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    Re: That darned old cocked hat
    From: George Huxtable
    Date: 2010 Dec 13, 14:41 -0000

    May I be forgiven for enjoying a chuckle or two about the current
    cocked-hat controversy, and whether the probability of being outside the
    cocked-hat is either 75%, according to simple logic, or 86%, according to
    John Karl's integration.
    Numerical simulations, by two Navlist members, backing my earlier Monte
    Carlo prediction (done for the analogous case of three landmark bearings)
    of 75%, seems to be drawing Karl into an increasingly desperate search for
    some mud to throw at the logical argument.
    But my chuckles are at the memory of the ructions that arose on-list, years
    and years ago, when I first introduced the argument that three-quarters of
    all observations would lie outside the cocked-hat. List reactions were
    split between those who were certain that every observation must lie within
    the cocked-hat, because that's what they had been taught, and those who
    were prepared to concede that a few observations might conceivably lie
    outside it, but regarded a figure of 75% as quite ridiculously high
    We've come a long way, since those days. This time round, no such arguments
    have been offered; not against the 75% figure that I have presented once
    again, and rather to my surprise, not even against the even-higher 86% that
    John has argued for. That must be some sort of progress, anyway.
    I hope we can discover, in the end, why these predictions disagree.
    Presumably, John and I are calculating subtly different quantities, and it
    will call for careful definition to decide what's what.
    contact George Huxtable, at  george@hux.me.uk
    or at +44 1865 820222 (from UK, 01865 820222)
    or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.

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