Recursively Yours

Yours to read, my new Mint column, Recursively Yours to read, my new Mint column, Recursively Yours to read, my new Mint column ... here.

(I called it "To Recurse, Perchance to Dream", Mint preferred "Recursively Yours").

In case the link does not work, the text is below. Comments, as always, welcome.

***
Our kittens have never stepped out of our flat. So I'm wondering about teaching them a foolproof method, call it the CatOut method, to find their way downstairs for a stroll. Now I'm sure they understand human-speak -- all right, I'm overly fond of felines -- so here's what I might whisper in their furry ears: "CatOut starts by checking if you're already on the ground floor. If so, you're done: race out to the road. If not, walk down one flight of stairs and do the CatOut from there."

Simple, right? So what happens when Aziz and Cleo do the CatOut at our fourth floor flat? They'll check: are we on the ground floor? No. Therefore, walk down one flight, to the third floor. Apply CatOut there. Meaning, they'll check: are we on the ground floor? No. Therefore, walk down one flight, to the second floor. Etc. In minutes, they'll shoot joyously out of the building, onto the road.

Look at it like this: We've defined their trip from a given floor in terms of the same trip from the floor below. We've defined it in a way that every computer science student will recognize: recursively.

Recursion is a profound and powerful idea. If you do it right, it works like a dream. But for me, its real appeal is that it's like saying: "You want to do this? Just go do it."

Or: "You want to learn how to swim? Jump in and start swimming." Best way to learn.

Because sometimes when you have a problem, detailed instructions get intense and complicated. Far better to just attempt a solution to a smaller but related problem, learning as you go. The power of recursion is precisely that it defines a task in terms of a simpler version of itself. By a clever bit of self-reference that, finally, reduces a daunting problem to a series of easy ones.

You specify an endpoint in which the task becomes trivial: if on the ground floor, run for the road. You specify a recursive case that reduces the task -- descend a flight of stairs -- because apart from the reduction the procedure is then identical: make the trip, but from one floor below.

Do this repeatedly, and CatOut becomes just a series of descents, one flight at a time. This way, you know Aziz and Cleo can reach the road from the ground floor, from the 10,679th floor, or even from the top of a building with an infinity of floors. (Though after descending a few million flights, you may hear a few yowls of protest. You have been warned.)

So yes, computer science students learn recursion, though not through the good offices of Aziz and Cleo. Instead, it works well, for example, for one of the earliest programming problems they tackle: calculating the factorial of a positive number.

The factorial, written with an exclamation mark, is what you get when you multiply all the numbers between 1 and the original number.

Thus 5! (read "five factorial") = 1 x 2 x 3 x 4 x 5 = 120.

And 100! = 1 x 2 x 3 x 4 x … x 97 x 98 x 99 x 100 = a number so large, I feel tired even trying to contemplate it, leave alone calculate it.

But while factorials quickly get large, you can tell a computer -- a stupid machine that can multiply two numbers, but no more -- how to calculate them via a short recursive procedure.

Note only that 5! = 5 x 4!, or 100! = 100 x 99! = 100 x 99 x 98!, etc -- you can break those down further. In English, the procedure looks like this: to calculate the factorial of a number, check -- is it 1? If so, the answer is 1 (the trivial case) and you're done. If greater than 1, the answer is the product of the number itself and the factorial of the number immediately below (the recursive step).

Do this repeatedly, and instead of an intimidating factorial calculation, the computer is left to do what it can: multiply pairs of numbers, a series of pairs. The power of recursion.

In my computer science days, my colleagues and I obsessed about writing what we called "elegant" software. We didn't always succeed, and it wasn't always clear what qualified as elegant in a particular situation. Yet we all recognized that it usually is clear, innovative and has a satisfying dash of panache.

And some of the most satisfyingly elegant stuff came from using this thing called recursion. Because if you get it right, recursion can substitute for chunks of clumsy programming.

"To recurse is divine", said the legendary computer scientist L Peter Deutsch. Me, I like learning by breaking things down, by doing, by simply getting going. That's what recursion's about, for me. Don't know much about divinity, but I'll take elegance every time.

My presence expected

A recent bit of email has me feeling privileged and delighted. That's because it is an invitation to an upcoming conference. And it has these excellent features.

