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The topologist’s world map (2020)

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Re: The topologist’s world map (2020)

#41

Post by Someone »

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?

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.

Re: The topologist’s world map (2020)

#42

Post by gmadsen »

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…

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

Re: The topologist’s world map (2020)

#47

Post by klyrs »

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 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.

Re: The topologist’s world map (2020)

#49

Post by _moof »

Zobat wrote: post #17

Places Iceland in America, but other than that really nice.

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.

Re: The topologist’s world map (2020)

#50

Post by whatshisface »

anonporridge wrote: post #40
School-Cotton wrote: post #37

Earlier quoted context omitted.

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_(g…

>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.

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