What's on your longitude?

[vtk]

I'll rephrase my previous post:

I just dislike lat-lon or loxodrome or similar methods of determining "direction" of one place relative to another because they place too much importance on cardinal directions, implicitly suggest that those cardinal directions are constant non-locally, and, in some cases, expose people's Mercator-like flat world view.

I didn't mean to say that latitude and longitude and the cardinal directions aren't useful for other purposes, or that they aren't based on measurable physical realities. 

Anyway, my great circle generator is now online.  http://vidthekid.info/misc/greatcircle.php  Your browser will download the result as a KML file, which most people would view in Google Earth.  (Note: when Google Earth loads the file, it may initially zoom to a really weird view where you may or may not be able to see the line.  But it shouldn't be too hard to find, just zoom out a bit more and spin the globe some...)  If you enter your home longitude/latitude and a direction of "0" or "180", you will get a line of longitude through your home (and around the other side of the planet).  If you enter your home longitude/latitude and a direction of "90" or "270", you get a line showing what is due east and west of your home, from the perspective of your home, as discussed above.

[english si]

implicitly suggest that those cardinal directions are constant non-locally

No cardinal directions are constant, that's the whole point of cardinal directions. If I travel 10 miles east, then travel 10 miles west from that point, I end up where I was - because east and west are constant (and opposite) vectors, wherever you are.

expose people's Mercator-like flat world view.

I'm trying to work out why you think this is: that using spherical coordinates exposes people's view that the earth is flat, not a sphere. It makes no sense

line showing what is due east and west of your home, from the perspective of your home, as discussed above.

No, you don't, as that is not what East and West are. Call them Turnwise and Widdershins if you wish, but they are vectors that aim to be constant wherever you are on the sphere.

If you travel your 'east' 10 miles, and then travel 'west' from there 10 miles, you end up somewhere else. While they are 180 degrees apart when you measure them, they are relative vectors depending on starting location (as opposed to the constant vectors that east and west actually are). I also, heading 'east' will change latitude - rather than being a vector that isn't at all north or south.

Lat-lon and East-West ways of explaining position and direction rely on the earth being spherical.

[Alps]

If I am "looking due east" while stationary, I agree that my line of sight in fact follows the great circle and not the latitude, because my line of sight is perpendicular to my vertical vector from the Earth's core. Conversely, if I am "traveling due east," I am constantly compensating and therefore following the latitude. The difference between the two at any given point is in fact zero by definition - one is a curve of large radius, and the other is a tangent to that curve.

[Duke87]

If I am "looking due east" while stationary, I agree that my line of sight in fact follows the great circle and not the latitude, because my line of sight is perpendicular to my vertical vector from the Earth's core.

No, your line of sight heads off into space over the horizon because the surface of the Earth is curved and a line is not.

But yes, if you project straight "down" from that line of sight to the Earth's surface, you get the great circle.


Actually, this would make for an interesting alternate definition of facing Mecca, where you not only need to get the bearing right but also tilt your head down at the right angle to be looking directly at it in 3D space. At Mecca's antipode, you would look straight down.

[vtk]

English, you apparently misunderstand most of what I dislike and/or why.  But that's okay; it's only my preference and nobody else needs needs to understand it.

But I would like to clarify one point, and then ramble a little.  The cardinal directions are not constant.  East in Ohio is quite a different direction from East in Poland.  (Substitute any other compass azimuth in that sentence and it's still true.)  You can travel East, following a curve of constant latitude, and say correctly that you have been travelling due East the whole time; but you have not been going in the same direction the whole time, because East changed gradually as you moved.  Likewise following a great circle path isn't without its own change in direction, but that change is minimal for given endpoints.

If you and I start in Columbus and you follow the 40th parallel around the world while I stay here, I'll watch you depart due east of me, but after a while you'll be northeast of me. Then north of me, then northwest of me, and then finally you'll arrive again from due west.  At least, that's how I'll perceive your journey – part of that's my vantage point, and part of that's my choice.

[english si]

If you and I start in Columbus and you follow the 40th parallel around the world while I stay here, I'll watch you depart due east of me, but after a while you'll be northeast of me. Then north of me, then northwest of me, and then finally you'll arrive again from due west.  At least, that's how I'll perceive your journey – part of that's my vantage point, and part of that's my choice.

Well yes, American* that is how circles work... All the time I would be objectively due east of you, following that circular vector (something you would expect on a sphere). I'd also never get more objectively north or south than 40N - a great circle would be on 40N for a tiny amount of time, and then get to 40S (where the antipode is).

