AND, why not? What are the arguments against, using degrees NOW that do not warrant a re-consideration (to hold horses) after 25-30 years, when I pleaded for The Metric Second? If time unit and arc-angle are NOT tied togather, the situation shall go back to where 'metrication started' and caused the failure of French experiment. I had done this exercise and showed that *grad, gon or The Metric degree* were the only solution to tie up 'loose ends in metrication'.First off, we probably all agree that minutes of arc and seconds of arc shouldnot be used for ANY modern purposes.
In my reply usma27190 to Bruce Hubbart in usma27188, I reproduce:
I wish the world had embraced decimal angles and the 1/100000 day second. Then [...] the geographic coordinates and grids on maps would already be tied to kilometers.There are TWO ways to think of THIS.
(1) Time and angle could have been tied earlier: using the day of 20hx100mx100s & dividing the circle into 400-metric degrees i.e. making the 'quadrant on 100-metric degree or *gon* as I learnt later'. This defines Nautical Kilometre; as in my base paper The Metric Second (1973); or
(2) Time and angle could be tied now: using the day of 24hx100mx100s & keeping the circle of 360- degrees unchanged BUT making the 'quadrant of 90-degree and each degree further divided into 1-degree x100 arc-minutes x100 arc-seconds. This defines Nautical Kilometre; as in my posts to USMA list, where I define METRE as:
*�Metre (m') is the distance traversed by light, in vacuum, during the time interval, 1/97059575.22TH of the decimal second�. Since�1/100TH of one degree� is to be the Nautical Kilometre; length distance METRE can be seen as 1/100000th of the degree.*
What lacks had been and perhaps it may still be the 'political will' to implement?
I fear the entire purpose shall get derailed, in arguments, if far reaching effects are ignored again - like these were kept aside, 200 years ago. THIS time, it shall be the education of masses to: plead for 'quad or milliquad' AND NOT resort to call: *Nautical Kilometre as 1/100th of One Degree*, with no changes whatsoever to mathematical table etc.
Brij Bhushan Vij <[EMAIL PROTECTED]>
20031020/12:27 PM(IST)
Aa Nau Bhadra Kritvo Yantu Vishwatah -Rg Veda.
*****The New Calendar Rhyme*****
Thirty days in July, September:
April, June, November, December;
All the rest have thirty-one; accepting February alone:
Which hath but twenty-nine, to be (in) fine;
Till leap year gives the whole week READY:
Is it not time to MODIFY or change to make it perennial, Oh Daddy!And make the calendar work with Leap Week Rule! ***** ***** ***** *****
From: "John S. Ward" <[EMAIL PROTECTED]> Reply-To: [EMAIL PROTECTED] To: "U.S. Metric Association" <[EMAIL PROTECTED]> Subject: [USMA:27226] Re: Angles quads and milliquads Date: Sun, 19 Oct 2003 21:29:48 -0700
Hi Marcus,
Yes, indeed, I was aware of this when I wrote the text copied below. Yes, the
grade is already on calculators, a major advantage over the quad. No, I
don't think grades are generally taught in school, at least not from polling
friends from a variety of countries. Perhaps they were mentioned and most of
us just forget about them since they are so seldom used.
I think the most important point to focus on is whether or not mankind would
be better off measuring angles with the degree define as 1/360 circle, or
with something else. Readers of this list seem to mostly believe that the
preferred unit would be to divide the circle into 4*10^N base units.
First off, we probably all agree that minutes of arc and seconds of arc should
not be used for ANY modern purposes.
Secondly, let's remember that the original killer feature of the metric system
was to extend each base unit by the application of a prefix to make a new
unit that is 10^N the size of the base unit. The advantages are (obviously)
that then we can convert from any unit to any unit by simply shifting the
decimal place appropriately, among other things. This does NOT mean that the
selection of the base unit itself has to be a factor of 10 of something. The
base unit for electrical current is a good example. There's no particular
advantage of the particular definition chosen for the ampere. In fact, it's
pretty arbitrary! The important thing is that we can derive kA, mA,
microamps, etc. from the base unit. Furthermore, we can derive other units
from the ampere (volts, ohms, etc.) that can also be used as base units to
derive kV, mV, etc.
An important question to then ask is why not just stick with degrees? Degrees
are THE defacto-standard unit for angle world-wide. If we simply drop
minutes and seconds of arc and instead use centidegrees, millidegrees, etc.
then 99% of our objections to degrees go away. Furthermore, the second
killer advantage of SI is to have a single, unambiguous global standard.
Degrees are exactly that.
The problem is cartography. That's it! Is it worth it for the world to
replace a broadly accepted ubiquitous international standard with some other
unit just to fix cartography? I will say this: EITHER we stop measuring
angles in degrees in favor of quads or grades or whatever OR we give up
trying to use angles for latitude and longitude and define a meter-based
geographical coordinate system.
Until 30 years ago, it wasn't possible to separate angles and geography, as
cartography was based on astronomical angle measurements. Nowdays, however,
electronic navigation can sidestep the problem. If I fight my perfectionist
urges hard enough, I start to think that this would be a lot more practical
solution than deprecating degrees.
I think it's a bad idea to base the standard datum on a reference surface over
500 meters below sea level. Is your reference surface a perfect sphere? I'm
afraid I just don't see the advantages. At the surface (where it matters),
your great circle grade will still not be 100 km.
John
On Sunday 19 October 2003 16:58, Ma Be wrote:
> 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
>
>
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