on 2005-10-17 08.57, m.f.moon at [EMAIL PROTECTED] wrote: > I realize that the subject of off base and at the risk of going even further, > let me describe a use of fractions in a very practical example. A few years > ago while attending a meeting of a navigation specification review, I > commented as did others on the correctness of a set of equations for polar > regions. I was offered the "opportunity" of evaluating these for > applicability, i.e., would they produce correct and useful results. As I did > not have access to a computer nor calculator nor even my trusty slide rule I > wondered what I was going to do as I didn't want to spend hours in tedious > hand arithmetic. I certainly know how to long multiplication and division but > not at 10 o'clock an night. I realized I could do most of the work doing > simple fractions to deal with the various spacings and parameters. In a short > while I convinced myself and the others the next day of the appropriateness of > the equations. > Had I been trained in the most modern ways of school arithmetic as being > taught in the local schools, the solution of my problem would have been out > of reach. > marion moon
Dear Marion, Whilst I agree that a knowledge and ability to use fractional calculations can at some odd moments be useful, I suspect that this is not one of them. The issue here is much deeper and it goes back to the origins of the metric system in the 1790s and the subsequent refusal of the world navies (led by the British Navy?) to have anything to do with the metric system. In 1799, the world's sailors, and there were many of them, were offered a sound practical world view based on the idea that the distance along any meridian was 10 000 kilometres from the Equator to either the North or South Poles. They rejected this idea preferring to retain the jargon based hodge podge of measures based on the more or less random selections of Babylonian astronomers. Had the metric system been chosen for navigation in the early 1800s, the fractional problems you faced would simply not have existed. One other issue was the matter of having a sensible method within the metric system for measuring angles. There is currently not a practical unit for measuring plane angle as an integral part of the metric system. The radian is a ratio that is simply not practical for sailors, air pilots, or especially builders. I believe that the creators of the metric system clearly intended to have a practical unit for plane angle when they decided to use the quadrant as the first and foremost metric unit (instead of the seconds pendulum). Recall that the first definition of the metre was based on the size of the plane angle of a quadrant. Plane angle in this respect is even more fundamental and basic that the metre itself! The quadrant once it was used to define the metre was then subsumed behind the name 'metric' system and we have rarely recognised its existence (and importance) since. I believe that the world still needs the quadrant as a practical unit in navigation and especially for building. As the SI chooses not to recommend or promote a useful unit of plane angle, the world's builders, sailors and air pilots are condemned to use the old Babylonian degrees, minutes, and seconds with all their calculation problems and inefficiencies indefinitely into the future. Cheers, Pat Naughtin P.S. I have written on this topic on the USMA list previously, perhaps before your time here. I promoted the idea of a unit called a quad defined as equal to a plane angle of one quadrant. From this definition a milliquad would equal 10 kilometres along any great circle of the world, and a milliquad would equal 10 metres. Please let me know if you would like more details of this suggestion.
