NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Peter Fogg
Date: 2010 Dec 11, 06:59 +1100
Peter,
On your side you have questioned and opposed George's reasoning, because in your view if the cocked hat were reduced to just one single point - which may very well happen since absolutely nothing forbids it - allocating a 25% probability to just this unique point makes no sense at all for you.
I would take position here only on one point Peter, namely your remark itself mentionned here-above. While I am sometimes under the impression that math might happen to be taught differently on each side of the Atlantic Ocean now and then :-) , I can see absolutely nothing which forbids to allocate a full 25% probability onto just one single point. So, I do not think that your view point - or at least what I have understood about it - is a counter example to George's results.
*******
I do find it a fascinating idea, since it follows a certain logic, even if it can be contradicted by another proposition that is also, apparently, quite logical: If 3-objects were able to be observed and expressed as position lines without error then these lines would meet at a point; the fix position...
The other apparent contradiction is that practical navigators tend to take a small triangle as an indication of little error, and a large triangle as an indication of significant error, and for practical purposes this makes sense. Yet John Karl and his proposal has reminded us that the larger the triangle the better the chance that it actually contains the fix position, while if the triangle becomes particularly small the chances of it containing the fix position, logically, approach zero.
