NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Cocked hats, again.
From: George Huxtable
Date: 2007 Mar 15, 21:42 -0000
From: George Huxtable
Date: 2007 Mar 15, 21:42 -0000
Gary appears to be still finding it difficult to accept the 1 in 4 argument for the probability of a fix-triangle embracing the true position of an observer. First, I ask him if he has seriously considered the statistical argument that has been put forward in support of that argument, and whether he has found any holes or flaws that cause him to reject its conclusions. He has put forward a counter example, which I have done my best to follow, ignoring the mock-biblical language. To me, it doesn't address the point in question. It applies only to the restricted situation where the intercepts are several sigmas from the true position, and that applies to a tiny fraction only of possible observations. So even if Gary's conclusion, in those rare situations, is correct, it has little relevance, on average, to the 1 in 4 question. That applies to the whole gamut of possible triangle, large ones and small ones, hardly any of which will correspond to Gary's rare example. Going to his figure 6, that shows a probability of 1/4 of the true position being in each of those 4 quadrants, which is fair enough. But what will be the actual distribution of possible positions? It will correspond to a crowd of dots, like a swarm of bees, centred on where the two position lines cross. Nearly all the observations will lie near the centre of that shaded area, and hardly any near the edges, because Gary has chosen to put its boundary several sigmas away from the crossing point. So when he chooses, in figure 11, to restrict the area further, by imposing a limit on its possible distance from the new diagonal position lines, that may cut off two corners of the shaded area, but will exclude none (or hardly any) of the possible observations. So when he writes- "Diagram 11 shows that the northwest and southeast quadrants now have somewhat more than a one in four chance and the southwest and northeast each have somewhat less than a one in four probability", that isn't so. Although the areas may differ, the populations of those four areas will differ only insignificantly. Any argument based on such rare events has no bearing on the statistical distribution of the vast majority of observations, which will lie near the centre of his picture. Finally, a request. If Garry has more sketches to send, I ask him to scan several such diagrams to each sheet, as I'm now getting submerged in paper. George. contact George Huxtable at george@huxtable.u-net.com or at +44 1865 820222 (from UK, 01865 820222) or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK. --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to NavList@fer3.com To , send email to NavList-@fer3.com -~----------~----~----~----~------~----~------~--~---