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    Re: Position lines, crossing.
    From: Peter Fogg
    Date: 2006 Dec 11, 08:48 +1100
    George writes:

    List members will appreciate the difficulties we are faced with in
    trying to convince others about the realities of a cocked hat.
    Already, three have put their heads up in defence of their cherished
    illusions; Peter Fogg, Bill, and Robert Eno. No doubt, others will
    join them. We've seen it before.
     
    Indeed we have. George is well and truly launched on one of his favourite hobby-horses. One that seems to me to be very much a case of creating an unnecessary mountain out of a mole-hill.
     
    Let's say that our conscientious navigator, alarmed by this talk of "dangerous illusion" (that the position lies at the centre of the triangle) decides to systematically enlarge the triangle (or other shape) formed by enclosing LOPs. To be on the safe side each position line is moved away from the original by 100 miles. Now the chances of the actual position not being bounded by the enclosing LOPs is negligible. Phew. That's a relief.
     
    What else has changed? Nothing. The only position that can be calculated from this shape, or the original, is exactly the same, and lies at the centre (least squares) of either the small or the large shape. One is virtually certain to contain the actual position, the other less so, but nothing else has changed or can be changed without additional data.
     
    Is this a "cherished illusion"? I don't think so. George, if you can show us how a more accurate position can be derived from the same data then that would be useful. On the other hand, if you are just saying that the calculated position is not necessarily the same as the actual position, then that seems pretty futile.

     

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