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    Re: Still on LOP's
    From: Bill Murdoch
    Date: 2002 May 6, 16:56 EDT

    Bill Murdoch  wrote:

    > I am still having a hard time with the 25% of the time you are inside
    > the cocked hat rule.  It just does not 'feel right'.  I have played
    > around with the Excel spreadsheet map that I mentioned a week or so
    > ago, and I can not get the calculations to work like I think they
    > should.

    > We have been discussing LOPs in two-dimensional (surface) navigation.
    > I have what may be a simpler question.  What rule applies in
    > one-dimensional navigation?  Let's say you are a tightrope walker,
    > getting nervous, and want to know exactly where you are on the rope.
    > You whip out your sextant and with a little skill and calculation plot
    > two POPs (points of position).  The two POPs are not in the same spot
    > (naturally).  What is the chance that you are between the two POPs?
    > What is the chance that you are to one side of both?  What is the
    > chance that you are on the other side of both?

    Then Mike Wescott wrote:

    Answers: .5, .25, .25

    Usual assumptions apply: no "systemic errors", equally probable that error
    is + or -. If both are plus, they're both on one side of you. If both are -
    then they're both on the other side of you. If #1 is + and #2 is - then
    one is one each side. Likewise, if #1 is - and #2 is +. Four equiprobable
    possibilities and 2 of the four have you between the POPs: 50% and 1 in
    four (25%) for each of the other two possiblities.

    This is where I 'fell off the train'.  If we stand to the side and watch the tight rope walker, we see along the rope from left to right POP#1, tight rope walker, and POP#2.  It is just as likely that the tight rope walker is to the left or the right of POP#1, and it is also equally likely that he is to the left or the right of POP#2.  If he is to the left of both, he is to the left of POP#1.  If he is to the right of both, he is to the right of POP#2.  If he is to the right of POP#1 and to the left of POP#2, he is between the two POPs.  If he is to the left of POP#1 and to the right of POP#2, he is not on the rope.  I understand + +, - -, and + -.  I do not understand - +.  Or, am I missing much more?

    Bill Murdoch
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