When talking about digital ethics I often begin with a run-through of how the tools, models and workflows we use are taken for granted, with rare concern for how they mislead. And the longer we use them the less they are questioned. In truth we really need to regularly revise and redesign all the tools we use. All tools simplify, which makes them vehicles for potential harm when the risks of oversimplification are not talked about, or worst-case: forgotten.
The world map is my go-to example. The flat, visual portrayal of the world in two dimensions based on the Mercator projection has been so commonplace in classrooms worldwide that this map is widely embedded in collective consciousness as a plausible truth. In my experience too few are taught to question it, even by their teachers. Which is disadvantageous of course, because the world – believe it or not – has never been flat.
Here is the two-dimensional map you most likely know best, using the Mercator projection:
Consider your relationship to this map. In your head you likely use it to think about distances between countries, and of course the shapes and sizes of countries and continents. Greenland and Africa, for example, look to be essentially the same size. In reality of course Africa is about 14 times larger than Greenland.
The Mercator projection was originally presented by Flemish geographer and cartographer Gerardus Mercator back in 1569. Its purpose was to be used for maritime navigation and it served this purpose well since throughout the projection North is up and South is down, while local shapes and directions are maintained. So when using this projection on a map scaled for navigational use it's easier to find your way.
This perhaps makes sense to you. But should it? Obviously, nobody puts a world map in their lap and navigates based on that. The Mercator projection is used for local navigation on a much smaller scale, where it makes sense. The world map is what happened when the same projection was extended to include the whole world.
Consider the full modern representation of a world map based on the Mercator projection that includes Antarctica. Remember, Antarctica hadn't yet been discovered when Mercator first introduced the map. Now, think about how long the top and bottom sides of the map are. They are just as long as the equator. That whole horizontal stretch of distance at the top and bottom should essentially be small dots. Those are the poles, where the north and south converge, respectively.
What is happening in the Mercator projection is that the further something is from the equator, the bigger it appears, because it is necessarily stretched out horizontally. A world map based on the Mercator projection is constructed as if the world was a cylinder rather than a globe. Antarctica is of course nowhere as big as it appears here.
This also means that Europe and North America appear much larger than they really are in comparison to Central Africa and South America. Another favorite example of mine is Sweden superimposed on Madagascar. On a world map based on the Mercator projection Sweden appears to be at least twice the size of Madagascar. In reality, as shown below, Madagascar is 30% larger.
There is another non-intuitive effect of flattening the globe in this way. It's about how the curvature of the Earth is misrepresented. When drawing straight lines between countries they would in reality be curved and seemingly curved lines can in fact be mostly straight. Allow me to elaborate.
In my talks I show this image of the world where a curved line, almost like a sinus curve traverses the map. One end of the line starts in Pakistan and it passes between the African mainland and Madagascar, dips below Africa and South America, and ends up in Russia, in a place known as Kamchatka Karia.
I then ask: what is this line?
Many people are naturally stumped by this question. The answer is that this line represents the longest distance you can sail across the world in a straight line without hitting land. It represents a distance of 32,000 kilometres. And yes, you read that right: this is a straight line.
The assertion of this being the longest distance in a straight line across water originally came from Reddit user Patrick Anderson (kepleronlyknows) in 2012. It was later confirmed by researchers Rohan Chabukswar and Kushal Mukherjee in 2018.
To give you more evidence, in the video below this line is shown on a 3D representation of the globe using Google Earth. Here it becomes evident that the line is in fact straight.
If you have ever travelled on a long-distance flight you may have followed the flight path on a screen on the plane. You may have wondered why the flight path doesn't follow a straight line but instead appears curved. In reality the flight path is more straight (along the curvature of the earth) than you may suspect. It's the map that isn't straight.
As a further example of the skewed perspective provided by the Mercator projection, see the video below where I use the service thetruesize.com to show how Kenya, a country on the equator, would appear if it was further north or south on the map. The effect of the distortion is extremely clear as Kenya further north expands to almost the size of Greenland.
Addressing the problems
By making this the default map in classrooms for centuries, with little context given to the reasons for its appearance, many people have necessarily had a truly twisted view of what the world looks like. There have been many different projections proposed and presented over these centuries, but none have really gained the same popularity as the Mercator one.
