Wheel of Time Messageboard: You don't understand your own model... by Shannow

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You don't understand your own model... Shannow Send a noteboard - 18/12/2009 11:38:05 PM

One: Why would the Tower restrict themselves to the middle? They won't stop anyone who is too strong from joining them. But they do stop people who are too weak from joining them. 37.5% of all channelers, in fact.

They don't stop stronger women. Stronger women are obviously rarer, and as we know, just one woman of Cadsuane's strength has come in the last six hundred years.

The truth is that Sharina isn't representative of the majority of channelers who are never found. For every one Sharina that is found, there are hundreds of Kin or other women who could learn, who are WEAKER than the average Aes Sedai. There are only 6 women stronger than Nynaeve, but there are thousands of female channelers. So people of that level are simply very rare, and VERY far above the average woman in strength.

Of course Sharina isn't representative of the majority of channelers out there! What is it in my model that makes you think any such thing?
A representative of the channeler out there is probably one of the older Novices who will definitely be Aes Sedai, but who isn't strong enough to make the Aes Sedai jump through hoops whooping in joy.

There is no sensible reason why the White Tower would restrict stronger channelers from joining them. The reason that Cadsuane is the strongest modern channeler, is because a woman of her strength is exceedingly rare. Not because the Tower are deliberately excluding stronger channelers. But they are deliberately excluding weaker channelers.

Who said it was deliberate? I said that it just so happens that the Tower has rarely seen someone stronger than Moiraine in the past thousand years. Doesn't mean women stronger than Moiraine are common. To the contrary, they keep getting rarer the farther up you move away from her.

I challenge you to provide a mechanism by which stronger channelers are excluded from the Tower.

The mechanism of plot convenience?

No, logic says someone like Cadsuane is far above average strength.

And that is exactly what I'm saying with my model too. If you put Cadsuane at strength 65, she is a pretty rare person. While the calculation is too difficult for me to carry out quickly, given the large number of channelers we're talking about (say 20,000 women distributed over a bell curve), I'd say that the difference in strength between Daigian and a woman of strength 50 would have to be less than one standard deviation to allow for 37.5% of women to be below her.
I'd argue that Caduane would lie in a similar position above 50, making her rare indeed. As rare as Daigian, in fact, who is uniquely weak in the weighted subset of the Tower, and still pretty rare in all the channeling population. Women like Morghase or Lanfear are further than even two standard deviations from the mean. 99% of the population falls withing 2 standard deviations, and Lanfear, Morghase, and some of the stronger Forsaken represent that last one percent, that vanishingly rare species of a very strong or very weak channeler.

Two:

Even if, as you suggest, Moiraine is close to average strength, that means that Moiraine is above 50 in strength. And since we know that Egwene is stronger than Moiraine and Melaine combined, that means Egwene must be at 100 strength or more.

Where do we know this from? For god's sake, Silviana, a woman weaker than Moiraine, can shield Egwene alone.
In battle, Egwene may well be able to tackle both Moiraine and Melaine. But they should be able to shield her easily.

That means Egwene is stronger than the strongest woman, Lanfear, who is at 100. How do you explain that in your quirky model?

I don't see why Egwene has to be stronger than Lanfear, sorry.

I agree that Dagian is less than one standard deviation from the mean. If she was one standard deviation below the mean, only 16% of women would be weaker than her. Since 37.5% are weaker than her, we know she is much closer to the average woman than one standard deviation. In fact, only 12.5% of women fall between her and the average woman. That means the average woman is not far above Dagian in strength.

But here's where you don't seem to grasp the implications of your own model. Let me put it to you simply.

1. The strongest possible woman can only be twice as strong as the average woman (who sits on 50 strength).

2. Aviendha provides a direct quote stating that Egwene can overpower Amys and Melaine combined. Amys is equal to Moiraine in strength, and Melaine is equal to a very strong Aes Sedai.

That means that BOTH of them would fall above the average strength woman, hence BOTH of them would be more than 50 strength.

So for Egwene to be stronger than both of them combined, she would have to exceed 100 in strength.

This is impossible, since in your model, Lanfear sits on 100, and everyone else has to be lower than that.

Do you understand now?

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The One Power Bell Curve: Proof that it is not centered on 50% of the strongest channeler's strength Shannow - 18/12/2009 08:37:55 AM 1328 Views

I always thought the curve was one sided Asha'man Warder - 18/12/2009 01:17:32 PM 734 Views

The Curve only refers to the channeling population, not to non-channelers. Shannow - 18/12/2009 01:56:25 PM 747 Views

I would say that your sample is flawed. RugbyPlayingAshaman - 18/12/2009 05:02:02 PM 816 Views

well said *NM* darius_sedai - 18/12/2009 05:12:40 PM 382 Views

It doesn't matter... Shannow - 18/12/2009 10:02:38 PM 671 Views

But, it sort of does. RugbyPlayingAshaman - 18/12/2009 10:43:08 PM 724 Views

So you're saying that no modern Aes Sedai are even of average strength? Shannow - 18/12/2009 10:51:01 PM 797 Views

