I pondered the question, "What if I head due north? Where have I already been on my exact longitude?" So, I traced it out. Here's what I found:
My longitude comes ashore at the Trump Taj Mahal in Atlantic City, crosses the east corner of Great Adventure, and passes through Rutgers just east of New Brunswick. It heads up through Edison and my apartment to downtown Middletown, NY and passes just west of Johnstown on its way to Long Lake in the Adirondacks (NY 28N/30 junction). It crosses into Quebec just east of Fort Covington, NY, between QC 132 and 138, and scrapes Ontario twice, running through Voyageur Provincial Park the second time. After heading west of Lachute, civilization starts disappearing; it crosses the TCH (QC 117) a few kilometers northwest of Ste-Agathe-Nord, and the last place I could drive to on my line of longitude is latitude 51, along the roads around Réserve Faunique Assinica and Lac Mistassini.
Longitude is sort of boring for those of us in the west, because of the way South America goes east- latitude is more interesting. That said, the furthest north I can drive is the Fort Smith Highway in the NWT, the largest city on my longitude is Drumheller, Alberta (pop 8,029), and the furthest south I can drive is Mexico Highway 1 in Baja California Sur. I am at the same longitude as the Great Salt Lake, but that's it.
The only towns my longitude hits in the USA, Canada, and Mexio are Gila Bend AZ, Wickenburg AZ, Dugway UT, Deer Lodge, MT, Drumheller AB, and Stettler AB. It does come quite close to Lethbridge.
I-15 crosses my longitude five times- 4 times in Montana and once in Utah. My longitude crosses I-90, I-15, I-86, I-84, I-80, I-40, I-10, and I-8.
My longitude is about 200 feet east of the southern terminus of US 93.
My longitude goes through Valencia, Spain, the Western suburbs of London, UK, and Scarborough, UK, where the northernmost roads in my longitude are found (Most notably A165).
Some time ago I found the Greenwich meridian (24' East of mine) goes through a town named Berbegal (Spain, near where I live), and therefore I no longer call it the Greenwich meridian, but the Berbegal meridian.
Broad brush strokes - a couple of miles corridor (what I can see on the 500m/2000ft zoom level on google):
Arctic Ocean - North Sea - Whitby, western Lincoln suburbs, Rushden, me, Slough, Guildford, Angers, Saintes, Bordeaux, just w of Alicante - Mediterranean - Oran, just e of Winneba - Atlantic Ocean
The Sahara is worse than knowing that there's nothing beyond Mexico/California before the South Pole. I got to the point, thinking it was broken as there was about 500 miles of nothing, except at one point the Algeria/Mali border - just ceaseless beige until south of the Niger, then it was broken up a bit more, with the odd road, or village name, or green area.
CNGL (at 24' West) is about 11 arcminutes east of me (at roughly 35' West) - corresponding to next to no time. We both had solar noon 59 minutes ago. Roughly going through Beverley, Hessle, Sleaford, Luton (yuck), Watford (my birth-place), Goring-by-Sea in the UK, that's about 10 miles west of my longitude at these latitudes.
Hudson Bay
Lake Superior
Upper Michigan
Lake Michigan
Grand Rapids, MI
Anderson, IN
Jeffersonville, IN/Louisville, KY
Corner point common to TN/AL/GA
Tuskegee, AL
Panama City, FL
Gulf of Mexico
Caribbean Sea
Trujillo, Honduras
Lake Nicaragua
Western Costa Rica
Pacific Ocean
My longitude goes through Lake Michigan and the north and south poles. :-D
Quote from: Steve on May 09, 2013, 12:25:28 AM
I pondered the question, "What if I head due north? Where have I already been on my exact longitude?" So, I traced it out. Here's what I found:
My longitude comes ashore at the Trump Taj Mahal in Atlantic City, crosses the east corner of Great Adventure, and passes through Rutgers just east of New Brunswick. It heads up through Edison and my apartment to downtown Middletown, NY and passes just west of Johnstown on its way to Long Lake in the Adirondacks (NY 28N/30 junction). It crosses into Quebec just east of Fort Covington, NY, between QC 132 and 138, and scrapes Ontario twice, running through Voyageur Provincial Park the second time. After heading west of Lachute, civilization starts disappearing; it crosses the TCH (QC 117) a few kilometers northwest of Ste-Agathe-Nord, and the last place I could drive to on my line of longitude is latitude 51, along the roads around Réserve Faunique Assinica and Lac Mistassini.
