The priest is usually an exceptionally good thinker/reasoner/philosopher – maybe 4-7 standard deviations from the mean.
I hope you are not talking about normal distribution, because for it, 7 standard deviations means about 1 in 10^12, that is, 1 in 1,000,000,000,000, far too much for the humanity to date.
I’ve heard (in conversation) that distributions of human abilities (such as IQ) have fat tails compared to normal distributions, so +7 SD would be more common than 1 in 10^12. I haven’t found a good reference for this yet… if anyone else has one I’d like to see it.
Not an answer to your question, but according to this, at most about 1 in 200 people are at least at +7 SD if the distribution is unimodal and symmetric (unimodal for the theorem to apply, symmetric so you can divide by 2). 200 seems like a uselessly low number, so I’m now regretting having pointed people at that theorem previously. :-)
ETA: though, even the useless 1 in 200 bound seems like an unrealistically high level of reasoning ability for priests.
I thought of that, but decided that the OP wasn’t taking it into account, and so the error was worth pointing out (which turned out to be correct). On the other hand, I don’t see how one can establish a linear scale of ability. IQ measure, for example, is often defined based on calibration in a form “1 in X”, and then giving, say, 16 points above/below 100 for each standard deviation to the area in normal distribution weighting 1/X. This also allows to cross-check IQ tests with other g-factor tests, competitions, etc.
Since I like Wikipedia, I probably looked at that exact table (showing percentages of values within one to 7 standard deviations) and thought, “the last 4 look good” (4-7 standard deviations) without actually counting the number of 9s after the decimal. While that describes my relationship with accuracy pretty well, I should have been more careful before posting. I did want to account for the fact that the best philosopher/priest figure in history (perhaps Aristotle, Jesus or Muhammad) would have a lasting influence on religion. Yet only about 100 billion humans have ever been born—not that I remotely knew that.
One of these people invented empirical science and formal logic and was, for the purposes of his own time, an atheist and materialist (in comparison to just about everyone else). The other two heard voices and started cults.
I suppose this is trivial but lets try to have pride in past rationalists who fought the good fight before it was popular. We need heroes for rationalist children and philosophers and scientists are all we got. (Not uncritical pride mind you, Aristotle was wrong about a great deal).
I hope you are not talking about normal distribution, because for it, 7 standard deviations means about 1 in 10^12, that is, 1 in 1,000,000,000,000, far too much for the humanity to date.
I’ve heard (in conversation) that distributions of human abilities (such as IQ) have fat tails compared to normal distributions, so +7 SD would be more common than 1 in 10^12. I haven’t found a good reference for this yet… if anyone else has one I’d like to see it.
Not an answer to your question, but according to this, at most about 1 in 200 people are at least at +7 SD if the distribution is unimodal and symmetric (unimodal for the theorem to apply, symmetric so you can divide by 2). 200 seems like a uselessly low number, so I’m now regretting having pointed people at that theorem previously. :-)
ETA: though, even the useless 1 in 200 bound seems like an unrealistically high level of reasoning ability for priests.
I thought of that, but decided that the OP wasn’t taking it into account, and so the error was worth pointing out (which turned out to be correct). On the other hand, I don’t see how one can establish a linear scale of ability. IQ measure, for example, is often defined based on calibration in a form “1 in X”, and then giving, say, 16 points above/below 100 for each standard deviation to the area in normal distribution weighting 1/X. This also allows to cross-check IQ tests with other g-factor tests, competitions, etc.
Since I like Wikipedia, I probably looked at that exact table (showing percentages of values within one to 7 standard deviations) and thought, “the last 4 look good” (4-7 standard deviations) without actually counting the number of 9s after the decimal. While that describes my relationship with accuracy pretty well, I should have been more careful before posting. I did want to account for the fact that the best philosopher/priest figure in history (perhaps Aristotle, Jesus or Muhammad) would have a lasting influence on religion. Yet only about 100 billion humans have ever been born—not that I remotely knew that.
Aristotle, Jesus or Muhammad…
One of these people invented empirical science and formal logic and was, for the purposes of his own time, an atheist and materialist (in comparison to just about everyone else). The other two heard voices and started cults.
I suppose this is trivial but lets try to have pride in past rationalists who fought the good fight before it was popular. We need heroes for rationalist children and philosophers and scientists are all we got. (Not uncritical pride mind you, Aristotle was wrong about a great deal).