Are you sure it's the same bell curve from the AoL? BlackAdder - 18/12/2009 11:11:19 PM 764 Views

The Tower is restricted to the middle... fionwe1987 - 18/12/2009 05:35:03 PM 889 Views

Two things... Shannow - 18/12/2009 09:28:25 PM 731 Views

The culling theory... Phelix - 18/12/2009 09:36:34 PM 662 Views

The culling theory applies to the ENTIRE population, not just Aes Sedai... Shannow - 18/12/2009 09:42:31 PM 790 Views

Yes, but Aes Sedai take it to a new level... Phelix - 18/12/2009 09:48:59 PM 852 Views

Re: Yes, but Aes Sedai take it to a new level... Shadowkiller - 18/12/2009 10:06:15 PM 653 Views

Several more things... fionwe1987 - 18/12/2009 11:26:19 PM 826 Views

You don't understand your own model... Shannow - 18/12/2009 11:38:05 PM 840 Views

So RJ was wrong about Bell Curve distribution? darius_sedai - 19/12/2009 06:03:24 PM 745 Views

Re: So RJ was wrong about Bell Curve distribution? Sidious - 19/12/2009 06:10:52 PM 701 Views

Its simple really... fionwe1987 - 19/12/2009 06:15:23 PM 716 Views

So, Aviendha trumps RJ? A woman who, as late as tGS, doesn't know what she's doing with the OP? fionwe1987 - 19/12/2009 06:12:42 PM 723 Views

Age-Related Sample Bias Shadowkiller - 18/12/2009 06:41:03 PM 686 Views

I have no problem with that...but it implies that the average woman today isn't at 50% of Lanfear... Shannow - 18/12/2009 09:46:00 PM 814 Views

Partially agreed... Shadowkiller - 18/12/2009 10:13:46 PM 696 Views

Well, the Aes Sedai are the only group that we have detailed strength info about... Shannow - 18/12/2009 10:26:48 PM 797 Views

Sharina is AS ... she'd be dead in a few years if she hadn't gone to the Tower *NM* darius_sedai - 28/12/2009 01:08:20 AM 822 Views

A thought that occured to me, and I'd like your opinion... Phelix - 18/12/2009 07:38:29 PM 686 Views

Well Sharina isn't a sparker and she's the strongest AS darius_sedai - 18/12/2009 07:57:17 PM 694 Views

Yes... Phelix - 18/12/2009 08:01:57 PM 778 Views

Is it just my bad memory or is one of the wondergirls not a sparker? Gher - 18/12/2009 10:12:59 PM 677 Views

I think it's just a bad memory... Phelix - 18/12/2009 10:19:25 PM 671 Views

Easier sulution, and real example. amirebram - 18/12/2009 10:03:20 PM 728 Views

And that is indeed the solution I feel most comfortable with... Shannow - 18/12/2009 10:08:40 PM 698 Views

Re: And that is indeed the solution I feel most comfortable with... Sidious - 19/12/2009 11:39:31 AM 939 Views

Agree, but a little more curvy is better

amirebram - 19/12/2009 11:17:16 PM 628 Views

*facepalm* BlackAdder - 18/12/2009 10:13:16 PM 721 Views

That's just the normalized value graphed on a log scale. amirebram - 19/12/2009 11:20:41 PM 686 Views

Dude, Seriously? Shadowkiller - 18/12/2009 10:19:25 PM 720 Views

Indeed, and that's why I propose that... Shannow - 18/12/2009 10:31:23 PM 702 Views

So RJ used two separate scales, one actual one relative, to explain the same thing?

fionwe1987 - 18/12/2009 11:33:20 PM 638 Views

Yes, "Bell Curve" does not mean Gausian. Or normal distribution. amirebram - 19/12/2009 11:24:10 PM 684 Views

I'm sorry, but I've never heard of a non-Gaussian bell curve. Can you prove its existence? *NM* fionwe1987 - 20/12/2009 03:24:22 AM 403 Views

Maybe people in my field just use the term in a non-technical way. We do things with ... amirebram - 21/12/2009 07:24:43 PM 645 Views

It does to RJ Shadowkiller - 20/12/2009 03:12:30 PM 766 Views

Yes, "Bell Curve" does not mean Gausian. Or normal distribution. amirebram - 19/12/2009 11:24:11 PM 659 Views

That's because outliers in IQ tests are excluded form the curve. *NM* fionwe1987 - 18/12/2009 11:31:23 PM 405 Views

Really?!?! then what is the definition of a IQ of 200? amirebram - 19/12/2009 11:28:18 PM 998 Views

You can have IQ's above that... fionwe1987 - 20/12/2009 05:09:44 AM 710 Views

I said that in the other post and was half torn to pieces *NM* Sidious - 19/12/2009 11:38:25 AM 351 Views

