The topologist’s world map (2020)(tafc.space)
tafc.space
The topologist’s world map (2020)
https://tafc.space/qna/the-topologists-world-map/
70 comments
The geography of the USA, bordered by massive oceans and weak/friendly neighbors along with being a huge and productive landmass with a unified culture, is one of the many reasons why it is unbelievably overpowered as a country, and unlikely to lose its dominance anytime soon.
China might be competitive in terms of massive, productive landmass, but it simply will never be as secure in its borders as the US with strong and less friendly neighbors all around it. That will hold it back from surpassing the US as the dominant superpower. Ditto India, Russia, Brazil, and any potential rising powers in Africa.
By far, the biggest threat to US dominance is balkanization. Fracturing the union and creating deeper geographic divides in American culture would create enough internal strife to hamstring its power. Maybe that's inevitable over time for such a large landmass and the unique conditions of American colonization were never going to last more than a couple hundred years before it started falling apart.
China might be competitive in terms of massive, productive landmass, but it simply will never be as secure in its borders as the US with strong and less friendly neighbors all around it. That will hold it back from surpassing the US as the dominant superpower. Ditto India, Russia, Brazil, and any potential rising powers in Africa.
By far, the biggest threat to US dominance is balkanization. Fracturing the union and creating deeper geographic divides in American culture would create enough internal strife to hamstring its power. Maybe that's inevitable over time for such a large landmass and the unique conditions of American colonization were never going to last more than a couple hundred years before it started falling apart.
Why exactly does having strong rivals on your borders make you any less likely to become a superpower? Is your argument that before China gets strong enough to be considered a superpower, their neighbors will invade them? Or is that they’ll feel insecure about their borders, and allocate resources to their military rather than economic development?
Both arguments seem far-fetched. War with one’s neighbors is never guaranteed, even though there’s a risk of it. And they’d have to spend an unrealistically huge portion of their gdp on border defense for that to make development impossible.
Both arguments seem far-fetched. War with one’s neighbors is never guaranteed, even though there’s a risk of it. And they’d have to spend an unrealistically huge portion of their gdp on border defense for that to make development impossible.
Honestly, it might not be as significant of a problem anymore, because nukes changed the game.
Russia and China, or India and China, will never outright invade each other ever again, because of mutually assured destruction. Only countries without nukes have to worry about their sovereignty being violated, e.g. Ukraine. This also means that the geopolitical Schelling point, https://en.wikipedia.org/wiki/Focal_point_(game_theory), is that every nation state must either 1) have nukes or 2) vassal themselves to a nuclear power, e.g. non nuclear powers in NATO. Again we see an instructive example in Ukraine. They surrendered their nukes after the Soviet Union collapsed for the promise of sovereignty. But promises don't mean anything on the question of sovereignty. Only real world power matters. Might makes right.
But large borders with populous and powerful neighbors still matter, because you still have to commit resources to control those borders to prevent unchecked migration from disrupting your internal economies. The US experiences that problem with Mexico. I imagine a future where India starts experiencing wet bulb temperature events where hundreds of thousands or millions die overnight, which triggers mass migration north. Or perhaps a future where Siberia becomes more temperate and hospitable draws Chinese people try to move north as well.
Russia and China, or India and China, will never outright invade each other ever again, because of mutually assured destruction. Only countries without nukes have to worry about their sovereignty being violated, e.g. Ukraine. This also means that the geopolitical Schelling point, https://en.wikipedia.org/wiki/Focal_point_(game_theory), is that every nation state must either 1) have nukes or 2) vassal themselves to a nuclear power, e.g. non nuclear powers in NATO. Again we see an instructive example in Ukraine. They surrendered their nukes after the Soviet Union collapsed for the promise of sovereignty. But promises don't mean anything on the question of sovereignty. Only real world power matters. Might makes right.
But large borders with populous and powerful neighbors still matter, because you still have to commit resources to control those borders to prevent unchecked migration from disrupting your internal economies. The US experiences that problem with Mexico. I imagine a future where India starts experiencing wet bulb temperature events where hundreds of thousands or millions die overnight, which triggers mass migration north. Or perhaps a future where Siberia becomes more temperate and hospitable draws Chinese people try to move north as well.
>Only real world power matters. Might makes right.
