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Subject: Re: Still on LOP's
WSMurdoch@XXX.XXX
Date: Mon May 06 2002 - 16:56:05 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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