NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Tables vs. Calculators
From: Robert Eno
Date: 2002 Sep 21, 11:32 -0400
From: Robert Eno
Date: 2002 Sep 21, 11:32 -0400
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 PearsonTo: 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@LISTSERV.WEBKAHUNA.COM] On Behalf Of Chuck Taylor > Sent: Friday, September 20, 2002 7:32 AM > To: NAVIGATION-L@LISTSERV.WEBKAHUNA.COM > 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 > >