* It contains the acronyms IPR, R&D, HRM, CEO, NKC, ICT, OM and possibly a few more I missed, of which I know the full forms of just three.

* It informs me that the organizers are "happy" that they have got, as an "active partner", a company or organization or something that I have never heard of.

* It "solicits my suggestions" to make the conference a "purposeful event", even though I am hard pressed to come up with any suggestions apart from "you probably don't want me there".

* It "expects my presence" on all three days of the conference.

* It asks me to "take active part" in the conference "by paying an appropriate registration fee."

* It invites me "as a respected Technology Management professional worldwide", which I didn't know I was. In fact I suspect they don't know either that I am that respected TMpw, because the letter is addressed to "Dear Sir/Madam".

Fifth from the bottom

When I was there two weeks ago, someone mentioned Bilaspur's position in some recent quality of life ranking of 200 Indian cities. It was fifth from the bottom, he told me.

This surprised me. Why wasn't it ranked at the bottom?

And since it wasn't, what kind of hellholes languish below Bilaspur?

I mean, what a ghastly place this second-largest city in Chhattisgarh is. For anyone who says Chhattisgarh is a well-run state, I can only say, visit Bilaspur. If this is the Pride of Chhattisgarh, I shudder.

Some thoughts, stream-of-consciousness style.

When it's not raining, there's dust everywhere from the endless construction. When it is raining there's mud and slush everywhere, great huge expanses of mud. There's a flyover under construction over a railway crossing: the ramps from both sides seem complete, but the flyover remains unfinished. Been that way for 7-8 years, I'm told, and certainly it hasn't progressed by so much as a laid brick since my first visit, 18 months ago. Thus the heavy traffic on that road -- both directions -- has to crawl for half a km along a narrow road and over the tracks. The state this road is in beggars description. It is simply a long series of craters. It runs alongside a huge pool of stagnant rainwater into which we saw, one evening as we waited at the level crossing, several men peeing, taking turns. Another evening, a truck mired in the mud, its driver standing knee deep in the water we had seen people peeing in, and scratching his head.

But the road beggars description only until you see other roads in the city. One has even deeper craters over an even longer stretch. As we careened over them in a rickshaw one night, the person beside me said, resignedly, it's been like this for three years.

In an upscale residential neighbourhood -- judging by the houses there -- once-new sewage pipes have simply been left on the side of the road. Also there at least 18 months. Beside them is the open drain, in which you can almost see mosquitoes breeding with abandon.

Piles of sand and rubble everywhere. Some sprawl across three-fourths of the road. Invisible at night, you wonder how people don't drive smack into them. The garbage that's simply lying around. A "ring road" that's been laid in concrete, but not completed, so suddenly the concrete gives way to mud, and getting onto it from feeder roads means traversing a ramp of packed mud, and when it rains that ramp is worn away so you have to drive up and over a one-foot height difference between the surfaces … the traffic, the impossibility of taking a simple walk in any direction that's more than a minute long because you run into mud, or traffic, or construction …

In this chaos and anarchy, this post-post-modern vision of what all of India's cities might one day be, people travel and sell and buy and fight and take out processions. They live. I don't know how.

Nawab of Pataudi

To remember a man today, these few words.

Who wrote that he had "never forgotten the spectacle of my Oxford contemporary, the Nawab of Pataudi (one of India's greatest cricketers, even after losing one eye) fielding for the university and throwing the ball with devastating speed and accuracy at the wicket"?

Go well, Mr Khan.

Uncertainly yours, the cat

My new math/science effort for Mint is in the paper today: Uncertainly Yours, The Cat.

It's about Lajwanti the cat, errant electrons and a mirror too. I tried my usual -- work in the gratuitous mention of Lady Gaga -- but yet again, I wasn't able to manage it. So the count of Gaga mentions in my columns remains stuck at one, more's the pity.

And as usual, in case the link doesn't work, the text is below.

Your thoughts always welcome.

***
Postscript: Please read Rahul Siddharthan's debunking of my article, here. Live and learn.

***
With two cats at home, it's always a delight when they compete to rub themselves against my shin. So I sometimes wonder, why would anyone dream up a cat? "DD's lost it", you're thinking. But I would submit that the world's best-known cat, at least among physicists, is an imaginary one.

And get this: she never lived, but people say she's both dead and alive.

