There have been a lot of posts centered around One Power strength, and the bell curve. Having been on vacation, I've read these posts with enthusiasim and coy amusement (it's nice to get some good debate going on this board).
That said, I'd like to raise some points regarding things I've seen. I'm also going to leave male channelers out of this entirely because some posters froth at the mouth as soon as saidin and saidar are compared even from a distance.
That said, I'd like to raise some points regarding things I've seen. I'm also going to leave male channelers out of this entirely because some posters froth at the mouth as soon as saidin and saidar are compared even from a distance.
From what I've read, this seems to be the only board that has considered this point in detail. So, YAY us!
Previous Posts
1. As mentioned before, everyone is toying around with things they probably don't understand as well as they think they do. RJ was a physicist and knew his subject well, and most people here are not proficient at mathematics and statistics. It took some striking posts from people who actually knows their subject in the form of Abunderment and Amirebram to demonstrate the shocking misuse of the bell curve to demonstrate people's points. The most important thing about the bell curve is that it is a frequency distribution that describes the prevalence of a strength level. Therefore, if there are 20 levels of strength and the graph peaks at level 10, it does not mean that level 20 is twice as strong, despite this being the flawed contention of other posters. As mentioned in one of their posts, the data is not in the graph, merely the frequency of that data. Therefore, the bell curve statements by RJ are close to irrelevant when trying to work out the actual strengths of various women. We merely know from his statements how common certain levels of strength are.
1. As mentioned before, everyone is toying around with things they probably don't understand as well as they think they do. RJ was a physicist and knew his subject well, and most people here are not proficient at mathematics and statistics. It took some striking posts from people who actually knows their subject in the form of Abunderment and Amirebram to demonstrate the shocking misuse of the bell curve to demonstrate people's points. The most important thing about the bell curve is that it is a frequency distribution that describes the prevalence of a strength level. Therefore, if there are 20 levels of strength and the graph peaks at level 10, it does not mean that level 20 is twice as strong, despite this being the flawed contention of other posters. As mentioned in one of their posts, the data is not in the graph, merely the frequency of that data. Therefore, the bell curve statements by RJ are close to irrelevant when trying to work out the actual strengths of various women. We merely know from his statements how common certain levels of strength are.
Well, I'm a biophysicist/cell biologist, and I can tell you that yes, in a normal situation, a bell curve is used for statistical analysis. Rarely would you see "bell curve distribution" used as a property. That is because in real life, you can never assume that all outliers are taken care of.
Take height for example... can we put 7 feet as the absolute maximum? What if someone an inch or so taller comes up? Also, all data points do not have a representation... any real bell curve is only going to be applied on the basis of a statistical sampling.
While all that is fine, this is an imagined world. RJ had the ability to set an upper and lower limit to channeling ability, and he did. Wen can safely say there can be no one stronger than Rand/Lanfear, because that was a restriction RJ himself applied.
Another thing is that when RJ says channeling strength follows a bell curve distribution, he's using the term as a property of channeling strength among humans. RJ did not sample his characters and do some math and find out that there was a bell curve distribution.
Instead, by authorial fiat, he has decreed that channeling strength follows a bell curve distribution. That means all his channelers in the series will fit into the bell curve.
Knowing that, you can rest assured that the average strength woman is half as strong as the strongest woman. Whether that strength is designated as 50 or 5000 or 4445543 doesn't make an ounce of difference. What matters is that mean strength is exactly half the maximum, and this is the commonest strength found in the population.
And this is not a statistical result, but actual fact because RJ never went through the process of sampling channeler strength and doing some math. He decided how the distribution would be and applied it.
2. Secondly, one of the posters, an electrical engineer says that the term bell curve is used very loosely in his profession to describe anything with a peak that tapers off. There is no evidence that RJ's bell curve is one of a pure gaussian distribution. It's possible, but not probable, that he was describing this sentiment. If one professional can do it, it's not beyond belief that RJ could too.