Eh. Ignore the IQ value and draw it on a linear weight scale amirebram - 19/12/2009 11:26:23 PM 677 Views

Re: The One Power Bell Curve: Proof that it is not centered on 50% of the strongest channeler's stre Kieran - 19/12/2009 06:02:34 PM 641 Views

I like this idea Shadowkiller - 20/12/2009 04:01:28 PM 846 Views

Accidental Post *NM* Shadowkiller - 20/12/2009 07:11:09 PM 401 Views

Mathmatically this is very close to the system I proposed in another thread darius_sedai - 27/12/2009 01:23:51 AM 649 Views

Re: The One Power Bell Curve: taura-tierno - 27/12/2009 10:05:33 PM 791 Views

What makes you think Alviarin is "middling"? darius_sedai - 27/12/2009 10:28:13 PM 992 Views

Re: What makes you think Alviarin is "middling"? taura-tierno - 28/12/2009 03:19:14 PM 688 Views

Re: What makes you think Alviarin is "middling"? darius_sedai - 28/12/2009 03:30:44 PM 890 Views

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<quote id="62873">
<quote id="62869"><quote id="62808">
One: Why would the Tower restrict themselves to the middle? They won't stop anyone who is too strong from joining them. But they do stop people who are too weak from joining them. 37.5% of all channelers, in fact.</quote>
They don't stop stronger women. Stronger women are obviously rarer, and as we know, just one woman of Cadsuane's strength has come in the last six hundred years.
<quote>The truth is that Sharina isn't representative of the majority of channelers who are never found. For every one Sharina that is found, there are hundreds of Kin or other women who could learn, who are WEAKER than the average Aes Sedai. There are only 6 women stronger than Nynaeve, but there are thousands of female channelers. So people of that level are simply very rare, and VERY far above the average woman in strength.</quote>
<i>Of course</i> Sharina isn't representative of the majority of channelers out there! What is it in my model that makes you think any such thing?
A representative of the channeler out there is probably one of the older Novices who will definitely be Aes Sedai, but who isn't strong enough to make the Aes Sedai jump through hoops whooping in joy.
<quote>There is no sensible reason why the White Tower would restrict stronger channelers from joining them. The reason that Cadsuane is the strongest modern channeler, is because a woman of her strength is exceedingly rare. Not because the Tower are deliberately excluding stronger channelers. But they are deliberately excluding weaker channelers.</quote>
Who said it was deliberate? I said that it just so happens that the Tower has rarely seen someone stronger than Moiraine in the past thousand years. Doesn't mean women stronger than Moiraine are common. To the contrary, they keep getting rarer the farther up you move away from her.
<quote>I challenge you to provide a mechanism by which stronger channelers are excluded from the Tower.</quote>
The mechanism of plot convenience? :P
<quote>No, logic says someone like Cadsuane is far above average strength.</quote>
And that is exactly what I'm saying with my model too. If you put Cadsuane at strength 65, she is a pretty rare person. While the calculation is too difficult for me to carry out quickly, given the large number of channelers we're talking about (say 20,000 women distributed over a bell curve), I'd say that the difference in strength between Daigian and a woman of strength 50 would <i>have</i> to be less than one standard deviation to allow for 37.5% of women to be below her. 
I'd argue that Caduane would lie in a similar position above 50, making her rare indeed. As rare as Daigian, in fact, who is uniquely weak in the weighted subset of the Tower, and still pretty rare in all the channeling population. Women like Morghase or Lanfear are further than even two standard deviations from the mean. 99% of the population falls withing 2 standard deviations, and Lanfear, Morghase, and some of the stronger Forsaken represent that last one percent, that vanishingly rare species of a very strong or very weak channeler.
<quote>Two:

Even if, as you suggest, Moiraine is close to average strength, that means that Moiraine is above 50 in strength. And since we know that Egwene is stronger than Moiraine and Melaine combined, that means Egwene must be at 100 strength or more.</quote>
Where do we know this from? For god's sake, Silviana, a woman weaker than Moiraine, can shield Egwene alone. 
In battle, Egwene may well be able to tackle both Moiraine and Melaine. But they should be able to shield her easily. 
<quote>That means Egwene is stronger than the strongest woman, Lanfear, who is at 100. How do you explain that in your quirky model?</quote>
I don't see why Egwene has to be stronger than Lanfear, sorry.</quote>

But here's where you don't seem to grasp the implications of your own model. Let me put it to you simply.

1. The strongest possible woman can only be twice as strong as the average woman (who sits on 50 strength).

2. Aviendha provides a direct quote stating that Egwene can overpower Amys and Melaine combined. Amys is equal to Moiraine in strength, and Melaine is equal to a very strong Aes Sedai.

That means that BOTH of them would fall above the average strength woman, hence BOTH of them would be more than 50 strength.

So for Egwene to be stronger than both of them combined, she would have to exceed 100 in strength.

This is impossible, since in your model, Lanfear sits on 100, and everyone else has to be lower than that.

Do you understand now?
</quote>

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