Achilles and the Tortoise

There are a lot of simple sounding puzzles that leave you befuddled (for lack of a better word). Here’s a simple one that is so disturbing brilliant, which apparently puzzled Greek mathematicians for ages. I stumbled on this 2 months back, and I stumbled again on it today and thought it deserved a post. Read the following and Enjoy!

Zeno of Elea (circa 450 b.c.) is credited with creating several famous paradoxes, but by far the best known is the paradox of the Tortoise and Achilles.

The original goes something like this:
The Tortoise challenged Achilles to a race, claiming that he would win as long as Achilles gave him a small head start. Achilles laughed at this, for of course he was a mighty warrior and swift of foot, whereas the Tortoise was heavy and slow.

“How big a head start do you need?” he asked the Tortoise with a smile.
“Ten meters,” the latter replied.
Achilles laughed louder than ever. “You will surely lose, my friend, in that case,” he told the Tortoise, “but let us race, if you wish it.”
“On the contrary,” said the Tortoise, “I will win, and I can prove it to you by a simple argument.”
“Go on then,” Achilles replied, with less confidence than he felt before. He knew he was the superior athlete, but he also knew the Tortoise had the sharper wits, and he had lost many a bewildering argument with him before this.
“Suppose,” began the Tortoise, “that you give me a 10-meter head start. Would you say that you could cover that 10 meters between us very quickly?”
“Very quickly,” Achilles affirmed.
“And in that time, how far should I have gone, do you think?” “Perhaps a
meter – no more,” said Achilles after a moment's thought.
“Very well,” replied the Tortoise, “so now there is a meter between us. And you would catch up that distance very quickly?”
“Very quickly indeed!” “And yet, in that time I shall have gone a little way farther, so that now you must catch that distance up, yes?”
“Ye-es,” said Achilles slowly.
“And while you are doing so, I shall have gone a little way farther, so that you must then catch up the new distance,” the Tortoise continued smoothly.
Achilles said nothing.
“And so you see, in each moment you must be catching up the distance between us, and yet I – at the same time – will be adding a new distance, however small, for you to catch up again.”
“Indeed, it must be so,” said Achilles wearily.
“And so you can never catch up,” the Tortoise concluded sympathetically.
“You are right, as always,” said Achilles sadly – and conceded the race.

At the first look, it does seem like Achilles would never catch the tortoise if the tortoise had a head start because there are infinite micro distances to cover. But, as explained in the solution link, all the small half-values intimately add up to a finite number which is when Achilles would meet the tortoise head to head. In Mathematics, it is the sum of 0.5 + 0.25 + 0125 + .. which ultimately sums upto 1 (and not infinity as it looks from the explanation provided by Tortoise). Simple, yet so brilliant. I wish mathematics was taught using such examples!

Image Courtesy: Link

Meaning of Life

One subject I've researched so much about in the past year. The Meaning of Life. Not that I got philosophical over the past year, but the sheer realization that the human psyche has tried and failed to get the answer to this one question for all the 60,000 (or whatever) years we've been here in planet earth gives me goosebumps. One simple and yet the most complicated question. I've tried to read so much about it over the past year, and everything I've read has made me both enlightened as never before and more confused as never before.

Anyway, a little bit of humour doesn't hurt anybody!

The most common Petrol Bunk fraud

When I think about the frauds I’ve personally faced, particularly down south here in Chennai, two bunch of frauds top the ranking chart. Number one is, obviously, the auto-wallah frauds. I don’t have a count of the different types of frauds they do, but they keep reinventing and coming up with a newer fraud like twice every week. They come up negotiation fraud, meter fraud, distance fraud, route fraud, one-way fraud, traffic-jam fraud, and innumerable combinations of these. And there’s only one real way to avoid getting into this fraud – not choosing autos as a mode of transport, which is what I recommend to most people permanently stationed in Chennai.

There’s another type of common fraud that I’m witnessing these days in the petrol bunks. The first time I was caught off-guard was 6 months back. I had asked the bunk guy to load Rs. 500 worth of petrol. He showed me the ‘Zero’ reading initially and started loading petrol, and suddenly stopped when the reading showed Rs. 100. This is the point to watch out. When you tell them you had asked for Rs. 500 worth of petrol and not for Rs. 100, they pretend as though they didn’t hear it properly the first time. They then reset the meter (but the reading never really goes back to zero, and they don’t ask you to watch the reading this time) and start loading till Rs. 400 and stop there. Since the reset from 100 to zero never happened and yet they stop at 400, you easily lose Rs. 100 in the process - especially if you did not notice the reading properly before the second phase of the loading. Even if you had noticed, the bunk guy is going to insist that the meter was reset before loading the additional Rs. 400. I have also noticed that they sometimes press the so-called ‘reset’ switch, but the reading does not go back to zero.