Given that the people who claim ownership and ensure distribution of this map have historically been white and rich representatives of the countries in the northern hemisphere, we may have a clue to the reason for its persistence. Why would any of these representatives and leaders have wanted their countries to suddenly appear smaller in favor of poorer countries? But perhaps more obviously: the map is centered on Europe and is a source for adopting global east and west naming conventions.
Beyond a possible colonial preference of minimising the visual significance of South America, Africa and India, there are further dilemmas. In a world facing a climate crisis, understanding the interplay of weather phenomenons (and displacement of people as an effect of heat, drought, flooding and conflict) relies on a firm understanding of the world's systems and structure. While I doubt many scientists rely on the Mercator projection for this type of research, communicating important findings can prove challenging when the majority of the world has a deeply ingrained misunderstanding of the world's appearance.
Similarly, conflicts arise with regards to national ownership of water masses based on erroneous assumptions about size and relative distances.
Say hello to Authagraph
I first stumbled upon the Authagraph projection in 2016, but it was invented already in 1999. Japanese architect Hajime Narukawa proposed an innovative approach to mapping. In 2016 it earned him the Good Design Award.
First of all, the map does a much better job at preserving the relative size and area of land and water masses, while reducing shape distortion. It is also designed to avoid dead ends, allowing the spherical nature of the world to be visualised by simply expanding the map in any direction. You can choose, and are encouraged to, center the map on any part of the world to ensure that your perspective is relevant to what you are trying to learn.
Here is an official version of the map centered on the Pacific Ocean, and another one below it centered on Europe. See if you recognize your part of the world and if this way of presenting the world gives you any aha moments.
Illustration from Authagraph showing how one can choose one's own perspective from the expanded map, centering on the area of interest:
Granted, this map is still not perfect (it's still not a globe) but remains one of the best attempts yet at representing the world in flat, two dimensions. In a map based on this projection, Australia and Brazil suffer the most from distortion. The concept behind the map's tetrahedron roots are explained through the image below.
- A spherical surface is divided into 96 regions.
- The divided regions are mapped on 96 regions on an inflated tetrahedron while it maintains their area ratios.
- The divided regions on an inflated tetrahedron are flattened to be a tetrahedron while it maintains the area ratios.
- A rectangular world map is obtained by cutting out the tetrahedron.
- The obtained rectangular world map.
Sadly the Authagraph map is still a proprietary model, and its equations have not been released or published. So it can not easily be reproduced or used in GIS software. This of course has led many people to dismiss it completely. For a deeper dive, read this review of tetrahedral projections.
These are the key learnings my research on maps has brought me:
- Just because a tool is a huge success for one application does not mean it can be applied indiscriminately for other, seemingly related purposes.
- The longer we use a tool without questioning it, the more of a truth it becomes no matter how wrong it is.
- We can truly believe we understand a tool without really doing so.
- If we use a tool to navigate but don't understand where the tool is wrong, we can draw all the wrong conclusions and end up in bad places.
- We need to be always questioning and revising our tools and models to improve them for the purpose we are using them for.
- People will fight to maintain and keep a faulty tool if they appear to gain from it, even if they learn it is wrong. Be wary of tool colonisation efforts.
- Proprietary tools will face a much bigger struggle in gaining traction. If you want to help better the world, open source is your friend. Open source also opens up for incremental improvements through crowdsourcing.
Thank you for reading. I feel like this with this post I can claim to have changed the world for at least some number of people. Do share and help others gain new perspectives as well! 😊
Links and tools and other stuff related to the conundrum of map projections
Compare real sizes:
Nick Finck pointed me to this hilarious scene from the TV series The West Wing, where representatives from The Organization of Cartographers for Social Equality argue for the Gall-Peters projection map to replace the Mercator projection.
Other projections of note
- Several people have noted that the Authagraph reminds them of the Dymaxion. In several reviews I have seen people mention that the Authagraph indeed seems inspired by the Dymaxion projection, but this does not seem to be confirmed by an official Authagraph stakeholder.
- The Dymaxion map projection projects the globe onto an icosahedron, a geometric shape with 20 sides. The Authagraph projection was created by equally dividing a spherical surface into 96 triangles. These triangles were then projected onto a tetrahedron, which helped maintain the proportions of land and water, and enabled unfolding it to a flat rectangle. Neither would of course be of much use for navigating.
