Dear Marcus, Thanks for your thoughts. However, it is Monday morning, here in Geelong, so I won't get a chance to consider your arguments for a few days.
Cheers, Pat Naughtin LCAMS Geelong, Australia -- on 20/10/03 5:02 AM, Ma Be at [EMAIL PROTECTED] wrote: > 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 >