This feline was the creation of the great German physicist Erwin Schrödinger, who died 50 years ago. Seeking to understand Heisenberg's Uncertainty Principle, fundamental to modern physics, he thought of a cat. I mean, the last thing I expected to hear about in college was a purely hypothetical cat. Yet generations of students the world over know this one well.

Absent mathematical jargon, the Uncertainty Principle says something simple: the act of measuring something affects that measurement. For example, it is impossible to determine both the location of an electron and the speed at which it moves. If you measure its speed accurately, this process of measurement itself makes its location hard to pin down, and vice versa. The uncertainty in one measurement, Heisenberg tells us, depends on the uncertainty in the other.

Looked at another way, measurement decides the state of the electron.

This is not such a mysterious idea. Imagine an anthropologist visiting a tribal village to study its inhabitants. His very presence will disturb the state of the village: we all behave differently when strangers come visiting. By observing, the anthropologist affects what he wants to observe. He never gets a "true" picture of the village.

Sure, but why is this important? Traditionally, physics nurtured the idea that nature's laws tell us the past and future. If we can fully describe the state of the universe right now, for example, we can deduce its state at any other time. Heisenberg shattered this romantic notion. Not only is there uncertainty in the properties of things, the act of measuring properties itself increases uncertainty. You cannot determine the state of the universe at a given time; life is not predictable.

Now this is fine with tiny particles like electrons that nobody can see anyway. What about ordinary objects?

What about, say, cats?

That very question occured to Schrödinger. His famous thought experiment went something like this. Put Lajwanti the cat into a box. Also put in a device that, when turned on, might or might not emit a single electron. That is, over a minute, the chances are exactly 50-50 that it emits an electron. If it does, it also releases a poisonous spray, goodbye Lajwanti. If it doesn't, she lives to fight another minute.

Seal the box and put it far enough away that you can't tell what's going on inside. Turn on the device for exactly one minute. What happens to the cat?

Trivial question, right? The answer: we don't know. The Uncertainty Principle reminds us that we can't predict the behaviour of the device: even if we pinpoint the location of its every electron, we have no idea about their motions, no way to determine their behaviour during that minute, no way to tell if one will be emitted. Thus we don't know if Lajwanti is alive or dead.

Until, of course, we walk over to the box and open it to hear -- let's hope -- the loud miaow of a bewildered cat. Only then do we actually know that she survived her uncertain ordeal.

With the box sealed, we know only that Lajwanti is either alive or dead. This must seem blindingly mundane. But it is entirely consistent with the laws of physics to think of her, before opening the box, as simultaneously alive and dead. Here's the crucial idea: the act of opening the box and looking in on Lajwanti -- taking a measurement, in other words -- is what puts her definitely into one of those two states: alive, we hope.

What's the point? What's so profound about a cat shut into a box?

Well, there's the effect of measurement, the idea of uncertainty, and more. But perhaps the deepest yet simplest point is this: reality takes shape only when we observe it.

We know an electron is emitted only when we detect it. The anthropologist learns something about tribal customs only when he actually observes a tribe, even if that affects their behaviour. We find out poor Lajwanti's fate only when we open Schrödinger's box.

Haven't we all wondered on these lines before? If I turn my back to the mirror, is my image really there? If there's nobody to hear, does a tree that falls in a forest make a sound?

Is there reality without observation, existence without consciousness?

Schrödinger's cat shows that the laws of physics might answer those questions with "no". That may be too extreme for people who believe reality surrounds them without needing to be looked at.

Then again, Lajwanti herself isn't real.

Ink Salon

I'll be speaking at INK Salon Mumbai this evening (Friday September 16).

Can't tell you yet what I will say, except that it's about a cot. If that's enough of a temptation for you, be there. Or be elsewhere.

Beating someone

Serious shouting and screaming from somewhere close by, an hour or two ago. Sounded like people were angry enough to kill each other. I walked over to see if there was something I could do to prevent sudden murder. It's a bungalow behind a high wall, can't see anything but the shouting is getting louder and fiercer. Then three people emerge from a gate, walking backward, gesticulating, shouting and being shouted at. A slender young woman, a young man who is probably her husband, and an older man who must be his father.

Four people. The woman is carrying a small baby.

The young man shouts in desperation at the father, a mixture of Marathi and Hindi: "Baba, start your scooter! Let's go!"

