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    Re: The Darn Old Cocked Hat - the sequel 1
    From: John Karl
    Date: 2013 Mar 13, 10:33 -0700

    My one more try:

    1. Hammo Ix’s calculation (http://fer3.com/arc/img/122753.celnav%20error%20part%201.pdf) makes no sense in terms of probability since the result has the dimensions of length, not a probability. If a quantity has the wrong dimensions, it’s not right. I don’t know, nor has anyone explained, what it does mean, if anything. So we can’t say his result and mine are opposite sides of the same coin, or correct results to different questions, when we don’t even know the significance of his result.

    2. As I’ve, and many others, have said before, this cocked hat question is indeed academic – for geeks interested in the subject. One result (assuming only previously determined normal distributions of measured altitudes) is that the MPP is always inside the hat at the symmedian point. Moreover, as I’ve shown from a variety of plots, reasonable points near the MPP inside the hat are just as good in practice – the more important result.

    3. And yes, accuracy is not a concern in the open ocean. But in intimidating waters, or making a landfall to a small low island, accuracy sure peaks our interest.

    4. Finally, I’m interested in this geeky subject because of the subtle concepts. It’s attractive like the barely perceivable smile of a beautifully mysterious woman. Compare the Goudsmit result of the true ship’s position being outside the hat 75% of the time, with the symmedian result. They are both correct results to two different questions (but only the last one is relevant for CN). It requires some intriguing thought to see why this is true.

    Happy Thoughts,

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