Talk:2519: Sloped Border - Revision history

172.71.222.220 at 04:01, 20 May 2025

2025-05-20T04:01:34Z

172.71.222.221 at 03:59, 20 May 2025

2025-05-20T03:59:56Z

162.158.90.23 at 09:45, 29 September 2021

2021-09-29T09:45:06Z

108.162.241.143: Pointing out the self-intersecting nature of any sloped boundary surface based on a curved boundary line on the Earth's surface

2021-09-28T03:31:41Z

Pointing out the self-intersecting nature of any sloped boundary surface based on a curved boundary line on the Earth's surface

172.70.42.129 at 13:15, 25 September 2021

2021-09-25T13:15:29Z

ProphetZarquon: Multinational highrise

2021-09-25T05:27:57Z

Multinational highrise

172.68.65.107 at 20:17, 24 September 2021

2021-09-24T20:17:47Z

172.69.90.15 at 15:35, 24 September 2021

2021-09-24T15:35:55Z

162.158.159.95: Oddly shaped borders where bridges carry one territory over another

2021-09-24T14:21:09Z

Oddly shaped borders where bridges carry one territory over another

Angel at 09:21, 24 September 2021

2021-09-24T09:21:14Z

← Older revision		Revision as of 04:01, 20 May 2025
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	If the border surface is tilted off vertical and also following a curved line on the surface, at sufficiently high altitude the border surface can self-intersect in a complex manner, producing enclaves of air/space/underground which are disconnected from the country that they belong to. That is, assuming you count the parity of border crossings to identify which country owns the space. You could also make a greedy border so the first time you cross is you are in the other country and stay there even in the detached enclaves. The enclaves would be even more exciting where the borders of three countries meet. I'm not even sure how the parity counting would work, when you are in country A and cross the B/C boundary. [[Special:Contributions/108.162.241.143\|108.162.241.143]] 03:31, 28 September 2021 (UTC)		If the border surface is tilted off vertical and also following a curved line on the surface, at sufficiently high altitude the border surface can self-intersect in a complex manner, producing enclaves of air/space/underground which are disconnected from the country that they belong to. That is, assuming you count the parity of border crossings to identify which country owns the space. You could also make a greedy border so the first time you cross is you are in the other country and stay there even in the detached enclaves. The enclaves would be even more exciting where the borders of three countries meet. I'm not even sure how the parity counting would work, when you are in country A and cross the B/C boundary. [[Special:Contributions/108.162.241.143\|108.162.241.143]] 03:31, 28 September 2021 (UTC)

−	:Think of a a string of bits as determining your country, so if you had two countries, 10 would mean “in country A”, and 01 would be country B, and crossing an AB boundary means XORing with the bit string. Using this logic extended to three bits, if we are in A and cross a BC boundary, then we exit 100 and enter 111. We are in A B and C at once. This is a coherent but very silly answer, so thus I love it. [[Special:Contributions/172.71.222.221\|172.71.222.221]] 03:59, 20 May 2025 (UTC)	+	:Think of a string of bits as determining your country, so if you had two countries, 10 would mean “in country A”, and 01 would be country B, and crossing an AB boundary means XORing with the bit string 11. Using this logic extended to three bits, if we are in A and cross a BC boundary, then we exit 100 and enter 111. We are in A B and C at once. This is a coherent but very silly answer, so thus I love it. [[Special:Contributions/172.71.222.221\|172.71.222.221]] 03:59, 20 May 2025 (UTC)

← Older revision		Revision as of 03:59, 20 May 2025
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	If the border surface is tilted off vertical and also following a curved line on the surface, at sufficiently high altitude the border surface can self-intersect in a complex manner, producing enclaves of air/space/underground which are disconnected from the country that they belong to. That is, assuming you count the parity of border crossings to identify which country owns the space. You could also make a greedy border so the first time you cross is you are in the other country and stay there even in the detached enclaves. The enclaves would be even more exciting where the borders of three countries meet. I'm not even sure how the parity counting would work, when you are in country A and cross the B/C boundary. [[Special:Contributions/108.162.241.143\|108.162.241.143]] 03:31, 28 September 2021 (UTC)		If the border surface is tilted off vertical and also following a curved line on the surface, at sufficiently high altitude the border surface can self-intersect in a complex manner, producing enclaves of air/space/underground which are disconnected from the country that they belong to. That is, assuming you count the parity of border crossings to identify which country owns the space. You could also make a greedy border so the first time you cross is you are in the other country and stay there even in the detached enclaves. The enclaves would be even more exciting where the borders of three countries meet. I'm not even sure how the parity counting would work, when you are in country A and cross the B/C boundary. [[Special:Contributions/108.162.241.143\|108.162.241.143]] 03:31, 28 September 2021 (UTC)
		+
		+	:Think of a a string of bits as determining your country, so if you had two countries, 10 would mean “in country A”, and 01 would be country B, and crossing an AB boundary means XORing with the bit string. Using this logic extended to three bits, if we are in A and cross a BC boundary, then we exit 100 and enter 111. We are in A B and C at once. This is a coherent but very silly answer, so thus I love it. [[Special:Contributions/172.71.222.221\|172.71.222.221]] 03:59, 20 May 2025 (UTC)

