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The topologist’s world map (2020)

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Re: The topologist’s world map (2020)

#31

Post by messe »

richardhod wrote: post #11

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 s…

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

Re: The topologist’s world map (2020)

#32

Post by malwrar »

todorstoyanov wrote: post #22

Fascinating how protected by their geography are USA, Canada, Ireland and maybe UK. 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…

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.

Re: The topologist’s world map (2020)

#33

Post by anonporridge »

todorstoyanov wrote: post #22

Fascinating how protected by their geography are USA, Canada, Ireland and maybe UK. 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…

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.

Re: The topologist’s world map (2020)

#34

Post by ouid »

ogogmad wrote: post #10

For people who have time to burn being uselessly pedantic, is this a topologist's world map up to homotopy equivalence or homeomorphism? [edit] 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…

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.

Re: The topologist’s world map (2020)

#36

Post by trynewideas »

hammock wrote: post #29

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?

> 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.

Re: The topologist’s world map (2020)

#37

Post by School-Cotton »

anonporridge wrote: post #33
todorstoyanov wrote: post #22

Fascinating how protected by their geography are USA, Canada, Ireland and maybe UK. 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…

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 stron…

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.

Re: The topologist’s world map (2020)

#38

Post by School-Cotton »

wnkrshm wrote: post #3

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.

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.

Re: The topologist’s world map (2020)

#39

Post by cwmma »

richardhod wrote: post #11

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 s…

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.

Re: The topologist’s world map (2020)

#40

Post by anonporridge »

School-Cotton wrote: post #37
anonporridge wrote: post #33

Earlier quoted context omitted.

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 stron…

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 gu…

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.

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