Dear Marcus and All, I have renamed,
Re: [USMA:21338] Re: Calendar Proposals - the Alternatives as, Angles � quads and milliquads. Underlying a lot of the discussions that we have had is still the mindest issue concerning hundreds and thousands � and I'm not discussing fairy bread at a children's party. Like the originators of the original metric system you favor dividing many units into hundreds (you prefer centimetres, grads, grades, or gons, and centilitres), whereas, based on my experience with more recent metrication, I favor dividing most units into thousands (I prefer millimetres, millilitres and milliquads). As I've pointed out previously I believe that this is largely a mindset issue. You were brought up in Brazil where metric units have been normal for so long that the 'hundreds' of the original metric system are still the major mindset. On the other hand I was introduced to SI in Australia in the mid 20th century by which time such people as builders, engineers, architects, and many others had come to the realisation that, not only did division by 1000s make their work easier, it also made training and conversion from old metric systems much simpler. As an example of this simplicity let me list a complete set of units for building a house in Australia. 1000 mm = 1 m 1000 m = 1 km 1000 mL = 1 L 1000 L = 1 m^3 1000 g = 1 kg 1000 kg = 1 t 1 m x 1 m = 1 m^2 As a challenge, you might compare this with the set of units needed to build a house in Brasil or Canada. I will now make some remarks about your arguments in favor of gons as a unit of angle. I have interspersed some thoughts. > gon: I don't know the history of the word gon, but grads and grades (like degrees) are products of the late 18th century where they were common words to refer to parts of larger units. In this context I suspect that the word grad is simply a short term for gradation that only later became a slang term. Grads and grades of plane angle were simply the marks that divided up a quadrant into a hundred parts. In the late 18th century it was clear that the unit of plane angle was the quadrant; which was in turn divided by 100 gradations. It sounds to me like the idea of using prefixes such as centiquadrants had not yet been developed as we know them. By the time that grads had established themselves as an alternative to centiquadrants (or centiquads as I would say today) the grad or the grade was well establish as an alternative word, but not as a part of a rational prefixed system. BTW. As a challenge, could you define grads, grades, or gons for me without referring � in any way � to a quadrant (and circles of four quadrants I will regard as a copout). > - no "flaws" concerning the powers of 10 issue I outlined above > - more adequate for the aviation, nautical and cartographic industries (for > instance, up to 3 digits, centigon = 1 km, % association) Shortcuts and rules of thumb can and will be devised to suit any system. For example, I could say that 100�milliquads of angle at the centre of the Earth is equivalent to 1�km on the surface. And in many ways I find this a superior correlation as it does not contain the possibility of directly confusing plane angle with distance since one is (in numerical terms only) 100 times the other. The fact that you immediately identified this as a flaw is, I suspect, largely due to that fact that you, personally, are inclined toward using a 'hundreds' mindset. If you have a 'thousands' mindset it doesn't matter that 100�milliquads of angle at the centre of the Earth is equivalent to 1�km on the surface because the number 100 is not anathema to a 'thousands' mindset person. In my opinion the flaws you refer to simply disappear if you have a mindset based on 'thousands'. > - infrastructure for education already in place > - already enjoys public awareness I am surprised that you claim this when you have already said that you had never heard of a gon until Joe Reid pointed it out to you last week. However, having said that, I too heard about grads, grades, and gons in senior secondary school mathematics or physics classes but others at my school (who didn't take these subjects) would never have heard of grads, grades, and gons in any of their course. Secondly, I have never heard grads, grades, or gons ever referred to in any of the media. To the general public, grads, grades, and gons are simply a non-event and they always have been. On the other hand quadrants (a.k.a. right angles) surround us all constantly. > - does not require decimal points or prefix for most applications Whereas quads, milliquads, microquads and nanoquads never require decimal points. You use the strengths of SI prefixes to choose the most appropriate (decimal point free) submultiple. Specifically, if one milliqad (equivalent to 10�kilometres on the Earth's surface) is a problem then use 100�microquad (equivalent to 1 kilometre) or one microquad (equivalent to 10�metres on the Earth's surface). I can't think of a practical use for a nanoquad so I won't explore it here! on 2002/07/23 04.26, Ma Be at [EMAIL PROTECTED] wrote: > On Sat, 20 Jul 2002 10:02:07 > Pat Naughtin wrote: > ... >>> Don't mention it, Pat. I'd have no quablles with your approach. However, I >>> think that one point to consider is that the unit grade *already* exist. I >>> know it'd be two words and I know it didn't... "catch on" and all, but it >>> would be easier to try to gather momentum for something that already IS >>> there >>> than for something "completely" new, even in concept (i.e. like the use of >>> milli attached to it). >> >> In a funny way, I think that it would be more appropriate to introduce the >> 'new' unit quad rather than re-adopting the grade, grad, or gon. We