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Re: Math gurus...Is it possible to find the missing variable... Tor Send a noteboard - 23/11/2012 02:59:12 PM
Assumption: Morgase is the weakest channeler possible. Since she is 1 out of 105 million that makes her 5.730 729 SD below the mean. See the standard deviation chart on wikipedia that I linked to in the original post.

Assumption: The bell curve is symmetrical and not skewed in one direction or the other. I know some of you disagree (but please humor me for a minute).

Since I don't like strengths less than 0 what I want to do is assign Morgase a strength equal to 1 unit of power. If I assign Morgase 1 unit of power do I have enough information to figure out the mean? In other words if 1 unit of power is equivalent to 5.730 729 SD below the mean can't I figure out the mean? If so, what is the mean?

If it is impossible to figure out the mean using Morgase equal to 1 unit of power and Morgase equal to 5.730 729 SD below the mean, then what other variables need to be known in the math equation


There are two parameters that make up a normal distribution, the mean and the standard deviation. If you assume that Morgase is strength 1, and that she is 5.7 standard deviations below the mean, then you could calculate the mean if you knew the standard deviation, or you could calculate the standard deviation if you knew the mean. If you know neither, then you're out of luck.

Technically, knowing Morgase's power and deviation from the mean gives you one equation with two unknowns, which you can't solve.

However, if you have two persons for whom you know the power, and where they fall in the distribution, then that would give you two equations with two unknowns, and you could solve to find both the standard deviation and the mean.

So, if you for example decided that Lanfear is at power 100, and 5.7 standard deviations above the mean, then the mean is 50.5 and the standard deviation 8.7.

However, there are some problems with this approach, as I see it. Firstly, I don't think we have enough information to say that Morgase is unique in her weakness. Secondly, I don't think there is any reason to assume that the distribution has symmetric endpoints. Rather, I think the case can be made for the opposite. If Lanfear is the top, and the bottom is essentially zero, then the mean would be at half the strength of Lanfear. I don't think that agrees with what we see in the books, which must be the ultimate test.

Finally, I don't actually see why knowing the mean and the standard distribution is really that interesting. Placing any given character on the scale is still going to be a matter of comparing quotes and building a hierarchy of people with known strengths, and it seems to be impossible to reach a consensus on even the most frequently described characters.

In my opinion, discussing the normal distribution isn't really helping, in particular since it seems to me that the distribution is mostly being used as a tool to sound scientific, with complete disregard for what the actual data, i.e., the descriptions of character's strength in the books, says.

For example, it has been suggested that if the mean is 50, and the standard deviation is 83, then every character will fall within one standard deviation from the mean. And while this is true, the consequence of this is that channelers of Lanfear's strength should be almost as common as channelers of average strength.

Personally, I think it would be interesting in itself to know the mean and the standard deviation, but I also think that the 20% of the 1000 novices clearly demonstrate that Jordan wasn't sufficiently consistent in the design of his world for it to be meaningful to discuss these things.

