Wednesday, September 9, 2009

Mathematical Induction Disproved

A long time ago, in a land far, far away, a Java programmer had way too much time on his hands...

A truly momentous event. As I was having lunch today, I happened to think of maths. Now, this, in itself, is astounding - maths being something I usually reserve for my worst nightmares. I'll tell you how it all began. Pay attention, folks. Innocuous, the setting may be. But that is true also for Newton and his apple; Goodyear and his rubber...

I was having lunch inside the building, facing the elevators. It was way too hot outside, and there were other reasons, too - I am not at liberty to divulge those. I was watching the elevator lights, indicating them going up and down. I had nothing better to do because I was sitting next to Ashutosh. Most of you probably don't know Ashutosh, and so wouldn't have a clue why sitting next to him makes you watch elevator lights. But that's a story for another day.

It was then that an interesting observation came to me. Only the people who had more than a floor to walk took the elevators. That is, those who were on the 5th floor (I was on the 6th) were quite content to walk up and down. My mind chose this moment to wander onto the topic of mathematical induction. If I remember my maths correctly (my maths teacher would probably reckon that it's debatable whether I ever knew any to forget - but we all have our critics), then what it states is as follows.

To prove something, you first prove that the thingy is true for X = 1 (or, was it 2? - anyway, it's probably not very important). Then, you go on to prove that if it is true for X = N, then, it is also true for X = N + 1. Sounds convoluted? Well, this is why millions of kids the world over choose to go into the Arts once schooling is over.

Applying all that crap to the elevator problem, you get the following results. Please follow it carefully. This is really important.

To prove : WE DON'T NEED ELEVATORS. (I think the caps are mandated by the MI committee.)

Let us take the "X = 1" case. That is, you're on the first floor. There are no "why"s here, by the way. So... first floor. You don't need to take the elevator to go to any other floor (say N) - unless, as everyone knows, there's a fire. This is because going from the 1st floor to the Nth floor can be broken up as - from the 1st floor to the second floor; from the second floor to the third floor ... from the (N - 1)th floor to the Nth floor - that is, a sequence of movements of only one floor each. And, since, we've already proved, through direct observational analysis, that people don't use elevators for movements of only one floor... You get my drift?

Now, the "X = N" case. Let us assume that you're up on the Nth floor. Now, even here, to go to any other floor (say M - we've already used up N), you don't need the elevator. Just substitute "N" for "1", and "M" for "N" - the original "N" - and you're good to go.

If you've followed the argument so far, and if you're still here, you'll realize that if it holds for "X = N," then, it should also hold for "X = N + 1" - unless, of course, the (N + 1)th floor has very high ceilings. That is, to repeat, any movement from the (N + 1)th floor to any other floor can also... blah blah blah.

And that's it. I think we're done and dusted here. But I need to wrap it up all formally with a sentence that begins with "therefore".

Therefore, we can safely assume that if the hypothesis is true for X = N, it is also true for X = N + 1.

The long and short of it is that, according to mathematical induction, we've just proved that MOST PEOPLE DON'T NEED ELEVATORS.

But we all know how ridiculous that statement is. Of course, we need elevators. Because if we didn't, why do all these buildings have elevator shafts?

The inescapable conclusion, therefore, is that MATHEMATICAL INDUCTION IS FALSE. Which leads us, sadly, to conclude that a lot of theorems being accepted as true by mathematicians are in fact without valid proof.

So... any chance of a retrospective correction of my score of 8% in the second-term Plus Two maths exam?

Saturday, July 4, 2009

The Indian Highway Code

1) Whenever you feel the need to stop your vehicle, do not waste time on trivialities like signalling or getting your car to the side of the road. Simply stop your car in the middle of the road, and turn on the hazard warning lights. Turning on the warning lights gives you the right to stop where you please, for as long as you please, regardless of any pileups behind you. For extra effect, carry a newspaper with you that you may peruse while exercising your fundamental rights. This occupies your tiny little mind while waiting for your spouse to finish shopping, and also makes it easier to ignore all those idiots gesticulating at you.

