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Peter Hakel wrote-

| The issue may be partly of terminology; what George calls a "blunder" may
be an
| unavoidable occurrence in a process whose probability distribution
inherently
| has a "fat tail."

There will inevitably be additional blunders of such a nature that it's
difficult or impossible to apply any sort of distribution to them. A
noted-down digit, misread or badly written in dim light. The mistake, that
almost every navigator makes at least once, of exactly reading a micrometer
drum, but  reading the scale-of-degrees as one too many, especially when
the minutes approach 60. Or the similar error, made by Lewis and Clark
again and again, of getting the seconds-hand of a chronometer carefully
right, but making a one-minute error in reading the minutes hand. Such
errors will never be eliminated. A good observer may well strangle some at
birth, but then any such pre-filtering will have its own effect on the
resulting distribution of errors.

But just as Peter suggests, it may well be that for some reason the
distribution of altitude errors may indeed have a fatter tail than the
traditional Gaussian model would imply. Before we accept that, it needs to
be convincingly demonstrated that it really is so, and by how much. Such
evidence, relating to sextant altitudes, might exist, but Frank has not yet
demonstrated it in a convincing manner.

| I think Frank's point
| is that they may even be applicable to imperfect human navigators on
small boats
| in bad weather attempting to do their best with sextants of varying
mechanical
| quality.

Yes, but as I pointed out, under different circumstances such as bad
weather, the breadth of the resulting distribution will then change. If
those results are then conflated with observations made under better
circumstances, the merging will create a misleading appearance of a
non-Gaussian distribution.

 | This may be one of those things that just might lead to intriguing
results upon further study.

Indeed, it might. First, it needs to be demonstrated that such a shape of
error-distribution really does apply to our observations at sea. Then, if
that's found to be the case, it needs to be quantified, and finally, we
need to learn how to apply that knowledge to make the most of our
observations.

George.

contact George Huxtable, at  george{at}hux.me.uk
or at +44 1865 820222 (from UK, 01865 820222)
or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.

   

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