NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Still on LOP's
From: Martin Gardner
Date: 2002 Apr 20, 07:32 -0700
From: Martin Gardner
Date: 2002 Apr 20, 07:32 -0700
My point, and I do have one... As this discussion continues, I think it drifts perilously from George's start, into muddy and shoal water: Here's where I stand - I have no reason to doubt probability ellipses, even if I can't calculate them. I believe they tell us as much as we would want to know about where we are. What I wanted to do was follow George and see if a much simpler geometric analysis could - just for the hell of it - give us a single number for the chances we were inside the hat. For me, taking simplified probability distributions, etc. goes the wrong way: I have the greatest confidence that these approaches, simulations, numerical methods, etc, will ultimately give us ellipses - the hard way. The scariest suggestion I have heard, and I can't recall who said it, was that perhaps there is no single number that defines our likelihood of being inside the hat in all cases. Somebody who does understand the ellipses might find an example where the 90% ( or 85%, or 92%) ellipse lies entirely outside the hat, or entirely within it - that would convince me there's no single value for the odds of being inside the hat, and I could move on with my life. Martin