blundered into. You’ve seen and read about many many others like this pair.

But what happens with this one? A cycling federation announces that they will call her in for trials, once this lockdown lifts. Ivanka Trump (!) praises her “beautiful” love for her father and the federation’s announcement. Voila: one strand in this blanket of migrant misery has been successfully painted as a heartwarming story of guts and glory that — believe! Just do it! — may even bring India Olympic glory one day!

* PM Modi flew to West Bengal to get a first-hand look at the devastation caused by cyclone Amphan, a great natural disaster. As he should, of course.

PM Modi has also been flying all over the country to get a first-hand look at the devastation caused by the lockdown — the streams of desperate migrants on foot and in concrete mixers and being hosed down with bleach and more, of course — a great manmade disaster. As he should, of course.

But wait. Oops. My mistake. Only one of those flights actually happened.

* PM Modi flew to West Bengal to get a first-hand look at the devastation caused by cyclone Amphan, a great natural disaster. He was met at the airport by the state’s governor, one Jagdeep Dhankar. Two photos have emerged of that meeting and a subsequent one between the two men: this one and this one.

Take a look, for the governor’s posture in both says everything you need to know about him. And I need say no more.

* Out for walks last evening and this morning, I ran into a substantial crowd both times — on foot, scooters, cars, cycles — outside a particular store. I’m talking easily a hundred people, all male. Many without masks. Distancing? Forget it. The owner of the store must have been anticipating trouble, because standing outside the entrance were two hefty bouncers in deep blue shirts, wielding long sticks.

Curiously, the store itself was actually closed. Both times. Were these men waiting for it to open? Likely, but why so long? (Last evening the crowd was nearly unchanged twice that I passed during my walk, 45 minutes apart).

So what does this store sell? Liquor.

There’s a commentary buried in there, I suspect. (Full disclosure: I love my vodka and rum).

* A woman is desperate to get to her home in a distant corner of India. She has her father with her. She chooses her only option: to cycle home. 1200 km, with him riding pillion. You don’t need me to tell you that this is just one more wrenching story from this migrant tragedy that we have blundered into. You’ve seen and read about many many others like this pair.

But what happens with this one? A cycling federation announces that they will call her in for trials, once this lockdown lifts. Ivanka Trump (!) praises her “beautiful” love for her father and the federation’s announcement. Voila: one strand in this blanket of migrant misery has been successfully painted as a heartwarming story of guts and glory that — believe! Just do it! — may even bring India Olympic glory one day!

* PM Modi flew to West Bengal to get a first-hand look at the devastation caused by cyclone Amphan, a great natural disaster. As he should, of course.

PM Modi has also been flying all over the country to get a first-hand look at the devastation caused by the lockdown — the streams of desperate migrants on foot and in concrete mixers and being hosed down with bleach and more, of course — a great manmade disaster. As he should, of course.

But wait. Oops. My mistake. Only one of those flights actually happened.

* PM Modi flew to West Bengal to get a first-hand look at the devastation caused by cyclone Amphan, a great natural disaster. He was met at the airport by the state’s governor, one Jagdeep Dhankar. Two photos have emerged of that meeting and a subsequent one between the two men: this one and this one.

Take a look, for the governor’s posture in both says everything you need to know about him. And I need say no more.

* Out for walks last evening and this morning, I ran into a substantial crowd both times — on foot, scooters, cars, cycles — outside a particular store. I’m talking easily a hundred people, all male. Many without masks. Distancing? Forget it. The owner of the store must have been anticipating trouble, because standing outside the entrance were two hefty bouncers in deep blue shirts, wielding long sticks.

Curiously, the store itself was actually closed. Both times. Were these men waiting for it to open? Likely, but why so long? (Last evening the crowd was nearly unchanged twice that I passed during my walk, 45 minutes apart).

So what does this store sell? Liquor.

There’s a commentary buried in there, I suspect. (Full disclosure: I love my vodka and rum).

## May 18, 2020

### Turned to beggars, one by one

My friend Nity walked with some migrants. So have some others. Through their accounts, I know second-hand what so many of my fellow-Indians are reduced to in this time of lockdown.