The latter isn't just a rephrasing of the former but an expression of assent to it, and most people probably don't mean that.
The latter isn't just a rephrasing of the former but an expression of assent to it, and most people probably don't mean that.
It's often hard to tell if a person making an ugly statement is saying it with approval that this is the way things ought to be, or if they are saying it as an observation of harsh reality and they aren't attaching a moral judgement to that observation. Many people then assume the former and label the speaker as malicious when they are simply sharing their observation.
In my view, "might makes right" is simply an observation of harsh reality. Ignoring that reality is folly.
In my view, "might makes right" is simply an observation of harsh reality. Ignoring that reality is folly.
Historically, over the span of centuries war with strong neighbors is certain.
U.S. already had multiple wars where their geography kept their infrastructure and citizens safe. Other countries got obliterated and lost their superpower trait.
U.S. already had multiple wars where their geography kept their infrastructure and citizens safe. Other countries got obliterated and lost their superpower trait.
Trade is a bigger issue than purely military. The US gets to dictate the terms of trade with Canada and Mexico, and they are pretty dependent on US trade. It's a large geopolitical advantage
> Trade is a bigger issue than purely military.
Hard disagree there. Trade has only taken priority because we've had such a long period of peace. Logistics fuel military power, but it turns out trade only happens when the more powerful party assents to it, if they do not then the weaker state may decide to inflict it's own trade relations on the weaker nation.
Many people in 1913 that trade was the most important factor in determining politics, that the global trade networks would prevent a truly large and terrible war, and that money was mightier than the musket.
It turns out that when the lights start to go out, when things start to go bad, and it becomes a matter of survival the power that matters is not trade but your ability to feed the pitiless war machine, and at that point your trade agreements mean squat if you don't have the ability to enforce those trade agreements with the barrel of gun.
It's not polite, it's not civilized, it's not fair, but just like the people raised in the Victorian era were given a rude awakening in the trenches of the Somme and the fields of Verdun about how circumstantial civilized behaviors are; so to will we be find our own base natures soon brought to the fore if we continue to pray to the false god of economic progress, and give offerings upon the altar of money in hopes of forestalling the looming crises we face.
Hard disagree there. Trade has only taken priority because we've had such a long period of peace. Logistics fuel military power, but it turns out trade only happens when the more powerful party assents to it, if they do not then the weaker state may decide to inflict it's own trade relations on the weaker nation.
Many people in 1913 that trade was the most important factor in determining politics, that the global trade networks would prevent a truly large and terrible war, and that money was mightier than the musket.
It turns out that when the lights start to go out, when things start to go bad, and it becomes a matter of survival the power that matters is not trade but your ability to feed the pitiless war machine, and at that point your trade agreements mean squat if you don't have the ability to enforce those trade agreements with the barrel of gun.
It's not polite, it's not civilized, it's not fair, but just like the people raised in the Victorian era were given a rude awakening in the trenches of the Somme and the fields of Verdun about how circumstantial civilized behaviors are; so to will we be find our own base natures soon brought to the fore if we continue to pray to the false god of economic progress, and give offerings upon the altar of money in hopes of forestalling the looming crises we face.
I wouldn't draw too strong of conclusions from this map. It does show relative proximity to things like oceans but doesn't show lakes, rivers, mountains (as you note), jungles, and other natural features that, from a geopolitical standpoint, have created and prevented conflict throughout history.
Well in ancient and medieval times many cities were built in easy to defend locations.
UK got invaded on several occasions historically speaking.
USA/Canada are relatively new countries and had not enough time to diversivy in order to create competing ethnicities.
UK got invaded on several occasions historically speaking.
USA/Canada are relatively new countries and had not enough time to diversivy in order to create competing ethnicities.
France's geography is actually also insane as a protection : ocean, seas, mountains or vast forest.
The site is currently being hugged to death, so if you find its resources exhausted, try the archived version from a couple of hours back:
http://web.archive.org/web/20221219173909/tafc.space/qna/the...
http://web.archive.org/web/20221219173909/tafc.space/qna/the...
This is beautiful, especially with the colors on the top right - though I have a nitpick that it is missing an entire continent (probably because it doesn't show up in a list of countries): Antarctica
Edit: I now realize it's only supposed to show the graph national borders, though on a political world map, Antarctica is still shown. In a topological fashion, it could be added as a white circle around the entire map.
