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    Re: AP terminology
    From: Frank Reed
    Date: 2009 Nov 14, 18:27 -0800

    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
    
    
    
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