Well, when challenged, said poster came up with no proof. Search the net for "bell curve distribution". You'll find zero mentions of a non-normal bell curve distribution.
It may well be that they use the term bell curve locally. Meaning that in a given range, a curve follows the normal distribution, and then takes on a different shape. Needless to say, the whole curve cannot be called a bell curve.
Lastly, if RJ meant some weird sort of bell curve, I don't see why he wouldn't have specified that.
3. Any of the radical strength levels could be outliers - we don't even know which ones. It's possible that women above Egwene in strength are such women. It's even probable that Morgase is an outlier considering she is very much weaker than even Sorilea. Morgase can only touch saidar one in a thousand times and is profoundly weak - there is a vast potential for strength levels between a woman like her and a weak woman like Daigian.
Exactly! But you put Daigian at strength 10, and then ask us to belive the existence of many strength levels between 1 and this, as well that 37.5% of the population falls in this range. The implication of that last is that 37.5% of the population also lies in the range 90-100, which I hope you will agree with me is ridiculous.
4. It is wrong to assume that Moiraine has a potential strength of 50 out of 100. Moiraine has been used as the mean-median-mode on several occasions in previous posts, which is not supported by the text. The reason this was done was to promote plausibility to this IMO weak theory : by claiming that the strongest Aes Sedai is half as strong as Lanfear you can at least gain some credibility compared to a theory that Lanfear is twice as strong as Vandene (or the true median strength). However, we know from Elayne in ACoS (Next door to a weaver) that Sheriam's strength is uncommon in women, and thus the true peak in female strength is far below this. This means that Moiraine is far above the peak in female strength, which has always been true. Once again, the bell curve cannot be used for exact data, only channeler prevalence at particular levels.
But Elayne bases her statement on her experience in the White Tower. Which is a vastly skewed sample. Whichever way you look at it, there need to be women stronger than Sheriam/Moiraine in a sample, yet the Tower provides none. It is indeed a vastly screwed sample.
For myself, I believe that Moiraine is actually a step above the peak of 50, and that peak is instead filled with women of around Anaiya's strength.
5. RJ changed his own ideas. Brandon says there are two strength lists - one with Nynaeve at the top, one with her not at the top. The latter list probably includes the Forsaken, we don't know. Still, he couldn't apply the bell curve to the first list and hold it steadfast by adding a range of channelers above Nynaeve later. He also couldn't set a bell curve on the second list considering it wasn't drawn up yet. Therefore, the curve is vague at best.
We have absolutely no clue when the Bell Curve was decided upon. Before the first list? Between the first and the second? After? Speculating on this is useless.
True female strengths
A rather pompous heading for so contentious a result!
So what is the strength of the average woman? Well, Egwene says in TPoD (Beginnings) that out of 1000 novices, most by far would never reach the shawl. However, RJ said that using a bell curve, 62.5% of women would attain the shawl. One must assume that everyone above the median value and 12.5% below it will attain the shawl. Daigian, being the weakest woman in the Tower is therefore in the vicinity of this level, which by definition means that 37.5% of women are weaker than her. This is factual evidence from RJ. We also know from TPoD (Alliances) that Sorilea is weak enough in the Power to make Daigian look strong, which reinforces the idea that many women fall into this one-third void of weakness below Daigian.
We see from Galina in ACoS (Spears) that none of the Shaido Wise Ones are truly weak in the Power, though she could break through the weakest's (Micara) shield with little difficulty. Galina says that few women in the Tower are as strong as her, meaning she is probably as strong as Sheriam. We've been told that most women in the Tower treat Daigian little better than a servant and Galina is unlikely to be much better when referring to low strength levels. It's therefore not unreasonable to assume that all of the Shaido Wise Ones are stronger than Daigian.
Therefore - about a third of women are weaker than Daigian in the Power. Most of Egwene's one thousand novices are weaker than Daigian by far meaning they fall into this area - which is proof that Egwene's sample is skewed. The Shaido are also skewed, however, being stronger than they should be, with none of their number being weak in the Power. Therefore, true sampling is still not present in the series that we know of.