But I also know simply by looking out my window on any given evening, and these days I don’t even need to look, I just need to keep an ear peeled. First-hand knowledge, too. On any given evening, there are anywhere between 25 and 40 people scattered around the nearby junction, waiting for food. From a distance, the women sit like so many dhobi-bundles, the men stalk about like long-legged storks. There seem to be occasional random generous people who stop and hand out food, but there’s clearly also an organized effort by young men on scooters. Two on each, the pillion man facing backwards to make the hand out go more smoothly. I once stopped to ask them who they were: residents of the nearby fishing “village”, really a densely-populated collection of ramshackle and not-so-ramshackle houses. A slum pocket, really. “We just decided to bring food for these people daily,” a pillion rider told me. "These people and watchmen in all these buildings, some of them are not getting any food. Then his partner revved their scooter and they sped off to the south, off to offer food to some others who needed it.

My ear now knows too. Because every evening, a cop comes by on a gleaming Bullet mobike, stops in the middle of the junction and uses his horn liberally to scatter the small horde. Some evenings he goes on with this for a couple of hours: the people he shoos away seem to want to come back almost immediately. From my window, I can see some of them remonstrating with him.

Who are these people and what’s to become of them?

Then there’s our pal A who sells us vegetables at the same corner, and our pal G who operates a taxi and who waits for business at, yes, that same corner too. Both have come by in recent times to ask for a little cash, their shame and anguish at needing to ask evident even through their masks.

What’s to become of us if a lockdown turns too many of us into beggars? Beggars that cops must be deputed to disperse? Beggars who wait for food?

But I also know simply by looking out my window on any given evening, and these days I don’t even need to look, I just need to keep an ear peeled. First-hand knowledge, too. On any given evening, there are anywhere between 25 and 40 people scattered around the nearby junction, waiting for food. From a distance, the women sit like so many dhobi-bundles, the men stalk about like long-legged storks. There seem to be occasional random generous people who stop and hand out food, but there’s clearly also an organized effort by young men on scooters. Two on each, the pillion man facing backwards to make the hand out go more smoothly. I once stopped to ask them who they were: residents of the nearby fishing “village”, really a densely-populated collection of ramshackle and not-so-ramshackle houses. A slum pocket, really. “We just decided to bring food for these people daily,” a pillion rider told me. "These people and watchmen in all these buildings, some of them are not getting any food. Then his partner revved their scooter and they sped off to the south, off to offer food to some others who needed it.

My ear now knows too. Because every evening, a cop comes by on a gleaming Bullet mobike, stops in the middle of the junction and uses his horn liberally to scatter the small horde. Some evenings he goes on with this for a couple of hours: the people he shoos away seem to want to come back almost immediately. From my window, I can see some of them remonstrating with him.

Who are these people and what’s to become of them?

Then there’s our pal A who sells us vegetables at the same corner, and our pal G who operates a taxi and who waits for business at, yes, that same corner too. Both have come by in recent times to ask for a little cash, their shame and anguish at needing to ask evident even through their masks.

What’s to become of us if a lockdown turns too many of us into beggars? Beggars that cops must be deputed to disperse? Beggars who wait for food?

## January 26, 2020

### That awful moment of parity between the religions

I've covered the ground in this essay before, but two things: 1) It bears repeating, it bears repeating, because the myth it seeks to debunk keeps getting regurgitated. 2) I thought I'd explain the actual mathematics behind the debunking.

So here you are. Myth: Muslims are soon going to outnumber Hindus in India. Debunking: below.

Myths need busting, and often over and over again. Often too, it’s a futile exercise, because to some, the myths are more seductive than any busting. Yet especially in this fog of accusations and hatred we’re living through right now in this country — the wrangle over the CAA and NRC, I mean — it’s especially important to keep on with the busting. I’m going to attempt just that in this column, but by using some of what this column is about: mathematics.

I’m repeatedly amazed at how much of the defence of the new Act is couched in terms of extreme hatred of Muslims. That by itself should be a red flag, a sign of something amiss. Yet the hatred keeps flowing. And too often, it finds expression in population numbers. Muslims are increasing their numbers, goes this argument, much faster than Hindus. Which means, goes this argument, that the time is just around the corner when Muslims will outnumber Hindus in India.

