Yes, Sidious' scale is a relative scale not an absolute one - Edit 1
Before modification by BlackAdder at 18/12/2009 12:23:39 AM
First, RJ told us Egwene and co. come one step below the Forsaken and Moiraine and the strongest Aes Sedai a step below them. You completely ignore this by placing Moiraine at 25, Egwene at 40 and Moghedien at 65! A wider range of numbers called one below the other I've never seen.
Second, by placing the strongest AS at 25 and the weakest at 10, you raise some startling implications from RJ's comments on the Bell Curve.
First, 62.5% of channelers (male or female) are strong enough to be Aes Sedai by modern standards. By your placement, this means 37.5% of women are weaker than Daigian.
But if we take a bell curve distribution to the strength range of 1 to 100, this means strength range 90 to 100 will also consist of roughly 37.5% of channelers. The only way to avoid this is to have a skewed bell curve, which RJ has said the distribution is not.
The worst, though, is the assumption made that the 21 levels are not evenly distributed. Most of the lists you and Sidious come up with have AS from 10-25, with increments of 1 since we know there are a load of levels among the AS. However, there are sudden jumps when you go from Moiraine to Cadsuane and then Caddy to Egwene, and then on to the Forsaken. On exactly what basis are you making the assumption that the 21 levels are not equally distributed in the strength range of 1 to 100? Especially with a bell curve distribution showing that RJ gave a load of thought to this.
For gods sake, if the range of a bell curve is 1 to 100, then the variable will cluster around the mean, meaning the highest number of women will be of strength 50. This is a mathematical fact, not a matter of perspective. And yet, you want to place someone of as rare strength as Egwene below this point and also all of the Aes Sedai?
Second, by placing the strongest AS at 25 and the weakest at 10, you raise some startling implications from RJ's comments on the Bell Curve.
First, 62.5% of channelers (male or female) are strong enough to be Aes Sedai by modern standards. By your placement, this means 37.5% of women are weaker than Daigian.
But if we take a bell curve distribution to the strength range of 1 to 100, this means strength range 90 to 100 will also consist of roughly 37.5% of channelers. The only way to avoid this is to have a skewed bell curve, which RJ has said the distribution is not.
The worst, though, is the assumption made that the 21 levels are not evenly distributed. Most of the lists you and Sidious come up with have AS from 10-25, with increments of 1 since we know there are a load of levels among the AS. However, there are sudden jumps when you go from Moiraine to Cadsuane and then Caddy to Egwene, and then on to the Forsaken. On exactly what basis are you making the assumption that the 21 levels are not equally distributed in the strength range of 1 to 100? Especially with a bell curve distribution showing that RJ gave a load of thought to this.
For gods sake, if the range of a bell curve is 1 to 100, then the variable will cluster around the mean, meaning the highest number of women will be of strength 50. This is a mathematical fact, not a matter of perspective. And yet, you want to place someone of as rare strength as Egwene below this point and also all of the Aes Sedai?
It is quite simple, really. In your model, the average channeler lies on 50, and the strongest possible channeler will lie on 100. Therefore, on your model, the strongest possible channeler is only double the strength of the average channeler. This is completely inconsistent with the text.
Instead, we see that the vast majority of channelers are very weak, and that everyone we see as being average strength channelers are actually very strong channelers. Even the normal Aes Sedai.
So, we know that 37.5% of women are weaker than Dagian who is say a 10 on the strength scale. Then, 12.5% of women fall between Dagian and the average woman - who is say a 15 on the strength scale.
That means, in this simple example, half of women fall below 15 which is still below the average Aes Sedai strength of 20. So this half of all women would include the Kin and all other women who are even weaker than Dagian, as well as weak Aes Sedai who fall above Dagian, but still below the average Aes Sedai strength.
To continue this example, we can then say that 62.5% of women fall below 20 - which is the average Aes Sedai strength. That would mean that 1 woman in 3 is stronger than the average Aes Sedai.
So you can see that to get to women like Nynaeve you are talking about 4 or 5 standard deviations from the mean - if the mean is 15 and Nynaeve is on 75.
Nynaeve appears to be 1 in 10 000 in terms of strength, so how many standard deviations from the mean would that be? I forget and I don't have my old textbooks handy. 3 standard deviations includes something like 97.5% of cases, and 4 standard deviations something like 99.95 of all cases. So Nynaeve might even be 5 standard deviations from the mean.
The point is, you cannot view the mean as being 50 on the strength scale. Because then you limit the strongest possible woman to being only double as strong as the average woman - which is refuted by the examples in the text.
Unless you take Egwene and Elayne to be of average strength - which is ridiculous, as they are among the strongest women in the Tower for 1000 years.
This Bell Curve cannot be centered on 50 strength, because RJ has stated that the vast majority of channelers in the Age of Legends were fairly weak, with only rare individuals being of great strength. It is the sheer numbers of channelers that allowed so many strong individuals to exist, because even though they were a very tiny percentage of the overall channelers, this small percentage still amounted to hundreds of thousands of channelers. Those who weren't of great strength, simply chose not to become Aes Sedai.
Remember, if 3% of the population could learn to channel, out of 5 to 10 billion or so that means around 100 million channelers.
And yet, according to RJ the number of Aes Sedai numbered in the hundreds of thousands to the low millions. So that's only about 1% of all possible channelers. The strongest 1%. And the Forsaken were probably the strongest 1% out of that 1%. Really the best of the best category.
So clearly, if you take the entire channeling population, the Bell Curve is centered far closer towards the bottom than to the top.