Edit: I now realize it's only supposed to show the graph national borders, though on a political world map, Antarctica is still shown. In a topological fashion, it could be added as a white circle around the entire map.
Antarctica isn’t shown for the same reason the bottom of the ocean or the surface of the moon aren’t shown: there are no countries there.
Adding cells that don’t correspond to a country (like your proposed white circle) would make the map less accurate.
Adding cells that don’t correspond to a country (like your proposed white circle) would make the map less accurate.
Then you get onto the definition of what a country is - there are many countries claiming land in Antarctica.
Indeed, but those claims don’t really reflect any on-the-ground reality, and the majority of countries don’t recognize them.
There are many disputed territories shown - Palestine (especially the bit bordering Jordan, which bares no relation to the facts on the ground), or Taiwan which is shown when only a dozen countries recognise it. Northern Cyprus which is defacto a different state to Mainland Cyprus isn't shown, but the UK military bases are shown. Gibraltar is erroneously shown as part of the UK, but the Falklands aren't shown at all -- nor are many other island territories. Hong Kong and Macau aren't shown as separate to China.
It's difficult to know what the definition for inclusivity is.
It's difficult to know what the definition for inclusivity is.
> It was at some point while I was thinking about adding extra countries to represent seas that it was time to call the automation quits, and just make the map manually. This has some advantages – I get to choose the overall layout, it’s much easier to include stylistic elements, and I don’t have to spend ages describing to a computer what common sense is.
An all too familiar situation.
An all too familiar situation.
For people who have time to burn being uselessly pedantic, is this a topologist's world map up to homotopy equivalence or homeomorphism?
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I think I get how to encode a hypergraph as a topological space. Let S be a set consisting of two kinds of points: Nodes and hyperedges. Endow it with a topology whose base consists of singleton sets containing only single nodes, and sets containing a hyperedge together with all the nodes it's connected to. In particular, a hyperedge cannot be in an open set unless it's accompanied by the nodes it's connected to. Observations are: The resulting space is usually not T2 or T1, but is always T0; connectivity of the hypergraph is equivalent to connectivity of the topological space; the Sierpinski space results from using a graph with one node and edge.
I don't know what that accomplishes except validate the intuition that graph theory is somehow connected to topology.
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I think I get how to encode a hypergraph as a topological space. Let S be a set consisting of two kinds of points: Nodes and hyperedges. Endow it with a topology whose base consists of singleton sets containing only single nodes, and sets containing a hyperedge together with all the nodes it's connected to. In particular, a hyperedge cannot be in an open set unless it's accompanied by the nodes it's connected to. Observations are: The resulting space is usually not T2 or T1, but is always T0; connectivity of the hypergraph is equivalent to connectivity of the topological space; the Sierpinski space results from using a graph with one node and edge.
I don't know what that accomplishes except validate the intuition that graph theory is somehow connected to topology.
Homotopy equivalence of what? This isnt really a topological space. It is a pair of spaces, one of which is contained in the other, (the sphere and the borders). This changes the category, morphisms are now pairs of morphisms and must preserve inclusion.
The answer is neither, since there is no continuous map that increases the number of connected components of a space and there are more islands than show up on the map.
There are other obstacles as well, alaska adds a piece to canada's boundary, this changes the fundamental group of the subspace, which is an invariant of homotopy type, and so the reduced version cannot be homotopy equivalent to the subspace with alaska's boundary included.
The answer is neither, since there is no continuous map that increases the number of connected components of a space and there are more islands than show up on the map.
There are other obstacles as well, alaska adds a piece to canada's boundary, this changes the fundamental group of the subspace, which is an invariant of homotopy type, and so the reduced version cannot be homotopy equivalent to the subspace with alaska's boundary included.
Is there a mathematical reason why, on the US map, only three types of lines are needed to generate this map- vertical, horizontal and one diagonal?
Does that notion generalize to all border maps and if so why?
Is it related how border maps can all be colored with only four colors?
Does that notion generalize to all border maps and if so why?
Is it related how border maps can all be colored with only four colors?
> Is there a mathematical reason why
No. Here's another topological map of the contiguous US that's all rectangles, arranged in a triangle: https://www.reddit.com/r/MapPorn/comments/gy2jq6/the_topolog...
