The Monty Hall Problem

A couple of days ago, a friend discussed an interesting puzzle.  The puzzle concerns probabilities and I found it very intriguing.  I thought I’ll write about it.  The puzzle is popularly known as the Monty Hall problem.  The problem is described as follows.

A friend, Monty, invites you to play a game where you have a chance to gain big.  He brings you to a large hall with three large doors named, say, A, B and C.  He says that behind one of the doors, he has parked a gleaming new car, and behind each of the other two, he has managed to make a goat stand quietly.  If you win the game, you take the car.  He asks you to choose a door.  Say you choose B.  He now opens another door and shows you a goat behind it.  Say, he opens C, and shows you a goat peacefully ruminating behind it.  He then asks you whether you want to switch your choice from your original door B to the remaining door A.  You can either opt to switch your choice, or retain your old choice.  Whatever your decide in response to this offer defines your final choice.  He opens the door of your final choice and if you find a car behind it, you win.  If you find a goat behind it, you lose.

The puzzle is, if you were playing this game, would you switch your choice when offered, or retain the original choice?

My immediate answer, like most people, was that it does not matter.  Since two doors remain, and one of them has a goat and the other a car behind it, there is no need to change my choice.  The probability of a car being there behind my original choice B, must be equal to the probability of a car being there behind the other door A, which is equal to 1/2.  However, on deeper thinking this turned out to be a fallacy.

If I do not switch my choice from B to A when offered, the goat that my friend shows me behind C makes no difference to me.  I simply stick with my earlier choice of B.  The only way in which I can win in this case, is if the car is behind B.  The probability of this is 1/3, since the car could be behind A, B or C with equal likelihood.

Now, if I switch my choice from B to A, the situation is a little more interesting.  The door C does not have a car as the friend has shown.  I win if A, and not B, has a car behind it.  In other words, the only way I win is if my original choice B does not have a car behind it.  And the probability of this event is 2/3.  So, the chances of my winning are doubled if I switch my choice from B to A!

Background noise

Why is the mind so noisy?  There are sounds in the mind, voices, chatter, thoughts emerging and falling all the time.  It is difficult to sustain quietude beyond a few moments.  Whenever I try to quieten the sounds in my mind, a stray thought would begin somewhere, a piece of silly music or a stupid song would start playing in the mind and the quietness is shattered.  It is not easy to quieten the mind for long.

What are these thoughts that keep the mind occupied?  Like a computer worm that replicates itself and occupies memory, or like a virus that occupies the processor and slows down a computer, these thoughts exhaust our mental resources.  So much so, that we lose sight of reality, and our vision of reality is distorted by the thoughts that occupy our mind.  The mind, in its purest form, is free of emotions like anger, frustration, sorrow or hatred.  It is thoughts that give rise to such emotions.  A stray thought arises in my mind, which tells me that I’m a victim of someone’s neglect.  The feeling of self-pity then immediately overcomes my mind.  The self-pity then leads to anger or hatred against the person whom I blame for my pitiable condition.  The mind is capable of taking action based on such feelings of pity, anger or hatred that arise out of noise in our minds.  As we can expect, action that is a result of noise is likely to be arbitrary or random, and such arbitrary actions can cause repentance later, leading to more feeling of self-pity, more anger, more hatred, and more anxiety.

For a few days, I’ve been trying to observe the thoughts in my mind.  Sometimes, the thoughts are absolutely meaningless, such as a piece of music or a phrase from an advertisement, or a song that plays over and over again.  Sometimes, there are thoughts of meaningless but comic violence, such as slapping someone or insulting someone, and a part of my self laughs at the comedy.  Some of these thoughts are unmentionable, and all of these thoughts are utterly worthless.

Sometimes, there are thoughts in the form of conversations.  I need to take a decision about something, say, about the topic of the next blog post.  My mind is split into two, and one part of the mind proposes ideas about what I should be writing to another part of my mind!  The proposal is in the form of words, and if I pay attention and quickly note down the words and sentences, I can even keep a record of such thoughts!  I’ve noticed that such mental conversations are highly biased by social prejudices, irrational beliefs and a lot of nonsense.  I’ve noticed that several of my key decisions are taken after such unconscious conversations in my mind!  I do not like this way of deciding at all.  I would rather prefer to take decisions with a calm mind, free of all biases and beliefs.  But for that, I need to quieten my mind, and to sustain the quietude.  That is the only way to ensure that my behavior is not a result of meaningless background noise, but is a manifestation of my pure consciousness.

