NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: That darned old cocked hat
From: George Huxtable
Date: 2010 Dec 13, 14:41 -0000
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. George. 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.