I'm not sure how much I'd overthink this map, since it appears to have been created as a puzzle for children to help them understand the concept of topology: https://www.1001mathproblems.com/2015_11_01_archive.html
> Does that notion generalize to all border maps and if so why?
No.
> Is it related how border maps can all be colored with only four colors?
If you're talking about the four color map theorem? Instinctively, my answer's no, but it might be a fun thing to prove.
No. Here's another topological map of the contiguous US that's all rectangles, arranged in a triangle: https://www.reddit.com/r/MapPorn/comments/gy2jq6/the_topolog...
I'm not sure how much I'd overthink this map, since it appears to have been created as a puzzle for children to help them understand the concept of topology: https://www.1001mathproblems.com/2015_11_01_archive.html
> Does that notion generalize to all border maps and if so why?
No.
> Is it related how border maps can all be colored with only four colors?
If you're talking about the four color map theorem? Instinctively, my answer's no, but it might be a fun thing to prove.
For more maps like this, there are a bunch of quizzes on Sporcle that ask you to label the nodes of a graph, where the nodes are states/provinces/countries and the edges are borders: https://www.sporcle.com/playlists/Alcas/graph-y-geography
> Is it related how border maps can all be colored with only four colors?
Actually, that's not generally true. Michigan, for example, violates the axioms behind the four color theorem -- if regions are allowed to have multiple disconnected pieces, a map could theoretically require arbitrarily many colors. For a more pathological example, consider that US embassies are considered "US soil" in an island of their host nation. I'm rather curious about the chromatic number (that is, the smallest number of colors required) of the world map under that consideration.
Actually, that's not generally true. Michigan, for example, violates the axioms behind the four color theorem -- if regions are allowed to have multiple disconnected pieces, a map could theoretically require arbitrarily many colors. For a more pathological example, consider that US embassies are considered "US soil" in an island of their host nation. I'm rather curious about the chromatic number (that is, the smallest number of colors required) of the world map under that consideration.
Embassies are not considered to be foreign territory. The host country gives special privileges to the guest country in accordance with the Vienna Convention.
But there can be an enclave of one country inside another (first-order enclave), as well as enclaves inside enclaves. Dahala Khagrabari was a third-order enclave, an enclave of India inside an enclave of Bangladesh inside an enclave of India in mainland Bangladesh. It was ceded to Bangladesh seven years ago as part of a border gore cleanup treaty.
https://en.wikipedia.org/wiki/Dahala_Khagrabari
But there can be an enclave of one country inside another (first-order enclave), as well as enclaves inside enclaves. Dahala Khagrabari was a third-order enclave, an enclave of India inside an enclave of Bangladesh inside an enclave of India in mainland Bangladesh. It was ceded to Bangladesh seven years ago as part of a border gore cleanup treaty.
https://en.wikipedia.org/wiki/Dahala_Khagrabari
Don't ruin my joke.
I used to date somebody who lived across from the Kenyan embassy in DC. The embassy had a few designated parking spaces, but only until 6:30 PM -- about the time I might arrive for a date.
I liked to think that I was parking in Kenyan territory. I was not, for numerous reasons, but it made me happy anyway. Just be out by 6:30 AM.
(It didn't become Kenya again until 9, but it was a travel lane during rush hour. That's why the spot was always open: the signs were so confusing that nobody wanted to park there first.)
I used to date somebody who lived across from the Kenyan embassy in DC. The embassy had a few designated parking spaces, but only until 6:30 PM -- about the time I might arrive for a date.
I liked to think that I was parking in Kenyan territory. I was not, for numerous reasons, but it made me happy anyway. Just be out by 6:30 AM.
(It didn't become Kenya again until 9, but it was a travel lane during rush hour. That's why the spot was always open: the signs were so confusing that nobody wanted to park there first.)
I would think horizontal and vertical line segments (or, by extension, straight line segments with two different orientations; take the map with only horizontal and vertical line segments and apply a shear mapping (https://en.wikipedia.org/wiki/Shear_mapping) and a rotation) are sufficient.
That’s basically what this is, if you draw it on a pixel grid.
That’s basically what this is, if you draw it on a pixel grid.