My whole problem with your idea is that east is different in Colombus than in Madrid or Beijing (both just about at 40N), or even Indianapolis and Philadelphia. And, because I will actually be travelling north and south at certain points, and east at precisely two points (Colombus and the antipode), I wouldn't travel through Philly, Indianapolis, Madrid or Beijing - despite them being on a line that isn't north or south at all.

You make direction about where you, as an observer, are - where I am they are different directions: 10000km along your east line, I would be heading due south by my, the travellers, reckoning. That's not a good, or useful way to describe direction!

You are taking 2-d geometry and imposing it onto a 3-d sphere.

*calling me 'English' like it's my name? do you not understand adjectives?

[vtk]

What's east of me is not the same as what's reached by travelling east. To me, those are two different concepts.  That's my whole point. When you insist that they are the same, it sounds to me as if you are the one imposing 2D geometry on a 3D sphere.  It all amounts to a differing opinion on the definition of "is east of".  Clearly I won't persuade you to adopt my definition, but I want at least for you to understand my definition and recognize that it makes sense in its own way.  In recognition of your definition's validity, I'll make a loxodrome KML generator soon, which will (for example) show a line that runs constantly due southwest starting in Buckinghamshire. (Meridians and parallels are the special cases of loxodromes for the directions north/south and east/west.)

And yes, I called you "english" as if it's your name. Not because you are from England, but because your "name" on the forum appears as "english si".  I simply shortened it, like how Bill Clinton calls his wife Hillary and not Hillary Clinton.  Do you expect me to know your real name?  That may or may not be a reasonable expectation, but I have trouble with that sometimes.

[jp the roadgeek]

Baffin Bay, Nunavut, Hudson Strait, Shawnigan PQ, Trois Rivieres PQ, Smuggler's Notch ski area, Killington/Pico ski area, Stratton Ski Area, New Haven, CT, NWS Brookhaven Laboratory, TWA Flight 800 Memorial, Mayaguana, Western Haiti, Venezuela, Columbia (100 mi east of Bogota), Peru, Pacific Ocean, Chilean coastal region, Antarctica just west of the peninsula, South Pole,

[kphoger]

Actually, what's on your latitude isn't necessarily due east or west of you. For that, you want the great circle which reaches maximum latitude as it passes through your home.

I have never heard this interpretation before!  so your definition of "due east" is to follow a route which is the precise circumference of the earth, and crosses the equator twice, going through your antipodal point as well?

one result of this interpretation is that if you live at the north pole, the south pole is due east of you - and you may choose any pair of opposing longitude lines to get there.

I do not believe this to be the correct mathematical definition, but it does yield an interesting locus of points.

Yes, your summary of my interpretation is correct. Whether or not it is correct depends on whether you're thinking about traveling constantly due east, or looking due east from a stationary point.  But I'm pretty sure Muslims at the same latitude as Mecca don't face due east or west when they prey, but rather in the great-circle direction.

Bear with me, as I have not taken a math course in probably eight or nine years.  Can you explain to me why you think of "east" (for example) as traveling along a great circle at all, and why you choose to include a location's antipode rather than any other point in determining the path of that circle?  Is it because that circle will always form a right angle with the meridian?  It just seems totally counterintuitive to say that, when agentsteel53 was in Puerto Natales, Patagonia, he was directly east or west of Lake Baikal (Ulan Ude, Buryatia).

[agentsteel53]

Bear with me, as I have not taken a math course in probably eight or nine years.  Can you explain to me why you think of "east" (for example) as traveling along a great circle at all, and why you choose to include a location's antipode rather than any other point in determining the path of that circle?  Is it because that circle will always form a right angle with the meridian?  It just seems totally counterintuitive to say that, when agentsteel53 was in Puerto Natales, Patagonia, he was directly east or west of Lake Baikal (Ulan Ude, Buryatia).

if you look in a direction in such a way that the horizon is level, you will have half of the earth to either side of you.  consequently, you must be looking down a great-circle line. 

at your location, there are an infinite number of great-circle lines, each corresponding to one direction you could be looking in.  each of those great circles, by definition, goes through your antipodal point.

to make this easier, assume you are at the south pole.  each of your great circle possibilities is a pair of longitude lines, and thus passes through your antipodal point: the north pole

so, to generalize, assume you are choosing your own location to be the "south pole", ignoring the earth's axis, and draw longitude lines, which are great circles... if the south pole is in Puerto Natales, then the north pole is in Ulan Ude. 

[A.J. Bertin]

I just had a chance to look at my own line longitude from my neighborhood in Grand Rapids, Michigan.

