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
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
How many standard deviations is Lanfear
15/11/2012 06:04:39 PM
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Hmm...
15/11/2012 07:25:34 PM
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see we CAN agree on stuff
15/11/2012 07:56:12 PM
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18/11/2012 08:37:22 PM
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Re:
18/11/2012 11:07:17 PM
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Re:
19/11/2012 05:16:00 AM
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Re:
19/11/2012 03:13:01 PM
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They only reject 37.5%, not 62.5%
19/11/2012 03:19:19 PM
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Re: They only reject 37.5%, not 62.5%
19/11/2012 04:01:43 PM
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Re: They only reject 37.5%, not 62.5%
19/11/2012 09:04:04 PM
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Hmmm...
20/11/2012 02:08:40 AM
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Perhaps, but Egwene is also being a bit dramatic in the scene as she managed
20/11/2012 04:28:57 AM
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Nope...
20/11/2012 03:13:13 PM
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I believe she is being over dramatic
20/11/2012 03:26:24 PM
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Keep believing that...
20/11/2012 03:30:14 PM
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*shrugs*
20/11/2012 03:49:10 PM
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Tired and forkroot are the same now?
20/11/2012 03:55:22 PM
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No it's the literary device
20/11/2012 04:04:28 PM
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Impossible. Daigian is exactly 0.32SD below the mean
19/11/2012 11:06:04 AM
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You keep saying that, but it is either a linear or a non-linear distribution
19/11/2012 09:09:32 PM
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That's the whole point. Thanks for finally seeing it.
19/11/2012 09:43:27 PM
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keep believing that ... but you making up numbers isn't really relevant *NM*
20/11/2012 04:29:44 AM
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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
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Ugh. I hate power level discussions. For real world applications, it should be kind of meaningless
16/11/2012 10:28:49 PM
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I don't really agree
18/11/2012 08:40:53 PM
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Perhaps, but we've seen that a MUCH weaker Channeler can win in a duel
19/11/2012 09:13:48 PM
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Re: Perhaps, but we've seen that a MUCH weaker Channeler can win in a duel
20/11/2012 08:10:01 AM
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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
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You have proven nothing, except that you have an opinion *NM*
18/11/2012 02:21:35 AM
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You simply don't get it. It is mathematically a fact. There is no opinion involved.
18/11/2012 02:19:40 PM
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Only because you've assigned numeric values. That you created.
18/11/2012 02:40:51 PM
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It doesn't matter what figure you use...
18/11/2012 03:01:56 PM
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What if Daigian is one third Lanfear's strength?
18/11/2012 04:37:58 PM
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Sure you can
18/11/2012 10:09:31 PM
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Re: Sure you can
18/11/2012 10:54:50 PM
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You're right, though its 37.5%
19/11/2012 12:21:29 AM
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Oops, typo!
19/11/2012 02:54:25 AM
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Again, not possible, due to Daigian being just 0.3SD below the Mean
19/11/2012 08:37:01 AM
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Egwene is definitely not 2x Amys...
19/11/2012 04:05:12 PM
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Re: Egwene is definitely not 2x Amys...
19/11/2012 05:55:02 PM
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Egwene is about as strong as Melaine and Amys combined
19/11/2012 09:19:50 PM
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Re: Egwene is about as strong as Melaine and Amys combined
20/11/2012 02:11:26 AM
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Forkroot in every case
20/11/2012 04:32:26 AM
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No!
20/11/2012 03:15:16 PM
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I'm not going to go re-read the books to you on this
20/11/2012 03:39:46 PM
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You need to read it for yourself, since you're completely confused.
20/11/2012 03:54:26 PM
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Not going to argue this with you.
20/11/2012 04:09:44 PM
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Your own example disproved your point...
20/11/2012 04:39:25 PM
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let's see, she's both asleep and would need hours to regain her strength
20/11/2012 04:43:17 PM
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Enough!
20/11/2012 05:04:06 PM
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LOL ... whatever. You go on believing that ... no one else sees it this way. *NM*
20/11/2012 05:20:52 PM
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Re: Your own example disproved your point...
