Very good argumentation, John. Just please allow me to add a few more thoughts though to your already great thought process.
On Sun, 19 Oct 2003 21:29:48 John S. Ward wrote: >Hi Marcus, > >Yes, indeed, I was aware of this when I wrote the text copied below. Yes, the >grade is already on calculators, a major advantage over the quad. No, I >don't think grades are generally taught in school, at least not from polling >friends from a variety of countries. Perhaps they were mentioned and most of >us just forget about them since they are so seldom used. > 'Course. However, the fact remains and which was my very point: DESPITE the fact that this may not be used, people *know* that there are 100 gr to a quarter circle, just like there are 90 degrees to it! But your point is taken. It comes to me as a surprise though because last time I checked both Canada and Brazil, for instance, included grade teaching in their curricula. >I think the most important point to focus on is whether or not mankind would >be better off measuring angles with the degree define as 1/360 circle, or >with something else. Readers of this list seem to mostly believe that the >preferred unit would be to divide the circle into 4*10^N base units. > True, and I'd say with good reason. Again, it goes to the fabric of using a *purely decimal system*. More on this below. >First off, we probably all agree that minutes of arc and seconds of arc should >not be used for ANY modern purposes. > Excellent. We both strongly agree on this one. However, please notice that marine and air foggeys continue to insist on using them, not so much the second, but *certainly* the minute! Why? Precisely because of its association with the nautical mile crap! >Secondly, let's remember that the original killer feature of the metric system >was to extend each base unit by the application of a prefix to make a new >unit that is 10^N the size of the base unit. The advantages are (obviously) >that then we can convert from any unit to any unit by simply shifting the >decimal place appropriately, among other things. This does NOT mean that the >selection of the base unit itself has to be a factor of 10 of something. The >base unit for electrical current is a good example. There's no particular >advantage of the particular definition chosen for the ampere. In fact, it's >pretty arbitrary! The important thing is that we can derive kA, mA, >microamps, etc. from the base unit. Furthermore, we can derive other units >from the ampere (volts, ohms, etc.) that can also be used as base units to >derive kV, mV, etc. > However, this is not the point though here, John. What one must take into account now is the relationships that would emerge from the USE of this 'unit'. It is important that one finds *key* associations with key situations that should be decimal in nature. And here is the brink of the question. Why choose an arbitrary 36 "units" for a full circle, too? Why not pick a specific common "slice" and assign it a decimal value? Here is another indication why the use of grade would be academically "perfect" (it goes without saying that this is also somewhat true of the quad, but not as clearly so!). We associate the spectrum of angles to be contained in a quarter circle. Supplementary angles and others bigger than 180 degrees, "self-repeat" or collapse into these ones! Alas, if everyone associates 100% as representing the ENTIRE spectrum of phenomena being investigated, why not use it to study and relate to the quarter circle? >An important question to then ask is why not just stick with degrees? Degrees >are THE defacto-standard unit for angle world-wide. If we simply drop >minutes and seconds of arc and instead use centidegrees, millidegrees, etc. >then 99% of our objections to degrees go away. Why not? Because there is a lot more to it than just the degree aspect. Navigation, time zone, cartography... All these guys work with a system that incorporates concepts like arc-angle, 24 hour zones and whatnot. The use of the grade would greatly facilitate terrestrial associations on projections since the earth is nearly a sphere and the errors between this assumption and the ideal of a perfect sphere are not too detrimental. True, perhaps academically speaking the best would be to fix the size of the meter to fit a "perfect" 40 Mm on the "average" surface we currently use, like SEA level, but... this would truly open up a can of worms here... Please note that originally the creators of the metric system found it to be important to come up with a "unit" that would end up with a "round" number around the planet (in this case they assumed that it would be 40 Mm). This conceptual work was done with a reason, John. It's regrettable that in reality there is a difference of some 31 km for that association to be "just perfect" on a surface level we call SEA level. More on this later. > Furthermore, the second >killer advantage of SI is to have a single, unambiguous global standard. >Degrees are exactly that. > ? I must respectfully disagree. It's not because the present 60-60-24 hour construct is "universal" (global) that it is THE best or most adequate system to use. We all know and most can even *PROVE* that there are inefficiencies and significant serious problems with this framework, like the constant need for conversion factors and whatnot. The exact very thing why we fight so hard to have the SI system the ONLY true universal system for mankind. Therefore, I'm sorry, but I canNOT be happy with accepting something just because it's being globally used! We're unfortunately wasting countless money by sticking to a mediocre system, even if EVERYBODY uses it! Imagine the incredible amount of time and money our civilization would save if we used a perfect decimal time construct, for instance. But, no, most (even here) continue to argue the old "cost card" to disregard adopting a different framework. This