NavList:

 

Yes.  But only one of them is correct.  Its that correct one we are working towards.  Having the right slope to begin with tends to be quite useful, instead of deriving an incorrect one.

We have that slope.  And thus the knowledge that all the sights, freed of error, are on that slope.

Yes, you're back to averaging.  Bill, what can I say?  All sights are not created equally.  Some are better than others.  The good ones tend to be closest to that slope.  What you seem to be arguing for is regression analysis, which treats all sights as being of equal importance and derives a line, a line with arbitrary slope from them, as blindly dictated by them.  Wrong approach.  Since we know the slope, we know the line on which a perfect series of sights must lie.

 

Enough or not, how many obs can you make and record within 5 minutes of time, Bill?  This is how a scribe, another person to time and record the sights, becomes so useful.  Remember that the slope line is really an arc, which limits how much of it we can approximate as a line.

Look, this (current) discussion began because George acknowledged that some sort of analysis of a series of sights, to reduce error, is useful.  Now we seem to be stalemated into an inability on the part of some to comprehend that slope analysis is a better method of reducing random error than averaging.  Whatever.

This was only part of the larger story, which was that the resolution of error is best considered as a 2-pronged approach:

1.  Reduce random error at source, via use of slope analysis.  If, despite all evidence to the contrary, you (or anyone else) prefers to use some sort of averaging, then feel free.  Go for it.  Actually, though, I suspect that this viewpoint is one beloved only of armchair navigators, who don't use either method.  All theory and no practice!

2. Having reduced random error as best as can be done, treat remaining error as systemic and find the fix at the centre of the shape.  The great advantage of this approach is that you arrive at a useful endpoint, a singular fix, that is as free of both kinds of error as it can be practically rendered.  Such a more useful approach than just moaning that the position is not knowable, due to 3 times more chance of the fix being outside than inside the shape.  Due, incidentally, to random error, with systemic error conveniently overlooked.

This discussion has caused me to reflect on the nature of supposedly 'rational' orthodoxy, so rigidly on display here, and so obviously upset by all this heretical talk:  "intuitive approach",  "think about what the data points mean, instead of just blindly number-crunching" and suchlike blasphemies.

Such irony. The closed mind that has decided in advance just what is permissible, in this case the reduction of random error, and anything else must be wrong.  We might as well be back in the Dark Ages.

I would have thought that a truly rational approach necessarily involves an open mind, one willing to put to one side preconceptions in order to consider a fresh approach. 

An example: Once Newton set down his 'Laws' (of Motion, etc) they became the foundation of physics and indeed of much modern science.  To question them seemed unthinkable (and they are still taught in schools as an essential base, even though we now have other models).

It took an extraordinary, an obviously open and a particularly imaginative mind to put them to one side and conjure up how matter, time, light, gravity and velocity could all be interrelated.  Now we accept that Einstein has produced better models of the nature of the universe than we had before, even while we struggle to comprehend them.

I'll say it just one more time: if you want to understand slope analysis then start using it.  That will be about a zilliom times more instructive than arguing about how it might work or not.