[HN Gopher] The topologist's world map (2020)
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The topologist's world map (2020)
Author : bo0tzz
Score : 204 points
Date : 2022-12-20 12:05 UTC (10 hours ago)
(HTM) web link (tafc.space)
(TXT) w3m dump (tafc.space)
| sylogizmo wrote:
| 508'd, so I guess the comments will make sense tomorrow.
| hammock wrote:
| 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?
| Someone wrote:
| 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.
| trynewideas wrote:
| > 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.
| klyrs wrote:
| > 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.
| joshuaissac wrote:
| 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
| jfengel wrote:
| 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.)
| abbusfoflouotne wrote:
| > 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.
| culi wrote:
| 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
| twic wrote:
| > 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.
| BenoitP wrote:
| I wonder how it would look like if we considered France's borders
| with the Netherland (at Saint Martin) and Brazil (at French
| Guiana).
| Someone wrote:
| 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.
| 082349872349872 wrote:
| I still find a Spilhaus projection more informative, but this is
| defo interesting!
| roter wrote:
| Definitely if you're an oceanographer. Interesting link here
| [0].
|
| [0]
| https://storymaps.arcgis.com/stories/756bcae18d304a1eac140f1...
| hoseja wrote:
| That tiny Canada-Panama striped tail containing the entirety of
| North and Central America is funny.
| 082349872349872 wrote:
| This map tends to give vertex-like countries large areas, and
| vice-versa.
| MonkeyClub wrote:
| 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...
| [deleted]
| ecommerceguy wrote:
| Just think if the Diomede islands were uplifted somehow, poof
| Russia and the USA have a border.
| thriftwy wrote:
| In winter there kind of is - I think you can walk by ice
| sometimes.
| lastofthemojito wrote:
| But don't expect a warm welcome if you make the trip:
| https://www.nbcnews.com/id/wbna12152629
| todorstoyanov wrote:
| 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 idea seems genius to me.
| anonporridge wrote:
| 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.
| umanwizard wrote:
| 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.
| anonporridge wrote:
| 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.
| whatshisface wrote:
| > _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.
| anonporridge wrote:
| 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.
| eftychis wrote:
| 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.
| gmadsen wrote:
| 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
| xkcd1963 wrote:
| 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.
| gat1 wrote:
| France's geography is actually also insane as a protection :
| ocean, seas, mountains or vast forest.
| malwrar wrote:
| 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.
| [deleted]
| ogogmad wrote:
| 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 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.
| ouid wrote:
| 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.
| joshlemer wrote:
| Canada actually now has a land border with Denmark!
| https://en.wikipedia.org/wiki/Hans_Island
| glitcher wrote:
| I like how the Panama Canal is represented by the gap in the name
| Pan|ama. Nice work overall!
| richardhod wrote:
| 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.
| tomtomtom777 wrote:
| 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.
| [deleted]
| mannykannot wrote:
| 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.
| cwmma wrote:
| 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.
| messe wrote:
| 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
| mc32 wrote:
| Also it does not seem to account for overseas
| territories/d'outre-mer, but that's understandable.
| pimlottc wrote:
| 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.
| adammarples wrote:
| 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.
| ISL wrote:
| https://web.archive.org/web/20221219173909/https://tafc.spac...
| TchoBeer wrote:
| What's going on by Israel-Egypt
| hydrogen7800 wrote:
| Egyptian territory on both sides of the Suez canal.
| HPsquared wrote:
| Could be a nice basis for a board game.
| pjmorris wrote:
| Topographical Risk!
| Zobat wrote:
| Places Iceland in America, but other than that really nice.
| _moof wrote:
| Iceland emerged (is still emerging?) from the rift between the
| North American and Eurasian plates. Roughly speaking everything
| west of Thingvellir 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.
| lastofthemojito wrote:
| That's not wrong geologically:
| https://www.icelandtravel.is/attractions/bridge-between-cont...
|
| Obviously not the cultural convention though.
| [deleted]
| forgotpwd16 wrote:
| The no-text version looks like Gallifreyan writing.
| wnkrshm wrote:
| 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.
| umanwizard wrote:
| 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.
| iso1631 wrote:
| Then you get onto the definition of what a country is - there
| are many countries claiming land in Antarctica.
| glxxyz wrote:
| Prior art:
| https://upload.wikimedia.org/wikipedia/commons/4/48/Hereford...
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