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    Re: Cocked hats, again.
    From: Peter Fogg
    Date: 2007 Mar 17, 10:34 +1100

    Let's assume that the careful and conscientious navigator has done everything possible to eliminate both random and systematic error. This should result in two effects:

    1. A relatively small shape formed by enclosing LOPs (which could even be a triangle, somewhat belying the 'careful and conscientious' assumption, but never mind).

    2. A small standard deviation representing the small residual errors.

    This small shape has here been greatly enlarged for clarity. Our CC&W (careful, conscientious and worried) navigator is nevertheless concerned by the 25% / 75% argument and decides to enlarge the LOPs, each by one standard deviation.

    (Please excuse drafting irregularities)

    Our CC&WN is somewhat reassured by knowing that, on average, there is a 70% chance that this larger shape encloses the position.

    But being such a good worrier; decides to enlarge the shape by another standard deviation, leading to a better than 90% chance that, on average, this larger shape encloses the position.

    Well goodo. Now our CC&WN is reassured that this augmented, somewhat larger, though still relatively small – THANKS TO EARLIER WORK DONE TO ELIMINATE ERROR – shape is overwhelmingly likely to enclose the position.

    Great. But what has happened to the fix?

    Nothing. It is still exactly (drafting irregularities aside) where it always was. At the calculated centre of the shape. Enlarging the LOPs proportionally cannot change it. There is still no improved calculated fix.

    There is no greater, or lessor, chance of ending up on those rocks thanks to this exercise.

    It really is an exercise in futility. Somewhat similar to this argument.

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