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 The Earth is not a sphere.  In general the local vertical does not go through the center of the Earth.  I would expect international law to be based on the local vertical (easily measured since antiquity by plumb bob or similar) rather than the line though the Earth's center (requiring surveying precision not widely available till the late 20th century).  Or perhaps international law just defines the Earth as flat.[[Special:Contributions/172.68.65.107|172.68.65.107]] 20:17, 24 September 2021 (UTC)
 ...it probably does, alongside Pi being 4. ;) [[Special:Contributions/172.70.42.129|172.70.42.129]] 13:15, 25 September 2021 (UTC)
 If the border surface is tilted off vertical and also following a curved line on the surface, at sufficiently high altitude the border surface can self-intersect in a complex manner, producing enclaves of air/space/underground which are disconnected from the country that they belong to. That is, assuming you count the parity of border crossings to identify which country owns the space. You could also make a greedy border so the first time you cross is you are in the other country and stay there even in the detached enclaves. The enclaves would be even more exciting where the borders of three countries meet. I'm not even sure how the parity counting would work, when you are in country A and cross the B/C boundary. [[Special:Contributions/108.162.241.143|108.162.241.143]] 03:31, 28 September 2021 (UTC)

← Older revision		Revision as of 03:31, 28 September 2021
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	The Earth is not a sphere. In general the local vertical does not go through the center of the Earth. I would expect international law to be based on the local vertical (easily measured since antiquity by plumb bob or similar) rather than the line though the Earth's center (requiring surveying precision not widely available till the late 20th century). Or perhaps international law just defines the Earth as flat.[[Special:Contributions/172.68.65.107\|172.68.65.107]] 20:17, 24 September 2021 (UTC)		The Earth is not a sphere. In general the local vertical does not go through the center of the Earth. I would expect international law to be based on the local vertical (easily measured since antiquity by plumb bob or similar) rather than the line though the Earth's center (requiring surveying precision not widely available till the late 20th century). Or perhaps international law just defines the Earth as flat.[[Special:Contributions/172.68.65.107\|172.68.65.107]] 20:17, 24 September 2021 (UTC)
	...it probably does, alongside Pi being 4. ;) [[Special:Contributions/172.70.42.129\|172.70.42.129]] 13:15, 25 September 2021 (UTC)		...it probably does, alongside Pi being 4. ;) [[Special:Contributions/172.70.42.129\|172.70.42.129]] 13:15, 25 September 2021 (UTC)
		+
		+	If the border surface is tilted off vertical and also following a curved line on the surface, at sufficiently high altitude the border surface can self-intersect in a complex manner, producing enclaves of air/space/underground which are disconnected from the country that they belong to. That is, assuming you count the parity of border crossings to identify which country owns the space. You could also make a greedy border so the first time you cross is you are in the other country and stay there even in the detached enclaves. The enclaves would be even more exciting where the borders of three countries meet. I'm not even sure how the parity counting would work, when you are in country A and cross the B/C boundary. [[Special:Contributions/108.162.241.143\|108.162.241.143]] 03:31, 28 September 2021 (UTC)

← Older revision		Revision as of 13:15, 25 September 2021
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	The Earth is not a sphere. In general the local vertical does not go through the center of the Earth. I would expect international law to be based on the local vertical (easily measured since antiquity by plumb bob or similar) rather than the line though the Earth's center (requiring surveying precision not widely available till the late 20th century). Or perhaps international law just defines the Earth as flat.[[Special:Contributions/172.68.65.107\|172.68.65.107]] 20:17, 24 September 2021 (UTC)		The Earth is not a sphere. In general the local vertical does not go through the center of the Earth. I would expect international law to be based on the local vertical (easily measured since antiquity by plumb bob or similar) rather than the line though the Earth's center (requiring surveying precision not widely available till the late 20th century). Or perhaps international law just defines the Earth as flat.[[Special:Contributions/172.68.65.107\|172.68.65.107]] 20:17, 24 September 2021 (UTC)
		+	...it probably does, alongside Pi being 4. ;) [[Special:Contributions/172.70.42.129\|172.70.42.129]] 13:15, 25 September 2021 (UTC)

