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+1 *NM* Sidious Send a noteboard - 30/10/2012 09:17:07 AM
A Bell Curve by definition means that the distance from the weakest to the strongest channeler is intersected at exactly the 50% mark by the mean (the average channeler). Any skewing of the distribution would mean that the term “Bell Curve” cannot be applied to the distribution. Instead, it would then be either a positively or negatively skewed distribution. But not a Bell Curve.

So the basic rule is that the average channeler has to be exactly half as strong as the strongest channeler. Or to put it differently, a channeler x standard deviations away from the mean on the weak side, must be exactly as far from the mean as a channeler x standard deviations away on the strong side.
RJ has also said that 62.5% of channelers are strong enough to become Aes Sedai. This means that Daigian – who is the weakest possible Aes Sedai – lies exactly on this margin. And it then means that 12.5% of all female channelers lie between Daigian and the average strength woman.

Since it has been strongly suggested that Lanfear is the strongest possible woman, we therefore know that 12.5% of all female channelers lie between Daigian and the channeler who has 50% of Lanfear’s strength.


Ugh, just lost half an hour of typing. I'll try again.

I've never delved into a one power discussion before, but as a stats teacher I thought I might be of some use.

To the above, and especially the bolded - yes the first statement is correct, assuming that's what RJ said, but it has nothing to do with the second statement. The second one is fallacious.

An example given above had a mean of 1 and a standard deviation of 4.1, but that was a little abstract, so why don't we use a real example? The average male height in the US is 5 foot 10 or so. That doesn't mean that the maximum possible male height is 11 foot 8, no one has ever even come close to that. All that it means is that if you took all the males in the US, added up their heights, and divided by that number of males, you'd get a mean of 5 foot 10. Shortest or tallest has no relation to that mean, in and of itself.

The second component to a bell curve is standard deviation, sort of like an 'average spread' of the curve. The standard deviation is around 3 inches (according to a quick internet search) for male height. According to the way that normally distributed data are distributed (the bell curve follows certain rules, and most things in nature are normally distributed, which makes it a heck of a lot easier to analyze stats), that just means that 68% of all males will be between 5 foot 7 and 6 foot 1 (+ or - 1 standard deviation from the mean). But even if you're 3 SD's above the mean, or even if you're the tallest man in the world, it doesn't relate to the mean at all, any more than any number or place on the normal curve does.

(note: of course, with dwarfism there would actually be a little bump in the lower part of the real distribution of height, but let's say we're talking about 'height of people not affected by a physical condition' )

In this power example, then, Lanfear can be ten times stronger than the average Aes Sedai, a hundred, whatever - ratio isn't relevant to a normal curve. Normal curve only talks in terms of probability, so if Lanfear was 3 standard deviations above the mean, it would mean that there's only a .15% chance of someone being stronger than her in the population (as 99.7% of all scores fall within +/- 3 SD of the mean, and the rest has to be split on both ends, meaning .15% below 3 SD below the mean and .15% above 3 SD above the mean). My guess is that Lanfear is even rarer, maybe 4 or 5 SDs above the mean. Regardless, that is meaningless (no pun intended) with regards to her strength relative to other channellers. She could be 1000 times as strong as the channeller that sits perfectly at the middle of the distribution, or 1.5 times as strong. She can still fit perfectly fine into a bell curve of channellers.

