Very good, Pat. It was with great interest that I read your arguments put forth in favor of the quad.
However, despite careful consideration of these I still believe that there are critical advantages to adopting the grade. And this despite its "attachment" to, as you correctly put it, the percentage framework, as opposed to the more usual engineering concept of powers of 3. But then again here is the beauty of the SI system in that one is NOT obliged to adhere necessarily to powers of 3 to devise decimal applications and have them work nicely. There is a lot more to discuss on this and I fully agree with your position that this aspect deserves a closer look. Since this is a very extensive mail I'll try to keep it short to what I believe would matter most, ok? Before I begin I must thank you for your usual thoroughness and willingness to revisit this important issue. Well done, my friend! :-) On Sat, 18 Oct 2003 15:05:29 Pat Naughtin wrote: >Dear Marcus and All, >... >In 2002, July, Marcus challenged me to support a suggestion that I had made >that a new unit, quad, should be created to measure the quantity of plane >angle. It has taken me this long to get around to it. > Actually this was much less as a "challange" than it was to lay before us the pros and cons surrounding these two proposals. Since you were at the time the main proponent of the quad I was curious to learn what you could bring to the table in its support. And I'm really happy that you did it in such rigorous way here. Once again, well done. However, after careful study of it I must confess I'm still favoring the grade slightly and I hope I'd be able to build a convincing case, if not here now, later on when I have the time to summarize it, ok? >This posting is in four parts: >1 Some definitions >2 Arguments for quads >3 Arguments for grads, grades, and gons >4 Some reflections on mindsets > >Definitions >... The word quad also fits well >with the SI concept of using prefixes as it is a short monosyllabic word. > If shortness is of such an essence, fine, I'd go along with the adoption of the word gon. But I don't think this has that much weight in terms of its being a decisive factor though. And, since, as you put it, grade is much more known, shouldn't we perhaps forget about adopting the gon after all, for practical purposes? Just a question for food for thought. In addition, if one would actually be using a lot more a prefixed quad, as in milliquad, wouldn't we be in actual and effective fact killing this argument altogether??? In other words, it would be "rare" for us to use a prefixed grade, but it would be far more "popular" to use milliquads. Therefore, for shortness sake, in the end, grade becomes more convenient from this perspective, wouldn't one say? More on this later on below. ... >Arguments for quad > >1 I think that it would be more appropriate to introduce the 'new' >unit quad rather than re-adopting, and trying again to re-introduce, the >grade, grad, or gon. We should recognise that grads, grade, and gons have >all failed... Honestly, I wouldn't call the lack of adoption of the grade on a global scale a failure. Why? Simple, because it CONTINUES TO BE TAUGHT *everywhere*! Even if only for "curiosity" purposes. My point is, if, for educational purposes, the grade continues to be taught why not take advantage of this to perhaps make such teaching increase in importance if industries end up choosing to be supportive of it? >5 The grad, grade, or gon does not exist without reference to a >quadrant; 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). > While interesting the above point is somewhat "academic" and not as relevant per se IMHO. Why do I say that? Well... Think about it. How do we define the meter (and so many other units of measurement), for instance? We're told that it's a fraction travelled by the speed of light!!! Alas, why would it be bothersome to define a grade as 1/100 th of a quadrant of a circle, or, better yet, 1/400th of a full circle??? (well... you asked me to define the grade without a reference to a quad!... ;-) :-) ) Aren't we being a little too pragmatic here or something? >6 There is a very interesting 'problem' with the grade in the fact >that the kilometre accuracy would mean the use of the defunct unit >'centigrade', which is still often confused with degrees Celsius. > Indeed, here we do have this... "coincidence". However, the context is clearly different. I mean there is no chance for one to confound these two when the issue is presented, wouldn't you say? True, it doesn't excuse it, and true it IS a con to the use of grade. But, would this be decisive against it? That's IMV the fundamental question. A lot of us are willing to shift prefixes to capital letters when it comes to positive powers of 10, right? Well... 