← Older revision		Revision as of 05:27, 25 September 2021
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	Wouldn't sloped borders also have interesting consequences underground when mining, building tunnels etc. ? [[Special:Contributions/162.158.88.239\|162.158.88.239]] 08:39, 23 September 2021 (UTC)		Wouldn't sloped borders also have interesting consequences underground when mining, building tunnels etc. ? [[Special:Contributions/162.158.88.239\|162.158.88.239]] 08:39, 23 September 2021 (UTC)
		+
		+	:That was my immediate concern as well: Residents of a single building could be divided between two jurisdictions, by residing one above the other. Mining & water rights & airspace might be similarly complicated. If airspace ended earlier than international waters, & undersea oil fields extended even beyond that... Oh, wait. 👀
		+	:[[User:ProphetZarquon\|ProphetZarquon]] ([[User talk:ProphetZarquon\|talk]]) 05:27, 25 September 2021 (UTC)

	I introduced into the explanation a hint of the more precise problem with airborne geometry upon spherical (or, possibly, geodesic) coordinates. The shallower the angle, the more possible that the 'curves with the ground' altitude calculation is to actually wrap itself all the way round the Earth before (presumably), whatever altitude limit there is to make space the same upper edge as International Waters are to horizontal edges. Taking the Liechtenstein case, as above, you could easily enclose them in a 'pyramidal' (or wedged, if not applied from all around them) air-claim by angling over them - ''or'' greatly increase their air-claim over neighbours if the angle is away. With inverse issues for the Mineral Rights issue. You need to agree in advance what happens when angled boundaries hit perpendicular ones, ''and'' whether the 'rhumbs' projected from the border mash together when equidistant points on a crinkly border project their own air-distance line. ''And'' if it is from an agreed surface level datum or local ground level, with the complications that arise from both cases. (Yeah, I originally thought there were about four different bones of contention that need to be ironed out in the codicil on curvature, but I now think there's about six of them needing strict definition, not counting the compound cases which further may need specifying in advance or forever requirev adhoc arbitration.) And none of this even takes account of Relativity and curved ''space'' frame of reference that might very subtly shift whatever reference you just agreed upon, if you let it go high enough. [[Special:Contributions/172.70.34.165\|172.70.34.165]] 12:05, 23 September 2021 (UTC)		I introduced into the explanation a hint of the more precise problem with airborne geometry upon spherical (or, possibly, geodesic) coordinates. The shallower the angle, the more possible that the 'curves with the ground' altitude calculation is to actually wrap itself all the way round the Earth before (presumably), whatever altitude limit there is to make space the same upper edge as International Waters are to horizontal edges. Taking the Liechtenstein case, as above, you could easily enclose them in a 'pyramidal' (or wedged, if not applied from all around them) air-claim by angling over them - ''or'' greatly increase their air-claim over neighbours if the angle is away. With inverse issues for the Mineral Rights issue. You need to agree in advance what happens when angled boundaries hit perpendicular ones, ''and'' whether the 'rhumbs' projected from the border mash together when equidistant points on a crinkly border project their own air-distance line. ''And'' if it is from an agreed surface level datum or local ground level, with the complications that arise from both cases. (Yeah, I originally thought there were about four different bones of contention that need to be ironed out in the codicil on curvature, but I now think there's about six of them needing strict definition, not counting the compound cases which further may need specifying in advance or forever requirev adhoc arbitration.) And none of this even takes account of Relativity and curved ''space'' frame of reference that might very subtly shift whatever reference you just agreed upon, if you let it go high enough. [[Special:Contributions/172.70.34.165\|172.70.34.165]] 12:05, 23 September 2021 (UTC)

← Older revision		Revision as of 20:17, 24 September 2021
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	If, say, planes define the border by the top of the mountain range, underground defines the border by the longest mines built by either country, and ground level is halfway up the mountain side, but angled to allow structural supports to be at a right angle to the slope.... And then you start defining curves to merge the various points into a uniform line plot..... This might almost make sense. And it probably returns to vertical once you get below the mines, or above the aircraft. [[Special:Contributions/172.69.90.15\|172.69.90.15]] 15:35, 24 September 2021 (UTC)		If, say, planes define the border by the top of the mountain range, underground defines the border by the longest mines built by either country, and ground level is halfway up the mountain side, but angled to allow structural supports to be at a right angle to the slope.... And then you start defining curves to merge the various points into a uniform line plot..... This might almost make sense. And it probably returns to vertical once you get below the mines, or above the aircraft. [[Special:Contributions/172.69.90.15\|172.69.90.15]] 15:35, 24 September 2021 (UTC)
		+
		+	The Earth is not a sphere. In general the local vertical does not go through the center of the Earth. I would expect international law to be based on the local vertical (easily measured since antiquity by plumb bob or similar) rather than the line though the Earth's center (requiring surveying precision not widely available till the late 20th century). Or perhaps international law just defines the Earth as flat.[[Special:Contributions/172.68.65.107\|172.68.65.107]] 20:17, 24 September 2021 (UTC)