Father yells and shakes his fist at whoever is inside. Something wondering about the caste of those inside, and pronouncing his own. Young man shouts at him again, "Get on your scooter! NOW!" Father won't stop yelling.

Eventually the woman starts walking toward me, which seems to prompt the father to get on his scooter. She says as she comes closer, cradling her baby, "They are beating our bahu in there."

The father and son draw alongside on their scooters. The father shouts in my face, "They are beating my bahu! Would you be able to tolerate it? I can't! My bahu!"

The woman settles herself on the seat behind her husband and the two scooters roar off down the road, with the father still shouting.

And I'm left scratching my head. Who were they talking about?

postAnna, #3

Third in the occasional series.

At Raipur station yesterday, long lines to buy tickets. Crowds even more than usual because incessant rains have flooded several roads. When I get to the window, I ask for a ticket to my destination. The man at the counter says there's a superfast about to come in, and I can buy a ticket for it and board. "Only thing is," he says, "you'll have to speak to the ticket checker to allot you a seat, and pay him."

"I'll get a receipt, right?" I ask.

"Receipt or no receipt is up to him," says the man.

***
Previous: postAnna, #1, postAnna, #2.

postAnna, #2

The second in an occasional series.

Seen today on a narrow but car-heavy one way street: a grey Honda Civic, driving at high speed the wrong way.

Also today: somebody I know called a foreign exchange dealer to ask about buying some said exchange for an upcoming trip abroad. The dealer said: if you want it officially, X is the price, bring a copy of your passport and ticket and I'll give you a bill. But if you want it unofficially, Y (about a rupee less than X) is the price. No bill.

***
Previous: postAnna, #1.

Not necessarily a century

I've been writing a column in Housecalls magazine for over a year now. The September-October issue carries "Not Necessarily a Century". It's readable online, but it's probably easier read below.

Comments welcome.

***
These words, soon after the end of a cricket Test at Lords. In which, perhaps you'll remember, England hammered India by a huge margin. And in cricket, as it often happens, there are some life lessons.

The result of the match, you'd think, would be the primary concern of Indian fans when it started five days earlier. You'd think Indian fans would be urging the team, silently or otherwise, to play to win, first and above all. I'm sure there were some fans like that. Except that if you read and heard all the pre-match hoopla about the game, you'd be forgiven for thinking that victory wasn't on too many people's radars. What was, instead, was a certain cricketer's personal milestone.

Sachin Tendulkar's 100th international century, of course. Ah, what poetry if he scored it here at Lords, the venerable home of cricket, where he has never done well. What joy if he got his name on the famous honours board at Lords. What perfect number magic, if in this 100th Test between India and England, in this 2000th Test match of all time, he managed to score his own 100th hundred.

Yet I don't remember seeing in any of this breathless adulation one simple thought: what if we won? What if Tendulkar scored a century while crafting a famous Indian victory? For surely that's what teams play the game for, to win. Surely not to provide a vehicle for one player to achieve greater heights than he already has.

Our obsession with such heights, I believe, encourages us to lose sight of what's important. Like, in this case, winning a Test match.

Now I can hardly suggest that the Indian team itself was similarly obsessed with Tendulkar's records and lost the Test right there. After all, there are plenty of exemplary cricketers in that team -- Dravid, Raina, Kumar, Sharma -- who fought hard all the way. But there's something to be said about this adulation of a man for his individual records, mighty though they are, in a team game.

In fact, there's something larger to be said.

If you merely look around, much of our country's landscape is dotted with adulation like this. Think of giant cutouts of whoever the current Chief Minister is in Tamil Nadu or Karnataka; think of how that cutout culture is spreading elsewhere. Think of the enormous statues of Mayawati in a new park on the outskirts of Lucknow. Think of the crowds that collect outside Amitabh Bacchhan's home every day, jostling for a glimpse of the man. Think of the obsequious reverence with which we greet the rich, famous and powerful: whether Anil Ambani or Bal Thackeray or, yes, Sachin Tendulkar. Think of men tattooing "JJ" on their bodies to mark Jayalalitha's birthday, enough tattoos to match the lady's age.

Because they reach a certain place in life, we turn these people into figures on a pedestal, give them flowery titles, worship and adore them. Thus Tendulkar is "God", and at least one book about him actually puts that word in its title. Jayalalitha is "Puratchi Thalaivi", or "Revolutionary Leader". Anil Ambani is MTV's "Youth Icon."