We see from Galina in ACoS (Spears) that none of the Shaido Wise Ones are truly weak in the Power, though she could break through the weakest's (Micara) shield with little difficulty. Galina says that few women in the Tower are as strong as her, meaning she is probably as strong as Sheriam. We've been told that most women in the Tower treat Daigian little better than a servant and Galina is unlikely to be much better when referring to low strength levels. It's therefore not unreasonable to assume that all of the Shaido Wise Ones are stronger than Daigian.
Therefore - about a third of women are weaker than Daigian in the Power. Most of Egwene's one thousand novices are weaker than Daigian by far meaning they fall into this area - which is proof that Egwene's sample is skewed. The Shaido are also skewed, however, being stronger than they should be, with none of their number being weak in the Power. Therefore, true sampling is still not present in the series that we know of.
This is what I've been saying all along. There has indeed been no true sample in the series, though the Wise Ones as a whole must come close, as must the Windfinders, since we can reaosnably assume both find all learners and definitely all sparkers.
We know that Siuan is less than 50% as strong as she used to be. She said that even if Nynaeve healed her to 50% of her previous strength, most Aes Sedai would be as strong, and a great deal would be stronger. Therefore, most Aes Sedai lie between 50-100% of Siuan's original strength. But not all - Siuan despite being weakened is not the weakest woman in the Tower. She's possibly a third as strong as she used to be, and total Aes Sedai strength may lie between 20 - 100% of her original strength. This, I believe is a range of 5-25 out of a potential of 100, though that is my personal theory.
Siuan's case proves nothing about actual strength though. Put her at 55 or 60 and you'll still have the same kind of results.
Therefore we can assume the following ...
- Almost all of Egwene's novices are weaker than Daigian. (<37.5% on the bell curve)
- Hundreds of Shaido Wise Ones are as strong as Daigain. (>37.5% on the bell curve)
- 1000 Aes Sedai are stronger than Daigian. (>37.5% on the bell curve)
- This sample of about 3000 channelers shows that about 1/3 of women cannot reach the shawl whereas 2/3 can, just like RJ said.
- Almost all of Egwene's novices are weaker than Daigian. (<37.5% on the bell curve)
- Hundreds of Shaido Wise Ones are as strong as Daigain. (>37.5% on the bell curve)
- 1000 Aes Sedai are stronger than Daigian. (>37.5% on the bell curve)
- This sample of about 3000 channelers shows that about 1/3 of women cannot reach the shawl whereas 2/3 can, just like RJ said.
Agreed.
Absolute strength
Some small inferences...
- Egwene is strong enough in the Power to overwhelm both Amys and Melaine. Amys is as strong as Moiraine, and Melaine a little weaker. Therefore because Egwene is said to be even stronger than this, she is stronger than a strong Aes Sedai and an average Aes Sedai combined. We already know factually that Siuan (Amys's strength) was once twice as strong as some Aes Sedai, and that most women in the Tower are as strong as that, and a great deal stronger. So let's place average Aes Sedai strength at 1 and Amys/Siuan at 1.25. Therefore Egwene is at least 2.25 in strength even if you look at it rather negatively. Aviendha said that she was even stronger than this, but she's at least this strong.
Some small inferences...
- Egwene is strong enough in the Power to overwhelm both Amys and Melaine. Amys is as strong as Moiraine, and Melaine a little weaker. Therefore because Egwene is said to be even stronger than this, she is stronger than a strong Aes Sedai and an average Aes Sedai combined. We already know factually that Siuan (Amys's strength) was once twice as strong as some Aes Sedai, and that most women in the Tower are as strong as that, and a great deal stronger. So let's place average Aes Sedai strength at 1 and Amys/Siuan at 1.25. Therefore Egwene is at least 2.25 in strength even if you look at it rather negatively. Aviendha said that she was even stronger than this, but she's at least this strong.