Does it run into anything of note in South America?
Mike
I'm aligned with Brooklyn and the Bronx, straight through the Botanical Gardens.
Going north.... The northern terminus of I-29, six bazillion lakes, the North Pole.
Going south.... Fort Worth (TX), Corpus Christi Bay, South Padre Island, the part of México's Highway 150(D) that crosses over itself in the mountains, the South Pole.
88 degrees, 08 minutes west (http://en.wikipedia.org/wiki/88th_meridian_west). It passes through Canada's Arctic, Hudson's Bay, Ontario, Lake Superior, Michigan's UP (Keweenaw Peninsula), Wisconsin (Milwaukee), Illinois (including Joliet), skips by Indiana along the Wabash River, Kentucky, Tennessee, Alabama, Mobile Bay, south into Mexico's Yucatan and Quintana Roo, through Belize, Honduras, and El Salvador before entering the Pacific Ocean.
Mine skirts the western edges of Hudson Bay and Lake Superior, and then crosses the Mississippi River five times and US-61 seven. On the other side of the Gulf of Mexico, it passes straight through Guatemala City. It also goes through the Galapagos archipelago, either through San Salvador or Santa Cruz.
I live not too far east of San Diego, along longitude -116.937 or thereabouts.
south of me:
most of my town of Lakeside
the town of El Cajon
the western shore of Lower Otay Reservoir
with only a few dozen feet margin of error, the northbound truck lanes of the Otay Mesa border crossing with Mexico
the east half of Tijuana
Puerto Nuevo, a small poblado on the water just off Mexico highway 1D
and that's it, 'til Antarctica
heading north:
the 67 freeway, and a tiny bit of Lakeside
a crossing of 67 where it is a four-lane undivided arterial
a final crossing of 67 where it turns east to head into Ramona
astonishingly little until I note that I am in line (~10 feet margin of error) with the KSDW transmitter tower in the Palomar Mountain area
Hemet, the boundary between Beaumont and Banning, and smack down the middle of Big Bear Lake
avoid Barstow, but hit the logistics base immediately to the east of it
Fort Irwin, and then Death Valley. Cross into Nevada about a quarter mile west of Daylight Pass Road, which is NV-374
clip the western edges of the Nellis Air Force training range
cross US-50 just east of the NV-376 junction
almost exactly the center of town in Battle Mountain
cross into Idaho about 3 miles east of the triple point with Oregon and Nevada
the next town is Homedale, many miles north. we head just west of its city hall by about a block
cross into Oregon briefly at a bend in the Snake River.
back into Idaho, where we miss Weiser to the east, and therefore alas not cross old US-630, the shortest route in the system at 3 miles.
cross into Oregon one last time, and then into Washington only about 3000 feet west of the triple point
cross between Washington and Idaho either 3 or 5 times, depending on the accuracy of my measurement, ending up in Idaho
clip the western outskirts of Genesee ID, a few feet within where I was once not given a traffic ticket (32 in a 25) in 2006 on Cow Creek Road
clip the westernmost 500 feet or so of Lake Coeur d'Alene
cross into British Columbia about 3 miles east of the triple point with BC, ID, and WA
cross into Alberta across the Continental Divide, just south of Mount Dent
cross the Yellowhead Highway - our last major east-west paved road - between Hinton and Edson, AB
cross into Northwest Territories about a mile east of the MacKenzie highway.
(//www.aaroads.com/shields/blog/photos/117022.jpg)
I am astonished that this place is almost exactly due north of where I currently live!
cross the MacKenzie highway for the last time out in the absolute middle of nowhere, along the north shore of Caen Lake
cross into Nunavut in the middle of an unnamed lake, around latitude 66.882
cross back into Northwest Territories around latitude 69.906, on Victoria Island
our last land is a bay on the north shore of Prince Patrick Island around latitude 77.321
Quote from: Dr Frankenstein on May 09, 2013, 01:52:33 PM
I'm aligned with Brooklyn and the Bronx, straight through the Botanical Gardens.
