NavList:

   

Reply

George,

Your 25/75 probability is NOT an average over all possible cocked hats. 
It is true for each and every cocked hat. The shape of the hat does not 
enter into your prove.

Herbert Prinz


On 2010-12-13 16:20, George Huxtable wrote:
> In an attempt to understand better what John Karl has been telling us, I
> have just returned to his posting of 8th December, and to his linked file
> at-
>
> http://www.fer3.com/arc/imgx/Darned-Old-Cocked-Hat.pdf
>
> John shows us a cocked hat, without defining its angles, and claims that-
>
> "Second, the probability that the ship is outside the cocked hat is 84%".
>
> I had taken this to be a general statement about all cocked hats,
> independent of their geometry, in the same way that my figure of 75% was an
> average over all possible cocked hats around ab observer.
>
> But reading on, more carefully this time, I see that he then poses another
> example, when one of the interior angles exceeds 120 degrees. Again, John
> doesn't tell us about the actual geometry, but now states- "(But still the
> probability that the ship is outside the hat is 94% in this example)".
>
> So, the calculated probability varies between one hat-shape and another,
> and John's figure of 86% seems to apply only to one particular shape.
>
> So, can we compare that with the 75% prediction at all, which averages over
> all conceivable hats? To do so, John would need to arrive at some sort of
> global average, over all possible geometries according to some sort of
> weighting function. Perhaps he can help to resolve my confusion.
>
> George.
>
> contact George Huxtable, at george{at}hux.me.uk
> or at +44 1865 820222 (from UK, 01865 820222)
> or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
> ----- Original Message -----
> From: "John Karl"
> To:
> Sent: Wednesday, December 08, 2010 10:22 PM
> Subject: [NavList] That darned old cocked hat
>
>
> That darned old cocked hat seem to keep popping up.  I’ve given this some
> thought lately and have computed some examples to investigate questions --
> such as where the point of maximum probability is.  I’ve thought for a long
> time, and still do, that this is all perhaps rather interesting
> academically, but of no practical importance for a navigator who is only
> interested in the safety of the ship.  In that case you’re never sure where
> you are better than the known random-error distances from each LOP.  (Ocean
> racing or armed combat might have different objectives.)
>
> The linked PDF file gives my results and observations.  I’d be glad to run
> off other examples if anyone is interested.
>
> JK
> ----------------------------------------------------------------
> NavList message boards and member settings: www.fer3.com/NavList
> Members may optionally receive posts by email.
> To cancel email delivery, send a message to NoMail[at]fer3.com
> ----------------------------------------------------------------
>
> 
File: 

   

>
>
>
>
>
>

   

Reply