Archive for Fevereiro, 2008
Paradox 2… Theseus
Raises the question of whether an object, which has had all its component parts replaced, remains fundamentally the same…
otis…
The sun is shining more than usual. Days are getting longer, people are getting happier. I’m still the same.
Paradox 1… St. Petersburg
In a game of chance, you pay a fixed fee to enter, and then a fair coin will be tossed repeatedly until a tail first appears, ending the game. The pot starts at 1 dollar and is doubled every time a head appears. You win whatever is in the pot after the game ends. Thus you win 1 dollar if a tail appears on the first toss, 2 dollars if on the second, 4 dollars if on the third, 8 dollars if on the fourth, etc. In short, you win 2^(k−1) dollars if the coin is tossed k times until the first tail appears.
What would be a fair price to pay for entering the game? To answer this we need to consider what would be the average payout: With probability 1/2, you win 1 dollar; with probability 1/4 you win 2 dollars; with probability 1/8 you win 4 dollars etc. The expected value is thus,
This sum diverges to infinity, and so the expected win for the player of this game, at least in its idealized form, in which the casino has unlimited resources, is an infinite amount of money. This means that the player should almost surely come out ahead in the long run, no matter how much they pay to enter; while a large payoff comes along very rarely, when it eventually does it will typically far more than repay however much money they have already paid to play. According to the usual treatment of deciding when it is advantageous and therefore rational to play, you should therefore play the game at any price if offered the opportunity. Yet, in published descriptions of the paradox, e.g. (Martin, 2004), many people expressed disbelief in the result. Martin quotes Ian Hacking as saying “few of us would pay even $25 to enter such a game” and says most commentators would agree.
23,5 Exquisite
Trashing, trashing. All she was doing. Trashing. Lying while believing. Refusing to see what was actually there to everybody’s acceptance. The self indecent and induced fakeness of her pain, the fear of non existing ghosts. The wounds were not healing, they kept bleeding in sequence. One after the other. She was cutting her own flesh over and over again. The bathroom floor had white and black square tiles. Aligned in sequence, white against black, good against evil, happiness against darkness.
That particular day it was sunny outside and at least birds were singing. The windows of her bedroom were covered, protecting her own little depressive corner of the world. Self pity some may say. Laying in the bathtub, hanging bleeding wrists were dropping blood over a white tile. One after the other until drops merged together to form an invading sea. When birds stopped singing, there were no more white tiles. All was red, all was blood. Her skin was white. Darkness in her bedroom was still intact, protected. She wasn’t there anymore.