- Hajime Narukawa's own website does have several posts mentioning the Dymaxion: "Fuller intended for the map to be unfolded in different ways. Peeling the triangle one way shows an almost contiguous land while peeling it in a different way shows connected oceans surrounded by land."
- Read more: Buckminster Fuller’s Map of the World: The Innovation that Revolutionized Map Design (1943)
There are many ways to get across the point of distortion in the Mercator map and other equirectangular variants. Here are some you may enjoy. I have seen most of these on Reddit but original sources are unknown. If missing, I am happy to add creator credit if the origin is identified.
The Russia-Africa controversy
Update April 17, 2023: In the image below a long line across Russia is shown to be indicating a much shorter distance than a visibly shorter line across Africa. It's one that many people find hard to accept and that has been the subject of debate, involving Twitter Community Notes and the Encyclopedia Britannica.
Tomas Pueyo tweeted a link to this blog post with this image as an example. And now Twitter has something called Community Notes that can be used by others to call out factual mistakes. In this case the Community Notes have been attached to his tweet with the following text, entitled "Readers added context they thought people might want to know":
False. Russia is east-west 5,600 miles (9,000 km) north-south 1,500 to 2,500 miles (2,500 to 4,000 km). Africa is east-west 4,600 miles (7,400 km) north-south 5,000 miles (8,000 km). britannica.com/place/Africa britannica.com/place/Russia
The first thing to note is that this comment does not attempt to measure the exact lines in the image but instead uses numbers from the Encyclopedia Britannica entries to assert that the supposed distances in the image could not be true. The second thing to note is that Britannica is misleading everyone when it comes to Russia. And that the distances shown in the image are in fact correct.
I had to check this on Google Earth to confirm that it is accurate. It is!
He then goes on to demonstrate how he finds no way of measuring Russia to be 9,000 km across.
My first interaction with Community Notes...& they're incorrect! Although the @Britannica entry does say Russia is 9,000km wide, I can find no way of measuring it that wide using @googleearth , even if you go from Kaliningrad to Cape Dezhnyov, or Lavry to the Kuril Islands...
To illustrate this point he added some images:
Here is what happens if we head 9000km east from Kaliningrad:
Here is what happens if you head east from Kaliningrad to Cape Dezhnyov, and continue to 9000km...:
And here is what happens if we head 9000km from Kaliningrad to the Kuril Islands, and continue to 9000km...:
Yes, it would appear that the Encyclopedia Britannica is rather wrong about the distance East-West of Russia. And the Community Notes on Twitter are more harmful than helpful in saying something is false when it is actually true.
My favorite part of course is when Scafidi questions how the Britannica measurement of Russia can be so wrong ("contiguous Africa is wider than contiguous Russia") and shows that would happen if we applied the same standards of measurement to Africa:
The only way to measure Russia as wider than Africa is to BOTH start the measurement in the Kaliningrad exclave AND cross a sea (either the Sea of Okhotsk or sea of Japan). But if those are the new rules, then I'm measuring Africa as 10,500km wide, starting in Cabo Verde (an African country and member of @_AfricanUnion) and ending on the Mauritian island of Rodrigues, the easternmost point of Africa. 🤣
As you will have understood by now, the size of Africa is of course repeatedly underestimated. And the Mercator projection has a lot of responsibility in this misconception. Also: you can't always trust Britannica, or Twitter's Community Notes.
The True Size of Africa
This XKCD cartoon has been mentioned to me quite a lot.
Stefan Will – July 20, 2023
Apropos the straight line example, the sinusoidal shape reminds me of what circular satellite orbits look like when projected onto a mercator map. And it's hard to argue that those aren't "straight".
pb – April 8, 2023
Is it possible that the Mercator projection is commonly used in the USA simply because all of the early colonists arrived by sea and that's just the maps that they brought along? In Poland, the Mercator projection is simply shown as an example of an equiangular map, if at all, while the "standard" world map used in classrooms and school atlases uses the equal-area hyperelliptical projection.
crazy canuck – April 8, 2023
Thank you for this recap, I keep coming back to it to remind myself of the true size of countries, including Canada, which isn't as big as it seems.
Levent Heitmeier – April 5, 2023
This is definitely one of the best articles i have ever read.