Looking north, the only places of any significance are Traverse City, MI, the Hudson Bay, and the North Pole. Looking south, these are the places I found:

• Kalamazoo, MI (the west side of town)
• Gas City, IN
• Louisville, KY (the far east end of the city)
• Edmonton, KY
• Jasper, TN (the east side of town)
• Piedmont, AL
• Tuskegee National Forest (AL)
• Newton, AL
• Slocomb, AL
• Springfield, FL (an apparent suburb of Panama City)
• Eastern Honduras
• Western Nicaragua
• Northwestern Costa Rica
• South Pacific Ocean
• South Pole

This was fun to explore!

[kphoger]

Bear with me, as I have not taken a math course in probably eight or nine years.  Can you explain to me why you think of "east" (for example) as traveling along a great circle at all, and why you choose to include a location's antipode rather than any other point in determining the path of that circle?  Is it because that circle will always form a right angle with the meridian?  It just seems totally counterintuitive to say that, when agentsteel53 was in Puerto Natales, Patagonia, he was directly east or west of Lake Baikal (Ulan Ude, Buryatia).

if you look in a direction in such a way that the horizon is level, you will have half of the earth to either side of you.  consequently, you must be looking down a great-circle line. 

at your location, there are an infinite number of great-circle lines, each corresponding to one direction you could be looking in.  each of those great circles, by definition, goes through your antipodal point.

to make this easier, assume you are at the south pole.  each of your great circle possibilities is a pair of longitude lines, and thus passes through your antipodal point: the north pole

so, to generalize, assume you are choosing your own location to be the "south pole", ignoring the earth's axis, and draw longitude lines, which are great circles... if the south pole is in Puerto Natales, then the north pole is in Ulan Ude. 

So, if I look due east by the compass, my theoretical line of sight (if not extending into outer space) would go through my antipode.  Right?  So, if you looked due east from a hotel in Puerto Natales, then you would supposedly be looking directly towards Ulan Ude?  That makes sense, although I still contend that your line of sight would extend into outer space.

[NWI_Irish96]

I just had a chance to look at my own line longitude from my neighborhood in Grand Rapids, Michigan.

Looking north, the only places of any significance are Traverse City, MI, the Hudson Bay, and the North Pole. Looking south, these are the places I found:

• Kalamazoo, MI (the west side of town)
• Gas City, IN
• Louisville, KY (the far east end of the city)
• Edmonton, KY
• Jasper, TN (the east side of town)
• Piedmont, AL
• Tuskegee National Forest (AL)
• Newton, AL
• Slocomb, AL
• Springfield, FL (an apparent suburb of Panama City)
• Eastern Honduras
• Western Nicaragua
• Northwestern Costa Rica
• South Pacific Ocean
• South Pole

This was fun to explore!

Sounds like you are just a couple miles east of me.

[The High Plains Traveler]

To the north, my Longitude (about 104° 46' W) passes through Aurora, CO, just west of DIA; just misses Regina, SK to the west, hits the east end of Lac La Ronge, and passes through the Barren Grounds of Nunavut. I'm looking for tours now.

To the south, it passes just west of Durango, Mexico, and enters the Pacific at La Manzanilla. Liquid water and ice from there south. A pretty unexciting piece of longitude.

[agentsteel53]

So, if I look due east by the compass, my theoretical line of sight (if not extending into outer space) would go through my antipode.  Right?  So, if you looked due east from a hotel in Puerto Natales, then you would supposedly be looking directly towards Ulan Ude?  That makes sense, although I still contend that your line of sight would extend into outer space.

no, your line of sight would indeed go into space.  if you travel in a straight line along your initial line of sight: the horizon falls away and you keep going straight, and you gain elevation and reach what is defined to be 'space' eventually.

your line of site, as projected down (toward the center of the earth), and in no other direction off to the side, would indeed be a great circle and go through your antipode. 

so, assume you looked east and fixed your line of travel to be in that direction.  you walk straight forward, treading over the earth in the same direction without changing course.  you are traveling a great circle, and it is the concept of "east" which has changed direction on you.  Natales and Ulan Ude are opposite of each other, and you just happened to start out east when leaving Natales, but your direction changed since your great circle is tangent to an east-west meridian only at Natales (and again at Ulan Ude).

[kphoger]

Yeah..... that didn't help at all.     Perhaps it's best understood by turning a globe on its side and asking if the "new" lines of latitude actually run east-west?  After all, if the earth is a sphere (almost), then what holds true for north-south ought to hold true for east-west–especially if we're talking about common sense as it relates to common observation.



If we can't come to grips with the red lines being truly east-west and the blue lines being truly north-south, then perhaps we need to reevaluate our conceptions?