2) The correct lane to be on just before turning right is the lane on the extreme left. And the lane on the extreme right is of course what you shall use to turn left. The middle lane is reserved for those free souls who prefer to live life on the edge, and decide at the last nanosecond which direction they'd like their car to point to. To add to this, if driving on an undivided road, the correct procedure to turn right is to switch on the turn signal, and then move over to the lane for oncoming traffic about half a kilometer before you turn. Proceed calmly. It is for the oncoming traffic to fend for itself; after all, you have switched on the turn signal.

3) If you're on a divided highway, and for some reason wish to turn around, do not waste time and fuel waiting for a break in the divider. Simply turn your car right round on the side of the road you currently are on. Since you are a conscientious citizen, you would want to keep to the left side of the road. While this would mean that you are on the fast lane for oncoming traffic, and the potential collision velocity could be in the region of 200 kph, don't let that bother you too much.

4) Red lights are more suggestions than rules. As in, "If it doesn't put you off, and there isn't too much going on in your life right now, you might consider stopping here." Feel free to honk at anyone who stops for over 5 seconds at a signal.

5) A recent scientific study has concluded that honking like a fucking idiot for no apparent reason makes you really popular with the ladies. It seems it makes them want to take you home and have wild sex with, through the night.

6) A friend of mine told me that while abroad, he came upon this 4-way intersection where the traffic lights had failed. It seems all the cars stopped, and then proceeded to cross the intersection one at a time in the order of whoever reached first. He said that he hoped to see something like this in Pune soon. The point of this story is NOT that we should all strive for the day when this will happen here. The point is that you should not be telling things like this in a moving vehicle within earshot of the driver. He may fall off his seat laughing, resulting in a serious accident.

7) As long as you keep a distance of 5 millimeters between your front bumper and the rear bumper of the car ahead of you, you are NOT tailgating. Further, so long as you honk or flash your lights, you are, by law, entitled to see the slower car ahead of you vanish into thin air within the next 2 seconds.

8) So there's this long-lost friend of yours that you want to catch up with. What do you do? Are you thinking, "Invite him/her over to your place, or set up a dinner or coffee meeting?" Aha, got you there! The correct procedure is to get two bikes, rush to the busiest road in your vicinity, and then have a long, leisured conversation while the two of you ride side-by-side at about 20 kph. This is known as synchronized riding. The Indian government, sensing a couple of guaranteed golds, is lobbying hard to make this an Olympic sport.

9) If you happen to own a bicycle, or a vehicle that hits the red line the moment you touch about 15 kph, the centre of the road is your spot. You own it.

10) The correct thing to do, while coming upon a car waiting to cross a very busy highway is not to wait behind it, as commonly believed, but to pull up alongside it so that you are now blocking his/her vision on one side. Since that car is also blocking your vision on one side, the two of you can now proceed to glare at each other for about 5 minutes. And then both of you, half blinded, may vault your vehicles ahead simultaneously, resulting in a nice, chaotic traffic jam. There are several advantages to this over the traditional "waiting behind the first car" approach. I will blog about them once I find out what they are.

11) If you're a passenger-ferrying vehicle, think nothing of stopping as far towards the middle of the road as possible when letting your passengers out. After all, population control shouldn't be something that's left just to contraceptives. On this topic, if you're a bus driver, it's all right to do an Orson Welles and ask yourself whether you'd really care if one of those little dots you see from your perch high up stopped moving.

12) If you're a truck driver doing 15 kph, and happen upon another truck doing 14.5 kph, attempt to overtake immediately! After all, it is the dream of any motorist who takes his or her car out on the expressway to sit and stare at the exhausts of 2 trucks for half an hour. (I feel a little guilty about this one. In my experience, trucks are the best behaved vehicles outside of city limits (please note that I am not including those homicidal maniacs who masquerade as intercity bus drivers in this category), and those guys do have their schedules to keep.)

13) Within city limits at night, you shall travel only by high beam. Also, if by some accident, you happen to be on low beam, please do remember to switch to high beam the moment you spy a car coming in the other direction. This is a form of friendly greeting.

14) Be really economical with all kinds of turn signals and lights (except, of course, with the above-mentioned high beam). Those things wear out fast. Really.

15) If you're a pedestrian, think nothing of crossing the road at the exact moment the light turns green for the vehicles. Motorists love jamming on the brakes, stalling their engines, and being rammed from behind. That's what we live for.

