NavList:

Alan, you wrote:
"I'm simply taking as correct, the numbers produced by a "black box", which more often than not are correct"

You were talking about a GPS receiver, but you have also just described a nineteenth century chronometer! Seriously, while celestial certainly has a lot of that "do-it-yourself feeling", and that's a big part of why we enjoy it, it is also in many ways a "black box" activity. A fair case could be made that the chronometer is the earliest example of a black box. It has no "user-serviceable" parts and no means of testing it (on its own) to determine whether it is behaving properly. It normally shows no visible signs of failure. Yet these "black boxes" have been essential to celestial navigation two hundred years. In the earliest period, this was seen as a near-fatal flaw in the concept of the chronometer. A chronometer was seen as worthless without lunars for testing, and some argued, with some reason, that this implied that chronometers were little more than a luxury. As the nineteenth century progressed, the simple method of polling was developed: carry several chronometers and let them vote. It's still used with mission-critical black box systems. To put it in the same terms as some recent comments on GPS, "the best backup for a chronometer is another chronometer".

It's also worth remembering that the astronomical data published in the various nautical almanacs is simply handed down to us from the clouds. The Nautical Almanac is also a "black box". Few practicing navigators have had any means to judge whether the data on refraction and other altitude corrections, let alone the ephemeris data themselves are correct.

Incidentally, in the last 18th century through the first half of the 19th century (with rapidly decreasing frequency), navigators could use "lunars" as a completely independent check on chronometers. Yet they found them difficult to trust. I have speculated recently that this was, in part, because lunars were not a "black box" calculation. When you as sole navigator can see all your work laid out before you, and when you know that you have made various conscious choices of clearing methods to use and details to include or exclude, there is much more room for self-doubt. On some early ships with enough competent navigators aboard, the "polling method" used later for chronometers could also be applied to lunars: have three junior officers each independently work and clear their lunars and treat each of them as "black boxes". Majority rules, simple as that.

-FER

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