You are about 2'25" west of me.
Heading south, my longitude passes through the east end of Crooked Island in The Bahamas; a bit west of Les Cayes, Haiti; down through Colombia (Bogota is about 10' west) barely missing Venezuela; Peru; a bit of the western extreme of Brazil; back out to ocean again about 80 km east of Yauca, Peru; back onshore near Ancud, Chile; and out into the Antarctic ocean in a remote area of Tierra del Fugeo.
Combine this with a latitude thread, and anyone who posts in both gives up their exact home location.
This isn't as easy as I'd hoped it would be, as it seems bounding-box display on OSM is currently broken. Let's see if I can get Google Earth to draw a nice longitude line for me...
North to south: Various large islands of eastern Nunavut; Hudson Bay; wilderness of Ontario; some unnamed roads and then the TCH (GE doesn't identify it with a number) just east of Mattice; Buchannan Lake; more wilderness, apparently; highway 101 and civilization again; TCH again just west of Iron Bridge; Lake Huron, including that pass of water just east of Cockburn Island; Near-miss of some islands just off Alpena, MI; come ashore and cross M-25 in a light residential area northeast of Caseville; cross I-69 just east of the Wilder Rd interchange near Lapeer; cross I-75, I-96, I-94, I-75 again in Detroit suburbs; embarking across Lake Erie at Estral Beach and coming ashore just east of Reno Beach, OH; cross the Turnpike a few miles east of Elmore; cross US in its eastern interchange with US 23, and US 23 a few miles south; cross Scioto River a bit upstream from Green Camp; cross I-70 just about at its closest point to my home; cross US 40 / National Road through the eastern arches of a 40s-vintage concrete arch bridge; cross I-71 not particularly near anything; Deer Creek Lake and associated State Park; cross US 50 just east of Bainbridge; a cemetery on an illogically-sharp bend in OH 772; Ohio River between Garrison and Vanceburg; approximate a jaggy part of the Carter—Lewis county line in Kentucky; I-64 west of Olive Hill; mostly farmland across the western tip of Virginia; I-81 near Morristown, TN; the east end of Douglas Lake; I-40 near Newport; Great Smoky Mts Nat'l Park, passing near Mt Guyot; Extreme NE Georgia, estreme W South Carolina, then into Georgia again; I-85 near Carnesville; the center of Carnesville; I-20 just W of Greensboro; Oconee Lake and Sinclair Lake a few times each; I-16 in the GA-112 interchange; I-75 a few miles north of the Florida—Georgia border; I-10 a few miles east of the Lee rest area; into the Gulf of Mexico at Horseshoe Cove; miss Loggerhead Key by several miles; Cuba, crossing a few miles east of an invisible town Google calls Puerto Escondido, the western Caribbean Sea; nicking Honduras and Nicaragua at the mouth of the Coco river, then grazing Nicaragua again; Costa Rica; Gulf of Dulce and into the Pacific; missing South America by a hundred miles or so; Antarctica, including the Ellsworth Mountains.
I live in the Town of Glenville, New York, slightly east of the Village of Scotia and the City of Schenectady.
Things that are directly due south of me include the tip of Breezy Point, which many of you may be familiar with due to the destruction that was caused by Sandy. Pass through parts of Harlem, the eastern part of Roosevelt Island, just east of the George Washington Bridge. Cross the Hudson River a few times and even go through ritzy Alpine, NJ. Pass just east of downtown Beacon, NY and through the famed Bowtie interchange in Poughkeepsie, Franklin D. Roosevelt's backyard at his estate in Hyde Park and the Kingston-Rhinecliff Bridge. After passing just east of downtown Saugerties, the next place of note is Schenectady.
Going north, I go through some scenic country in the Adirondacks. Things of note include the eastern arm of the Great Sacandaga Lake, Wevertown, just west of Lake Tear of the Clouds, just east of downtown Lake Placid and Whiteface Mountain. I cross the border into Canada at Franklin Centre, which is where NY 189 becomes QC 209. Cross the St. Lawrence in Melocheville, Ile Perrot, so not far from Montreal. Last thing of note that I noticed was that the longitude line passed east of St. Jerome, Quebec.
