Dear Marcus, I haven't forgotten our discussion, I've just been a little busy.
Our discussion of measures of plane angle has taken on the appearance of a bush fire that is burning on many fronts. Let me summarise. We agree that: 1 The issue of plane angle measures needs to be reconsidered. 2 The radian is not a suitable unit for popular or common use We disagree about: 1 The angle to use as an SI unit: you favor the circle while I favor the right angle (which I call a quad). 2 The number of divisions: you favor 100 divisions in a circle while I favor the division of the right angle by 1000 (into milliquads). 3 You favor a connection between clock angles and plane angles while I prefer to break any nexus between them and to consider the best alternatives for each separately. Do you think that this is a fair representation of our respective positions? Cheers, Pat Naughtin CAMS Geelong, Australia > On Thu, 27 Jun 2002 08:11:33 > Pat Naughtin wrote: >> Dear Marcus and All, >> >> Thank you for your kind thoughts. I have interspersed some remarks. >> > You're welcome, Pat. :-) Let's then take a look at your remarks below. > ... >> Let's take one thing at a time (tee hee). I disagree that we should maintain >> the nexus between angle and time. This connection has now outlived its >> worthlessness. > > Well... I'm very sorry for saying this, Pat, but I honestly can't see how we > could even do that as these ARE intrinsically connected for at least two > applications that I can see, aviation and time zones. > > Please let me explain, at least the latter one, since it's the simpler to go > about. > > Time zones around the world are defined based on their longitude location on > the sphere of our planet, which is basically an "angle". In other words, in > order for us to define where on earth it's, say, 14:00, we need to check the > location's "angular" position on the surface of our planet, which will prevail > for a *segment* thereof (nowadays, usually a 15-degree "slice" per hour of > time). > > Tiing this to aviation/navigation, it would be much easier for aviation folks > to deal with latitude/longitude issues if they could relate decimal angles and > distances with decimal time. It would be a real no-brainer. Not so, though, > with this stupid 65-deg 13' 15" crappy stuff surveyors insist on pushing on us > (and it's very unfortunate that this thing is plaguing GPS instruments and > all... !#$%#$...) > > True, not all time zones are rigorously thus defined, it's currently actually > quite a mess. However, we *could* fix that when introducing decimalization to > these entities, or, if not, at least retain the principle. I'm certain that > with technology becoming more and more a part of our lives, that the > introduction of this more rigorous "mathematical" approach to time/location > would make everybody's lives much easier (again, I'm aiming at the future > here, Pat). > >> The connection between angle and time has inhibited progress >> in the measurement of both angle and time - now is the time (more tee hee) >> to separate the two so that we can move forward. >> > Please, see my comments above. However, I'm not sure that such 'connection' > has indeed been inhibiting 'progress' in both fields. I'd say that > professionals in *both* fields are to blame for this (plus, evidently, > people's resistance to change...), since they haven't been bold enough to > volunteer definitive changes to both areas. > ... >> One obviously good way to break the nexus between angle and time would be to >> choose the right angle as the SI base unit of plane angle and leave the >> circle to the time and calendar folk. >> > (One additional personal note/observation before I proceed though is that I > wouldn't want to see this 'nexus' broken. I personally like this > "parasitical" relationship between both of these concepts. Perhaps maybe > because of my aviation background, I don't know. Still... And even if we do > "succeed" in breaking this 'nexus' I'd still think that if there were an > advantage somewhere, somehow to use a hypothetical "reconnection" between > them, it would certainly be easier and more straigthforward if structurewise > they were both decimalized and "related" to each other the way(s) I proposed) > > I'm not sure I understood your digression about angle above. Angles and > circles are intrinsically "connected" entities (at least that's what we learn > at school, especially in trigonometry classes...). So when one talks about, > say, 'right angles' one is talking about a section of a circle. > > I just sense that there could be serious definitional difficulties with your > approach, Pat. > >> As a side issue here we could consider the practicalities of introducing a >> circle into (say) the building industry by telling all of the trades that a >> circle is an angle. This will take some time. >> > ? I'm no 'builder', or of the profession, but from what I know I'd say that > they already