This is supposed to be a terrifying thought. One scare-monger spelled out his fears about this in an article, long before we had even heard of the CAA: “Non-Muslims now rarely venture into areas of India where Muslims are in large numbers, fearing unpredictable, irrational behaviour or violence directed at them.” Given that kind of fear, the prospect of Muslims actually outnumbering Hindus in this land, this man wanted his readers to believe, is self-evidently a horrible one for us all.

Well, it is indeed a horrible prospect, but not for the reason the haters like him hold tight to their puny chests. Let me explain, using numbers we actually have rather than empty rhetorical flourishes like “where Muslims are in large numbers”.

In August 2015, the Registrar General and Census Commissioner released population data by religion from India’s 2011 Census. Taken from there, consider the population growth of the various religions in the decade 2001-2011. The Hindu population increased by 16.8% in those ten years, Muslim by 24.6%, Christian 15.5%, Sikh 8.4%, Buddhist 6.1% and Jain 5.4%. The result, as of 2011, was that 79.8% of Indians were Hindu and 14.2% Muslim. Other faiths each accounted for far smaller fractions of our population, which the Census found was just over 1.2 billion.

That is, in 2011 we had about 958 million Hindus in India, and 170 million Muslims.

With me so far? Now if we assume the same growth rates persist (which we cannot, but I’ll return to that) — 16.8% per decade for Hindus, 24.6% for Muslims — we can project both populations to the time in the future when Muslim numbers will equal Hindus. When will that be?

To answer that, we need some relatively elementary, if a little involved, arithmetic. Bear with me as I explain.

Here’s the issue: the 958 million Hindus are growing at a rate of 16.8% every decade, and the 170 million Muslims at 24.6% every decade. One decade from now (or actually from 2011, but let’s not quibble), the two populations will have increased by these amounts:

Hindus: 958m x 16.8% = 161m

Muslims: 170m x 24.6% = 42m

That is, one decade from now the respective populations will be:

Hindus: 958m + 161m = 958m x 1.168 = 1.119 billion

Muslims: 170m + 42m = 170m x 1.246 = 212m

Since we assumed the growth rates don’t change, we can do just the same calculation for the decade that follows. The increments in those ten years will be:

Hindus: 1.119b x 16.8% = 188m

Muslims: 212m x 24.6% = 52m

And thus the respective populations two decades from now:

Hindus: 1.119b + 188m = 1.119b x 1.168 = 958m x 1.168² = 1.307b

Muslims: 212m + 52m = 212m x 1.246 = 170m x 1.246² = 264m

We could keep doing these laborious calculations for decade after decade, of course, searching after every iteration for the point when Muslim numbers will equal Hindus. But no doubt you recognize this growth as equivalent to the notion of compound interest — and we know how to calculate that. Thus, three decades from now, the populations will be:

Hindus: 958m x 1.168³

Muslims: 170m x 1.246³

And to generalize this, some number “n” decades from now, the populations will be:

Hindus: 958m x 1.168ⁿ

Muslims: 170m x 1.246ⁿ

So now we ask, for what value of n will these two be equal? That is, we want:

958m x 1.168ⁿ = 170m x 1.246ⁿ

Rearrange this equation:

958/170 = (1.246/1.168)ⁿ, or 5.635 = 1.067ⁿ

I wouldn’t hold it against you if your eyes are glazing over by now. Lots of calculations, I know. But we’re almost done. Your high-school mathematics memories will tell you that at this point, we use logarithms, and that gives us:

log 5.635 = n x log 1.067, or n = log 5.635 / log1.067 = 27.

There we have it. At those growth rates, it will take 27 decades, or 270 years, for the Muslim population to catch up to the Hindus.That is, the hate-mongers are quaking in their shabby boots — and asking us to do so as well — about something that will happen as we, or actually our descendants many generations over, close in on the 24th Century. Are you really going to worry about what might happen in the year 2290 AD?

But even if the haters do quake about that, let’s ask another question: assuming these growth rates, how many Hindus and Muslims will there be in India in 2290? In other words, what is 958m x 1.168

Answer: 64 billion. 64 billion Hindus and 64 billion Muslims. Think of it. This, in a nation that today has a total of 1.3 billion Indians. This, meaning 100 Indians for every single Indian living today: 100 Indians crowding that spot where you sit reading this, 100 Indians jostling for the tiny standing space you occupy in the 8:27 Churchgate fast, 100 Indians sharing one seat to watch Deepika Padukone in a rerun of Chhapaak, just as they were going to do this week. This, and remember we have not accounted for Christians and Sikhs and Buddhists and other varieties of Indians, not forgetting other denizens of India such as cows and dogs, cars and bookshelves, trees and playgrounds.