> It was at some point while I was thinking about adding extra countries to represent seas that it was time to call the automation quits, and just make the map manually. This has some advantages – I get to choose the overall layout, it’s much easier to include stylistic elements, and I don’t have to spend ages describing to a computer what common sense is.
Though this is casually thrown out by the author and empathetically chuckled at by most of us, I this points to a problem worth exploring. In the wake of the hype around recent AI advancements, we can often view computers and software as capable of anything. But often the limits of our current computing systems are made glaringly obvious, such as stylistic design and a "common sense" disconnect articulated here. An area worth our attention and a domain possessing potential for innovation.
Though this is casually thrown out by the author and empathetically chuckled at by most of us, I this points to a problem worth exploring. In the wake of the hype around recent AI advancements, we can often view computers and software as capable of anything. But often the limits of our current computing systems are made glaringly obvious, such as stylistic design and a "common sense" disconnect articulated here. An area worth our attention and a domain possessing potential for innovation.
While I generally agree with this sentiment, I don't know if this is a good example.
This doesn't really seem like an impossible problem to me so much as a really complicated one. Something that could likely be solved algorithmically without even the use of AI.
Perhaps it could take information like the size and/or population of different countries to make best guesses on how large to make different parts of it. Even if it produces a best guess that you can then clean up in Inkscape it'd be a tremendous contribution to this task
This doesn't really seem like an impossible problem to me so much as a really complicated one. Something that could likely be solved algorithmically without even the use of AI.
Perhaps it could take information like the size and/or population of different countries to make best guesses on how large to make different parts of it. Even if it produces a best guess that you can then clean up in Inkscape it'd be a tremendous contribution to this task
That tiny Canada-Panama striped tail containing the entirety of North and Central America is funny.
This map tends to give vertex-like countries large areas, and vice-versa.
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I like how the Panama Canal is represented by the gap in the name Pan|ama. Nice work overall!
I still find a Spilhaus projection more informative, but this is defo interesting!
Definitely if you're an oceanographer. Interesting link here [0].
[0] https://storymaps.arcgis.com/stories/756bcae18d304a1eac140f1...
[0] https://storymaps.arcgis.com/stories/756bcae18d304a1eac140f1...
Canada actually now has a land border with Denmark! https://en.wikipedia.org/wiki/Hans_Island
I wonder how it would look like if we considered France's borders with the Netherland (at Saint Martin) and Brazil (at French Guiana).
It has both as exclaves: the France-Netherlands border in the group of islands at bottom left (nitpick: technically not a border with the Netherlands because St Maarten nowadays is an independent country in the kingdom of the Netherlands), just above Cuba, and the Belize exclave at the top of Brazil, bordering Surinam.
The Kingdom of the Netherlands is the parent nation state, despite St Maarten's designation as a "country". It's no more an independent state than Scotland (which is to say, not independent).
(also sorry to be pedantic)
(also sorry to be pedantic)
Just think if the Diomede islands were uplifted somehow, poof Russia and the USA have a border.
In winter there kind of is - I think you can walk by ice sometimes.
But don't expect a warm welcome if you make the trip: https://www.nbcnews.com/id/wbna12152629
508'd, so I guess the comments will make sense tomorrow.
Places Iceland in America, but other than that really nice.
That's not wrong geologically: https://www.icelandtravel.is/attractions/bridge-between-cont...
Obviously not the cultural convention though.
Obviously not the cultural convention though.
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Iceland emerged (is still emerging?) from the rift between the North American and Eurasian plates. Roughly speaking everything west of Þingvellir is on the North American plate, everything east on the Eurasian. I would've given it two colors in the continent map, although now that I look at it again it the categories seem to be more cultural than geologic, which would place it squarely in Europe.
The no-text version looks like Gallifreyan writing.
What's going on by Israel-Egypt
Egyptian territory on both sides of the Suez canal.
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This gets Ireland so wrong it is unbelievable. Firstly the British isles are treated differently from all the other islands on the map, and it's hard to tell that there's even a blue line separating it from the rest of Europe.
Secondly, Ireland doesn't even have a blue line, which implies it is connected by land to Britain
And thirdly, Wales and Scotland should really be acknowledged, and at the same time you might suggest Northern Ireland as well.