20/11/2012 05:10:15 PM
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Barasine + Katerine isn't that much less than
20/11/2012 05:26:31 PM
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Re: Egwene is definitely not 2x Amys...
20/11/2012 02:26:47 AM
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Re: Egwene is definitely not 2x Amys...
20/11/2012 09:03:40 AM
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Re: Egwene is definitely not 2x Amys...
20/11/2012 02:59:08 PM
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None of this is backed by any evidence...
20/11/2012 03:24:12 PM
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who said Cadsuane was 1.5x Moiraine or more?
20/11/2012 04:03:13 PM
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Nope...
20/11/2012 04:41:35 PM
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wrong
20/11/2012 04:48:50 PM
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Better evidence? LOL!
20/11/2012 03:18:55 PM
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Huh? How did you come to that conclusion?
20/11/2012 04:40:56 PM
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BEcause Cadsuane is close on the heels of Egwene?
20/11/2012 05:10:50 PM
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I'm not arguing that. I agree that Cadsuane is pretty close to Egwene
20/11/2012 05:50:34 PM
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Interesting, but let's go with your figures...
19/11/2012 06:54:54 AM
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Indeed
19/11/2012 08:16:44 AM
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Rand is sort of a special case
20/11/2012 04:25:02 AM
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Regarding Mesaana...
20/11/2012 08:42:56 AM
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You continue to mix two things
20/11/2012 03:24:44 PM
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No
20/11/2012 04:54:19 PM
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You are mistaken
20/11/2012 05:04:40 PM
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Probably, but the AS have no idea what 37.5% means
19/11/2012 02:59:26 AM
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It's irrelevant
19/11/2012 03:46:42 AM
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Agreed. Daigian is the marker of the absolute bottom of Aes Sedai strength.
19/11/2012 06:55:41 AM
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Daigian
19/11/2012 08:12:19 AM
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It is a direct marker due to RJ's quote
19/11/2012 08:50:26 AM
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You missed my point
19/11/2012 09:08:42 AM
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Asmodean would never have made the comment about 13 weakest AS
20/11/2012 04:41:11 AM
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Re: Asmodean would never have made the comment about 13 weakest AS
20/11/2012 09:07:49 AM
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Re: Sure you can
19/11/2012 09:22:09 AM
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Care to explain this...
19/11/2012 05:06:28 PM
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Indeed
20/11/2012 07:16:37 AM
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Explained far better than I ever could. Bravo.
20/11/2012 07:30:29 AM
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Well duh.
20/11/2012 02:57:24 PM
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Incorrect.
20/11/2012 04:28:07 PM
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No
20/11/2012 04:44:16 PM
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You're integrating without lower limits...
20/11/2012 02:55:06 PM
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We are not talking about a normal distribution in any case
20/11/2012 04:44:24 AM
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Re: We are not talking about a normal distribution in any case
20/11/2012 07:02:47 AM
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You must tell me of this special math...
20/11/2012 03:10:09 PM
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Re: You must tell me of this special math...
20/11/2012 04:29:40 PM
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Morghase is a placeholder...
20/11/2012 04:45:42 PM
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Well...
18/11/2012 08:43:59 PM
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Re: Well...
19/11/2012 03:40:44 PM
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Wow.
19/11/2012 03:53:47 PM
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Well then you're both wrong I'm afraid
19/11/2012 06:09:36 PM
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Re: Well then you're both wrong I'm afraid
19/11/2012 07:42:58 PM
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this is why I think all of the Forsaken are very close in Power
20/11/2012 04:51:20 AM
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Re: this is why I think all of the Forsaken are very close in Power
20/11/2012 02:45:18 PM
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I think RJ went out of his way to keep strength a bit of a mystery
20/11/2012 08:42:44 PM
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Math gurus...Is it possible to find the missing variable...
21/11/2012 05:12:24 PM
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the problem is that the Mean is not going to tell us much really
22/11/2012 02:55:03 AM
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Re: the problem is that the Mean is not going to tell us much really
22/11/2012 03:15:33 AM
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I do not think you can calculate the Mean without knowing the Units of Power
22/11/2012 03:53:59 AM
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Re: Math gurus...Is it possible to find the missing variable...
23/11/2012 02:59:12 PM
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