For the authorities:-

1) All traffic lights shall be turned off at 9 PM, irrespective of how busy or dangerous the intersection is.

2) If you work in the RTO, and are responsible for issuing driving licenses, you shall grant the license to anyone who can drive a car in a circle on a football field, and reverse the car into a spot that is roughly 4 goalposts wide - provided s/he doesn't stall the vehicle more than 5 times during the course of the exercise, of course.

3) All traffic signs and directions will be in regional languages only. This is as Indians are really hospitable people, and do not like to burden their guests with unnecessary rules.

4) If there's some construction going on on the road, the correct place to leave the material while retiring for the day is on the fast lane, next to the divider. Also, a good way to let motorists know that there is construction going on is NOT to leave well-lit warning signs, as this may prove energy inefficient; but rather, leaving an unlit boulder (not that I've seen lit boulders) in the middle of the road.

5) No flyover or construction on a heavily-used road shall be completed before 5 years. We like our share of moral policing, and as Calvin's Dad would put it, hardships build character.

"I've seen things you people wouldn't believe. SUVs on the Golden Quadrilateral, hurtling towards me on the wrong side of the road. I watched headlights on high beam glitter in the dark near India Gate. All those moments will be lost in time... like lane discipline at an intersection in Pune... Time to die." - Roy Batty, Blade Runner.

Thus concludes Part Three of my "commute whinge" series. The UK version of the Highway Code is here.

Tuesday, June 2, 2009

Movie Turn-Ons, Part 3 (Sex and Violence... or Kiss Kiss Bang Bang)

The only reason I'm still on Orkut is that I created this community for B Movies (25 members and counting) about 15 months back, and don't want it deleted along with my account. Here's the description for it, in the hope that it gives you an irresistible urge to join...

"Bergman, Wenders, Kieslowski. The "Sultans of Cinema", as a recent ad goes... Now, these guys and their ilk are not bad, but this community is for people who fell in love with films watching cheesy science fiction, steamy exploitation thrillers, and gory horror movies on late-night television. Sure, watching a medieval knight grapple with weighty questions on life and death; or watching sombre meditations on the death penalty, parenthood and the like, has its attractions. But give us aliens in badly designed flying saucers invading earth, the undead terrorising the inhabitants of some nameless town, psychos attracted to naked girls in showers (no wait, scratch that - that's Hitchcock, no?), wise-cracking private eyes and their femmes fatales dealing with mind bending plots - all with a heady mix of bad acting, terrible dialogue, sex and nudity - any day. Here's to B Movies!"

The "films" section of my profile used to be a huge list of films and directors, which I've toned down to...

"Off the top of my head, De Palma, Bunuel, Almodovar, Kubrick, Herzog, Woody Allen, the Coens. Anything with Anthony Hopkins' Hannibal Lecter in it. Noir. Mood pieces. Vivid colours and grand camera movements. Humour. Decadence. Amorality. Snappy dialogue. Candles flickering in old mansions. Sex and violence - B movies, especially. The list goes on. Will watch anything, in short..."

Ignore the directors' list there, which really was a "top of my head" thing. What do the two have in common? Sex, violence and dialogue. Just goes to show how grounded I am, and how I've remained essentially the same person despite all the fame and fortune.

I already did a post on dialogue. Since it seems inconceivable to me that anyone could not appreciate good sex and violence in a movie, I will not go on about it. Pointless really. Would be like someone writing a whole passage on why watching a sunset is a beautiful thing... I will merely quote Pauline Kael, "The words 'Kiss Kiss Bang Bang' which I saw on an Italian movie poster, are perhaps the briefest statement imaginable of the basic appeal of movies.” (The quote goes on with some hogwash about how we despair when we realise how seldom movies are more than this, but let's not go into all that now - I wish women would try and see movies from guys' perspective sometimes...)

Oh, I also want to slip in a rhetorical question. Is there a genre that captures this very essence of movies - sex and violence (along with a healthy dose of moral ambivalence, great dialogue, and gripping, atmospheric photography) - better than noir?

