'(The Blog) With No Name', perhaps best described as a stream of notes and thoughts - 'remembered, recovered and (sometimes) invented'.

Thursday, July 05, 2012

Surely, you were NOT joking, Mr. Perelman!

I board a half empty bus at Ernakulam. It is 9 pm. The only vacant window seats are among the 10 or so reserved for women (which men can occupy only if there aren't female travelers).

I reason: "This is a late hour. And this is Kerala, where women don't dare to travel late - and even if they do, they make at most 1 in 20 of the passengers. So, at most 2-3 ladies may board on the way. And so, I can take a ladies' seat and safely sit for the full journey". To be doubly sure, I take the ladies seat farthest from the door.

More men get in and by the time the bus leaves the downtown, there are quite a few standing. No woman passengers in yet. I sit back.


Let me leave that dull narration and quote a bit from Yakov Perelman's little gem, 'Figures for Fun' (with a minimum of editing):


A girl asked "I have a hunch, the first person walking past our window will be a man. What is the chance that I am right?"

The young mathematician answered: "The probablity is half..."

And another asked: "And what is the probablity that the first two passers are men?"

Mathematician: ".... (some basic arguments)... so it is 1/2 times 1/2 that is 1/4!"


"And what will the chance be for 10 passersby all being men?"

Mathematician: "Oh, very small; it works out to 1/2 multiplied by itself 10 times, less than 1 in 1000! Nobody will bet on such a thing happening; no hope! I will bet a 1000 roubles that it wont happen."

Suddenly one of those present exclaimed: "I can take the bet; am willing to put up a rouble and win a thousand!"

Mathematician: "But don't you forget, the chance to win is one in a thousand!"

The Other Chap: "I don't care, I can bet a rouble against a thousand that the first hundred passers-by, not just the first ten, are all men!"

Mathematician: "With hundred passers, your chance of winning falls to er.. 1 in a number that is 1 followed by 30 zeros!"

TOC: "Impressive! I will still take the bet. What do you put up against my rouble?"

Mathematician: "Everything that I have, Everything!"

TOC: "That's too much. Make it your bicycle against my rouble for 100 passers-by. But I am sure you won't dare!"

Math: "I wont dare?! Of course, go ahead; I bet you my bike! I am not risking anything anyway!"

TOC: "Neither am I. If I win, I get a bike. If you do, I lose very little."

Math: "But don't you realize you will NEVER win? I have basically got your rouble in my pocket."

Now, an old professor spoke, addressing the Mathematician: "You seem to be missing something..."

Math: " What, Professor, you really think he has a chance?"

Prof: "Have you considered the fact that not all occurences are equally possible.. that the computation of probability will be correct only for equally possible events, isn't it? And here we have a situation where .... And do you not hear the military band?"

Math: "I do. But what is the connectio... Hey!" He rushed to the window and looked out and turned and said sadly: "I lost, bye-bye, my poor bike!"


And here is how my own journey went:

The bus halted briefly at Vyttila 'Hub', the main suburban bus station. A few more passengers, all men, got on. And just as we are about to leave, a woman in cleaning/maintenance staff uniform runs up and tells the conductor: "Please hold on. It's closing time. A few of us are coming!" And moments later, a dozen and more of uniformed ladies trooped in!

NOTE: Let me now nitpick a bit with the master of nitpicking. While its probabilistic analysis is perfectly even-handed in terms of gender, Perelman's story as a whole is not. It implicitly says the mathematician and the professor and the smart Alec are all men. The military band signifies an all-male march-past of soldiers and the only time females participate in the discussion is when a couple of girls ask the most elementary questions imaginable - then, as the heavyweights get involved, they 'discreetly fall silent'. Elsewhere in the book, some friends get together, someone suggests they play with brain teasers to pass time and a young woman, silent until then, objects: "I will quit if they involve algebra or geometry."


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