Wednesday, January 13, 2010
Friday, March 6, 2009
Monday, February 23, 2009
Pascal's Wager, extended
Rob at Wind Rose Hotel writes about Pascal's Wager.
Let's apply it to a slightly more complex problem...
Pascal's Wager proves that it's better for you to believe in God, but which God? Each religion offers you one: the benevolent God of Christianity, the harsh, unforgiving God of Islam, the indifferent God (if any) of Taoism and Buddhism, the capricious Gods of Hinduism and Paganism...
Let's extend the reasoning of Pascal's Wager to the case where there's choice between different Gods.
Assume for simplicity the possible choices are: (i) an harsh God (who punishes you unless you believe Him and behave exactly as His Prophets say), (ii) a benevolent God (who may perhaps forgive you if you didn't sin too much or even if you didn't believe in Him -- say you'll end up in Purgatory instead of Hell), and (iii) an indifferent God (who won't neither punish nor reward you -- this case is indistinguishable from the no-God one).
Suppose you choose to believe in the indifferent God, or in no Got at all; then, if the harsh God is the true one, you'll end in Hell (-1 points), if the true God is the benevolent one, you'll probably end in Hell as well, but perhaps not always, depending on your other sins (say -0.9 points). If the true God is indifferent, you have nothing to gain. Total score: -1.9 or so.
Suppose you choose to believe in the benevolent God. Then in the harsh God case you would be punished (-1), and rewarded in the case of a benevolent God (+1). An indifferent God wouldn't care to punish you. Total score: 0
Suppose you choose to believe in the harsh God. Then, if you're right, you'll be rewarded (+1). If the true God is the benevolent one, you'd probably be punished, but perhaps not always (say -0.9 points). In the case of an indifferent God, nothing happens. Total score: 0.1 points.
To summarize, this extended Pascal's Wager confirms the findings of the original one: you'd fare better believing in a God than not believing (or believing in an indifferent one).
Moreover, the harsher the God, the more convenient it is to believe in Him.
So I imagine the best option in the real world, according to Pascal's Wager, would be to convert to Islam, and perhaps hedge the bet by avoiding behavior that's sinful for Christianity (eg. taking more than one wife).
Let's apply it to a slightly more complex problem...
Pascal's Wager proves that it's better for you to believe in God, but which God? Each religion offers you one: the benevolent God of Christianity, the harsh, unforgiving God of Islam, the indifferent God (if any) of Taoism and Buddhism, the capricious Gods of Hinduism and Paganism...
Let's extend the reasoning of Pascal's Wager to the case where there's choice between different Gods.
Assume for simplicity the possible choices are: (i) an harsh God (who punishes you unless you believe Him and behave exactly as His Prophets say), (ii) a benevolent God (who may perhaps forgive you if you didn't sin too much or even if you didn't believe in Him -- say you'll end up in Purgatory instead of Hell), and (iii) an indifferent God (who won't neither punish nor reward you -- this case is indistinguishable from the no-God one).
Suppose you choose to believe in the indifferent God, or in no Got at all; then, if the harsh God is the true one, you'll end in Hell (-1 points), if the true God is the benevolent one, you'll probably end in Hell as well, but perhaps not always, depending on your other sins (say -0.9 points). If the true God is indifferent, you have nothing to gain. Total score: -1.9 or so.
Suppose you choose to believe in the benevolent God. Then in the harsh God case you would be punished (-1), and rewarded in the case of a benevolent God (+1). An indifferent God wouldn't care to punish you. Total score: 0
Suppose you choose to believe in the harsh God. Then, if you're right, you'll be rewarded (+1). If the true God is the benevolent one, you'd probably be punished, but perhaps not always (say -0.9 points). In the case of an indifferent God, nothing happens. Total score: 0.1 points.
To summarize, this extended Pascal's Wager confirms the findings of the original one: you'd fare better believing in a God than not believing (or believing in an indifferent one).
Moreover, the harsher the God, the more convenient it is to believe in Him.
So I imagine the best option in the real world, according to Pascal's Wager, would be to convert to Islam, and perhaps hedge the bet by avoiding behavior that's sinful for Christianity (eg. taking more than one wife).
Monday, February 9, 2009
On the Englaro case
I don't have a clear position on this case, but despite what Catholics say, I think that Mr.Englaro's position was a little more coherent than the one of the Italian government.
From what I understand, the parents' position is based on two amply-condivided principles.
The first principle is that a person has the right to refuse to be submitted to therapy. This principle is (at least implicitly) accepted by the Church. I remember reading some time ago of the case of a pregnant woman who, at risk of her own health, refused therapy that could have harmed the foetus she was carrying, and this behaviour was reported very favourably by the Catholic press. Moreover, when in a few years therapies based on embrional stem cells will become to be offered to patients, I suppose many Catholics will want to be able to refuse them as against their principles. Even Pope John Paul II is rumored to have requested to suspend therapies in the last days of his illness.
The second principle is that when patients are unable to express their will, relatives may testimony the patients' opinion. This is how consent is currently sought for in case of organ trasplant from brain-dead people, for example. This principle is also supported by the Church, that doesn't forbid organ donation.
The only aspect on which perhaps the protesters have a point is whether alimentation and hydration are or not to be considered a therapy. This is debatable, as the means by which Ms. Englaro was kept alive are everything but "natural".