Monday, March 30, 2009

You Complete Me

One of the first English movies I remember watching is "Superman". I watched the entire Christopher Reeve series, including the bad ones - of course, to a six-year-old, there is no such thing as a bad Superman movie. So anyway, while I'm not much of a comic-book reader, and am not a walking encyclopedia on their mythology, I do have a soft spot for superhero movies. Most guys do.

But one thing always puzzled me. Not the bad physics. That, I could take. I was never one to poke fun at the genre by pointing out the impossible physics. No one ever questions how Philip Marlowe could solve a case, let alone stay alive long enough to ever write all those books, do they? How did Scottie get off that roof in "Vertigo"? What are the chances of your meeting a girl who looks like Julie Delpy in a train, let alone her agreeing to walk around Vienna with you? Why should physics be on a higher pedestal? Every movie creates its own universe, and as long as it sticks to the rules it establishes, and doesn't cheat, it's fair game, I say.

Yes, I know. The puzzling thing. I speak from a rather limited exposure to the genre, but it's like this. Humanity gets along just fine (well, mostly) for a few millennia. So does Lois Lane, though maybe not for as long. And then Superman comes along. All of a sudden, Lois gets mugged, she gets killed (temporarily), we face evil geniuses helping investments in property along by doing a bit of nuking on the side, bad guys from Krypton arrive to establish a new order... so on and so forth.

Superman goes away. For 5 years, there's peace on earth. Lois gets married, has a son, wins a Pulitzer for an article on why the world doesn't need Superman. All in all, a happy life. And then Superman makes a come-back. Even as he's entering the stratosphere, Lois almost gets killed in a plane crash. The evil genius also has some new plans. Coincidence?

Take Peter Parker. When he was a nerd who worshipped Mary Jane from afar, the world and Mary herself were safe. A spider-bite, and a spider suit later, we have, in the course of less than half a decade and 2 sequels, in order - a Green Goblin, an Octopus Man something, a Sand Man, Green Goblin Jr, and an alien-infested jealous photographer. In the words of the man himself, "Where do these guys come from?" Mary Jane, who had no difficulty getting into her 20s, now faces threats to her life on a daily basis. Coincidence again, I ask you?

So "The Dark Knight" comes along to explain it all. A pretty nifty piece of film making, I thought, when I first saw it, but too self aware for its own good, I think now, having just rewatched it on DVD (yes, at 3 AM on a Monday morning; yes, I need to get a life). Had it been a light-hearted exploration of the sleight of hand practised by every superhero movie I've seen, a-la "The Incredibles" (if that is what that movie did - it is 3 AM, after all), I probably wouldn't have stayed up to write a post on it. However...

Batman asks the Joker, "Why do you want to kill me?" He replies, visibly resisting the urge to french-kiss the caped crusader, "I don't want to kill you! What would I do without you? Go back to ripping off mob dealers? No, no, you... you complete me."

Magicians are supposed to draw attention away from their trickeries. And yet, here you have a film that not only exposes a plot hole the size of a truck in all films of its kind, but also wallows in it with the kind of solemnity that makes me want to throw up every time I hear the word "Matrix".

If you really wanted to make a picture that poses questions as dark as the movie pretends it wants to ask, surely there are better vehicles than a big-budget money-spinner, with all the limitations that that entails? When it's as plain as day that the movie's about a rich, good-looking dude beating the crap out of the bad guys, why all the pretentious bullshit? Why take away from all those glorious action set pieces, the Batmobile, and all those gadgets that would put James Bond to shame, with endless talk on "sacrifices" and "rules" and "choices" and what not? Why all the gloom? Why so serious?

P.S. - As long as I'm still slightly drunk, sleepy and crabby, what's with all the "one man can make a difference" hogwash that keeps getting peddled in the Spidey movies? I mean, the man in question can swing from building to building, and also get off with just a slight headache on being slammed into buildings with enough force to take chunks of concrete off. Bah, humbug.

P.P.S. - In walks Tendulkar. He batted beautifully for his 58 yesterday. Hope he goes on for a ton today. Time for some superhero action...

P.P.P.S. - Damn, he got out. I'm off to sleep.

