On Wed, 24 Jul 2002 06:46:49 Pat Naughtin wrote: ... >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). > Well, Pat. Part of what you said above is indeed true, but it's not that simple, my dear friend.
Please bear in mind that we, long time metric users, have considerable more experience in **USING** the metric system. We have come to appreciate the convenience of using other prefixes in the SI system than most others. I do realize though that perhaps from a perspective of *transition* the approach to metrication that would "focus" on the engineering powers of 3 may indeed make sense. But, again, I'd you like to (hopefully...) understand that unlike many may think there IS a place for the use of the plethora of prefixes foreseen in the SI system. Talking about mindset is fine and is a very valid point, and I can see that from a perspective of someone growing up with mediocrities like ifp units folks would probably prefer to avoid learning and getting familiar with new stuff. So they'd favor doing it with as *little* a number of "units" as possible (so, please also allow me to suggest that there would be a natural tendency from you, guys - former ifp countries - to do this). What I'm trying to say is that there should be NO reason *whatsoever* to try to "impose" or "standardize" people's use of prefixes. The SI system is flexible and powerful enough that this small "mindset" differencial (as you put it) would not cause such a stir! >... 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. Granted! Please notice the qualifier though: 'it also made training and conversion' to the new system (my inclusion here) simpler. I can see where you're coming from. Just please note my above comments, too. I'd like to believe that they too deserve merit and consideration. So, in essence, if you guys felt that going to 1000 was better, wonderful! You won't find an opponent in me on this, but please consider the merits of using certain other prefixes, too, especially in the context of usage by peoples around the world. Percentages, like it or not, DO have its advantages and merits. Besides, it very much... "stuck"! ;-) > As an example of this >simplicity let me list a complete set of units for building a house in >Australia. > No need, Pat, I evidently can appreciate your point. Not much argument here. Just a small side note though to comment that unlike you we, Brazilian and other countrie's builders, find convenience and ease in using cm (perhaps mostly due to the fact that it would cut one more digit from construction data with the mm being used ONLY when it's necessary or required in some cases). ... >I will now make some remarks about your arguments in favor of gons as a unit >of angle. I have interspersed some thoughts. > Sure, let's take a look. >> 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. > I don't know much the history behind this either. Nonetheless I suspect that this may have a lot to do with scaling for purposes of reading, measuring and all. Dividing a right angle in 100 increments looks very adequate to the eye and for simple day-to-day activities. So, again, I suspect, this may have more to do with the practical aspect of this issue. >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). > ? I'm not sure I follow you, my friend. As I said before, our approaches are actually the *exact same one*! I.e., we both agree that the right angle should be associated, measurementwise with the number 1. The only difference between our approaches is in how many zeros we want to add after that! And my contention in favor of using 2 zeros, as opposed to none in your case seems to present some important advantages as I already highlighted before. In the end I just saw them enough of "power punches" to make a decision in its favor, *DESPITE* acknowledging your attempt to keep things within an... engineering "mindset", as you put it. .. >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. > ? I'm not sure I followed you (again, sorry if I'm seeming a little slow today...). We're trying to devise a system for navigation that would be convenient to navigators *on the surface of the earth*. 'Centre of the Earth' circle considerations and the like IMHO should not be of concern to this industry. The 'plane angle' issue and its association with distances does have merits. However, it's precisely for this reason that the navigation industry has apparently decided to make such an association. They figured that it would be advantageous for them to define the nautical mile vis-a-vis a minute of arc. I'm just respecting their wisdom, knowledge and experience and offering them a... "metric" alternative (while many here could probably protest and argue that that alternative would be the radian...) with which they could live. >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'. > Hmm... I don't think it's that, Pat. Please consider that the use of 'hundreds' in this case falls well within the scope of our present set of prefixes, as I tried to explain. What I mean is this. What decimal "size" would suit us well when it comes to defining the right angle? Using the quad we'd have the situation in which 1 km would be associated with 0.0001 quads. But we don't have a prefix for this, if we used 100 gons, we would (centi) (1 x 0 for the gon). "Normal" angles (for most applications even outside navigation industries this seems to be the case) are less than the right angle. If one uses the quad unit one would have to use a prefixed unit, just like we do with the kg, making it almost as the "de facto" standard, but then why not "rename" it to get rid of the milli prefix in it? With the 100 gon model we wouldn't have that difficulty (2 x 0 for the gon). For practical purposes (trust me on this, please) dealing with 2 digits is nearly always better/easier than dealing with 3, especially when one needs the ability to react quickly and/or do quick general simple calcs. This is behind why health industries deal mostly with centimeters for size of tumors for instance. When your life is on the line you want to deal with the littlest amount of digits and complicating factors as possible. Besides, percentages are a more pervasive concept in people's lives, perhaps more than "engineering" ones, making it nearly ideal for situations requiring speed. A jump to its use seems to have a natural magnet for acceptability in the minds of many (3 x 0 for the gon). Finally, devising a simple compass with subdivisions would "look" cleaner/neater with 100 units to the right angle compared to 1 000 mq (4 x 0 for the gon). (Note: And I'm not considering potential future benefits this could have if the time construct gets overhauled. But, granted, this one may hinge on what construct would win in the end...) Anyways... This is how I see it. >> - 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. Not the *word* gon, Pat. I knew about this via the word *grade*! >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. Hmm... Are you saying that you guys in Australia do not teach your children anymore about the various ways angles can be measured? I thought this would be covered regardless of the metrication project you underwent! Now, I'm surprised... > 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. True, of course, perhaps with the noted exception of France. But it doesn't change the fact that this "knowledge" sits there somewhere in people's memories. Just to show you my point. The other day I mentioned about this to my wife and she, unlike me, couldn't remember about the grade until I "refreshed" her memory, then she seemed to have conceded that sometime ago she may have been exposed to this (and I know she was because I know our educational system in Brazil fairly well, besides she's contemporary to me, similar age). > On >the other hand quadrants (a.k.a. right angles) surround us all constantly. > True, except that apparently it isn't exactly associated in people's minds (as I already commented earlier) as a *measurement unit*, but rather as an "object/property/entity" or something. >> - 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)... True, but why should we mess with bringing on board a yet another prefix, micro (plus the milli), into the picture, Pat, if we don't need to? By using 100 gons to a right angle this is would not happen, unfortunately not so with the quad though. Besides, why associate a figure 100 to 1 when we could use 1 to 1 (100 uq = 1 km versus 1 cgr = 1 km)? Another difficulty of falling back to 1 uq is that 10 m would be just too fine an accuracy and useless for normal grand navigational purposes. BTW this is a difficulty *inherent* with using ONLY engineering prefixes (so this part of my observation is not particularly addressed at the quad discussion) and another reason why I position myself on the side of allowing for the use of other intermediary prefixes if they would be helpful and/or more convenient for certain applications. Please note: **allowing**, as opposed to making mandatory the use of ONLY engineering powers of 10. Marcus Is your boss reading your email? ....Probably Keep your messages private by using Lycos Mail. Sign up today at http://mail.lycos.com