If I had the time and the inclination to work out the statistics, I would decide on some arbitrary scale for strength, like 0 to 100, then try to put a number to as many people as possible by a hierarchy of well documented comparisons, so other people could see what I had done and check my assumptions, and then I would draw the curve from those data and extract the mean and the standard deviation from that.
Fram kamerater!
This message last edited by Tor on 23/11/2012 at 03:04:07 PM
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How many standard deviations is Lanfear - 15/11/2012 06:04:39 PM 2071 Views
Well... - 15/11/2012 07:02:45 PM 1109 Views
Hmm... - 15/11/2012 07:25:34 PM 1206 Views
see we CAN agree on stuff - 15/11/2012 07:56:12 PM 1062 Views
- 18/11/2012 08:37:22 PM 957 Views
We've always been close with everything except the scale - 18/11/2012 10:29:07 PM 993 Views
Re: - 18/11/2012 11:07:17 PM 1163 Views
Re: - 19/11/2012 05:16:00 AM 989 Views
Re: - 19/11/2012 03:13:01 PM 994 Views
They only reject 37.5%, not 62.5% - 19/11/2012 03:19:19 PM 997 Views
Re: They only reject 37.5%, not 62.5% - 19/11/2012 04:01:43 PM 1203 Views
Re: They only reject 37.5%, not 62.5% - 19/11/2012 09:04:04 PM 950 Views
Hmmm... - 20/11/2012 02:08:40 AM 1016 Views
Perhaps, but Egwene is also being a bit dramatic in the scene as she managed - 20/11/2012 04:28:57 AM 974 Views
Nope... - 20/11/2012 03:13:13 PM 1025 Views
I believe she is being over dramatic - 20/11/2012 03:26:24 PM 922 Views
Keep believing that... - 20/11/2012 03:30:14 PM 1051 Views
*shrugs* - 20/11/2012 03:49:10 PM 1001 Views
Tired and forkroot are the same now? - 20/11/2012 03:55:22 PM 908 Views
No it's the literary device - 20/11/2012 04:04:28 PM 1029 Views
This is getting ridiculous... - 20/11/2012 04:43:13 PM 907 Views
You are missing my point completely - 20/11/2012 04:50:46 PM 870 Views
Impossible. Daigian is exactly 0.32SD below the mean - 19/11/2012 11:06:04 AM 973 Views
You keep saying that, but it is either a linear or a non-linear distribution - 19/11/2012 09:09:32 PM 1029 Views
That's the whole point. Thanks for finally seeing it. - 19/11/2012 09:43:27 PM 991 Views
keep believing that ... but you making up numbers isn't really relevant *NM* - 20/11/2012 04:29:44 AM 653 Views
Please show me a number that is made up. The 0.32SD for Daigian is a rule of statistics. - 20/11/2012 07:15:48 AM 954 Views
Go read Fionwe's post about it *NM* - 20/11/2012 02:33:19 PM 668 Views
Is that before or after she started juicing? - 15/11/2012 11:04:14 PM 967 Views
Wouldn't it be 1 in 105 million? - 21/11/2012 04:56:19 PM 819 Views
Are you sure that it is a normal distribution? - 16/11/2012 04:21:02 PM 1043 Views
Ugh. I hate power level discussions. For real world applications, it should be kind of meaningless - 16/11/2012 10:28:49 PM 943 Views
I don't really agree - 18/11/2012 08:40:53 PM 885 Views
Perhaps, but we've seen that a MUCH weaker Channeler can win in a duel - 19/11/2012 09:13:48 PM 959 Views
Re: Perhaps, but we've seen that a MUCH weaker Channeler can win in a duel - 20/11/2012 08:10:01 AM 930 Views
probably ... Lanfear/Cyndane is clearly remarkably skilled - 20/11/2012 02:35:09 PM 970 Views
Since I've proven that it's not a normal distribution in units of absolute strength, SDs don't apply - 17/11/2012 07:48:21 PM 989 Views
You have proven nothing, except that you have an opinion *NM* - 18/11/2012 02:21:35 AM 636 Views
You simply don't get it. It is mathematically a fact. There is no opinion involved. - 18/11/2012 02:19:40 PM 833 Views
Only because you've assigned numeric values. That you created. - 18/11/2012 02:40:51 PM 957 Views
It doesn't matter what figure you use... - 18/11/2012 03:01:56 PM 835 Views
