### February 08, 2006

## Applying Statistics

Yesterday I spent thw whole day at home with the flu, and god bless the Internet for these situations. Last night I was truly shaking with fever, and that ain't fun. However, today I'm OK even if I feel a bit funny still.

It occurred to me that often the discussion of issues such as religious or ideological fanatism seems to be framed in the wrong terms. For example, when one points to the ovious intolerance and fanatism of Islamists, almost always someone pops up to point out that there are Christian and Jewish extremists too.

The first flaw of these arguments is that one fanaticism does not excuse the other - especially for an agnostic like me.

The second is that meraly pointing to the existance of non-Muslim fanatics does indeed explain little.

I think it is necessary to consider things a bit more objectively, and this requires statistics. Statistical distributions describe the frequency of a variable across a population - for example, the height of adult males. The most common (I think) distribution is the Gaussian one, also called "normal distribution" or bell-curve. There are many more statistical distributions useful for different cases; for example blog traffic follows a power-law distribution: there are relatively little blogs with a very high traffic, and many more with low traffic.

The normal distribution is symmetrical and centered on the median value. For example, the median height of Italian males was 172 cm (If I remember correctly) a few years ago: this means that most males will be of that height or close, while there is only a small fraction of males much taller or much shorter. The median height of say, Filipinos is lower while Brits tend to be taller. Knowing the distribution function it is easy to calculate the probability of someone being taller or shorter than a specified value, and other interesting quantities.

Of course religious opinions are much more difficult to treat in this way; I think that at least two variables are required, one being the degree of belief and the other tolarence (something like this quiz). The normal distribution of two variables is represented as a three-dimensional surface with one single maximum, as you can see here. I expect that plotting these distributions for Jews, Christians and Muslims will show that Christian and Jews are centered on rather moderate and tolerant positions - while Muslims are centered on more fanatical and less tolerant positions.

Alternatively, the distributions may very well not be Gaussian (maybe they are Gamma), and thus skewed towards moderation for Christians and Jews but towards fanaticism for Muslims.

So yes, there are fanatics on all sides, and also very accomodant Muslims. But the distribution of "belief intensity" and tolerance is different, that's the point (and also, whether Islamists are a minority or not, they are enough to cause great trouble).

It occurred to me that often the discussion of issues such as religious or ideological fanatism seems to be framed in the wrong terms. For example, when one points to the ovious intolerance and fanatism of Islamists, almost always someone pops up to point out that there are Christian and Jewish extremists too.

The first flaw of these arguments is that one fanaticism does not excuse the other - especially for an agnostic like me.

The second is that meraly pointing to the existance of non-Muslim fanatics does indeed explain little.

I think it is necessary to consider things a bit more objectively, and this requires statistics. Statistical distributions describe the frequency of a variable across a population - for example, the height of adult males. The most common (I think) distribution is the Gaussian one, also called "normal distribution" or bell-curve. There are many more statistical distributions useful for different cases; for example blog traffic follows a power-law distribution: there are relatively little blogs with a very high traffic, and many more with low traffic.

The normal distribution is symmetrical and centered on the median value. For example, the median height of Italian males was 172 cm (If I remember correctly) a few years ago: this means that most males will be of that height or close, while there is only a small fraction of males much taller or much shorter. The median height of say, Filipinos is lower while Brits tend to be taller. Knowing the distribution function it is easy to calculate the probability of someone being taller or shorter than a specified value, and other interesting quantities.

Of course religious opinions are much more difficult to treat in this way; I think that at least two variables are required, one being the degree of belief and the other tolarence (something like this quiz). The normal distribution of two variables is represented as a three-dimensional surface with one single maximum, as you can see here. I expect that plotting these distributions for Jews, Christians and Muslims will show that Christian and Jews are centered on rather moderate and tolerant positions - while Muslims are centered on more fanatical and less tolerant positions.

Alternatively, the distributions may very well not be Gaussian (maybe they are Gamma), and thus skewed towards moderation for Christians and Jews but towards fanaticism for Muslims.

So yes, there are fanatics on all sides, and also very accomodant Muslims. But the distribution of "belief intensity" and tolerance is different, that's the point (and also, whether Islamists are a minority or not, they are enough to cause great trouble).

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