'K' ALSO coincides with the symbol for Kelvin, would it not? And yet, I still believe that most of us would support this proposal (myself included, BTW!...). True, it's a coincidence, but so what? I believe, again, that the context would make it unequivocal which one is which, agreed? The same could be said about the centigrade. >7 For aircraft navigation 1 milliquad would allow for an aircraft >navigating, on their own, to within 10 kilometres of an airfield and then >being navigated by the air traffic controller. > But a centigrade would be even better, since the accuracy is 1 km! All systems could be built to such accuracy (two decimal points). And given the fact that most aeronautical navigational airport approaches are within 5 km, centigrade would evidently be a lot more useful. >8 Using microquads as a small unit would describe a distance of 10 >metres on the surface of the Earth - this measure, within the wingspan of >most aircraft, should be sufficiently precise to allow for all aviation, >nautical and for most cartographic purposes. > Hmm... True, of course. However, we're talking about aerospace navigation here. I'm not aware of any grid or cartography data that requires less than 1 nautical mile precision. If you can devise an application that would require that much accuracy, Pat, I'm all ears, my friend... On the other hand, cartography at a very small scale, like you appear to suggest, could be provided to any number of decimal places. But I'm glad you brought this up because it reinforces my belief that we should create at least a couple of more prefixes here for 10 to 4 and 10 to -4! And sometime ago I suggested the 'ty' for the 10 to -4 since this would be very useful for the desktop publishing industry (remember, the typo thing? 1 ty = 10^-4 m). So, 1 tygr = 10 m, just like with the milliquad. >9 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) 100 times the other. > But if grids in general are built to two decimal places, the centigrade is *unique* and unequivocal, whereas 100 milliquads would suffer from the same problem the L/100 km ratio does! Again, this discussion appears to support that, at least *academically* one should devise and revisit the issue of availability of prefixes. There might be a strong case for the creation of even 4 new prefixes to complete the spectrum from 10 to 0 up to 10 to +/- 6, without exception. >10 The infrastructure for using quads is already in place in >educational institutions at all levels; every right angle need only be given >the additional measure of 'one quad'. Right angles (say in a furniture >building class) would still be called right angles as well as being measured >as one quad; the angles are 'right' because any angle smaller or bigger than >'1 quad' is a wrong angle. >... The above IMV would pose the exact same difficulty as renaming the grade to gon! True, everyone uses 90-degrees, but *everyone* knows it as 'right angle'! If you find this to be worth the effort, then, forcefully, you should also support the same procedure towards the gon. But, is this worth the trouble? I just wonder... >13 The claim that grads, grades, and gons are currently known by the >general community is, I believe, resting on rather shaky ground. When I >first heard about grads, grades, and gons in senior secondary school >mathematics or physics classes, others at my school (who didn't take these >subjects) would never have heard of grads, grades, and gons in any of their >courses. 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 non-existent and they always have been. Interesting yet though that despite this most people would know that there are 100 grades to a right angle, isn't it? Isn't it wonderful how decimal concepts are so simple for general folks to remember, EVEN IF THEY DO NOT USE IT??? This is just an aside comment not related to this discussion though BTW... :-) > On the other hand quadrants >(a.k.a. right angles) surround us all constantly and most people are aware >of them. > Yes, but the fact that they are NOT called 'quads' is a challenge, I'd say! True, it's a minor point, but still, it goes to familiarity, an aspect that speaks in favor of the grade, since this word is at least known by the general population. The introduction of a new word, especially in the context of measurements, appears to pose as a much more challanging issue to address. >14 Using suitable prefixes with quads, milliquads or microquads for >example, means that decimal numbers and decimal points might be avoided for >almost all applications. Using quads, milliquads, microquads and nanoquads >you might never require decimal points. You use the strengths of SI prefixes >to choose the most appropriate (decimal point free) submultiple. The same would hold true of centigrades though! But, again, I see much less need for the use to go beyond 10 to -4, and this one is yet to be required for navigational purposes. >Specifically, if one milliquad (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! > Very good. But why suffer the same problem as the likes of L/100 km? The centigrade is all one would need, Pat. And, actually, pilots would rarely deal