Yet perhaps we must remember that these are just more men and women, with qualities and foibles and failings like all men and women possess. Just people, really. What do we do to them, to us, when we turn from respect to worship?

Take Anna Hazare, for example, and the number of times he's been compared to Gandhi. ("Grandparents are taking children to see the Gandhi of this generation", said one ecstatic bit of mail someone forwarded to me when he was on his Jantar Mantar fast last April, a message that did not so much as mention what Hazare was fasting for). Why should he have to fill those oversized boots? And if we keep expecting him to fill them, should we be surprised when he fails, as he inevitably will? When we regularly mention both names in the same breath, in a mistaken excess of respect, we lay a burden on Hazare that nobody should have to carry. The comparison is unfair, above all, to Hazare.

But if we've all heard plenty of times about the dangers of putting people on pedestals, there's a subtler point here that worries me more. With a not-even subliminal parallel to Gandhi in place, our focus shifts: from the effort Hazare is making, to the man's character and moral stature, especially because he is stacked up against Gandhi. From the Lokpal Bill and how we can improve it, to what kind of man he is and what he did or did not do, prior to this moment in history, in Ralegaon-Siddhi and the Army.

The point, and it's a crucial one, is that Hazare does not have be "the Gandhi of this generation", or even to measure up to Gandhi in any sense, to make a difference to this country. His single-minded pursuit of the Lokpal Bill stands on its own, and can be judged on its own, certainly for the debate it has generated on the evils of corruption. I realize that we're unlikely to see grandparents taking children to see the Lokpal Bill. Yet if it comes to fruition and is able to curb corruption in this land, that's the achievement that will mark Hazare's place in Indian history. In exactly the same way, plenty of us now question the character of Gandhi and his colleagues from our freedom struggle. But what those men achieved speaks for itself.

Freedom is like that. Freedom from corruption might be like that too.

Back with cricket. Something I read on the morning of the last day of the Lords' Test summed up what I'm trying to say here. You will remember that India started that last day facing a long struggle even to save the game, let alone win. Tendulkar had been ill for most of the previous two days, and thus off the field. According to the rules, therefore, he could not come in to bat until nearing lunch time.

So that morning, someone wrote a short article titled "Why you don't want to see Sachin come out to bat". Since he would only be able to bat later in the day, it said, he would have "little time to get his 100th century even if he gets going." And therefore, "with India in a tight spot and battling to stay in the Test, this may well be one time that Indian fans could end up praying for Sachin to not come on the pitch at all."

Funny: with India in a tight spot and battling, one Indian fan -- me --  yearned for Tendulkar to bat us to safety, period. Yet going by this article, mine was by no means a universal yearning. Evidently there are people who would prefer that Tendulkar bailed out of trying to save the Test, because batting in such circumstances might interfere with his chances of scoring that century.

And so after England finished administering its Lords hammering, I wondered if these people were disappointed (as I was), and if so why. Because Tendulkar came out to bat after all? Because he get nowhere close to scoring a century?

Or because India lost?

Surrounded by a sea of mediocrity, of what most of us perceive as half-men and women, it's natural to long for heroes. That's fine as far as it goes. But it's worth remembering that what makes them heroes is what they do for those around them.

That may not necessarily include a 100th hundred.

The number of things

My current effort for my "A Matter of Numbers" column in Mint is titled "The Number of Things". Just in case you were curious, the answer is yes: the essay does mention svelte figures, though perhaps not quite the ones you're thinking of.

There's also a mention of "the beginning of this month, less than three weeks ago" -- which applied when I was writing the essay, but I overlooked the fact that it would be published in September. So if your brow furrows at that, put it down to my own clumsiness with numbers, which is exactly what I'm going on about anyway.

You'll find it here.

Though if you have difficulty with the link, the text is below (with the September mixup fixed).

Some clarifications for those of you who might not know a few references in here: a crore is 10 million. The Mauryan Empire ruled over much of India between about 325 BC and 180 BC. Antilla is the massive mansion India's richest man, Mukesh Ambani, has built for himself in Bombay. The Commonwealth Games were staged in Delhi last year, and turns out to have been one enormous cesspool of corruption.

Comments welcome!