consider it this way, don't they? (Please, anyone in the field > correct me if I'm wrong. Thanks) > >> Noting that the radian has already failed to become a popular unit of plane >> angle - with the continued use of Babylonian units - I believe that an angle >> that looked like an angle would have more success. A right angle looks like >> an angle, while a circle does not look like an angle. > > Let's please go in parts here. First, the radian issue. The main reason, I'd > say that the radian "failed" in popular parlance is the fact that it's > undeniably intractable and cumbersome. Referring to angles like pi over 4, > pi, pi over 2, etc, is a nuisance to practicality. (let's just please imagine > us creating a compass to measure angles with such "values" especially > considering that "round" values would have absolutely no significance, > usefulness or meaning, i.e. the scale would be useless, 1, 1.1, 1.2 rd etc...) > > Second, 'a circle does not look like an angle'. I don't think the case here > is a one of "looks", but of *definition*. We're told by academics that > circles (even the whole one) ARE angles, they're 360-deg ones. We even use > the artificiality of drawing a single straight line from the center of the > circle to the circumference of it (usually at the top) to denote this... > "angularity" (and some would even add a smaller circular arrow ending to the > left of this vertical line to indicate it). Again, I'm sorry for saying but I > don't know how to take your comments here, Pat. > >> On the other hand a >> circle looks like a circle and I know that it would take a long time and a >> lot of education to convince building workers (and the general population) >> that a circle is an angle. >> > Please, see my earlier comment, i.e. that it came as a surprise to me that > they wouldn't already. > >>> The tie-up to this approach would clearly be beneficial for aviation, >>> geographers, surveyors, etc, in the long run. >> >> Marcus, could you elaborate on these advantages. I do not have any >> experience in aviation so I cannot see any advantages of tying angle and >> time together. > > I'll try my best, Pat. Besides the examples I've cited earlier in this post I > can think of the following. For example, popularly, we, pilots (especially > fighter pilots), are used to say things like "2 o'clock" position, "4 > o'clock", etc when referring to angular positions in the sky. True, this may > sound like sillyness, but nonetheless in people's minds they do make this > harmless connection which in their thinking would convey information in > simpler terms than saying 270 degrees, or 120 degrees, etc. > > We do not per se use a connection time/location to do things in aviation. > However, if charts were gridded with decimal units, as opposed to stupid > nautical miles, simple navigational parameters could be more easily made. If > time were also decimalized "in tandem" with that we could benefit from it by > working in *either* approach. I.e. given a known flight speed we could just > look at city positions as if on a clock and come up with flight times, etc. > > For instance, say Chicago to Seattle is equivalent to 10 "hours" (where my > hours is the "new" hour, 100 hours in a day, 100 units in a circle) in my > "watch", or circle. Let's say the "rule of thumb" is 1.8 (i.e. it would take > 180 "hours" for the aircraft to complete a tour of the earth). Travelling > between two cities spaced 10 "h" apart would then take, 18 "h". GPS-based > instruments could even show a "slice" calibrated with final decimal time > scaling making this even more effortless! One could look at a slice of the > sphere and *read* time directly from the "watch" for *any* two cities apart!!! > Cool, isn't it? ;-) > >> My suspicion is that because the connection between angle and >> time has prevented development in either, we have simply retained the >> Babylonian measure because it is too difficult to change two things at once. >> When you try to reform time the angle folk squeal, and if you decide to try >> reform of angle the time folk scream. Either way, it is probably possible to >> reform one thing at a time if you can break the connection. >> > Hmm... You may be right. On the other hand, if we could get these 2 folks > together and show them how beneficial it could be for them to work together on > this one we could get something done. > ... >> The error is sleight; the value is close enough for almost all purposes. As >> we can quite comfortably say that a litre of water has a mass of a kilogram, >> so we can say that it is 10 megametres from the equator to the North or >> South Pole. >> > True. And I see this as another reason why this continued 'connection' could > work and be beneficial for both camps! My personal take, of course. > > Marcus > > > Is your boss reading your email? ....Probably > Keep your messages private by using Lycos Mail. > Sign up today at http://mail.lycos.com >