I strongly doubt this. If she is indeed so much stronger, I fail to see how Silviana alone can hold her shield.
I think if you place Siuan at 1.25, Egwene should be at 1.75.
- Egwene says that Rand is stronger than both she and Aviendha combined (TFOH - This place, this day). Egwene and Aviendha are not at full strength, but it doesn't matter because Aviendha's statement on Egwene's strength predates this. Now I agreed to leave men out of this debate, but Rand is pretty much as strong as Lanfear according to RJ himself. However, we know that he wasn't at his full strength yet - he equated Rahvin's strength to his own, and later Sammael's, and therefore was certainly not as strong as Lanfear at this point considering the strongest man and woman are a match. Therefore, double Egwene's minimum strength of 2.25 and get Lanfear's minimum strength of 4.5.
The same book has Moiraine stating that Egwene and Aviendha combined could overwhelm Lanfear or Graendal. Do you trust Egwene's word when she cannot even estimate Rand's strength, or Moiraine's, who has held a strong Forsaken and has also seen Lanfear and her strength in the Rings?
Further, in tFoH, Rand says Egwene and Aviendha were working at a distance that he himself had to strain to work at. He thinks they must be straining even more than him, based on what Egwene told him.
But consider this... Rand had an angreal, and was straining. Egwene and Avi were probably linked, and showed no more tiring than Rand. Does this mean they are weaker than him, or stronger than him? I'd say definitely the latter.
This once again fits into my own personal theory of female strength...
- Aes Sedai 20 (range 5 - 25)
- Egwene 50
- Nynaeve 90
- Lanfear 100
It's all very iffy, and I don't claim that it's totally accurate, but it keeps in line with most of the quotes in the series and with what the author has told us.
- Aes Sedai 20 (range 5 - 25)
- Egwene 50
- Nynaeve 90
- Lanfear 100
It's all very iffy, and I don't claim that it's totally accurate, but it keeps in line with most of the quotes in the series and with what the author has told us.
I'd personally say
Average Aes Sedai- 40
Average woman- 50
Siuan-55/60
Egwene-75
Nynaeve- 90
Lanfear- 100
As a small example Rand says that he can handle three women if they aren't too strong, but he might be in trouble if one if Moghedien or Semirhage (LoC - Gifts).
- 3 Aes Sedai = 20x3 = 60.
- 2 Aes Sedai + Semirhage = 20+20+85 = 125.
Lews Therin says he definitely cannot handle seven women (LoC - the Mirror of Mists) : 20x7 = 140.
- 3 Aes Sedai = 20x3 = 60.
- 2 Aes Sedai + Semirhage = 20+20+85 = 125.
Lews Therin says he definitely cannot handle seven women (LoC - the Mirror of Mists) : 20x7 = 140.
There's a problem with this, though. As I showed in another thread, four women who are all too weak to even be tested for Accepted can nearly match the effects Rand can. Three Aes Sedai should definitely be able to, whatever scale you follow, even though they cannot shield him. This statement is in sharp contrast to that.
Nynaeve vs Egwene/Elayne/Aviendha
There's been a lot of debate around this, and some posters such as myself believe that Nynaeve is much stronger than Egwene (90 vs 50), and others think they aren't too far apart (90 vs 80).
One can safely fall back on Moiraine's statement that Nynaeve is like a bonfire next to Egwene and Elayne. It's a statement of magnitude, if not of detail, and it at least means something.
There's been a lot of debate around this, and some posters such as myself believe that Nynaeve is much stronger than Egwene (90 vs 50), and others think they aren't too far apart (90 vs 80).
One can safely fall back on Moiraine's statement that Nynaeve is like a bonfire next to Egwene and Elayne. It's a statement of magnitude, if not of detail, and it at least means something.
Well, by that, Nynaeve should at least be twice as strong as Egwene, which is something even you disagree with. If you take it literally, it means Nynaeve should be thousand times as strong, which is ridiculous.