is really sad... Why? Firstly, because instead of focussing on **SCIENCE** they focus on market power to push a specific standard even if they know fully well that it's probably the worst there is!!! So, how can I as a scientist take this? Please tell me. Secondly, they "conveniently" overlook that in the long run we WOULD be MUCH better off by changing (even if it requires the entire planet to do it!) to that kind of system than to be content with getting global acceptance of a very flawed construct. And I'm talking about cost *ITSELF* (YES, the very lame argument many propose to reject change and progress here!... ;-) ) >The problem is cartography. That's it! Is it worth it for the world to >replace a broadly accepted ubiquitous international standard with some other >unit just to fix cartography? I will say this: EITHER we stop measuring >angles in degrees in favor of quads or grades or whatever OR we give up >trying to use angles for latitude and longitude and define a meter-based >geographical coordinate system. > Very good, John. I'm with you here. So, to answer your very pertinent question, I'd say a resounding YES. It IS worth it! But the benefits are apparently small and can only be perceived by a rigorous calculation. The problem though is that this calc seems to point towards "breaking even" in some 6 or 7 decades (or maybe even a century!...). And folks don't like that, so they prefer to put up with 60 minutes to an hour, 60 seconds to a minute and 24 hours to a day, for instance... What can I say?... Your second part of the paragraph above is a very pertinent and interesting aspect, a one which I understand and concur with. However, John, we would NOT need to see this as mutually exclusive, my friend! What I mean is that we COULD cut the cake and eat it, too, here!!! In other words, why not have EVERYTHING??? We can enjoy the advantages of the grade ALONG with what you suggested and NOT have to make a choice between one OR the other, you see! >Until 30 years ago, it wasn't possible to separate angles and geography, as >cartography was based on astronomical angle measurements. Nowdays, however, >electronic navigation can sidestep the problem. That is evidently been demonstrated to be true when GPS came along. No argument here. But, again, we don't have to "forget" about the angle situation necessarily. I firmly believe we can STILL have the best of BOTH worlds! If only we had a little bit of more good will to accept some changes... > If I fight my perfectionist >urges hard enough, I start to think that this would be a lot more practical >solution than deprecating degrees. > Well... Perhaps, but please consider that you would not necessarily have to sacrifice your 'perfectionist' stance in life for that... :-) >I think it's a bad idea to base the standard datum on a reference surface over >500 meters below sea level. ? John, perhaps you're not aware of or don't realize it, but there is an unsurmountable systemic problem with EVEN our current SEA LEVEL approach, my friend. Why? Because the earth EVEN on SEA level is NOT perfectly 40 Mm, or whatever the hideous nautical mile trash turns out to be! So, this is totally moot, my friend. On the other hand, why would this new UAR be important, you would ask? Good question, and the answer is a matter of a "perfect academic system structure"! There are two options here, either we take the inaccuracy associated with the surface of the earth and tolerate it, as it's presently done, or, we fix that by fixing the reference to a perfect one and build projections based on the UAR. So what if good part of places on earth would NOT be on UAR? Most are not on SEA level, either!!! What's the big deal if altitudes would be quoted as, say, 3500 m UAR, instead of 2969 m SEA (actually this would be more like 3000 m as flight levels and all are devised with round rational numbers vis-a-vis that reference)? FL's and whatnot would simply be redefined with the UAR in mind. This would evidently entail in practical terms a meager 31 m difference from their present "location". Hardly something to cause so much headache to the traveling community!... ;-) > Is your reference surface a perfect sphere? Evidently yes. > I'm >afraid I just don't see the advantages. At the surface (where it matters), >your great circle grade will still not be 100 km. >... But it's not 1.852 km per minute arc angle either!!! We continue to deal with approximations here, John. On the other hand you do have a point in the sense of my reference surface being somewhat farther below than our current SEA level "average". But the advantages of dealing with grade angles on a *perfect* sphere set up probably would outweigh such disadvantages. I concede I could be mistaken, though. Therefore I appeal to those professionals in the area to come up with refutations to my UNS idea proposal, not as a: "I-dare-you" attitude, but in the name of finding real solutions for mankind. It may be the case that I may need to revisit my entire proposal after all, I don't know. So far I haven't sensed too great difficulties with UNS usage. FL's calcs and all could be performed on *perfect* locations to render the system usage irresistibly attractive for navigational purposes, and now I'm talking more about on-board computer gizmos and things like that. Please let's also NOT forget that airplanes cover distances on the air and NOT on the surface. But sea boats and ships would be a different story (that's true...). But then again, computers can work wonders at any altitude level, UAR or non-UAR... Anyways, I've already spoken too much... Thanks a million for a very healthy discussion, John, I've been really enjoying this and hearing from you. Take care, Marcus ____________________________________________________________ Get 25MB of email storage with Lycos Mail Plus! Sign up today -- http://www.mail.lycos.com/brandPage.shtml?pageId=plus