should >> recognise that these have all failed and as the riddle goes: >> >> Q What would you be doing if you were a sadist, a masochist, and a >> necrophile all at the same time? >> A You'd be flogging a dead horse. >> > Pat, I understand where you're coming from. Perhaps though we should, first > of all, understand why the gon failed (if it really failed... from an > educational point-of-view it actually didn't as we continue to teach the > grade/gon(?) *everywhere* in this planet... We just didn't select to use it > in most places, unfortunately...). > > Secondly, I continue to believe that the "quad" has some nagging difficulties > like the ones I highlighted in my last post. It's just unfortunate that there > are 40 Mm in the circumference of the earth, instead of 4 Mm, or 4 Gm, etc. > ... >> But the quadrant is taught in all schools - constantly, and in my view quite >> effectively, already. The only problem is that it is not called the quadrant >> or a quad, it is called a right angle. Children draw angles of a quad in >> every square and rectangle they use, they cut angles of a quad out of paper >> and fabric. Apprentices in all trades are totally trained in the uses of >> angles of a quad on every job that they do. There is a vast difference >> between having 'already been exposed to it at one point in their lives' and >> the constant and necessary understanding that comes with constant daily >> contact in everything you do. Even every classroom the student sits in was >> designed and built using quads between all the walls, floors, and ceilings. >> > I see... True, we do that, but I doubt it that people tie this to the fact > that they have been drawing, cutting, etc, a (one) "quad". The right angle is > being treated as an... *object*, not as a potential *measuring device* that > has a unit value. When they draw any other angle they'd never associate it > with its being some 1.4, 1.6, whatever, of the quad, but rather 90, 110, 180 > degrees and so forth. > > Also, true, one could "introduce" the quad as actually being a unit, but then > we could run into all sorts of difficulties like the fact that most angles are > less than 1 hence generating decimal points which people appear to be > naturally averse to. Sure, "use the milliquad", as you proposed, but then > there is the meter question, the lack of an appropriate power of 10 for > certain applications, etc... So... Wouldn't it perhaps be more prudent to > revisit the grade/gon question, "for the first time"? The infrastructure is > ALREADY in place! It's still taught all over the world. So the cost of > having people learn it is practically zero! Suffice it for them to just > refresh their memories and start using it! This could be an irresistible > argument in its favor. > ... >> Thanks for pointing out this flaw. I recognize this difficulty. When I first >> considered this I was thinking of aircraft navigating (on their own) to >> within 10 kilometres of an airfield and then being navigated by the air >> traffic controller. >> >> Recognizing this flaw, I still consider it to be minor when compared to the >> overall benefits that the quad would bring. Currently, the SI is >> fundamentally flawed in that it does not have a base unit of plane angle. >> That is a far more significant flaw. >> > Agreed, Pat. But this is also adequately addressed by the grade/gon, isn't > it? In other words, the quad and the gon are actually the same thing but with > a different face (quad = 1, gon = 100). > > If we consider this issue from technical, economical, practical, etc > points-of-view I believe there would be more pros in favor of the gon than the > quad (despite the "smell" of failure attached to the gon). However, if you > disagree (and perhaps you do), let's please then consider what these are one > by one and in the end let's see whether pros outweigh the cons in favor of any > of these options. So far as I can tell this is a brief summary of the main > *differences* and advantages of the gon over the quad: > > There could be others, but the above is what I could quickly come up with. > Should you have a similar list of those in favor of the quad, please share it > with us for our analysis, Pat. Thanks. > >>> On the other hand we'd have a very interesting "problem" with the grade in >>> the >>> fact that the km accuracy would mean the use of "centigrade", a natural >>> confusion with the Celsius scale... ;-) >> >> You're absolutely right. And thanks, I hadn't thought of that one. >> ... > No problem, Pat. Joe, however, pointed out later on that there was another > name for the grade, the gon, which would adequately address that problem. I, > personally, must confess, I didn't know about it. On the other hand, if I, > being an academic, didn't know about it, it may be fair to say that probably > there would be many others out there who probably wouldn't either. Therefore, > just this... "name" change from grade to gon could possibly invalidate one or > two of my arguments in my list above... :-S (But, still, probably not enough > yet to sway me from my preference in favor of the gon/grade. The... > "breakers" to me are still the power of 10 issue, the use of decimal points > with the added fact that we would be condemning one to use a prefixed unit, > milliquad, most of the time, just like we do with the kilogram, this may > ultimately lead people to argue about why not eliminating this by renaming the > milliquad with some other name, just like we, here, do with the kilogram question... ;-) ) > > Marcus > > > Is your boss reading your email? ....Probably > Keep your messages private by using Lycos Mail. > Sign up today at http://mail.lycos.com > > ------ End of Forwarded Message