With regards to the problem of zero - practically, that's not so much a problem. As I've already mentioned, only .15% of the population falls below 3 SDs below the mean, and that number gets exponentially smaller with each SD you get away from the mean. Taking height as an example, then, as I said you're at 5 foot 1 when you're 3 SDs below the mean. You still have 20 more standard deviations to go before you get to zero, so by the time you get to zero, although there's practically a CHANCE that you could get someone who has zero height, the chances of that happening even assuming it was physiologically possible would be essentially one in infinity, close enough. So the fact that there are physiological limitations doesn't mean that a significant part of the population has power (or height, or whatever) slightly above zero and then hits a wall. For the most part, the zero cutoff is a non-issue in measurement, which is why it's perfectly acceptable to describe things as conforming to a bell curve, even when some of the extreme aspects of a bell curve aren't perfectly replicable in real life. I'd say RJ would be totally justified in describing power as fitting a bell curve, without having to qualify 'except for specific theoretic mathematical points that make very little difference in reality'.
Wheel of Time board admin
Fan of Lanfear
This message last edited by Sidious on 30/10/2012 at 09:17:45 AM
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The Bell Curve revisited - 29/10/2012 09:44:09 AM 1498 Views
Re: The Bell Curve revisited - 29/10/2012 10:21:27 AM 894 Views
That's incorrect... - 29/10/2012 10:26:49 AM 1468 Views
Re: That's incorrect... - 29/10/2012 10:36:32 AM 900 Views
RJ the physicist didn't know math, so that Shannow could be right... - 29/10/2012 02:11:19 PM 814 Views
Response to a few of your poorly researched points... - 29/10/2012 02:31:17 PM 760 Views
Re: RJ the physicist didn't know math, so that Shannow could be right... - 29/10/2012 02:37:33 PM 775 Views
Exactly... - 29/10/2012 02:39:30 PM 774 Views
there are dozens of reasons for this - 29/10/2012 08:18:18 PM 791 Views
Excellent point. - 29/10/2012 08:24:37 PM 820 Views
Re: there are dozens of reasons for this - 29/10/2012 09:07:35 PM 721 Views
Again I don't argue that genetics play no role - 30/10/2012 01:57:24 AM 697 Views
Re: Again I don't argue that genetics play no role - 30/10/2012 07:07:17 AM 723 Views
I don't think it plays much role in the plot - 30/10/2012 03:17:55 PM 876 Views
Once again just so,we are clear on my stance with Genetics and Strength - 30/10/2012 03:27:11 PM 736 Views
That the 1000 Novices aren't a random sample of the population? - 29/10/2012 08:23:47 PM 675 Views
And why would it be biased towards those with lower strength? - 29/10/2012 09:11:25 PM 681 Views
Absolutely no reason... - 30/10/2012 01:35:35 AM 782 Views
Re: Absolutely no reason... - 30/10/2012 06:43:54 AM 683 Views
Only if it was a random sampling. Which this is not. - 30/10/2012 01:58:34 PM 769 Views
That's exactly the point. I want you to explain why it wasn't random. - 30/10/2012 02:14:59 PM 691 Views
It wasn't random because it was a self-selected sample! - 30/10/2012 02:43:03 PM 707 Views
Re: It wasn't random because it was a self-selected sample! - 30/10/2012 02:47:30 PM 705 Views
Go read a stats text will you? - 30/10/2012 02:54:16 PM 701 Views
Done - 31/10/2012 09:34:11 AM 1372 Views
You seem to have perfected whining to a Talent... - 10/11/2012 10:14:19 PM 961 Views
Re: You seem to have perfected whining to a Talent... - 11/11/2012 11:37:16 AM 730 Views
Re: You seem to have perfected whining to a Talent... - 11/11/2012 07:14:48 PM 659 Views
Re: You seem to have perfected whining to a Talent... - 11/11/2012 08:33:59 PM 1399 Views
Re: You seem to have perfected whining to a Talent... - 11/11/2012 08:43:19 PM 924 Views
Still nothing? - 10/11/2012 03:33:15 PM 713 Views
Still doesn't explain the difference - 30/10/2012 07:01:53 PM 646 Views
Re: Still doesn't explain the difference - 10/11/2012 10:21:00 PM 730 Views
Yes that totally makes sense - 30/10/2012 08:07:16 AM 820 Views
Thank you! *NM* - 30/10/2012 10:19:15 AM 380 Views
That's not what happened... - 30/10/2012 02:01:52 PM 743 Views
Re: That's not what happened... - 30/10/2012 02:15:57 PM 706 Views
Who said it would? - 30/10/2012 02:44:17 PM 711 Views
let's not mix up "random" and "representative" - 30/10/2012 05:28:09 PM 775 Views
Doesn't mean RJ applied it to his series - 30/10/2012 08:23:29 AM 785 Views
But of course he did.. - 30/10/2012 02:13:07 PM 806 Views
I hate to get into these things - 29/10/2012 05:45:50 PM 849 Views
I would love for you to be right, because it would solve all our problems, but 0 is the challenge... - 29/10/2012 07:56:34 PM 807 Views
In the truest sense, you are probably right that it is skewed - 29/10/2012 08:20:52 PM 832 Views
Overwhelm Lanfear, not match her. *NM* - 29/10/2012 08:26:09 PM 412 Views
Truth is, Moiraine was being overly optimistic... - 29/10/2012 08:39:17 PM 751 Views
You're pathetic... - 30/10/2012 01:20:01 AM 693 Views
The quote isn't specific - 30/10/2012 08:32:36 AM 814 Views
Its highly specific... - 30/10/2012 02:15:38 PM 644 Views
Yet neither of them are at full potential and at least equal a Forsaken - 30/10/2012 03:45:24 PM 1299 Views
Honestly! - 30/10/2012 02:07:37 AM 743 Views
Re: In the truest sense, you are probably right that it is skewed - 29/10/2012 09:10:27 PM 748 Views
Lots of people mean perfectly normal distribution when they say it - 30/10/2012 05:25:35 PM 687 Views
Couldn't the Towers method of obtaining Aes Sedai be to blame? - 30/10/2012 12:04:01 AM 890 Views
Re: Couldn't the Towers method of obtaining Aes Sedai be to blame? - 30/10/2012 09:33:44 AM 814 Views
Are you sure about that? - 30/10/2012 12:03:43 PM 816 Views
Re: Are you sure about that? - 30/10/2012 12:19:34 PM 721 Views
That doesn't seem a coherent narrative to me - 30/10/2012 04:26:25 PM 1019 Views
Sharina did not have the Spark, nor did Nicola - 30/10/2012 05:16:40 PM 827 Views
Re: Sharina did not have the Spark, nor did Nicola - 30/10/2012 05:54:41 PM 712 Views
We do not know if Cadsuane or any of the Forsaken are Sparkers - 30/10/2012 10:33:55 PM 840 Views
you're confusing 2 things - 30/10/2012 04:27:32 AM 889 Views
+1 *NM* - 30/10/2012 09:17:07 AM 819 Views
Re: you're confusing 2 things - 30/10/2012 09:21:39 AM 789 Views
Not true... - 30/10/2012 11:49:57 AM 801 Views
One thing - 30/10/2012 05:23:17 PM 778 Views
That's the problem. The BC RJ has "built" has a minimum and a maximum value - 30/10/2012 05:48:55 PM 799 Views

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