Thom Sulfa – August 20, 2022:
The idea that retaining a map which distorting the sizes of countries is a Eurocentric conspiracy against equatorial countries was originally made by Peters when pushing his equal area projection in the 1970s and 80s.
It's a pretty tendentious argument though, since in addition to it obviously not being the original intent, people don't draw the conclusion that Greenland is a mighty state, the US is subordinate to Canada and the Middle East is a small and inconsequential backwater from map projections, and if people did gauge power and wealth from map projections, the Mercator projection would actually understate the actual relative power and influence of Western Europe anyway (and Peters massively overstates arid underpopulated regions and is barely any better at putting India's sixth of the world population in context).
Plus of course, the Mercator projection is still better for local navigation anyway for reasons not fully represented in this article. The author doesn't even get right the reason why the Mercator excels for navigation: constant rhumb lines. You set your course and you'll get to your destination without needing to correct (a great circle requires constant correction).
Per: Thanks for your input Thom. Yes, I don't think I myself would argue that the Mercator projection is a 'eurocentric conspiracy'. Rather, when I refer to 'colonial preference' my thinking is that the actions (or lack of actions) are often the result of bias and unawareness, and unwillingness to change that which works well enough to support one's own interests. So harm would potentially be caused by lack of care rather than insidious intent.
Of course there are a great many factors that will determine anyone's perception of geographical power structures, far beyond a map projection. But I believe it would be a mistake to discard a pervasive map projection as insignificant. This is also a very small part of the overarching point of the article, to encourage more rigid reflection and analysis of why some models prevail and others are discarded, and I do think these points are valid for that argument - even if the conclusion should be that the maps do not influence biased perception. I've added the example of China's world map to illustrate the idea that different countries will opt for different models of the same phenomenon, and often ones that align with self-image.
John Yesberg – August 21, 2022:
You describe that 32000km line as a "straight line", as though a line on the surface of a sphere can be straight. (To me, a straight line might be tangent to the surface at one point, or cross the surface at two points.) I think this would be a great opportunity to talk about great circles, rhumb lines, and other approximations of straight lines on projected geometries.
Per: While the context of this description hopefully gathers enough understanding to infer what I mean in this article, I do love this as a thought experiment. At what point is a straight line actually straight? If we take a piece of paper and draw a "straight" line with a ruler, is it this not a straight line because the paper itself is not perfectly flat but full of imperfections? If I ask you to walk in a straight line across my lawn, is that even possible? As it would seem, straight lines exist only in mathematics, and not truly within the real world. When it comes to sailing in a straight line, the human experience will often allow this 'clumsy' expression.
Sreader – August 21, 2022:
Sebastian Lague has an excellent video on this topic while trying to make a game that lets you deliver packages across the globe - https://www.youtube.com/watch?v=sLqXFF8mlEU
Per: Thanks for sharing! This was a really beautiful experiment and cool way of taking on the challenge of mapping the flat map onto the globe. I was especially intrigued by the mountain ranges below oceans. I haven't really written much about the topography of the world.
