A rich man lived upon a tall hill in a mansion and he was served by a devoted servant boy. One day, while sitting before a feast at his table, the man felt generous (or pity perhaps) and gave the skinny boy four delicious warm buns to enjoy. The boy thanked the man profusely in an effusive, over-the-top fashion, then threw one of the rolls on the ground, picked it up and crushed it, and then poured goats blood on it and offered it back to the man. "Why on earth did you do that" asked the shocked and perplexed rich man. "Because I wanted to prove to you how devoted I am to you by showing that I'm willing to suffer deprivation in your name". "What", asked the fellow again. "I'm showing that I'm willing to suffer deprivation to prove how devoted I am", said the boy. At which the man replied, "what kind of master takes pleasure in his servants suffering?"
This is an obvious metaphor for religious sacrifice, where some 'god' is supposed to have given us worldly bounty as a gift, and we in turn destroy part of it in a "sacrifice" as a means of giving it back and showing that we're willing to suffer for our beliefs. Now, the rich man can respond in one of two ways. He could enjoy the boy's suffering, and even carry this pathogenic mindset even further by instilling fear and guilt in the boy and convincing him that his suffering will "cleanse" his soul, OR he could be a decent person and see that this boy gets help.
The 'god' of the bible resembles the former option, not the latter. What this relationship takes the form of is obvious. It's sadomasochistic.
Now, lest you think I've got this all wrong, consider Church history and dogma regarding the "mortification of the flesh", the idea that virginity is "pure", and that the "Passion of the Christ" to some extent, helped pay for sins. It payed a "ransom" as Matthew put it. In fact, it seems that 'god' cannot forgive sins without the shedding of blood (Heb 9:22), and consider that Jesus is offered as an innocent virgin sacrifice to make 'god' happy, much like Jephthah's virgin daughter offered up as a human sacrifice to YHWH in Judges 11, which is remembered and honored even still, as the chapter tells us in it's closing verses.
Christianity often teaches that suffering is "good for the soul" as part of it's reoccurring dogmas.
Indeed. Jesus himself sacrificed of himself to the point of destruction, all the while telling us that this is the moral ideal, and that the fellow who planned this (his father) is morally right by insisting that Jesus be destroyed before he ('god') can manage to forgive other people for not being impossibly perfect. What greater example of martyrdom and masochism is there?
http://www.religious-vocation.com/redemptive_suffering.html
[[Saint Gemma Galgani, letters Jesus spoke these words; "My child, I have need of victims, and strong victims, who by their sufferings, tribulations, and difficulties, make amends for sinners and for their ingratitude."]]
[[Saint Faustina Kowalska, diary, January 1934, .279"And the Lord said to me; 'My child, You please Me most by suffering. In your physical as well as your mental sufferings, My daughter, do not seek sympathy from creatures. I want the fragrance of your suffering to be pure and unadulterated. I want you to detach yourself, not only from creatures, but also from yourself. My daughter, I want to delight in the love of your heart, a pure love, virginal, unblemished, untarnished. The more you will come to love suffering, My daughter, the purer your love for Me will be'."]]
Monday, November 10, 2008
The Two Envelopes Problem
This is one of my favorite problems, mainly because it's so simple and yet stumps so many people, especially the "smart" ones.
Look at what the Wiki page has to say about it.
"The two envelopes problem is a puzzle or paradox within the subjectivistic interpretation of probability theory; more specifically within Bayesian decision theory. This is still an open problem among the subjectivists as no consensus has been reached yet."
http://en.wikipedia.org/wiki/Two_envelopes_problem
Look at the complex mathematics applied on that page. It makes me laugh since the solution is so simple, but I digress.
Here's the "paradox".
(I'll word it my own way, but I won't change the essential nature of the problem).
You are seated at a table, and before you are two identical envelopes. You are told that each envelope has a card in it with a monetary amount written on it. One has a certain unknown amount and the other has twice that amount. You cannot see through the envelopes and you have no idea what amount of money is involved or which envelope has which card. You are to choose one of the two envelopes, and after doing so, you are free to swap one for the other and to keep swapping as long as you wish. After having settled on choosing one of the two envelopes, you may then, and only then, open up one of the envelopes, read the card and collect that amount of money from the person offering the game to you. However, there is catch (there's always a catch). You are obligated to (a) follow the goal, which is to obtain as much money as possible, and (b) you must follow an optimal strategy that will allow you to achieve this goal, and (c) then and only then, can you stop swapping envelopes and collect your money. Otherwise, you must continue to swap envelopes in pursuit of a higher amount.