What if Daigian is one third Lanfear's strength? - 18/11/2012 04:37:58 PM 978 Views
We have a limit for Daigian's strength, as you well know. - 18/11/2012 05:41:49 PM 931 Views
Are you kidding me? - 18/11/2012 09:07:38 PM 1090 Views
Sure you can - 18/11/2012 10:09:31 PM 990 Views
Re: Sure you can - 18/11/2012 10:54:50 PM 940 Views
You're right, though its 37.5% - 19/11/2012 12:21:29 AM 905 Views
Oops, typo! - 19/11/2012 02:54:25 AM 975 Views
Again, not possible, due to Daigian being just 0.3SD below the Mean - 19/11/2012 08:37:01 AM 926 Views
Egwene is definitely not 2x Amys... - 19/11/2012 04:05:12 PM 869 Views
Re: Egwene is definitely not 2x Amys... - 19/11/2012 05:55:02 PM 798 Views
Egwene is about as strong as Melaine and Amys combined - 19/11/2012 09:19:50 PM 915 Views
Re: Egwene is about as strong as Melaine and Amys combined - 20/11/2012 02:11:26 AM 942 Views
Forkroot in every case - 20/11/2012 04:32:26 AM 924 Views
No! - 20/11/2012 03:15:16 PM 907 Views
I'm not going to go re-read the books to you on this - 20/11/2012 03:39:46 PM 923 Views
You need to read it for yourself, since you're completely confused. - 20/11/2012 03:54:26 PM 886 Views
Not going to argue this with you. - 20/11/2012 04:09:44 PM 861 Views
Your own example disproved your point... - 20/11/2012 04:39:25 PM 951 Views
let's see, she's both asleep and would need hours to regain her strength - 20/11/2012 04:43:17 PM 848 Views
Enough! - 20/11/2012 05:04:06 PM 936 Views
LOL ... whatever. You go on believing that ... no one else sees it this way. *NM* - 20/11/2012 05:20:52 PM 623 Views
What a brilliant argument! - 20/11/2012 05:25:18 PM 969 Views
this is why I refuse to continue this debate - 20/11/2012 05:31:11 PM 886 Views
Re: Your own example disproved your point... - 20/11/2012 05:10:15 PM 981 Views
Barasine + Katerine isn't that much less than - 20/11/2012 05:26:31 PM 982 Views
Re: Barasine + Katerine isn't that much less than - 20/11/2012 05:31:50 PM 923 Views
Re: Barasine + Katerine isn't that much less than - 20/11/2012 05:42:53 PM 918 Views
Excuse me? - 20/11/2012 05:28:48 PM 974 Views
see we can agree on the relative strength of Egwene v. Forsaken - 20/11/2012 05:35:07 PM 922 Views
??? - 20/11/2012 05:37:01 PM 1001 Views
2 middling sisters - 20/11/2012 05:45:27 PM 943 Views
Re: Egwene is definitely not 2x Amys... - 20/11/2012 02:26:47 AM 856 Views
Re: Egwene is definitely not 2x Amys... - 20/11/2012 09:03:40 AM 904 Views
Re: Egwene is definitely not 2x Amys... - 20/11/2012 02:59:08 PM 939 Views
None of this is backed by any evidence... - 20/11/2012 03:24:12 PM 858 Views
who said Cadsuane was 1.5x Moiraine or more? - 20/11/2012 04:03:13 PM 859 Views
Nope... - 20/11/2012 04:41:35 PM 901 Views
wrong - 20/11/2012 04:48:50 PM 834 Views
My bad. Mized up 1/3 and 2/3. - 20/11/2012 05:05:05 PM 926 Views
gotcha *NM* - 20/11/2012 05:46:21 PM 583 Views
Better evidence? LOL! - 20/11/2012 03:18:55 PM 907 Views
Huh? How did you come to that conclusion? - 20/11/2012 04:40:56 PM 897 Views
Exactly *NM* - 20/11/2012 04:55:28 PM 869 Views
BEcause Cadsuane is close on the heels of Egwene? - 20/11/2012 05:10:50 PM 816 Views
I'm not arguing that. I agree that Cadsuane is pretty close to Egwene - 20/11/2012 05:50:34 PM 920 Views
Re: Better evidence? LOL! - 20/11/2012 05:00:47 PM 828 Views
Interesting, but let's go with your figures... - 19/11/2012 06:54:54 AM 971 Views
Indeed - 19/11/2012 08:16:44 AM 1010 Views
Rand is sort of a special case - 20/11/2012 04:25:02 AM 835 Views
Regarding Mesaana... - 20/11/2012 08:42:56 AM 908 Views
You continue to mix two things - 20/11/2012 03:24:44 PM 835 Views
No - 20/11/2012 04:54:19 PM 1058 Views
You are mistaken - 20/11/2012 05:04:40 PM 918 Views
