NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Still on LOP's
From: Rodney Myrvaagnes
Date: 2002 May 7, 23:12 -0500
From: Rodney Myrvaagnes
Date: 2002 May 7, 23:12 -0500
Maybe Michael will be kind enough to tell me where this goes astray: OI am going back to the triangle, since it seems to me the tight rope is equivalent to zeroing out the error in one of the LOPs. Assume that three LOPs are measured with symmetrical error distribution about the platonic lines that would intersect at the true position. Each LOP can be either side of the true position with equal probability. A navigator who has measured three LOPs has no way of knowing which side each line is on. Thus we consider 6 LOPs, with each pair straddling the true position. If we choose a cocked hat that includes the true position, then switching any of the LOPs for its mirror will produce a cocked hat that does not include the true position. If we take the mirror of all three however, we get another cocked hat that includes the true center. If I draw this out I get two triangles that include the true position, and six that do not. This would appear to get 1/3 inside, rather than the 1/4 everyone else gets. If I collapse one pair of LOPs to its center, I get two pairs that surround the center, and two that do not, for a 1/2 chance. On Tue, 7 May 2002 11:48:29 -0400, Michael Wescott wrote: > >Why in that order? > >You've just placed POP#1 and POP#2 in relation to each other, not to >mention the tight rope walker. And our tight rope walker's postion >with respect to POP#2 is no longer independent of his relationship to >POP#1. > >> It is just as likely that the tight rope walker is to the left or Rodney Myrvaagnes J36 Gjo/a "Anything really worth doing is worth doing badly." (I know who said it, but he can't defend himself now.)