Re: Math gurus...Is it possible to find the missing variable... - Edit 1
Before modification by Tor at 23/11/2012 03:04:07 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.