***
A lady I knew well was warm, well-read and knowledgeable: an all-round sweetheart. Sadly, she also suffered from a far too common affliction. She was a near-total innumerate. She went blank when faced with bank statements. Despite showing her that her investments brought her an income considerably greater than mine, she was convinced she was a pauper.

"I can't understand all these numbers!" she'd say with a helpless smile.

Many of us know about illiteracy, but how many are concerned about widespread innumeracy -- the inability to deal easily with numbers? (The mathematician John Allen Paulos made the term famous with his 1989 book, "Innumeracy: Mathematical Illiteracy and its Consequences"). Think of how often you've heard people saying "I hated maths in school!" Or "I'm a people person, not a numbers person!"

I'm just wondering, do we as easily talk up our difficulties with words? Have you heard people say, echoing the lady I knew, "I can't understand all these letters!"

And yet numbers are everywhere, all the time. Whether in the latest budget, or the latest gigantic scam, or the results from the last Census: numbers surround us, often with plenty of zeroes attached. If we don't understand them, we don't understand their impact. We don't fully understand issues that affect our lives every day.

But fear not! If you merely leap aboard a number wagon with me, we'll look more closely at some svelte figures -- ok, bad adjective -- we've heard of lately.

The Commonwealth Games mess, remember that? One report quoted an official thus: "The total CWG misappropriation may touch Rs 8000 crore, which is quite huge and alarming." Sure, but how huge? Well, let's say a CWG scamster was spiriting money away at the rate of one rupee per second, 24 hours a day, seven days a week. Pretty rapid misappropriation, I'd say. So how long would he take to fill his pockets with 8000 crore?

The answer: more than 2500 years. That is, to be done today, this rupee-a-second scamster would have had to start nearly two centuries before the Mauryan Empire.

Puts 8000 crore in perspective, no?

Rolling right along: In February, Pranab Mukherjee announced a "provision of Rs 1,64,415 crore" for defence services in this year's budget. "Needless to say," our Finance Minister continued, "any further requirement for the country's defence would be met." No doubt this set off the same applause in Parliament that previous Ministers have received for statements like "we will not compromise on national security!"

Applause is good, but what does that figure really mean? What is our military costing you and me?

For each Indian man, woman and child -- all 1.2 billion of us -- we will spend nearly Rs 1400 on defence this year. Compare to the allocation for education Mukherjee also announced: Rs 52,057 crore, or about Rs 430 for each of us. Break it down like that, and it's easier to see that not compromising on security costs our Central Government over three times as much as the imperative to educate you does.

Or try this. All through 2011, we will spend Rs 52,000 per second on defence. Going at that rate, our friend the CWG misappropriater need not have started his spiriting before the Maurya Empire. Nope: the second week of August, less than three weeks ago, would have sufficed, thank you.

And speaking of 1.2 billion of us. That's a whole lot of us, sure. But how many Indians, really, in terms we can understand?

Suppose you are sitting on a stool at the entrance to Bombay's Azad Maidan. Everyone in the country has been asked to file past you into the Maidan and it's your job to count them. Let's say you're ten times as efficient as the misappropriater: in every second that he spirits away a rupee, ten Indians pass and you count them.

If you started today, you'd be sitting on that stool counting Indians trudging past till June 2015. (Give or take a few bathroom breaks). That's how many Indians.

And why are they filing into Azad Maidan? This thought experiment further asks you to imagine building a wall around the ground. The idea is to cram Indians every which way into the resulting enclosure: cheek to fleshy cheek, layer upon bony layer. How high would the wall have to be to accommodate every single person in this country? A metre? Ten metres? Fifty?

The correct answer is -- drum roll please -- about 3 kilometres. There are a lot of us, you know.

And by the time the last Indian -- that's you, finally free of your stool -- leaps onto the quivering pile of fellow-citizens, we'd have built a structure even taller than Ambani's Antilla. About 20 times taller, in fact.

And from somewhere inside that quivering pile, you might just hear the lady I knew: "All right, I understand 1.2 billion! Too damned well! Now let me out!"

postAnna, #1

So maybe this will be the first in an occasional series, post Anna.

Seen today at a traffic signal about 5pm -- 2 taxis, 3 motorbikes with 2 riders apiece, 3 private cars and a small truck. All of which paid no attention to the red light.