This would be a fun exercise to look at latitude as well, lots of interesting things due west or due east of me.
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 could probably write a web service to create kml files of great circles with specified origin and direction. This could demonstrate the fact that if A is due east of B, B probably isn't due west of A.
Quote from: vtk on May 09, 2013, 09:09:24 PM
Combine this with a latitude thread, and anyone who posts in both gives up their exact home location.
eh, people generally know where I live.
Quote
This isn't as easy as I'd hoped it would be, as it seems bounding-box display on OSM is currently broken. Let's see if I can get Google Earth to draw a nice longitude line for me...
I had wondered what everyone's technique was. Mine was to use google maps's "what's here" function, in the right-click menu. that will load the latitude and longitude of whatever is clicked on. I started with my house, and made note of the longitude.
then I scrolled approximately north and when I ran into interesting things, I clicked "what's here", and replaced the reported longitude with the desired one, which yielded an arrow exactly on my longitude line, from which I could report the context.
Quote from: vtk on May 10, 2013, 08:44:02 AM
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.
Quote from: agentsteel53 on May 10, 2013, 12:01:52 PM
Quote from: vtk on May 10, 2013, 08:44:02 AM
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.
Quote from: vtk on May 10, 2013, 12:11:19 PM
looking due east from a stationary point.
I had not thought of it that way. you are absolutely correct.
QuoteBut 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.
I looked it up, and there is a well-specified direction for Muslim prayer at Amundsen-Scott polar station.
http://www.islamicfinder.org/prayerDetail.php?country=antarctica&city=South_Pole_-_Amundsen-Scott_Station_South_Pole&state=00&id=6&month=&year=&email=&home=2013-5-10&lang=&aversion=&athan=
that is defined to be 90 degrees latitude south, but given that a) the station is not located at the true pole, or even the ceremonial pole, and b) there is a well-defined vector for "direction to Mecca", the implication is that it is in fact 89.xxxS, xx.xxxE/W and those values are very well known.
given that the station shifts relative to the true pole, and any small change is magnified into a large difference in the "looking east" vector, I'll bet they have to adjust the direction to Mecca pretty frequently.
Actually I just found out there are two methods for determining direction to Mecca: great circle, or constant-compass/Mercator/loxodrome. Apparently there isn't universal agreement on which is right.
Regarding a mobile station near the South Pole, the great circle direction to Mecca would indeed swing wildly relative to local north, but would be quite stable relative to the orientation of the south-polar UTM zone. The shortest loxodrome, on the other hand, would always point nearly north, more closely constrained to due north as the station approaches the pole – the point at which north becomes nonspecific and the local direction of every nonmeridian loxodrome is undefined.
My great circle generator should be ready soon, by the way, featuring start-and-direction mode. Through-two-points mode will come at a later date.
Quote from: agentsteel53 on May 10, 2013, 12:01:52 PM
Quote from: vtk on May 10, 2013, 08:44:02 AM
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.
This methodology produces several weird consequences.
- two people heading due east from any two points on Earth will at some point have their paths cross
- as you head "east" your bearing gradually becomes further away from perpendicular to north-south
I would never have even thought of it, parallel latitude avoids these problems and is more real-world meaningful given how the earth rotates.
As for direction to Mecca, or any other point on Earth, I would determine that by measuring the distance along your latitude to Mecca's longitude, measuring the distance from there down that longitude to Mecca, and determining what angle makes the hypotenuse of that (admittedly distorted) right triangle.
The problem with the great circle definition is that it's not transitive. If point A is east of point B, point B is not west of point A (unless they're exactly opposite). I think you would have to define an "east pole" and "west pole" on the equator to make transitive great circle definitions.
I just dislike lat-lon or loxodrome or similar methods because they place too much importance on meridians and parallels (which aren't natural features) and, in some cases, expose people's Mercator-like flat world view.
Side note: everyone should own at least one globe.
Quote from: vtk on May 11, 2013, 07:37:21 AMI just dislike lat-lon or loxodrome or similar methods because they place too much importance on meridians and parallels (which aren't natural features)
Great circles certainly aren't natural features...
Meridians at least have natural phenomena all the way along them (noon at the same time).
QuoteSide note: everyone should own at least one globe.