with it, but with the grade itself (just like they do to come up with flight plans). Let's leave the 0.01 grade to on-board computers to handle if necessary. ... >Mindsets > >Underlying a lot of the discussions between Marcus and myself is the issue >of mindsets. In our two cases our main differences are between hundreds and >thousands - and I'm not discussing fairy bread at a children's party. Marcus >prefers to divide things into hundreds and I prefer to divide things into >thousands. > Not necessarily, my dearest friend! NOT necessarily. What may perhaps be the underlying problem here is my failure to explain that I respect the needs of particular applications. It just SO HAPPENED that when it came to these two applications I'd favor the centi prefix more than the milli! That's all! I do accept and understand where you're coming from. But, again I must highlight this. There is enough flexibility built into the SI system to accept that FOR SOME CASES the use of hundreds would outweigh the use of thousands. In aviation, for instance, I find it to be CRITICAL that one use THE LEAST amount of digits as possible! The hundreds fill that need very nicely IN THIS CASE. I'm NOT advocating this to be the case *universally*! I obviously canNOT argue against the power of the powers of 3 framework. But I CAN when it comes to certain applications. >Marcus, based on his experience in Brasil (adopted metric measures in 1862) >and Canada, prefers dividing many units into hundredths, such as centimetres >and centilitres, and in the case of plane angles into grads, grades, or gons >(1/100th of a quadrant). > Correction: I do NOT favor centilitres actually!!! I'm into milliliters instead! However, I might see why some would prefer centilitres. >Whereas, based on my experience with the recent metrication in Australia, I >favor dividing most units into thousands; I prefer millimetres, millilitres >and, in the case of plane angles, milliquads. > And I have no beef with that. If the use of millis helped, like you argued, wonderful! But please accept the fact that this may NOT be necessarily so EVERYWHERE or IN ANY CIRCUMSTANCE! So, my message is, let's be sensitive to the needs of specific trades and accept that sometimes what may work here may not work there. >As I've pointed out previously I believe that this is largely a mindset >issue. Marcus was 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 and therefore much faster. > Perhaps this may actually not be as much a matter of mindset, my dear friend, as it is of looking at the *ACCURACY* issue! Let me explain. Millimeters work great with construction because that is the minimum accuracy required for things to work there. However, hundreds here fulfill the needs just as well on a slightly "macrolevel". What I mean is that in general terms one would not need to refer to lengths of stuff ALL THE TIME to that accuracy! Therefore, centimeters would be just fine, you see. But, now with aviation, I see no need at all for us to go beyond the simple kilometer, hence I see no need to delve into an accuracy larger than the centigrade. If one uses the quad, for instance, one would have to resort to deciquad, a quite unusual prefix one should agree... In addition, percentages are entities that are with us so often that EVERYONE relates to them practically immediately, you see. It's all around us: money matters, performance, school grades... you name it! But in the end, I'm not sure this is indeed so much a question of mindset, even though I grant you that we may indeed be more accustommed to using percentages there. But then again, this may also be true around here (you may just not realize it that much). So, in conclusion, I'd like to say that the "unit" to be used should be tied to the question of *accuracy* and trade requirements than necessarily the question of powers of 3. That's why I defended the typo for instance for desktop publishing, because *for that application* 10 to -4 would be just perfect a prefix, you see. I'd venture say that the thing that perhaps hindered the SI system usage taking hold in that industry is *PRECISELY* the lack of a 10 to -4 "unit". At least I can see some effort in that direction by the Japanese with their Q thing. The flaw though in their approach was that they fell prey to the inch-mentality and defined that as 0.25 instead of 0.1 of the millimeter. What can I say?... >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 > Yes, Pat, no argument here, evidently. But please accept the fact also that in general overall terms one would NOT need to refer to dimensions of rooms, places and stuff beyond the centimeter, i.e. why refer to the size of my room as 12 500 by 16 500 mm if simply saying 12.50 by 16.50 m would do, you see? Excellent discussion though. Cheers, Marcus ____________________________________________________________ Get 25MB of email storage with Lycos Mail Plus! Sign up today -- http://www.mail.lycos.com/brandPage.shtml?pageId=plus