Thursday, January 22, 2009


The following's a slightly rewritten version of the only article of mine that's ever been printed. Not that its "published" status is any indication of quality. It was my school magazine, and they also published an article named "My Cat" by an eight-year-old. But still, that I grasped, at a fairly young age, the simple fact that the easiest way to the top lies in the politics of hate, probably heralds a promising future in the corridors of power. There's still a long way to go, of course. To that end, I'm studying, with keen interest, the Israeli propaganda machine, which is currently engaged in getting away with murder. Citing "self defense", for instance, seems to work miracles in the PR world - even if you deny that very right to the people whose lands you're illegally occupying, and whom you're starving through an economic blockade that's lasted 18 months so far. Meanwhile, here's my own little political manifesto...


I gripped the seat tightly to prevent myself from running up and down the bus, screaming with rage. Here I was, with barely fifteen minutes left to reach the theatre in time for the opening scene, and my fellow passengers and the bus driver were actively plotting against me. First of all, there was the number of bus stops on that route, that seemed to be one less than infinity, as the joke goes... I'm not sure that's quite all of the joke, but the thing is, I don't really remember the... I digress. Sorry.

Secondly, there was the speed at which some of the passengers were exiting the bus. A dying snail crawling to its death, would be a good description for one man's walk to the door, in particular. It was all I could do to restrain myself from aiming a carefully-timed kick at his rear to expedite his departure.

After one second less than eternity (I still cannot remember the punchline of that joke), my stop came. Elbowing all co-passengers out of the way, I was at the door, and even as the bus was slowing down, I was out of it and running alongside it with my face turned towards it, carrying an expression that said, "Look here fools. This is the way to get out of a bus." Obviously it wasn't. For, in the very next minute, I was lying on my back, clutching what was left of my face. A bloody lamppost.

I'm sure I have company here. It needn't necessarily have happened while jumping out of a bus. It might just as easily have been while cheerfully walking down the road, with a cool breeze ruffling your hair, and with the sunset behind your back, and you closing your eyes and smiling and thinking, "What a beautiful world this is!" Subsequent events, chiefly formulated by a solid object in your path, would convince you that this isn't such a beautiful world, after all. It isn't just the physical pain. Here you are, running alongside a bus with a contemptuous look on your face, or walking down the road with closed eyes and a blissfully happy face, and WHAM...

A recent survey by a leading magazine has shown that 58.65% of all road accidents are caused by vehicles colliding with lampposts. That they would have gone on to hit the wall beyond the lamppost had the lamppost not been there is besides the point. We're discussing cold, hard facts here and not hypothetical cases.

So the question is, all this death and destruction aside, do lampposts have anything that redeems them? Apart from population control, that is - which isn't an issue that earns too many votes, anyway. In everything that can be called art there is a quality of redemption, wrote Raymond Chandler. Lampposts aren't exactly art, and anyway the quote has nothing whatsoever to do with... why did I... well... ah yes... quality of redemption. Let's look at that, shall we?

Having done a lot of research on the matter, I gather that lampposts are primarily used as a means to guide at night idiots who haven't brought their torches. There's no redemption there; just aggravation. Is humouring them enough justification for the continued existence of this threat to life and property? Besides, even they require these monstrosities only at night. Ghosts and other assorted vampires and things disappear at the crack of dawn when their services are no longer required. But lampposts remain! Just today, as I was climbing out of bed to get ready for work, I counted three lampposts from my window... and this was at 11:30 in the morning.

So here I come to the crux of the issue. I'd like to invite all sensible people who have grasped the gravity of the situation, and also leading lights of the torch industry (heh heh; get it? leading lights of the torch... ahem... never mind), to join the newly-formed ALP (the Anti Lamppost Party) of which I am Founding (and so far, Only) Member and President. The broken lamppost is our symbol. My first official act, on becoming Prime Minister, will be to banish all lampposts from the street sides of India. Any lamppost found loitering near streets will be subjected to ten years of rigorous imprisonment and/or a fine of Rs. 50,000/-. On repeated loitering, the offending lamppost will be executed by the removal of its fuse. The time has come to draw a line on the pavement. Across this line, you do not illuminate!

I sincerely hope that the message has got through to you all. As I'm sure it has, please do consider a small donation to this noble cause. Social activism has its costs. I will leave you now to ponder over the views that I have just expressed. Thank you for your time.