Well yes, but you would still use lat and lon to describe position - if you note, the coordinates are angles and thus how you work with spherical objects.
And with axes you would have the axis of rotation as a blatantly obvious one (even if not trying to cross oceans and working out longitude by a clock and local noon...) and there isn't an obvious second axis (west and east poles), so the angle from the midpoint between north and south poles is a naturally obvious second measure.
And west and east as concepts exist because it bisects the N-S axis. W and E have to be a constant angle in relation to the measurable N-S axis and not dependent on where you started (partially as it then becomes hard to work out where west is as local west is a different direction to west-where-you-started), otherwise it's totally useless as a concept!
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.
Quote from: vtk on May 11, 2013, 02:08:50 PMimplicitly 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.
Quoteexpose 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
Quoteline 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.
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.
Quote from: Steve on May 11, 2013, 08:33:18 PM
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. (https://www.aaroads.com/forum/proxy.php?request=http%3A%2F%2Fimg833.imageshack.us%2Fimg833%2F1395%2Ftrollicons2288917697thu.png&hash=97ba5ba2bd5009e175b35ab98f30591820a499a9)
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.
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.
Quote from: vtk on May 12, 2013, 02:44:30 AMIf 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?
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.
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,
Quote from: vtk on May 10, 2013, 12:11:19 PM
Quote from: agentsteel53 on May 10, 2013, 12:01:52 PM
Quote from: vtk on May 10, 2013, 08:44:02 AM
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).
Quote from: kphoger on May 13, 2013, 01:14:54 PM
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.
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!
Quote from: agentsteel53 on May 13, 2013, 01:26:30 PM
Quote from: kphoger on May 13, 2013, 01:14:54 PM
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.
Quote from: A.J. Bertin on May 13, 2013, 01:47:31 PM
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.
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.
Quote from: kphoger on May 13, 2013, 02:37:40 PM
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).
Yeah..... that didn't help at all. :banghead: 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.
(https://www.aaroads.com/forum/proxy.php?request=http%3A%2F%2Fi1092.photobucket.com%2Falbums%2Fi410%2Fkphoger%2Fglobe_zps9c8355fc.png&hash=435e03b749b6588ec3b8854f9f5e3483f13d000c)
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?
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.
Quotewhat 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.
Quote from: agentsteel53 on May 13, 2013, 08:15:08 PM
Quotewhat 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:
(https://www.aaroads.com/forum/proxy.php?request=http%3A%2F%2Fi1092.photobucket.com%2Falbums%2Fi410%2Fkphoger%2Fglobe2_zpsc821788a.png&hash=9b3fb7cebe8ebbc1b05bd9b23b74dd1ab5c2ffb0)
Quote from: kphoger on May 13, 2013, 08:35:17 PM
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?"
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 earth doesn't rotate about the intersection of the great circle from my latitude and the equator.
Quote from: The High Plains Traveler on May 13, 2013, 10:39:41 PM
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.)
Quote from: kphoger on May 13, 2013, 10:59:57 PM
(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.
Quote from: vtk on May 12, 2013, 08:02:49 PMWhat'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'.
QuoteWhen 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.
QuoteIt 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.
QuoteAnd 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.
QuoteDo 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...
Quote from: english si on May 14, 2013, 04:14:22 PMYou 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".
Quote from: english si on May 14, 2013, 04:14:22 PM
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.
Bear with the devil's advocate, here. Turning the tables, one could just as easily wonder why you think north-south lines can be straight rather than curved. See the flipped globe illustration above. Do you have an answer to that that doesn't involve earth's rotation (which factors not one bit into how people think of directions). What I mean is, looking east out your window is functionally no different than looking north out your window, yet the lines described by "east" and "north" are not the same, i.e. straight or curved.
Quote from: agentsteel53 on May 14, 2013, 04:19:22 PM
Quote from: english si on May 14, 2013, 04:14:22 PMYou don't call Red Eric 'Red', do you.
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".
This whole time, I just figured it was an initialism, written in textspeak. I always say it to myself as
English, es i, which my brain comprehends as
English, metric system. :hmm:
Quote from: agentsteel53 on May 14, 2013, 04:19:22 PM
if your name were "prelude si" I would not hesitate to call you "prelude".