I became very conscious of this fraud after my first incident where I think (I still am not sure) I lost Rs. 100. The same fraud was tried twice on me after that, one as recently as the day before yesterday. This time, it was the Indian Oil bunk near the Kodambakkam Flyover in Chennai. Fortunately, I noticed that the meter reading did not go back to zero after the fraud ‘reset’ and shouted at him. They do not play with you if you consciously watch the reading throughout. They only play with you when you lose a moment of concentration and fail to watch the reading go back to zero during the mid-way reset. If you think you’ve been fooled into this, the best way to tackle this fraud is to ask them to show the petrol dispensing report from the machine – the log that contains all the dispensing activity for the day, which contains the time and quantity of petrol dispensed. I haven’t seen one personally, but I’ve been told that such a report can indeed be generated. You could also threaten to call the police as you go through the log with them, just to be on the safer side. In my experience, just raising the voice and being stern works most of the time.

This fraud is very difficult to control/eliminate because, unlike problems such as adulteration or fault meters, this can never really be tested and isolated. And the bunk owners can not be penalized since it’s the bunk operator who indulges in this. The only way to tackle this seems to be to consciously watch out for these frauds.

Donate rice playing a word game!

This is real interesting - a cute example of an amazing thought process.

For donating rice to poor nations, all you have to do is to play the word game in the website Free Rice. For every correct answer scored, the website donates 10 grains of rice to world's poorest nations.

FreeRice has already donated 1 billion grains of rice in 2 months.

You get to play vocab games (and some of us do that often) and you automatically donate rice.

The revenue concept is simple and sparkling in its sheer brilliance. The website uses advertisement revenue to pay for the rice, and the more the number of people who visit the site, better the ad revenue. I don't want to hazard a guess as to the possibility of ad tariff increase and its ceiling value as the traffic increases, but this is surely a brilliant thought.

Worst movie still of the century

Just watch this still.

Ok, honestly, I don't know how good this couple is actually gonna look in the movie, and I really don't think I'll watch this movie, but I think this has to be the worst still of the century. If this still makes anybody watch the movie, let me know. I'm just plain curious.

Yuk.

Pa's the answer to Splash

Just when you thought the B (or A2) segment of Indian cars got a little boring, there’s a lot of news to cheer up.

Almost all the cars in the segment are quite old. Santro has become an old-looking race horse, Zen Estilo never did justice to the Zen brand, Wagon-R and Indica have been around for a while and don’t really do justice in the looks department, and Spark is stuttering to even start, probably because of its Chevrolet association.

It was time for a change, and I think Hyundai has got it right. I10, or the Hyundai Pa as its known elsewhere, has arrived, and, with Maruti Suzuki’s Splash (Wagon-R’s cuter replacement) set to release next year, I10’s release has set the car-war rolling again. It’s refreshing to see some change in the hottest car segment in India.











It was time Hyundai replaced Santro coz of its dated design, and it was time Maruti had one solid product in the entry segment. I think Maruti somehow didn't have a real winner as far as the looks are concerned in this segment, probably because of its recent focus in Swift, SX4 and the Grand Vitara. B-Segment is really a cash cow in India, and products such as ‘I10’ and ‘Splash’ would just be the perfect bets to get the cash registers rolling for the two biggest car makers in India. I love the fact there are new options for the car buyer. A lot of other segments are boring for lack of competition. For example, you don’t have a real choice in ‘A’ segment – it’s just between the M800 and Alto, both from the Maruti stable. B+ Segment’s got Swift and Getz, but Swift is easily a no-brainer. Also, Skoda’s premium hatchback (Skoda Fabia) will be positioned in the C segment.

That said, the segment that could really do better is the entry level Segment ‘C’. If you are looking for a petrol car between 5L and 6L with a boot, there’s really no car that you could go with without thinking too much or compromising on one factor or the other. Esteem is from our grand-daddy’s generation, Logan looks boxy and sometimes yucky (and you don’t want to pay that much for a car that some just wouldn’t like), Indigo Petrol is not refined as the other ones in this segment, and Ikon has got maintenance issues. Of course, Hynudai Accent’s slow phase out was a case study example of killing a solid cash-cow of a brand.

In short, I would love to see some real action in this segment. I personally had to stretch to reach the SX4 since this segment was out of solid options. 2008 is going to be one fine year.