Dear John, Most (if not ALL) of the positive points you highlighted about the quad can ALSO be said of the grade! I'll try making that clear below as we go.
On Sat, 18 Oct 2003 19:55:13 John S. Ward wrote: >Yes Pat, I'm behind you 100%. Your proposal of the quad has big advantages >over degrees, minutes of arc, seconds of arc, grads, grades, gons, etc. I >like your points about the "centigrade" and the "centigon"! > The above points, though valid, are overshadowed by similar situations like I described in my reply to Pat (for instance, the day we turn small k to capital K and the "possible" confusion with the Kelvin unit). Though true, given the fact that angles can never be confounded with temperatures, we should not be annoyed by this similarity. >To strengthen your arguments, I suggest avoiding calling a quad the natural >unit of plane angles. The official SI unit for plane angles, officially >dimensionless but often called the radian, is arguably more natural than the >quad. However, the quad is far more practical for most non-scientific use, >so I suggest SI should define the quad and call it a unit accepted for use >with the SI, and discourage the use of degrees, etc. > We could *already* achieve that with the grade, whereas we would face a significant battle with the quad. First of all we'd need to get quad accepted as a word to replace 'right angle'. Then we'd have to have every country on earth accept its teaching, and THEN, ONLY then, we'd consider its status vis-a-vis BIPM's acceptance of it. >Quads have a couple coincidental advantages aside from the obvious ones you >pointed out, including: > >1 centiquad is about 1.11 degrees. Anyone who has a good intuitive feel for >degrees should have no problem adapting to the centiquad. > The same holds true with the grade, too! By the way it's NOT 1 cq = 1.11 degrees, but the other way around, i.e. 1 degree = 1.11 cq! Therefore, 1.11 grade = 1 degree. With the advantage that it's not *centi*quad, but the unit *itself* holding that relationship! >1 quad is about 1.57 radians. Thus a mq is 1.57 mradians, the microquad is >1.57 microradians, etc. Note that this is an important advantage, since the >quad will have to coexist with the radian. Again, because the definition of the quad and grade differs by only a decimal point (1 q = 100 gr), the relationship above is also true with the grade!!! >... >Realistically, replacing the 360 degree circle with the 4 quad circle faces a >major uphill battle, probably pretty close to impossible. Unfortunately I must concur with the above comment. However, I'd say some ray of hope to get the grade going again. If my UNS gets acceptance by the avionics industry we would have won a major battle!... ;-) > Nonetheless, I >propose the following path for the global adoption of quads: >... >2.) Try to get the attention of NIST and the BIPM, or at least of people >within NIST and the BIPM. > Interesting proposal. But one could think of doing the same with the grade. >3.) Keep in mind that angle measurement is intimately tied to astronomy. For >example, the 4-5 thousand year old origin of the "degree" is that it is >(almost) the angle that the earth sweeps out around the sun in one day. As >an astrophysicist, I can attest that dealing with coordinates measured in >degrees, minutes, and seconds of declination and hours, minutes, and seconds >of right ascension is a major pain! Indeed! We read you and I concur! > Getting astronomers to adopt the quad >would be a major victory and bring instant credibility to the unit. > Similar succes could also be achieved with the grade though... >4.) The second big arena where we need quad embracement is >geography/cartography. Actually I consider this to be THE major obstacle! One we get these guys to accept decimalization of angles (quad or grade) a MAJOR hurdle would have been overcome! > Keep in mind that while for great circle routes one >mq will be very nearly 10 km, it's not exact, both due to the error in the >original standard meter bar and because the earth isn't a perfect sphere. True, hence my proposal incorporating the needed UAR (universal altitude reference) of ~531 m below current SEA level. BUT, the mq does NOT have enough accuracy to serve its purpose for navigation. We'd need an **extra decimal place** to get it to the adequate 1-km minimum accuracy. And THIS is one of the major reasons for my choice falling on the grade scheme. Please note: mq: not enough, we'd need xxx.Y mq for it to be useful. So, if one would be using a decimal place ANYWAY, we might as well use what we already have at our disposal: the centi, while the 10 to -4 prefix does not yet exist and would be needed with the quad construct. Evidently if we support the creation of the ty (10 to -4), both would be in "equal footing" in THIS REGARD. ... >5.) If you get to the point where quads are being used, then you would have >to convince calculator manufacturers, software writers, measuring tool >manufacturers, etc. to all support quads. > And here there is a MAJOR victory for the grade, *ALREADY*! All calculators that I know of DO carry the grade! Therefore, from this point-of-view, grade already won!... ;-) >6.) Governments would have to globally require the quad be taught in schools >at all levels, including math, science, and vocational classes. But no such requirement would be needed for the grade, since this system ALREADY IS taught around the world, John!!! > Furthermore, >they would have to agree to outlaw degrees, minutes, seconds, grads, etc. > Here we both strongly agree! >I would like to point out a minor geometrical detail about the quad. We tend >to not use fractions with the metric system: 1/3 of a m or 1/3 of a kg have >no particular special meaning, and are better specified as 333 mm or 333 g, >rounded appropriately to the required precision. However, 30, 60, 120... >degree angles are geometrically special, conceptually exist independently of >how you measure them, are mathematically exact, and are a common angle in the >real world. To deal with this, you would sometimes need to use fractions. >For example, a "1/3, 2/3, 1 quad triangle" instead of "30, 60, 90 degree >triangle." At least we can say this inconvenience is pretty minor compared >to the inconvenience of angle measurements in degrees, minutes and seconds! > We, again, agree 100% here. True, these "special angles" would pose as a problem for either quad or grade, but this is a minor point indeed. Both would still be useful, especially because navigation falls on ANY angle from anywhere, so this is moot. >Pat, please forgive me for saying that your arguments against the quad are >anything but convincing. I only see TWO arguments against the quad: the >difficulty in overcoming 4000+ years of measurements in degrees, and the >necessary coexistence with radians. >... Agreed, again. But I see no major obstacle for both radian and grade coexisting peacefully. So... In summary, this is what makes (*TO ME*) the scale tip in favor of the grade vis-a-vis the quad in the end: 1) We'd have ONE less digit to deal with, just like it already is with the degree construct. Example: 58 gr versus 580 mq! (Notice 2 digits versus 3 with the quad), with all the advantages this would entail, like the statement of angles in airport runways, e.g. from 00 to 39 for the grade. Dealing with the minimum amount of digits is a practical must for flying personnel. 2) Required accuracy to 1 km -> 1 cgr versus 0.1 mq. Marcus ____________________________________________________________ Get 25MB of email storage with Lycos Mail Plus! Sign up today -- http://www.mail.lycos.com/brandPage.shtml?pageId=plus