...but that's MY nickname! :-D
Quote from: kphoger on May 13, 2013, 09:08:58 PM
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).
I grew up imagining East and West Poles at (0,0) and (0,180), both over open water. However, I could never figure out what that meant. Once I learned more about the North and South Poles actually having significance, I dropped that notion.
Quote from: english si on May 14, 2013, 04:14:22 PM
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'.
No, my definition of travelling east is the same as yours. It's my definition of what's due east of me that's on a great circle. Following that great circle (starting in an easterly direction) does involve changing direction a bit as measured in the traveller's local coordinate system, but not as much as you characterized in the above quote. The locally-measured deviation from local due east is never more than the latitude angle of the starting point, and certainly never west. *
As far as reciprocals, are we talking about the relative directional relationship between two points, or are we talking about travel? If I travel due east 1000 miles, then travel due west 1000 miles, I return to my starting point. But if I identify a point 1000 miles due east of me, and then go there, my starting point is 1000 miles away but not exactly due west. NE2 and I have already mentioned this phenomenon.
QuoteQuoteWhen 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?
I have made statements about what is east of me, and you say I'm wrong because something about traveling east. That's when you seem to insist that the two concepts (which you didn't quote) are the same.
I'm beginning to think that the problem is not 2D versus 3D thinking, but a choice of coordinate system. You seem to prefer a global spherical coordinate system of ρ,θ,φ – possibly converting to/from geocentric cartesian x,y,z when necessary for intermediate calculations. I prefer a global geocentric cartesian x,y,z, converting to/from spherical ρ,θ,φ for as necessary for communication, but I also think in terms of local cartesian x,y,z coordinate systems with the origin at a point on the Earth's surface and x and y aligned to east and north at that point. We've both been largely neglecting elevation in our discussion, so while you don't specify ρ, I don't specify local z. Both of those omissions make the earth Flat in different ways if the missing variable isn't reconstructed.
QuoteYou 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.
East is a direction, not a path. East is therefore not straight or curved. You can define a path whose direction is east at every point along its length, and you get a parallel of latitude. Or you can define a path which begins in the direction of east, but has no curvature; that's a line into space. Or you can define a path that begins in the direction of east, and has the minimum curvature required to follow the Earth's surface (there's a general term which eludes me for such a minimum-curvature path constrained to a surface) and then you get a great circle.
QuoteYour use of great circles may have merit, but to call it 'east' is just totally wrong.QuoteIt 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.
I'm certainly not saying that great circles define "east" as such a general term – that would indeed be wrong, unless someone defines an "east pole", which I'm not advocating. The collection of points that "are due east of" a given point on the Earth's surface lie on a great circle, as I define the phrase "is/are due east of". My definition is no broader than that. I'm certain I'm not the only person who supports that definition, though I won't assert it's a large number.
QuoteQuoteAnd 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.QuoteDo 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?
Who is Red Eric? I don't claim to be good at world history. And I wouldn't be surprised if folks called him Red, particularly on the Internet. Long ago I was a regular at a chatroom for nudists. Another frequent visitor used the handle "gay_nude_oz_guy". (Not meant to be overtly sexual, as it might be interpreted in a more general chatroom.) Many people just called him "gay" for short, even though "guy" was the noun.
Anyway, "english" isn't always an adjective; it can be a noun too. Understanding it as an adjective requires a noun to be modified, in this case "si" which is apparently a proper noun, your name – this was not clear to me before. I'm not familiar with many names which would shorten to Si, and I've never met anyone who does so, and besides, you didn't capitalize it. For that matter, had you capitalized it, I might have interpreted it as the symbol for Silicon. As it is, I thought the "si" in your name was spanish for "yes", and "english" was a noun (the language). Like if someone asked a Cuban merchant if he spoke English, and the merchant responded "English, sÃ", comedically demonstrating either an inability or unwillingness to consistently use the potential customer's preferred language. Frankly, I'm a little disappointed to learn that your forum handle isn't a joke about mismatched languages.
QuoteThat said, you seem to think that traveling due east means travelling west at some point
That is, at best, an exaggeration of an unwarranted generalization of what I said.* Have I clarified things in this post, or do I need to explain in more formal mathematical terms? Or should I just say you have misunderstood me and give up?
