NavList:

   

Reply

Geoffrey, to Peter H you wrote:
"And I don't think I agree with you anyway about just needing one parameter to characterise an LOP."

Peter Hakel writes in phrases that lead me to believe that his education was 
in mathematical physics (or something close --correct me if I've guessed 
wrong!). Saying that a path is "parametrized" by a single number fits in with 
that. What it means is that we can identify any point along an LOP with a 
single "index". Imagine a rather complex path on a piece of paper, like a 
signature drawn by pen in hand. Its coordinates have to be specified as x,y 
on the page, but I can "parametrize" the path by a simple index which could 
be a time index for example. Even though the path of the pen tip may cross 
its own path and may leave the page for a moment between words, it can't be 
in two places at once (no pairs of pens, no interfering quantum pens!) so if 
I make a "movie" of someone making a signature, I can specify where I am in 
the path made by the pen tip by a time index, t, in the video. That counts as 
parametrizing the path --I've uniquely identified every point in the path by 
the time when it was drawn. The path would still require to variable to 
describe it, x and y on the page. Those would be functions of the parameter: 
x(t) and y(t). Note that some other variable could be used, like the quantity 
of ink, q, remaining in the pen. We would then have x(q) and y(q). For a 
celestial circle of position, a potential parameter would be azimuth, azm, 
measured from the GP at the center of the circle. Then we would give the 
points on the circle in latitude and longitude as  Lat(azm), Lon(azm).

None of the above has anything to do with celestial navigation particularly. 
Nor does it have anything to do with any so-called "confusion" on the meaning 
of lines of position and the intercept method. The fact of the matter is that 
every student of celestial navigation brings their own background to the 
subject and they will attempt to re-phrase the rules and methods of celestial 
in the language that best fits their own background. Occasionally, this leads 
to erroneous "mappings" (there's my math and physics background coming into 
view) of the actual subject onto the copy in one's own head. In other words, 
people sometimes make connections based on their own personal analogies that 
are incorrect. Sometimes this can happen when normal, everyday meanings of 
words, can interfere with technical meanings. This is a much bigger problem 
for some students than others. Plenty of students, but I would say less than 
50%, get quite confused by the phrase "horizontal parallax" since the shift 
in the Moon's position *due to* the horizontal parallax is vertical, not 
"horizontal" in the normal meaning of the word. There are many cases of this 
in math and physics generally; functions have no "function" and work does not 
mean "work". John's contention that some students are confused by the very 
phrase itself "assumed position" is not inconceivable --I just haven't 
encountered it. We all just have to remember that we are all distinct 
students (and teachers) with unique ways of understanding concepts. The 
concepts exist objectively nonetheless, and it is certainly possible to have 
an idiosyncratic way of looking at things, a stretched analogy, that ends up 
being flat out wrong. But it's also possible to have a slightly different 
"spin" on a concept, like whether to define "AP" narrowly or broadly, that is 
simply a result of the individual path that each of us has taken to get to 
where we are... Which make me wonder, what parameter could we apply to that 
path...?

-FER



--~--~---------~--~----~------------~-------~--~----~
NavList message boards: www.fer3.com/arc
Or post by email to: NavList@fer3.com
To , email NavList+@fer3.com
-~----------~----~----~----~------~----~------~--~---

   

Reply