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    Re: That darned old cocked hat
    From: John Karl
    Date: 2010 Dec 13, 10:02 -0800

    Gary & George,

    Like one of you has said, this is subtle stuff – perhaps too subtle to get straight with the communication limitation of blogging (this is blogging, isn’t it?). I find it difficult to carry on without simply repeating myself, but:

    George and I are discussing VERY DIFFERENT topics. His “experiment” is compiling statistics of the frequency of occurrence of an simple definitive event – he’s simple COUNTING between two possible outcomes (in vs. out).

    My single 3-body fix compiles no statistics, does employ known prior knowledge of the LOP’s normal probability distributions, and then embarks on computing the probability distribution (probability/area) of the possible fix locations. This is INFERRING A PROBABILITY DISTRIBUTION given the individual LOP distributions (these two distributions are very different things). The inferred result depends both on the a priori LOP distributions and on the LOP positions. It’s also trivial to see that the location of the MPP is at the symmedian point of the hat. This symmedian is always on the inside of the hat, and is easy to plot, or to eyeball. This only determines the MPP, the true fix could be anywhere in the world since it’s probability distribution is non-zero everywhere.

    Since the above two topics are so different, I don’t know if George’s in/out 25%/75% is correct or not. I can say that I’ve not seen a convincing proof of it.

    Gary, your discussion at http://www.fer3.com/arc/m2.aspx?i=102348&y=200703 makes sense relative to my topic above, but it is employing a uniform distribution (not normal) when you say “..this is the only point on the planet the observer can be.” As I pointed out above, there is a finite probability everywhere if the individual LOPs are distributed normally. And since you’re discussing my topic above, not George’s, yours does not disprove George.

    Are we having fun yet?

    P.S. You might what to check out my post at http://fer3.com/arc/m2.aspx?i=114828
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