"Kama kuzungumza juu ya maadili digital mimi mara nyingi kuanza na kukimbia kwa njia ya jinsi zana, mifano na workflows sisi kutumia ni kuchukuliwa kwa uhakika, na wasiwasi nadra kwa jinsi wao kupotosha. """ Na kadiri tunavyowatumia kwa muda mrefu ndivyo wanavyotiliwa shaka kidogo. Kwa kweli tunahitaji mara kwa mara kurekebisha na kubuni upya zana zote tunazotumia. Vifaa vyote kurahisisha, ambayo inafanya yao magari kwa madhara ya uwezekano wakati hatari ya oversimplification si kuzungumza juu, au mbaya zaidi: kusahaulika. Ramani ya ulimwengu ni mfano wangu wa kwenda. "Mapambo ya dunia ya ""pana"" ya vipimo viwili, kulingana na makadirio ya Mercator, yamekuwa ya kawaida sana katika madarasa duniani kote, kwamba ramani hii imeingizwa kwa wingi katika fahamu ya pamoja kama ukweli wa kweli." Kwa uzoefu wangu ni wachache sana wanaofundishwa kuitilia shaka, hata na walimu wao. Ambayo ni hasara bila shaka, kwa sababu dunia - kuamini au la - haijawahi kuwa gorofa. "Kama unavyoona, ""Map"" ya 2D ni mfano wa ""Mercator"" na ""Mercator"" ni mfano wa ""Mercator"" na ""Mercator"" ni mfano wa ""Mercator"" na ""Mercator"" ni mfano wa ""Mercator"" na ""Mercator"" ni mfano wa ""Mercator"" na ""Mercator"" ni mfano wa ""Mercator"" na ""Mercator"" ni mfano wa ""Mercator.""" Katika kichwa chako unaweza kutumia kufikiri juu ya umbali kati ya nchi, na bila shaka maumbo na ukubwa wa nchi na mabara. Kwa mfano, Greenland na Afrika zinaonekana kuwa na ukubwa uleule. Kwa kweli, Afrika ni kubwa mara 14 kuliko Greenland. Mfano wa Mercator ulianzishwa na Gerardus Mercator mnamo 1569. Lengo lake lilikuwa kutumiwa kwa ajili ya usafiri wa baharini na lilitumika vizuri kwa kusudi hili kwani katika makadirio yote Kaskazini ni juu na Kusini ni chini, wakati maumbo na mwelekeo wa mahali hapo unadumishwa. Kwa hiyo wakati wa kutumia makadirio haya juu ya ramani scaled kwa ajili ya matumizi ya urambazaji ni rahisi kupata njia yako. Labda hilo lina maana kwako. Lakini je, inapaswa kufanya hivyo? Ni wazi, hakuna mtu anayeweka ramani ya ulimwengu kifuani mwake na kusafiri kulingana na hiyo. Mercator makadirio ni kutumika kwa ajili ya urambazaji wa ndani juu ya kiwango kidogo sana, ambapo ina maana. Ramani ya ulimwengu ni kile kilichotokea wakati makadirio yaleyale yalipanuliwa kujumuisha ulimwengu wote. Fikiria uwakilishi kamili wa kisasa wa ramani ya ulimwengu kulingana na makadirio ya Mercator ambayo ni pamoja na Antaktika. Kumbuka, Antaktika haikuwa bado imegunduliwa wakati Mercator alipoanzisha ramani hiyo kwa mara ya kwanza. Sasa, fikiria urefu wa pande za juu na za chini za ramani. Ni ndefu kama ikweta. Sehemu hiyo nzima ya usawa ya umbali juu na chini inapaswa kuwa nukta ndogo. Hizo ndizo ncha, ambapo kaskazini na kusini hukutana, kwa mtiririko huo. Mfano wa Mercator unaonyesha kwamba kadiri kitu kinavyokuwa mbali na ikweta, ndivyo kinavyoonekana kuwa kikubwa zaidi. Ramani ya ulimwengu inayotegemea makadirio ya Mercator hutengenezwa kana kwamba ulimwengu ni mviringo badala ya dunia. Antarctica ni bila shaka mahali popote kubwa kama inaonekana hapa. Hii pia inamaanisha kwamba Ulaya na Amerika Kaskazini zinaonekana kubwa zaidi kuliko ilivyo kweli ikilinganishwa na Afrika ya Kati na Amerika Kusini. Mfano mwingine ninayopenda ni Sweden iliyounganishwa na Madagaska. Katika ramani ya ulimwengu inayotegemea makadirio ya Mercator, Sweden inaonekana kuwa angalau mara mbili ya ukubwa wa Madagaska. Kwa kweli, kama inavyoonyeshwa hapa chini, Madagascar ni kubwa zaidi kwa