Even with the new law that forces alimentation and hydration not to be interrupted, I don't think a patient in those conditions could survive for long without any other kind of medicament or drug. An immobilized person would develop infections or trombosis without continuos treatment.
From what I understand, the parents' position is based on two amply-condivided principles.
The first principle is that a person has the right to refuse to be submitted to therapy. This principle is (at least implicitly) accepted by the Church. I remember reading some time ago of the case of a pregnant woman who, at risk of her own health, refused therapy that could have harmed the foetus she was carrying, and this behaviour was reported very favourably by the Catholic press. Moreover, when in a few years therapies based on embrional stem cells will become to be offered to patients, I suppose many Catholics will want to be able to refuse them as against their principles. Even Pope John Paul II is rumored to have requested to suspend therapies in the last days of his illness.
The second principle is that when patients are unable to express their will, relatives may testimony the patients' opinion. This is how consent is currently sought for in case of organ trasplant from brain-dead people, for example. This principle is also supported by the Church, that doesn't forbid organ donation.
The only aspect on which perhaps the protesters have a point is whether alimentation and hydration are or not to be considered a therapy. This is debatable, as the means by which Ms. Englaro was kept alive are everything but "natural".
Even with the new law that forces alimentation and hydration not to be interrupted, I don't think a patient in those conditions could survive for long without any other kind of medicament or drug. An immobilized person would develop infections or trombosis without continuos treatment.
Thursday, January 22, 2009
Why I'm skeptic about IQ
The main reason I'm skeptic about IQ has something to do with degrees of freedom, as used in physics. It doesn't sound possible that you can describe something as complex and multi-dimensional as the human intelligence using a single parameter.
Even cars, which are a lot less complex than the human mind, cannot be described with a single parameter. There's no such a thing as a Car Quotient, nobody calls a dealership and orders a 120 point car. The characteristics we look for in a car are multiple and independent: persons seated, trunk size, engine power, speed, mpg, price. No single parameter can summarize them all.
Yet IQ supporters maintain that a single parameter can summarize all mental power of a person. If it were so, then a IQ 120 person would be able to do everything a IQ 110 person can do, with capacity to spare.
As a Gedankenexperiment, take for example two famous Britons of the past: Shakespeare and Newton, and call IQ(S) and IQ(N) their respective IQs. Then either IQ(S) > IQ(N) or IQ(N) > IQ(S). If IQ(N) > IQ(S), that would mean that Newton could have written Shakespeare's plays? I don't think so. On the other side, IQ(S) > IQ(N), then Shakespeare could have written the Principia, which I find also improbable.
The fact that IQ test are composed of different parts, each used to measure a different facet or skill: short term memory, verbal ability, pattern recognition, arithmetics, etc. The final score is a weighted average of the score of the subparts. With different weights, the same test performance might result in different IQs. If the linguistic part is valued enough, then the Shakespeares will turn out with a greater IQ than the Newtons, if it is valued less enough, then all the Newtons will outperform the Shakespeares.
IQ supporters claim that the score of the different subtest are statistically correlated, so they all measure the same thing. If it were so, why have different subtests ? Actually, the correlation is not very high. To return to the car metaphor, we can see that also the car characteristics are also correlated: large cars on average seat more people, have a larger trunk, a more powerful engine, lower fuel efficiency and a higher price, than small cars. Then again, there are sport cars that are small, but have powerful engine and high price, or minivans with relatively small engines, so the average correlation cannot be used to describe a car.
Even cars, which are a lot less complex than the human mind, cannot be described with a single parameter. There's no such a thing as a Car Quotient, nobody calls a dealership and orders a 120 point car. The characteristics we look for in a car are multiple and independent: persons seated, trunk size, engine power, speed, mpg, price. No single parameter can summarize them all.
Yet IQ supporters maintain that a single parameter can summarize all mental power of a person. If it were so, then a IQ 120 person would be able to do everything a IQ 110 person can do, with capacity to spare.
As a Gedankenexperiment, take for example two famous Britons of the past: Shakespeare and Newton, and call IQ(S) and IQ(N) their respective IQs. Then either IQ(S) > IQ(N) or IQ(N) > IQ(S). If IQ(N) > IQ(S), that would mean that Newton could have written Shakespeare's plays? I don't think so. On the other side, IQ(S) > IQ(N), then Shakespeare could have written the Principia, which I find also improbable.
The fact that IQ test are composed of different parts, each used to measure a different facet or skill: short term memory, verbal ability, pattern recognition, arithmetics, etc. The final score is a weighted average of the score of the subparts. With different weights, the same test performance might result in different IQs. If the linguistic part is valued enough, then the Shakespeares will turn out with a greater IQ than the Newtons, if it is valued less enough, then all the Newtons will outperform the Shakespeares.
IQ supporters claim that the score of the different subtest are statistically correlated, so they all measure the same thing. If it were so, why have different subtests ? Actually, the correlation is not very high. To return to the car metaphor, we can see that also the car characteristics are also correlated: large cars on average seat more people, have a larger trunk, a more powerful engine, lower fuel efficiency and a higher price, than small cars. Then again, there are sport cars that are small, but have powerful engine and high price, or minivans with relatively small engines, so the average correlation cannot be used to describe a car.
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