It has been seven months since I posted.  And I want to resume posting.  So, this is a resumption!

(Inspired by the title of Satyanarayana’s blog.)

WordPress for Android

Just downloaded WordPress for Android and installed on my HTC Explorer. Have been using my desktop PC far lesser than earlier, since I got a data plan on my phone connection. So, perhaps, this app is a good way to stay in touch with my blogs…

Roads to Freedom

Picked up Bertrand Russel’s “Roads to Freedom” last weekend.  Here is a passage from the introduction in the book:

“The class war, like wars between nations, produces two opposing views, each equally true and equally untrue.  The citizen of a nation at war, when he thinks of his own countrymen, thinks of them primarily as he has experienced them, in dealings with their friends, in their family relations, and so on.  They seem to him on the whole kindly, decent folk.  But a nation with which his country is at war views his compatriots through the medium of a quite different set of experiences:  as they appear in the ferocity of battle, in the invasion and subjugation of a hostile territory, or in the chicanery of a juggling diplomacy.  The men of whom these facts are true are the very same as the men whom their compatriots know as husbands or fathers or friends, but they are judged differently because they are judged on different data.  And so it is with those who view the capitalist from the standpoint of the revolutionary wage-earner:  they appear inconceivably cynical and misjudging to the capitalist, because the facts up0n which their view is based are facts which he either does not know or habitually ignores.  Yet the view from the outside is just as true as the view from the inside.  Both are necessary to the complete truth; and the Socialist, who emphasises the outside view, is not a cynic, but merely the friend of the wage-earners, maddened by the spectacle of the needless misery which capitalism inflicts upon them.”

Seems to be very interesting reading!

Almost a dream!

Yesterday night, I had a dream.

I was in a room, that had a sea-facing window.  The window was rather wide and large.  I had some two friends with me, but I am not able to correlate their identity with any real-life individuals.  However, I was aware of the presence of some two individuals who must’ve been friends.  We were lying on three separate cots that were set at the window.  The window was low, at the same height as the cots.  I was on the leftmost cot, lying on my belly, had lifted my head and was looking out of the window.  I don’t remember seeing any color outside the window.  I think the sight was in black-and-white, but I clearly remember seeing a vast sea-front, and dark clouds in the sky.  One of the two friends commented that when such houses are constructed, they don’t keep the sea-facing side of the house towards south.  I remarked that if the sea is on the southern side of the house, the sea-facing side of the house is bound to be towards south.  I felt very clever for having made this remark.  I remember feeling very relaxed at this point.  I kept my head on the cot, and started falling asleep.

I think I awoke at this point, for some reason.  When I recollected the dream, I realized that in my sleep, I had dreamt about falling asleep!  Had I not woken up, perhaps I would have had a dream within my dream!

Coconut-Jaggery Rice (नारळी भात)

Prepared a sweet dish for Sankranti. नारळी भात, or rice cooked with coconut and jaggery.  And it turned out well.  Here is the recipe.

Ingredients

• Rice (I used Sona Masoori, though some recommend Basmati):  1 1/2 cups
• Fresh coconut, scraped or grated:  2 cups
• Jaggery, crushed or grated:  2 cups
• Cloves:  6 or 7
• Ghee:  3 tablespoons
• Broken cashewnuts:  10-12
• Raisins:  10-12  (other dry fruits such as almonds or unsalted pistachio can be added, as per taste)
• Powdered or crushed cardamom (elaichi) seeds:  4-5

Method

1. Wash the rice in enough water. Drain the water.  Leave the washed rice in a covered vessel for an hour.
2. Heat 3 cups of water till it boils.  Lower the flame and keep the water boiling.
3. Melt 2 tablespoons of ghee in a pan.  Fry the cloves in it for about half a minute.  Make sure the ghee does not burn or smoke.
4. Add the washed rice to the ghee in the pan, and fry for about three minutes.  The rice should be covered with ghee and should start to appear a little golden.
5. Add the boiling water to the pan.  Cover with a lid and let the rice cook.  I used a pressure-pan for easy cooking.
6. Once the rice is cooked, spread it in a shallow dish and allow it to cool.
7. Mix the coconut and jaggery in a bowl.  Add this mixture to the cooled rice, and mix gently.  Do not crush the rice while mixing.
8. Melt the remaining tablespoonful of ghee in a pan, and lightly fry the dry fruits.  Remove the dry-fruits from the pan using a spoon and keep them aside.
9. Now ad the coconut – jaggery – rice mixture to the remaining ghee.  On a low to moderate flame, cover with a tight lid and allow to cook.  I used the same pressure-pan without the weight-valve for this purpose.  Remove the lid every 2-3 minutes, and stir well.  Make sure the mixture does not burn at the bottom of the pan.  After about 15-20 minutes of cooking, the mixture becomes a little dry.  The jaggery melts completely into the mixture.
10. Once the mixture is dry, turn off the flame.  Add the crushed cardamoms and the fried dry-fruits.  Serve hot or after it cools.  Store in a cool place, after cooling, in a vessel covered with a lid.