asilimia 30. Kuna athari nyingine isiyo ya intuitive ya flattening dunia kwa njia hii. Ni kuhusu jinsi curvature ya Dunia ni misrepresented. Wakati wa kuchora mistari ya moja kwa moja kati ya nchi, kwa kweli itakuwa curved na inaonekana curved mistari inaweza kuwa kweli zaidi ya moja kwa moja. Hebu nijulishe mambo zaidi. Katika hotuba zangu mimi kuonyesha picha hii ya dunia ambapo mstari curved, karibu kama mstari sinus kuvuka ramani. Mstari wa kwanza unaanzia Pakistan na unapita kati ya bara la Afrika na Madagascar, kisha unaingia chini ya Afrika na Amerika Kusini, na mwishowe unafika Urusi, katika eneo linalojulikana kama Kamchatka-Karyia. Kisha nauliza: mstari huu ni nini? Ni wazi kwamba watu wengi wanashangaa na swali hilo. Mstari huu unawakilisha umbali mrefu zaidi ambao unaweza kusafiri kwa meli duniani kote kwa mstari wa moja kwa moja bila kugonga nchi kavu. Hii inamaanisha umbali wa kilomita 32.000. Na ndiyo, umesoma vizuri: hii ni mstari wa moja kwa moja. "Kutoka kwa ""mwisho wa mstari wa moja kwa moja"" kwenye Reddit, Patrick Anderson aliandika hivi: ""Kupitia mstari wa moja kwa moja, mimi na Patrick Anderson, nilipata mstari wa moja kwa moja kwenye Reddit." Utafiti huo ulifanywa na Rohan Chabokswar na Kushal Mukherjee mnamo 2018. Kwa mfano, katika video iliyo hapa chini, tunaonyesha picha ya dunia ya 3D kwa kutumia Google Earth. Hapa inakuwa dhahiri kwamba mstari huo kwa kweli ni wa moja kwa moja. Ikiwa umewahi kusafiri kwa ndege ya umbali mrefu, unaweza kuwa na kufuatilia njia ya ndege kwenye skrini. Huenda ukajiuliza kwa nini njia ya kuruka haifuati mstari wa moja kwa moja bali badala yake huonekana kuwa yenye kupinda-pinda. Kwa kweli njia ya kuruka ni ya moja kwa moja zaidi (pamoja na mwinuko wa dunia) kuliko unavyoweza kudhani. Ni ramani ambayo si moja kwa moja. Kwa mfano wa mtazamo wa kupotoka unaotolewa na makadirio ya Mercator, angalia video hapa chini ambapo ninatumia huduma ya thetruesize.com kuonyesha jinsi Kenya, nchi kwenye ikweta, itaonekana ikiwa iko kaskazini au kusini zaidi kwenye ramani. Athari ya kupotosha ni wazi sana kama Kenya zaidi kaskazini inaenea kwa karibu ukubwa wa Greenland. Kwa kufanya hii ramani ya default katika madarasa kwa karne, na kidogo muktadha aliyopewa sababu ya kuonekana kwake, watu wengi wamekuwa na mtazamo wa kweli twisted ya jinsi dunia inaonekana. Kwa karne nyingi, makadirio mengi yamependekezwa na kutolewa, lakini hakuna hata moja ambayo imepata umaarufu kama ule wa Mercator. Kwa kuwa watu wanaodai kuwa wamiliki na kuhakikisha usambazaji wa ramani hii wamekuwa wawakilishi weupe na matajiri wa nchi za kaskazini mwa dunia, tunaweza kuwa na clue kwa sababu ya kudumu kwake. Kwa nini viongozi hao wa nchi zao walipenda nchi zao zionekane kuwa ndogo kwa ajili ya nchi maskini? Lakini labda wazi zaidi: ramani ni katikati ya Ulaya na ni chanzo cha kupitisha kimataifa mashariki na magharibi majina mikataba. Zaidi ya upendeleo wa kikoloni unaowezekana wa kupunguza umuhimu wa kuona wa Amerika Kusini, Afrika na India, kuna matatizo zaidi. Katika ulimwengu unaokabiliwa na mgogoro wa hali ya hewa, kuelewa mwingiliano wa matukio ya hali ya hewa (na uhamisho wa watu kama athari ya joto, ukame, mafuriko na migogoro) hutegemea uelewa thabiti wa mifumo na muundo wa ulimwengu. Ingawa nina shaka wanasayansi wengi hutegemea makadirio ya Mercator kwa aina hii ya utafiti, kuwasiliana matokeo muhimu inaweza kuthibitisha kuwa changamoto wakati wengi wa ulimwengu una ufahamu wa kina wa kuonekana kwa