The topologist’s world map (2020)
tafc.space
tafc.space
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.
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.
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.
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.
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.
In my view, "might makes right" is simply an observation of harsh reality. Ignoring that reality is folly.
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.
U.S. already had multiple wars where their geography kept their infrastructure and citizens safe. Other countries got obliterated and lost their superpower trait.
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.
http://web.archive.org/web/20221219173909/tafc.space/qna/the...
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.
Adding cells that don’t correspond to a country (like your proposed white circle) would make the map less accurate.
It's difficult to know what the definition for inclusivity is.
You know the flat earthers would run wild with that map.
An all too familiar situation.
[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 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.
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.
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?
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.
That’s basically what this is, if you draw it on a pixel grid.
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.
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.
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.)
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.
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
[0] https://storymaps.arcgis.com/stories/756bcae18d304a1eac140f1...
(also sorry to be pedantic)
Obviously not the cultural convention though.
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.
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 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
And that last sentence is an extremely revisionist view of British history.
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.