Now, you select an envelope. Let's say that the one you selected is has 'n' amount written on it's card (that you still haven't seen). But before looking at the card, you reason that the other envelope that you didn't select has either 2n or one half n written on it's card. If you swap cards, you stand to lose one half n, or stand to gain 'n' amount, so you're obligated by the terms of the game to swap envelopes, but now THE SAME reasoning now applies to the envelope you just selected. The OTHER envelope not in your possession always has either half or twice the amount as your envelope, so again, you are obligated to swap envelopes, and yet again, the same reasoning applies so you must swap yet again...
The end result is that you must KEEP swapping and NEVER actually receive any money because by the rules of the game, you are never allowed to stop swapping and to open any envelopes.
What's wrong with this reasoning?
(Try reasoning it out for yourself before reading the following solution)
------------------------------------------------------------
Solution:
What's wrong is, as you may have guessed, how the problem is being considered. We're approaching the problem as if there are three possible amounts (.5n, n, 2n), when there are actually two possible amounts on the cards. Instead of calling the amount on the card selected "n", let's just say that one envelope has a card with 'x' amount, and the other has 2x. If you first selected 'x', then by swapping you stand to gain 'x' amount, (2x-x). If, on the other hand, you first selected 2x, then by swapping you stand to lose 'x' amount. (-2x+x = -x).
That's the answer. By swapping, you stand to either gain 'x' or lose 'x', so there is no obligation to swap envelopes because there is no advantage in doing so.
Look at what the Wiki page has to say about it.
"The two envelopes problem is a puzzle or paradox within the subjectivistic interpretation of probability theory; more specifically within Bayesian decision theory. This is still an open problem among the subjectivists as no consensus has been reached yet."
http://en.wikipedia.org/wiki/Two_envelopes_problem
Look at the complex mathematics applied on that page. It makes me laugh since the solution is so simple, but I digress.
Here's the "paradox".
(I'll word it my own way, but I won't change the essential nature of the problem).
You are seated at a table, and before you are two identical envelopes. You are told that each envelope has a card in it with a monetary amount written on it. One has a certain unknown amount and the other has twice that amount. You cannot see through the envelopes and you have no idea what amount of money is involved or which envelope has which card. You are to choose one of the two envelopes, and after doing so, you are free to swap one for the other and to keep swapping as long as you wish. After having settled on choosing one of the two envelopes, you may then, and only then, open up one of the envelopes, read the card and collect that amount of money from the person offering the game to you. However, there is catch (there's always a catch). You are obligated to (a) follow the goal, which is to obtain as much money as possible, and (b) you must follow an optimal strategy that will allow you to achieve this goal, and (c) then and only then, can you stop swapping envelopes and collect your money. Otherwise, you must continue to swap envelopes in pursuit of a higher amount.
Now, you select an envelope. Let's say that the one you selected is has 'n' amount written on it's card (that you still haven't seen). But before looking at the card, you reason that the other envelope that you didn't select has either 2n or one half n written on it's card. If you swap cards, you stand to lose one half n, or stand to gain 'n' amount, so you're obligated by the terms of the game to swap envelopes, but now THE SAME reasoning now applies to the envelope you just selected. The OTHER envelope not in your possession always has either half or twice the amount as your envelope, so again, you are obligated to swap envelopes, and yet again, the same reasoning applies so you must swap yet again...
The end result is that you must KEEP swapping and NEVER actually receive any money because by the rules of the game, you are never allowed to stop swapping and to open any envelopes.
What's wrong with this reasoning?
(Try reasoning it out for yourself before reading the following solution)
------------------------------------------------------------
Solution:
What's wrong is, as you may have guessed, how the problem is being considered. We're approaching the problem as if there are three possible amounts (.5n, n, 2n), when there are actually two possible amounts on the cards. Instead of calling the amount on the card selected "n", let's just say that one envelope has a card with 'x' amount, and the other has 2x. If you first selected 'x', then by swapping you stand to gain 'x' amount, (2x-x). If, on the other hand, you first selected 2x, then by swapping you stand to lose 'x' amount. (-2x+x = -x).
That's the answer. By swapping, you stand to either gain 'x' or lose 'x', so there is no obligation to swap envelopes because there is no advantage in doing so.
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