Here is a picture I took with a mobile phone.

Aerial View

Flew into Mumbai for the first time today. Had traveled to Mumbai in the past, but never flew in. The first feature that struck, about Mumbai as seen from the sky, was the tall buildings, that stand upright, as if sticking right out of the Earth. The second feature was a mass of black or blackened roofs, around the buildings. I later realized that these roofs are actually corrugated tin or asbestos roofs, primarily of slum houses. Perhaps that one sight itself conveyed something significant about the city.

I also remember the first aerial view of a few other cities. Hyderabad, from the sky, looks like it is spread out flat, without too many tall structures, with unplanned, chaotic growth.

Bangalore looks a a lot greener, with trees of various varieties showing up as various shades of green.

Kochi offers a bouquet of coconut palms! The sight of coconut palms, right up to the horizon, or right up to the sea-front, is a most glorious sight!

Would like to see how Delhi looks like.

Waves in the sea

A visit to a beach is a subtle, spiritual experience.  I had the opportunity to visit the Pondicherry beach a couple of months ago.  It is a short, rocky beach and the sea seemed to be noisy and a bit rough.  But the dynamics were just right for long walks along Goubert Avenue and a few silent moments of introspection!

The beach starts getting visitors from around 5 in the evening.  The crowd that throngs the beach is one of the most colorful and vibrant.  There are groups of men, relaxing after a day of hard work.  There are families socializing in the gentle breeze.  Vendors sell little toys for the children, many of them are battery operated with bright lights.

The guest-house at which we stayed was located right on the beach, so there was ample opportunity to click pictures of the waves in the sea.  Here are a few that I clicked.

Chennai Sky!

I was at Chennai the whole of last week on a work assignment.  I had carried my little camera with me hoping to find some time to click a few pictures.  However, it was not before Saturday evening that I could find some time to spend with the camera.  The time was around 5:15 in the evening, and the sun was setting.  I couldn’t find any subjects to click, so I thought I’ll click the sky.

 For a few moments, the sun was behind a cloud.  When massive clouds try to mask a radiant sun, his might is even more pronounced, as his brilliant light bathes the clouds and colors the sky!

“A good heart is the sun and the moon; or, rather, the sun and not the moon, for it shines bright and never changes.” - Shakespeare.

Large clouds are heavy and imposing.  Dark clouds bring darkness, lightning, thunder, melancholy and adversity!   But little white clouds are like a child’s laughter – light, innocent and fleeting.

“Every man, wherever he goes, is encompassed by a cloud of comforting convictions which move with him like flies on a summer day.” - Bertrand Russel.

 And, when it is turning dark, the feeling is sometimes gloomy.  When the sun is smothered and his light is failing, our minds unconsciously are led to contemplate about the day that was, the day that could have been, and the impending dark night.  A few birds seemed to be engaged in such a contemplative dialog..

“Be still, sad heart, and cease repining; Behind the clouds the sun is shining; Thy fate is the common fate of all; Into each life some rain must fall; Some days must be dark and dreary.” - HW Longfellow

When the darkness seems imminent, when the light seems to be entirely lost, the sun tears through a cloud.  Light pierces through darkness one last time, like a moment of optimism in a life of eternal despair.

“Our deepest fear is not that we are inadequate. Our deepest fear is that we are powerful beyond measure. It is our Light, not our Darkness, that most frightens us.” - Marianne Williamson.

On the flight to return home, I had a window-seat, but for most of the journey the sun was beating directly through the glass.  There was hardly a chance to click any pictures of the sky.  But just before the aircraft assumed its final course, there was this glimpse of the sky, the clouds, the elusive horizon, and the coastline…

“A cloud does not know why it moves in just such a direction and at such a speed...It feels an impulsion...this is the place to go now. But the sky knows the reasons and the patterns behind all clouds, and you will know, too, when you lift yourself high enough to see beyond horizons.” - Richard Bach.