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Subject: Re: Tables vs. Calculators
From: Robert Eno (enoid@XXX.XXX)
Date: Sat Sep 21 2002 - 11:32:31 EDT
Interesting argument. I have to agree. I reduce my sights using a simple
calculator and the spherical trigonometric formulas. It is fast and simple.
When I am engaged practicing my sight-taking at home, I always reduce a few
of them long-hand using the formulas in conjunction with tables of trig and
log functions.
Some will argue that a calculator is in itself, a black box, however, my
argument is that it is simply an anti-drudgery device. It is no different
than washing your clothes with a automatic washer, vs. a washboard and pail.
What I find most useful about using the formulas and calculator, as well as
trig and log tables, is that after a while, one develops a "feel" for the
answers. In otherwords, one can sense when the answer "doesn't look right".
This advantage is totally lost with most black box methods.
----- Original Message -----
From: Arthur Pearson <arthurpearson@XXX.XXX>
To: <NAVIGATION-L@XXX.XXX>
Sent: Friday, September 20, 2002 6:12 PM
Subject: Re: Tables vs. Calculators
> Chuck,
> Very well stated argument, I agree. Even for those of us who can't
> program, replicating table results with a calculator or a spreadsheet,
> or even solving problems with two different tables or methods and
> reconciling results, leads to a much better understanding of what is
> under the covers. I would argue that robust navigational practice should
> always be comparing the different sources and methods and applying
> judgment in the face of what are often inconsistent or conflicting data
> ("my DR says X, my fathometer says Y, my distance off that mountain
> suggests Z, I believe I am..."). The same applies to sight reduction in
> that comparing methods and their differences leads to a greater
> understanding what variables have the impact the accuracy of the
> results. My only real objection to any black box (from 229 to GPS) is
> when complete faith is placed in one and only one method of obtaining
> position.
> Arthur
>
> -----Original Message-----
> From: Navigation Mailing List
> [mailto:NAVIGATION-L@XXX.XXX] On Behalf Of Chuck Taylor
> Sent: Friday, September 20, 2002 7:32 AM
> To: NAVIGATION-L@XXX.XXX
> Subject: Tables vs. Calculators
>
> Sight reduction tables have long been widely used by celestial
> navigators. Why?
> The formulas for sight reduction by the law of cosines have long been
> known. The
> answer is pretty straightforward: Tables are used to save labor in
> performing
> calculations.
>
> One can perform sight reduction by the law of cosines with with a set of
> trigonometric tables (sines, cosines, etc.) and a pencil and paper.
> Multiplying
> and dividing 5-digit sines and cosines can be a bit tedious, however.
> The
> traditional solution was to use more tables, specifically tables of
> logarithms,
> so that multiplication could be converted to addition, and division to
> subtraction.
>
> The next logical step was to combine trigonometric an logarithm tables,
> so that
> one could look up, for example, the log-sine of an angle (the logarithm
> of the
> sine). Then came variations on the same theme, such as tables of
> haversines and
> log-haversines.
>
> Next came various other sets of tables intended to speed up the process
> of sight
> reduction by combining various steps, relieving the navigator of still
> more of
> the labor of computation. Examples include HO 214, Pub 229, Ageton's
> Tables,
> and numerous others produced by various hydrographic offices around the
> world.
>
> Many of us object to the exclusive use of "black boxes" such as GPS
> units on the
> grounds that it takes all the sport out of navigating if all you have to
> do is
> turn on the black box and observe your position (either the lat/lon or a
> mark on
> a chartplotter). We call it a "black box" because most of us don't fully
> understand how it operates, and we certainly can't duplicate its results
> by
> other means such as pencil and paper.
>
> We also believe that it is important to use the traditional methods in
> order to
> maintain our skills. Who knows, the black box may fail some day.
>
> I would argue that tables such as Pub 229 are an early form of "black
> box". At
> least many of us treat it as such. We open to the appropriate page and
> extract
> numbers, trusting on faith that they are correct. How many of us have
> tried to
> verify that those numbers are correct? I have. I can successfully
> reproduce
> the main tables by computer, but I have been stumped at trying to
> reverse
> engineer the the interpolation tables (difference and
> double-second-difference
> tables). I even asked the folks at NIMA who publish the tables, and
> they
> couldn't give me a satisfactory answer. If I can't program it, I don't
> trust
> it.
>
> I would be very grateful if one of you could provide me with a set of
> algorithms
> to reproduce the various difference and double-second-difference tables
> in Pub
> 229.
>
> How can we logically dismiss the use of the "GPS black box" while
> simultaneously
> embracing the "Pub 229 black box"? I'll grant you that the Pub 229
> black box is
> less susceptible to failure due to causes beyond the control of the
> navigator,
> but it still has many of the other characteristics of a black box. (It
> is
> certainly easier to carry a spare GPS than a spare set of the various
> volumes of
> Pub 229.)
>
> To me a calculator is less of a black box than a set of tables. I can
> reproduce the calculator's results using pencil and paper and a bit of
> time and
> effort. I could even reproduce the sines and cosines if I wanted to
> trouble
> myself with going through a Taylor series expansion. Because I can
> independently reproduce what a calculator does, I trust it. I don't
> trust
> tables that I can't reproduce. (I do trust the Ageton tables, because
> they are
> more easily reproduceable).
>
> In this sense, the use of a calculator is arguably less of a black-box
> operation
> than the use of sight reduction tables such as Pub 229. In that sense I
> would
> argue that the use of calculators (programmable or otherwise) is fully
> in
> keeping with the spirit of traditional navigation. The calculator
> simply does
> what you could do with more time and effort. There is nothing
> mysterious about
> it. Those who came before us weren't a bit shy about using such
> labor-saving
> methods as tables of logarithms. Why should we be shy about using more
> modern
> labor-saving devices?
>
> Chuck Taylor
> Everett, WA, USA
>
>
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