*Oh, wait, I think I figured out where you got that "travelling east includes travelling west" paradox. I guess I did sort of say that indirectly, but it's not as absurd as you color it. I really need to sleep right now, but I'll try to address that soon.
Quote from: vtk on May 15, 2013, 02:47:55 AM
As far as reciprocals, are we talking about the relative directional relationship between two points, or are we talking about travel? If I travel due east 1000 miles, then travel due west 1000 miles, I return to my starting point. But if I identify a point 1000 miles due east of me, and then go there, my starting point is 1000 miles away but not exactly due west. NE2 and I have already mentioned this phenomenon.
Buh? If you identify a point 1000 miles due east of you, and going due east 1000 miles does not get you to that point, something is very wrong with your terminology.
Quote from: NE2 on May 15, 2013, 04:55:35 AM
Buh? If you identify a point 1000 miles due east of you, and going due east 1000 miles does not get you to that point, something is very wrong with your terminology.
A point 1000 miles due east of me can be reached by travelling 1000 miles along a great circle path which is due east at my starting point. If I instead travel due east for 1000 miles – correcting my course along the way to keep a due-east heading – I reach a different point which is just shy of 1000 miles away from my starting point, and the direct direction (not the direction of the path I travelled) from start point to end point is a little off of east, as measured from either the start point or the end point.
...All of this assumes I am nowhere near the equator at any time in this scenario.
I think I'll make some graphics, animated if necessary, to illustrate the points I've made.
I understand what you mean, but your terminology really really sucks.
Quote from: NE2 on May 15, 2013, 04:55:35 AM
Buh? If you identify a point 1000 miles due east of you, and going due east 1000 miles does not get you to that point, something is very wrong with your terminology.
Quote from: vtk on May 15, 2013, 07:42:32 PM
A point 1000 miles due east of me can be reached by travelling 1000 miles along a great circle path which is due east at my starting point. If I instead travel due east for 1000 miles – correcting my course along the way to keep a due-east heading – I reach a different point which is just shy of 1000 miles away from my starting point, and the direct direction (not the direction of the path I travelled) from start point to end point is a little off of east, as measured from either the start point or the end point.
Quote from: NE2 on May 15, 2013, 04:55:35 AM
Buh? If you identify a point 1000 miles due east of you, and going due east 1000 miles does not get you to that point, something is very wrong with your terminology.
Quote from: vtk on May 15, 2013, 07:42:32 PM
A point 1000 miles due east of me can be reached by travelling 1000 miles along a great circle path which is due east at my starting point. If I instead travel due east for 1000 miles – correcting my course along the way to keep a due-east heading – I reach a different point which is just shy of 1000 miles away from my starting point, and the direct direction (not the direction of the path I travelled) from start point to end point is a little off of east, as measured from either the start point or the end point.
Quote from: NE2 on May 15, 2013, 04:55:35 AM
Buh? If you identify a point 1000 miles due east of you, and going due east 1000 miles does not get you to that point, something is very wrong with your terminology.
I think we've reached an impasse.
My terminology doesn't fit your expectations which are based on 2D Euclidean geometry, so it sucks? I suppose you are entitled to your opinion. I, however, believe terminology that depends too much on the cardinal directions being special is problematic. It causes people to get used to thinking about geography only from specific, possibly distorted perspectives. I like to be able to turn the globe around in my head and look at it any which way I want.
Latitude, longitude, loxodromes and the Mercator projection all have their uses, but they're not the only valid way of understanding geospatial relationships. The methods I've outlined work too, and to assert that they are inferior – not for any specific uses, but inferior in general – suggests a lack of objective thinking. I'm not the only one who thinks about geospatial relationships this way, either. The azimuthal equidistant projection has been around for a very long time.
There is not an applicable emoticon I can use here.
Your terminology is self-contradictory.
Quote from: NE2 on May 16, 2013, 12:26:04 AM
Your terminology is self-contradictory.
My terminology is nuanced.
Going south, I pass Cambridge, Boston, and Fall River. After a long stretch of ocean, I go into the Dominican Republic. I go into South America, and I miss Santiago by a few miles.
Going north, I pass the White Mountains, and I miss Quebec City by a few miles.