Secondly, Ireland doesn't even have a blue line, which implies it is connected by land to Britain
And thirdly, Wales and Scotland should really be acknowledged, and at the same time you might suggest Northern Ireland as well.
It seems correct to me.
The map shows the country "United Kingdom of Great Britain and Northern Ireland" (UK) without separating its constituent countries. This is what most political world maps do.
Ireland does border by land to the UK, at the border of Northern Ireland. This is shown with the black line.
Also it borders to the UK and all of the world's ocean bordering countries which is shown through the surrounding blue.
The map shows the country "United Kingdom of Great Britain and Northern Ireland" (UK) without separating its constituent countries. This is what most political world maps do.
Ireland does border by land to the UK, at the border of Northern Ireland. This is shown with the black line.
Also it borders to the UK and all of the world's ocean bordering countries which is shown through the surrounding blue.
It is a little inconsistent in that it shows the Bosporus dividing Turkey and even the Suez Canal dividing Egypt, but not the Irish Sea dividing the UK - though the first two are nominally continental boundaries.
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Well, if you're going to go down that route:
> the British isles
Many in Ireland[1] would consider that a rather loaded political term rather than neutral geographic one, and wouldn't use it to refer to Britain and Ireland.
> Secondly, Ireland doesn't even have a blue line, which implies it is connected by land to Britain
It's connected by land to the UK. Maybe there should be an additional blue line to denote the Irish sea, but it wouldn't exactly add any additional borders to the map, as GB is also an island.
> And thirdly, Wales and Scotland should really be acknowledged, and at the same time you might suggest Northern Ireland as well.
Why? The UK as a whole is already there. Ireland is a sovereign state in its own right, unlike Scotland, Wales and Northern Ireland which are just constituent parts of the UK. Do you think every US and German state should be there as well?
[1]: https://en.wikipedia.org/wiki/British_Isles_naming_dispute
> the British isles
Many in Ireland[1] would consider that a rather loaded political term rather than neutral geographic one, and wouldn't use it to refer to Britain and Ireland.
> Secondly, Ireland doesn't even have a blue line, which implies it is connected by land to Britain
It's connected by land to the UK. Maybe there should be an additional blue line to denote the Irish sea, but it wouldn't exactly add any additional borders to the map, as GB is also an island.
> And thirdly, Wales and Scotland should really be acknowledged, and at the same time you might suggest Northern Ireland as well.
Why? The UK as a whole is already there. Ireland is a sovereign state in its own right, unlike Scotland, Wales and Northern Ireland which are just constituent parts of the UK. Do you think every US and German state should be there as well?
[1]: https://en.wikipedia.org/wiki/British_Isles_naming_dispute
You misunderstand the status of these countries, which are countries. They have their own football teams. The only reason that they are largely ruled from Westminster is due to the the military strength of England.
They’re not sovereign states though. Having a football team doesn’t make something a country, I hope you realise how ridiculous that sounds.
And that last sentence is an extremely revisionist view of British history.
And that last sentence is an extremely revisionist view of British history.
Britain isn't on the map, the UK is. Boris forgot that the UK had a border with Ireland, don't be like Boris. The blue line of the channel could be thicker though.
Presumedly they are counting the land border between Ireland and Northern Ireland (as part of UK), but it’s confusing with the water boundary called out between UK and France.
Whereas I would call Northern Ireland an exclave colony, although in the current political status fittest part of the UK, much as Puerto Rico is part of the US, or the non-Russia Soviet States were part of the Soviet Union.
Also it does not seem to account for overseas territories/d'outre-mer, but that's understandable.
It's only Turkey, Panama, and Egypt that have a split in them, as they are places that have notable straits going through them. The UK is handled the same as Indonesia.
The weird thing about Wales and Scotland is that they complete independently in sports stuff not that they are excluded here, they are integrated parts of the UK with the same amount of autonomy as a large U.S. city.
The weird thing about Wales and Scotland is that they complete independently in sports stuff not that they are excluded here, they are integrated parts of the UK with the same amount of autonomy as a large U.S. city.
The remaining countries have too many neighbors and, accordingly, potential opponents. Look at the Balkans or part of Africa.
I live in Sofia, Bulgaria and it has always seemed silly to me that the reason our city was chosen as the capital was the fact that it is surrounded by mountains on all sides. Now with this war in Ukraine, this idea seems genius to me.