Whether you say 50 and 90 or 75 and 90, Moiraine's statement is pure bunkum.
However, I just want to throw in one small added debate, and that is growth in strength. We know that women grow in strength at a steady pace, and that the stronger you are the faster you grow. You also grow faster if you're forced. Now, compare the strength progression of these two women...
Books 1 and 2
minimal channeling ability
Books 1 and 2
minimal channeling ability
Actually, no. Siuan says Nynaeve is already as strong as most sisters in the Tower. Meaning where Egwene started at 0, Nynaeve was at 20 or 40, depending on which scale you follow.
Book 3
Nynaeve - as strong as any Sister in the Tower
Egwene - stronger than Liandrin
Nynaeve - as strong as any Sister in the Tower
Egwene - stronger than Liandrin
Nope. Elayne says Egwene is as strong as any Aes Sedai.
Book 4
Nynaeve - much stronger than Egwene (Egwene says that Rand handled her and Elayne like puppies, but that maybe Nynaeve would be able to challenge him. TSR - Playing with Fire)
Egwene - stronger than Moiraine.
Book 5
Nynaeve - as strong as Moghedien (in the last section of the previous book already). This already exceeds Egwene's maximum potential.
Egwene - stronger than Amys and Melaine.
Nynaeve - much stronger than Egwene (Egwene says that Rand handled her and Elayne like puppies, but that maybe Nynaeve would be able to challenge him. TSR - Playing with Fire)
Egwene - stronger than Moiraine.
Book 5
Nynaeve - as strong as Moghedien (in the last section of the previous book already). This already exceeds Egwene's maximum potential.
Egwene - stronger than Amys and Melaine.
She was already stronger than either of them. It would be interesting to know if Egwene was pretty close to her potential by now. IF she was, she wasn't far below Moggy.
Now, both women are growing in strength. They have probably reached their potential, but as late as WH that was in doubt. I think the strength progression speaks for its self, and shows a wide difference in potentials between the two women. Not only that, but Egwene has the 'advantage' in that she was forced, and Nynaeve the 'disadvantage' in that she was blocked. I'm sure some people will see it differently, but I think it's self-evident that Egwene is much weaker than Nynaeve, though both are women of rare strength.
That doesn't mean much. I cannot find the quote, but we are told that all three of them were forced, though Egwene's time with the Seanchan forced her the most. Egwene reached her potential remarkably fast. Elayne is yet to reach hers. Nynaeve may have, but she had a unique event like the Cleansing to speed her up. I doubt you can make any meaningful comparison.
The Tower does not exclude strong channelers, only weak ones. We know for a fact that 37.5% of all channelers are excluded because they are too weak. And since 37.5% of all channelers are weaker than Dagian, we know that only 12.5% of channelers lie between Dagian and the mean.
Therefore, Dagian is very close to the strength of the average channeler. And seeing as Dagian is only about half as strong as the average Aes Sedai, it seems very likely that the average woman falls between Dagian and the average Aes Sedai.
Meaning, and here's the important bit, that the average Aes Sedai is STRONGER than the average woman.
Proving that the Tower sample is skewed towards the stronger side of the strength range.
Yes. It's one of the few things we know about Aes Sedai - strength is one of the primary things they use to discard or accept initiates. As you say, only 12.5% of women are stronger than Daigian that lie below the median. The Tower is ultra-skewed though, and thus doesn't have very strong women, so their mean strength may be lower than say the Wise Ones, who have women like Therava, Tamela and Viendre to raise the average strength.
Siuan more than hints that most Sisters are above the median strength on the bell curve, after her fall from grace. She claims that most Sisters are at least half as strong as she used to be, which Daigian was not. There are no Forsaken strength women, but not very weak ones either - it balances out in a twisted way.
Wheel of Time board admin
Fan of Lanfear
Fan of Lanfear
One Power strength - critical analysis of previous posts and some further ideas
- 03/01/2010 07:59:24 AM
2342 Views
I support your view, with maybe a few comments to add...