← Older revision		Revision as of 15:35, 24 September 2021
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	This kind of thing can happen with tunnels and bridges. For example, the border between the City of London (north of the river) and the Borough of Southwark (south of the river) runs right down the middle of the Thames as you might expect. But the whole of London Bridge belongs to the City. So if you happen to be on a boat underneath the bridge and on the southern half of the river, you're in Southwark; while a passenger on a bus crossing the bridge directly above you is in the City. So the border really must be sloped - and curved - and, as you trace the arches of the bridge, in some places horizontal. [[Special:Contributions/162.158.159.95\|162.158.159.95]] 14:21, 24 September 2021 (UTC)		This kind of thing can happen with tunnels and bridges. For example, the border between the City of London (north of the river) and the Borough of Southwark (south of the river) runs right down the middle of the Thames as you might expect. But the whole of London Bridge belongs to the City. So if you happen to be on a boat underneath the bridge and on the southern half of the river, you're in Southwark; while a passenger on a bus crossing the bridge directly above you is in the City. So the border really must be sloped - and curved - and, as you trace the arches of the bridge, in some places horizontal. [[Special:Contributions/162.158.159.95\|162.158.159.95]] 14:21, 24 September 2021 (UTC)
		+
		+
		+	Note that the only data point we have is at ground level, and the knowledge that the border is at least somewhat vertically curved. For all we know, there may be specific plausible landmarks defining the border at different altitudes, and a from a long distance away, the border might appear to be essentially vertical.
		+
		+	If, say, planes define the border by the top of the mountain range, underground defines the border by the longest mines built by either country, and ground level is halfway up the mountain side, but angled to allow structural supports to be at a right angle to the slope.... And then you start defining curves to merge the various points into a uniform line plot..... This might almost make sense. And it probably returns to vertical once you get below the mines, or above the aircraft. [[Special:Contributions/172.69.90.15\|172.69.90.15]] 15:35, 24 September 2021 (UTC)

← Older revision		Revision as of 14:21, 24 September 2021
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	Just had the additional thought that this is probably creating additional borders, which will need more treaties. If the sloping border is quite shallow, there's a chance that the country on the left (with more airspace than ground) will now have an airborne border with whatever country is on the far side of the country on the right. And conversely for the mineral rights issue, the country on the right may now have an underground border with whatever country is on the far side of the one on the left. How does international law deal with a border treaty between two countries causing a non-signatory to have an extra border with one of them? Would those countries need to be consulted? --[[User:Angel\|Angel]] ([[User talk:Angel\|talk]]) 09:21, 24 September 2021 (UTC)		Just had the additional thought that this is probably creating additional borders, which will need more treaties. If the sloping border is quite shallow, there's a chance that the country on the left (with more airspace than ground) will now have an airborne border with whatever country is on the far side of the country on the right. And conversely for the mineral rights issue, the country on the right may now have an underground border with whatever country is on the far side of the one on the left. How does international law deal with a border treaty between two countries causing a non-signatory to have an extra border with one of them? Would those countries need to be consulted? --[[User:Angel\|Angel]] ([[User talk:Angel\|talk]]) 09:21, 24 September 2021 (UTC)
		+
		+	This kind of thing can happen with tunnels and bridges. For example, the border between the City of London (north of the river) and the Borough of Southwark (south of the river) runs right down the middle of the Thames as you might expect. But the whole of London Bridge belongs to the City. So if you happen to be on a boat underneath the bridge and on the southern half of the river, you're in Southwark; while a passenger on a bus crossing the bridge directly above you is in the City. So the border really must be sloped - and curved - and, as you trace the arches of the bridge, in some places horizontal. [[Special:Contributions/162.158.159.95\|162.158.159.95]] 14:21, 24 September 2021 (UTC)

← Older revision		Revision as of 09:21, 24 September 2021
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	Borders are usually vertical; what definition of "vertical", though? Some geodetic system? (Which one?) Local plumb line? Something else? [[User:Sabik\|Sabik]] ([[User talk:Sabik\|talk]]) 06:48, 24 September 2021 (UTC)		Borders are usually vertical; what definition of "vertical", though? Some geodetic system? (Which one?) Local plumb line? Something else? [[User:Sabik\|Sabik]] ([[User talk:Sabik\|talk]]) 06:48, 24 September 2021 (UTC)
		+
		+	Just had the additional thought that this is probably creating additional borders, which will need more treaties. If the sloping border is quite shallow, there's a chance that the country on the left (with more airspace than ground) will now have an airborne border with whatever country is on the far side of the country on the right. And conversely for the mineral rights issue, the country on the right may now have an underground border with whatever country is on the far side of the one on the left. How does international law deal with a border treaty between two countries causing a non-signatory to have an extra border with one of them? Would those countries need to be consulted? --[[User:Angel\|Angel]] ([[User talk:Angel\|talk]]) 09:21, 24 September 2021 (UTC)