[agentsteel53]

take that rotated globe, and draw a line straight up and down the middle of it.  that is a great circle that goes through,  oh I dunno, looks like Mexico City. 

it is tangent to a blue line (perhaps even the drawn blue line which goes through the center of the circle - it's a bit off but for the purposes of this conversation assume that the sixth blue line from the left is drawn just a bit to the right).  that blue line is the east-west line through Mexico City.  our new line, the great circle, is tangent to it, and goes east-west at Mexico City.

it does not go east-west other than at Mexico City (and Mexico City's antipodal point), and that is okay. 

what holds true for north-south ought to hold true for east-west

plenty of things do not hold true for east-west and for north-south.  latitude lines are all parallel; longitude lines all intersect at the poles, as one example.

[kphoger]

what holds true for north-south ought to hold true for east-west

plenty of things do not hold true for east-west and for north-south.  latitude lines are all parallel; longitude lines all intersect at the poles, as one example.

Right.  But, it seems reasonable to expect us to think of north and south as having the same relationship to each other as east and west.  Which is to say, it does now strike me as odd that we speak of going "due north" as following a great circle (line of longitude), whereas we speak of going "due east" as not following a great circle (line of latitude).

I'm just trying to wrap my head around the problem, and this is the way I'm thinking about it.

So here's my modified globe to reflect your suggestion:

[agentsteel53]

Right.  But, it seems reasonable to expect us to think of north and south as having the same relationship to each other as east and west. 

locally, sure, if you don't spend much time at the north or south pole. 

using great circles for east-west navigation does indeed cause quite a bit of trouble - mainly, their non-transitive relationship as NE2 pointed out, which makes absolute location references require more than just a "zero" line, rendering them functionally unwieldy.  this is why the standard latitude/longitude system is accepted so widely. 

but it is still interesting to think about "what lies on the great circle which passes through your location due east-west?"

[kphoger]

Basically, we just need an East Pole and a West Pole, and then we'd all be happy (as long as we switch to metric).

[The High Plains Traveler]

The earth doesn't rotate about the intersection of the great circle from my latitude and the equator.

[kphoger]

The earth doesn't rotate about the intersection of the great circle from my latitude and the equator.

Understood.  But, when people talk about going due north or due west, they typically don't have the earth's rotation in mind.  At least, when I look north up a highway, I don't think differently about it than when I look east down a highway.  It's only when I start thinking about the lines of longitude and latitude converging or not converging that I start to think differently about the directions.  And I now understand how that's sort of an artificial distinction, since I don't actually observe the rotation of the earth while driving down the road.

(And, yes, it would be weird for the earth to rotate about a point on its surface.)

[agentsteel53]

(And, yes, it would be weird for the earth to rotate about a point on its surface.)

very.  having a single point stay constant, as opposed to an axis, is very very strange to try to visualize for a three-dimensional object.

[english si]

What's east of me is not the same as what's reached by travelling east.

yes - the latter is a vector staying on the same latitude, the other is a positional statement.

London is east of me, even though the true vector has a large southerly component and I'd skim the northernmost suburbs if I travelled east.

Your version of 'traveling east' is a straight line that is only east at one point, but north, south and west at three others.It is also not reciprocal with 'traveling west'.

When you insist that they are the same, it sounds to me as if you are the one imposing 2D geometry on a 3D sphere.

1)where was I insisting they were the same?

You are the one treating east as a straight line as if the world was flat and thus a direction with a definition of 'perpendicular to north-south lines' can be straight, rather than curved.

Your use of great circles may have merit, but to call it 'east' is just totally wrong.

It all amounts to a differing opinion on the definition of "is east of".

Yes, and you are using a totally different one to everyone else.

And yes, I called you "english" as if it's your name. Not because you are from England, but because your "name" on the forum appears as "english si".  I simply shortened it, like how Bill Clinton calls his wife Hillary and not Hillary Clinton.

Yes, his first name. You don't call Red Eric 'Red', do you.

Do you expect me to know your real name?

I've given you a shorted version of my first name. What else do you need to not call me an adjective?

That said, you seem to think that traveling due east means travelling west at some point (that is some good doublethink there!), so a grip on concepts in the English language like adjectives might be lost on you...

[agentsteel53]

You don't call Red Eric 'Red', do you.

first I'd heard him called that... on this side of the pond, he is Eric (or Erik) the Red. 

that said, given that your username is all lowercase, it is not completely intuitive to parse "si" to be a shortening of a name.  (Simon, Silas, Siberian Husky, etc.)  if your name were "prelude si" I would not hesitate to call you "prelude".