This is the mirage-like prospect that a deep-seated hatred drives people to dream up and fear.

The truth should be apparent. The really horrible, fearful prospect is not that Muslims will outnumber Hindus. Instead, it’s that hundred-fold increase the calculations above suggest. If we are actually going to rack up numbers like those, we will have died out from overcrowding long before getting to that moment in 2290 AD, that dreadful prospect of Hindu-Muslim parity.

And here’s what makes that prospect even more mirage-like. The reality is that we cannot assume the same growth rates — Hindu 16.8%, Muslim 24.6% — will hold indefinitely. In the earlier decade, 1991-2001, Census 2001 figures showed that the Hindu and Muslim populations increased by 19.9% and 29.5%, respectively. Those numbers decreased to 16.8% and 24.6%, respectively. Obvious from those numbers is that growth rates are decreasing. There’s nothing unusual here; this is exactly what happens as a country develops. (Note too that the Muslim growth rate declined faster, decade to decade, than the Hindu growth rate). So since the country has continued to develop since the 2011 Census, the 2021 Census will certainly show further declines in these growth rates. That means even greater population projections than 64 billion, an even longer time to population parity than 270 years.

Welcome to the overcrowded wasteland of 25th Century India, perhaps. The pity is that the hatred in too many of us reduces us to such a wasteland right now.

So here you are. Myth: Muslims are soon going to outnumber Hindus in India. Debunking: below.

***

Myths need busting, and often over and over again. Often too, it’s a futile exercise, because to some, the myths are more seductive than any busting. Yet especially in this fog of accusations and hatred we’re living through right now in this country — the wrangle over the CAA and NRC, I mean — it’s especially important to keep on with the busting. I’m going to attempt just that in this column, but by using some of what this column is about: mathematics.

I’m repeatedly amazed at how much of the defence of the new Act is couched in terms of extreme hatred of Muslims. That by itself should be a red flag, a sign of something amiss. Yet the hatred keeps flowing. And too often, it finds expression in population numbers. Muslims are increasing their numbers, goes this argument, much faster than Hindus. Which means, goes this argument, that the time is just around the corner when Muslims will outnumber Hindus in India.

This is supposed to be a terrifying thought. One scare-monger spelled out his fears about this in an article, long before we had even heard of the CAA: “Non-Muslims now rarely venture into areas of India where Muslims are in large numbers, fearing unpredictable, irrational behaviour or violence directed at them.” Given that kind of fear, the prospect of Muslims actually outnumbering Hindus in this land, this man wanted his readers to believe, is self-evidently a horrible one for us all.

Well, it is indeed a horrible prospect, but not for the reason the haters like him hold tight to their puny chests. Let me explain, using numbers we actually have rather than empty rhetorical flourishes like “where Muslims are in large numbers”.

In August 2015, the Registrar General and Census Commissioner released population data by religion from India’s 2011 Census. Taken from there, consider the population growth of the various religions in the decade 2001-2011. The Hindu population increased by 16.8% in those ten years, Muslim by 24.6%, Christian 15.5%, Sikh 8.4%, Buddhist 6.1% and Jain 5.4%. The result, as of 2011, was that 79.8% of Indians were Hindu and 14.2% Muslim. Other faiths each accounted for far smaller fractions of our population, which the Census found was just over 1.2 billion.

That is, in 2011 we had about 958 million Hindus in India, and 170 million Muslims.

With me so far? Now if we assume the same growth rates persist (which we cannot, but I’ll return to that) — 16.8% per decade for Hindus, 24.6% for Muslims — we can project both populations to the time in the future when Muslim numbers will equal Hindus. When will that be?

To answer that, we need some relatively elementary, if a little involved, arithmetic. Bear with me as I explain.

