1.
The only problem with searching for a needle in a haystack is practically searching the entire haystack for the needle.
2.
There is nothing like majority rule (democracy).
In every political organism there will always be a ruling elite who are the minority.
The ruling elite is not elected by the voters but has itself elected by them.
3.
Wednesday, April 23, 2008
Thursday, April 17, 2008
How come ?
1.
The Two Envelope Paradox
You have a choice between two envelopes that contain money. You are allowed to look at one before you chose. You are told that one envelope contains twice as much as the other. You pick one (let's say A). You find 10/=. So, the other envelope (B ) must have $5 or 20/=. Do you keep this one or go select B?
Well look at the expected value of the other one. It is (1/2 x 5/=) + (1/2 x 20/=) = 12.50/=. Hmm, looks like you need to pick B. But wait, what if you had picked it first? The same analysis would have caused you to conclude that A was the better one. How come?
2.
The Unexpected Execution (Hanging) Paradox
A prisoner is told that he will be hanged next week but the day of the hanging will be a surprise. The prisoner realizes that if he wakes up Saturday morning and finds himself not dead, then he can't be hanged that day because it would not be a surprise. By induction, he then eliminates Friday and so on for every day of the week. But come Wednesday he was hanged -- much to his surprise -- as the judge promised. How come its a surprise?
3.
The black card paradox.
Consider a stack of 7 playing cards, all of which are red except one which is black. It is your job to assemble the cards in a stack face down with the black one in some position. It is my job to turn the cards over one at a time until I get to the black one.
Can you arrange the cards in the deck in such a way that at every position, I will not be able to deduce that the next card is a black one before I turn it over? That is, as I go through the stack, one at a time, I will not be able to correctly deduce that the next card is black.
You cannot put it in the bottom, 7th, position, for I can certainly deduce that it is black if I get down to the last card and I haven't seen a black one. So that rules out the 7th position. There seems to be no doubt about that. (It would seem even that the 7th card is useless and we might as well play the game with 6, but I will let that pass.)
What about the 6th position? Well when I get down to the 6th card, I can deduce that the it must be black since we have already eliminated the 7th position. So you can't use the 6th position either.
Now, I say the 5th position has exactly the same problem. We have eliminated the 6th and 7th haven't we? This continues until we eliminate the 1st position.
This implies that i can always know it the card is black.
How come?
The Two Envelope Paradox
You have a choice between two envelopes that contain money. You are allowed to look at one before you chose. You are told that one envelope contains twice as much as the other. You pick one (let's say A). You find 10/=. So, the other envelope (B ) must have $5 or 20/=. Do you keep this one or go select B?
Well look at the expected value of the other one. It is (1/2 x 5/=) + (1/2 x 20/=) = 12.50/=. Hmm, looks like you need to pick B. But wait, what if you had picked it first? The same analysis would have caused you to conclude that A was the better one. How come?
2.
The Unexpected Execution (Hanging) Paradox
A prisoner is told that he will be hanged next week but the day of the hanging will be a surprise. The prisoner realizes that if he wakes up Saturday morning and finds himself not dead, then he can't be hanged that day because it would not be a surprise. By induction, he then eliminates Friday and so on for every day of the week. But come Wednesday he was hanged -- much to his surprise -- as the judge promised. How come its a surprise?
3.
The black card paradox.
Consider a stack of 7 playing cards, all of which are red except one which is black. It is your job to assemble the cards in a stack face down with the black one in some position. It is my job to turn the cards over one at a time until I get to the black one.
Can you arrange the cards in the deck in such a way that at every position, I will not be able to deduce that the next card is a black one before I turn it over? That is, as I go through the stack, one at a time, I will not be able to correctly deduce that the next card is black.
You cannot put it in the bottom, 7th, position, for I can certainly deduce that it is black if I get down to the last card and I haven't seen a black one. So that rules out the 7th position. There seems to be no doubt about that. (It would seem even that the 7th card is useless and we might as well play the game with 6, but I will let that pass.)
What about the 6th position? Well when I get down to the 6th card, I can deduce that the it must be black since we have already eliminated the 7th position. So you can't use the 6th position either.
Now, I say the 5th position has exactly the same problem. We have eliminated the 6th and 7th haven't we? This continues until we eliminate the 1st position.
This implies that i can always know it the card is black.
How come?
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