Yes she did Darius! - 20/11/2012 05:27:36 PM 854 Views
Yet there is no duel - 20/11/2012 06:01:17 PM 837 Views
Explain the .3xSD thing to me... - 19/11/2012 04:58:57 PM 1077 Views
Probably, but the AS have no idea what 37.5% means - 19/11/2012 02:59:26 AM 862 Views
It's irrelevant - 19/11/2012 03:46:42 AM 930 Views
Agreed. Daigian is the marker of the absolute bottom of Aes Sedai strength. - 19/11/2012 06:55:41 AM 896 Views
Daigian - 19/11/2012 08:12:19 AM 917 Views
It is a direct marker due to RJ's quote - 19/11/2012 08:50:26 AM 943 Views
You missed my point - 19/11/2012 09:08:42 AM 878 Views
Re: You missed my point - 19/11/2012 02:18:33 PM 947 Views
Asmodean would never have made the comment about 13 weakest AS - 20/11/2012 04:41:11 AM 886 Views
Re: Asmodean would never have made the comment about 13 weakest AS - 20/11/2012 09:07:49 AM 862 Views
Which would make an average AS around a 30 - 20/11/2012 04:58:56 PM 732 Views
Re: Sure you can - 19/11/2012 09:22:09 AM 1006 Views
Care to explain this... - 19/11/2012 05:06:28 PM 848 Views
Indeed - 20/11/2012 07:16:37 AM 1069 Views
Explained far better than I ever could. Bravo. - 20/11/2012 07:30:29 AM 884 Views
Well duh. - 20/11/2012 02:57:24 PM 992 Views
Incorrect. - 20/11/2012 04:28:07 PM 978 Views
No - 20/11/2012 04:44:16 PM 954 Views
Re: No - 20/11/2012 04:48:36 PM 946 Views
That depends... - 20/11/2012 05:18:46 PM 817 Views
Re: That depends... - 20/11/2012 05:31:03 PM 1243 Views
You're integrating without lower limits... - 20/11/2012 02:55:06 PM 928 Views
Re: You're integrating without lower limits... - 20/11/2012 04:37:57 PM 958 Views
It matters. - 20/11/2012 05:22:40 PM 924 Views
We are not talking about a normal distribution in any case - 20/11/2012 04:44:24 AM 771 Views
Re: We are not talking about a normal distribution in any case - 20/11/2012 07:02:47 AM 959 Views
You must tell me of this special math... - 20/11/2012 03:10:09 PM 858 Views
Re: You must tell me of this special math... - 20/11/2012 04:29:40 PM 894 Views
Morghase is a placeholder... - 20/11/2012 04:45:42 PM 962 Views
Re: Morghase is a placeholder... - 20/11/2012 04:49:54 PM 1148 Views
Why? - 20/11/2012 05:23:29 PM 941 Views
Re: Why? - 20/11/2012 05:36:45 PM 1114 Views
Well... - 18/11/2012 08:43:59 PM 994 Views
Re: Well... - 19/11/2012 03:40:44 PM 975 Views
Wow. - 19/11/2012 03:53:47 PM 1017 Views
Re: Wow. - 19/11/2012 04:26:09 PM 1028 Views
Some points - 19/11/2012 06:03:00 PM 1030 Views
Well then you're both wrong I'm afraid - 19/11/2012 06:09:36 PM 869 Views
Re: Well then you're both wrong I'm afraid - 19/11/2012 07:42:58 PM 771 Views
this is why I think all of the Forsaken are very close in Power - 20/11/2012 04:51:20 AM 964 Views
Agreed - 20/11/2012 08:13:37 AM 994 Views
probably - 20/11/2012 06:18:45 PM 877 Views
Re: this is why I think all of the Forsaken are very close in Power - 20/11/2012 02:45:18 PM 906 Views
I think RJ went out of his way to keep strength a bit of a mystery - 20/11/2012 08:42:44 PM 913 Views
Indeed... - 21/11/2012 05:44:18 PM 886 Views
I agree - 22/11/2012 01:43:02 AM 1136 Views
Math gurus...Is it possible to find the missing variable... - 21/11/2012 05:12:24 PM 914 Views
the problem is that the Mean is not going to tell us much really - 22/11/2012 02:55:03 AM 979 Views
Re: the problem is that the Mean is not going to tell us much really - 22/11/2012 03:15:33 AM 1267 Views
I do not think you can calculate the Mean without knowing the Units of Power - 22/11/2012 03:53:59 AM 1069 Views
Re: Math gurus...Is it possible to find the missing variable... - 23/11/2012 02:59:12 PM 1197 Views
Disregard this post *NM* - 23/11/2012 03:02:24 PM 838 Views

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