Here’s the issue: the 958 million Hindus are growing at a rate of 16.8% every decade, and the 170 million Muslims at 24.6% every decade. One decade from now (or actually from 2011, but let’s not quibble), the two populations will have increased by these amounts:

Hindus: 958m x 16.8% = 161m

Muslims: 170m x 24.6% = 42m

That is, one decade from now the respective populations will be:

Hindus: 958m + 161m = 958m x 1.168 = 1.119 billion

Muslims: 170m + 42m = 170m x 1.246 = 212m

Since we assumed the growth rates don’t change, we can do just the same calculation for the decade that follows. The increments in those ten years will be:

Hindus: 1.119b x 16.8% = 188m

Muslims: 212m x 24.6% = 52m

And thus the respective populations two decades from now:

Hindus: 1.119b + 188m = 1.119b x 1.168 = 958m x 1.168² = 1.307b

Muslims: 212m + 52m = 212m x 1.246 = 170m x 1.246² = 264m

We could keep doing these laborious calculations for decade after decade, of course, searching after every iteration for the point when Muslim numbers will equal Hindus. But no doubt you recognize this growth as equivalent to the notion of compound interest — and we know how to calculate that. Thus, three decades from now, the populations will be:

Hindus: 958m x 1.168³

Muslims: 170m x 1.246³

And to generalize this, some number “n” decades from now, the populations will be:

Hindus: 958m x 1.168ⁿ

Muslims: 170m x 1.246ⁿ

So now we ask, for what value of n will these two be equal? That is, we want:

958m x 1.168ⁿ = 170m x 1.246ⁿ

Rearrange this equation:

958/170 = (1.246/1.168)ⁿ, or 5.635 = 1.067ⁿ

I wouldn’t hold it against you if your eyes are glazing over by now. Lots of calculations, I know. But we’re almost done. Your high-school mathematics memories will tell you that at this point, we use logarithms, and that gives us:

log 5.635 = n x log 1.067, or n = log 5.635 / log1.067 = 27.

There we have it. At those growth rates, it will take 27 decades, or 270 years, for the Muslim population to catch up to the Hindus.That is, the hate-mongers are quaking in their shabby boots — and asking us to do so as well — about something that will happen as we, or actually our descendants many generations over, close in on the 24th Century. Are you really going to worry about what might happen in the year 2290 AD?

But even if the haters do quake about that, let’s ask another question: assuming these growth rates, how many Hindus and Muslims will there be in India in 2290? In other words, what is 958m x 1.168

^{27}?Answer: 64 billion. 64 billion Hindus and 64 billion Muslims. Think of it. This, in a nation that today has a total of 1.3 billion Indians. This, meaning 100 Indians for every single Indian living today: 100 Indians crowding that spot where you sit reading this, 100 Indians jostling for the tiny standing space you occupy in the 8:27 Churchgate fast, 100 Indians sharing one seat to watch Deepika Padukone in a rerun of Chhapaak, just as they were going to do this week. This, and remember we have not accounted for Christians and Sikhs and Buddhists and other varieties of Indians, not forgetting other denizens of India such as cows and dogs, cars and bookshelves, trees and playgrounds.

This is the mirage-like prospect that a deep-seated hatred drives people to dream up and fear.

The truth should be apparent. The really horrible, fearful prospect is not that Muslims will outnumber Hindus. Instead, it’s that hundred-fold increase the calculations above suggest. If we are actually going to rack up numbers like those, we will have died out from overcrowding long before getting to that moment in 2290 AD, that dreadful prospect of Hindu-Muslim parity.

And here’s what makes that prospect even more mirage-like. The reality is that we cannot assume the same growth rates — Hindu 16.8%, Muslim 24.6% — will hold indefinitely. In the earlier decade, 1991-2001, Census 2001 figures showed that the Hindu and Muslim populations increased by 19.9% and 29.5%, respectively. Those numbers decreased to 16.8% and 24.6%, respectively. Obvious from those numbers is that growth rates are decreasing. There’s nothing unusual here; this is exactly what happens as a country develops. (Note too that the Muslim growth rate declined faster, decade to decade, than the Hindu growth rate). So since the country has continued to develop since the 2011 Census, the 2021 Census will certainly show further declines in these growth rates. That means even greater population projections than 64 billion, an even longer time to population parity than 270 years.

Welcome to the overcrowded wasteland of 25th Century India, perhaps. The pity is that the hatred in too many of us reduces us to such a wasteland right now.

## 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

1/

Take my word for it: those three terms alone give a value for

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.

***

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.

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! :-)

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! :-)

John

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