- 03/01/2010 02:58:05 PM
1056 Views
where is this phantom quote of Egwene "not standing a chance"
- 03/01/2010 05:20:20 PM
757 Views
Here's the real quote
- 03/01/2010 05:38:59 PM
815 Views
Well that quote perfectly illustrates the skewed way in which you interpret the evidence...
- 03/01/2010 06:18:22 PM
780 Views
I also think the quote is specific
- 03/01/2010 06:34:38 PM
781 Views
Skill not Strength is the key that and the potential that another FS was with her
- 03/01/2010 06:51:46 PM
799 Views
Bah
- 03/01/2010 07:13:01 PM
742 Views
Who's arguing that?
- 03/01/2010 07:34:21 PM
716 Views
What ARE you arguing?
- 03/01/2010 07:43:06 PM
782 Views
That there is far more to strength in her quote!
- 03/01/2010 08:05:20 PM
678 Views
Re: That there is far more to strength in her quote!
- 04/01/2010 09:40:05 AM
878 Views
and where do I ever say Elayne is only a small step below Moghedien?
- 04/01/2010 03:08:37 PM
777 Views
You more than imply it with your own list
- 04/01/2010 03:39:06 PM
784 Views
and you are fixated on simple strength to the exclusion of everything else
- 04/01/2010 05:05:54 PM
729 Views
Re: and you are fixated on simple strength to the exclusion of everything else
- 04/01/2010 06:46:45 PM
1120 Views
Tiny Unimportant Objection to "Bell Curve" Point
- 03/01/2010 03:09:55 PM
877 Views
Re: Tiny Unimportant Objection to "Bell Curve" Point
- 03/01/2010 04:39:25 PM
783 Views
I've got a slightly revised opinion than my last post
- 03/01/2010 05:16:39 PM
989 Views
Re: I've got a slightly revised opinion than my last post
- 03/01/2010 06:31:09 PM
913 Views
It's actually not that complicated ... simple math actually
- 03/01/2010 07:08:52 PM
786 Views
Yes, but to think that RJ put that much effort into it is improbable
- 03/01/2010 07:19:13 PM
791 Views
I'm being harsh with one poster who continues to mis-quote things!
- 03/01/2010 07:56:17 PM
707 Views
Re: I'm being harsh with one poster who continues to mis-quote things!
- 04/01/2010 09:50:38 AM
822 Views
Re: I'm being harsh with one poster who continues to mis-quote things!
- 04/01/2010 03:26:10 PM
897 Views
Re: I'm being harsh with one poster who continues to mis-quote things!
- 04/01/2010 03:52:19 PM
768 Views
You are talking out of both sides of your mouth
- 04/01/2010 05:09:15 PM
717 Views
Dude
- 04/01/2010 06:21:28 PM
672 Views
Dude, please go back to Fionwe's post
- 04/01/2010 06:35:03 PM
712 Views
A reply...
- 03/01/2010 06:02:33 PM
719 Views
The Tower sample is skewed allright, but to the upper side of the strength range...
- 03/01/2010 06:36:45 PM
853 Views
I agree - Aes Sedai are stronger in the Power
- 03/01/2010 07:26:45 PM
920 Views
Re: A reply...
- 03/01/2010 07:09:55 PM
847 Views
I think distance is related to Strength
- 03/01/2010 07:21:46 PM
765 Views
amusing side note
- 04/01/2010 05:22:39 AM
709 Views
Which is exactly what I envisage the AOL distribution to have looked like...
- 04/01/2010 07:03:51 AM
659 Views
Re: Which is exactly what I envisage the AOL distribution to have looked like...
- 04/01/2010 03:29:47 PM
735 Views
It may sound silly, but did you look at One Power values in the Wheel of Time CCG?
- 05/01/2010 12:56:41 AM
1163 Views
Re: It may sound silly, but did you look at One Power values in the Wheel of Time CCG?
- 05/01/2010 07:33:21 AM
813 Views