ulimwengu. Vivyo hivyo, migogoro hutokea kuhusiana na umiliki wa kitaifa wa misa ya maji kulingana na dhana zisizo sahihi kuhusu ukubwa na umbali wa jamaa. Authograph ni moja ya programu za kwanza za picha za picha za picha za picha za picha za picha za picha za picha za picha za picha za picha za picha za picha za picha za picha za picha za picha za picha za picha za picha za picha za picha za picha za picha za picha za picha za picha za picha za picha. Mhandisi wa majengo Mjapani Hajime Narukawa alipendekeza mbinu mpya ya kuchora ramani. Mwaka 2016 alipewa tuzo ya Good Design Award. Kwa mfano, ramani ya dunia inaonyesha jinsi ardhi na maji yalivyo na ukubwa na ukubwa wa kipekee, na hivyo kupunguza kasoro za umbo. Pia ni iliyoundwa ili kuepuka mwisho imara, kuruhusu asili ya dunia ya mviringo kuwa visualized kwa tu kupanua ramani katika mwelekeo wowote. Unaweza kuchagua, na unahimizwa, kuelekeza ramani kwenye sehemu yoyote ya ulimwengu ili kuhakikisha kwamba mtazamo wako unahusiana na kile unachojaribu kujifunza. Hapa kuna toleo rasmi la ramani iliyoelekezwa kwenye Bahari ya Pasifiki, na nyingine iliyo chini yake iliyoelekezwa Ulaya. Angalia kama unatambua sehemu yako ya ulimwengu na kama njia hii ya kuwasilisha ulimwengu inakupa wakati wowote wa aha. Picha ya Authograph inaonyesha jinsi mtu anaweza kuchagua mtazamo wake mwenyewe kutoka kwa ramani iliyopanuliwa, ikizingatia eneo la maslahi: Kwa kweli, ramani hii bado si kamilifu (bado si dunia) lakini bado ni moja ya majaribio bora bado ya kuwakilisha ulimwengu katika gorofa, vipimo viwili. Katika ramani inayotegemea utabiri huo, Australia na Brazili ndizo zinazopatwa na kasoro nyingi zaidi. Dhana nyuma ya mizizi tetrahedron ya ramani ni alielezea kwa njia ya picha hapa chini. Kwa mfano, dunia imegawanywa katika sehemu 96. Sehemu za 96 za tetrahedron zimegawanywa katika ramani ya mkoa wa 96 na kuunganishwa na mkoa wa 96 wa tetrahedron. - Mikoa iliyogawanywa kwenye tetrahedron iliyoinuliwa ni flattened kuwa tetrahedron wakati inadumisha uwiano wa eneo. - Ramani ya ulimwengu yenye umbo la mstatili hupatikana kwa kukata tetrahedron. - Ramani ya ulimwengu yenye umbo la mstatili iliyopatikana. Kwa kusikitisha ramani Authagraph bado ni mfano wa wamiliki, na equations yake hawajaachiliwa au kuchapishwa. Kwa hiyo haiwezi kuigwa au kutumiwa kwa urahisi katika programu ya GIS. Bila shaka, hilo limewafanya watu wengi walishindane nalo kabisa. Kwa ajili ya kuzama kina, kusoma hii mapitio ya tetrahedral makadirio. Hizi ni mafunzo muhimu utafiti wangu juu ya ramani imeleta mimi: - Tu kwa sababu chombo ni mafanikio makubwa kwa ajili ya maombi moja haina maana inaweza kutumika indiscriminately kwa madhumuni mengine, inaonekana kuhusiana. - Kadiri tunavyotumia chombo bila kukiuliza, ndivyo kinavyokuwa kweli hata kiwe kibaya kadiri gani. - Tunaweza kuamini kweli tunaelewa chombo bila kweli kufanya hivyo. Kama sisi kutumia chombo navigate lakini si kuelewa ambapo chombo ni makosa, tunaweza kuvuta wote hitimisho makosa na kuishia katika maeneo mabaya. - Tunahitaji kuwa daima kuhoji na kurekebisha zana zetu na mifano ya kuboresha yao kwa ajili ya kusudi sisi ni kutumia yao kwa. Watu watapigana ili kudumisha na kuweka chombo kibaya ikiwa wanaonekana kupata kutoka kwake, hata ikiwa wanajifunza ni makosa. Kuwa makini na juhudi za tool colonization. - Vifaa vya wamiliki watakabiliwa na mapambano makubwa zaidi katika kupata traction. Kama unataka kusaidia ulimwengu bora, chanzo wazi ni rafiki yako. Open chanzo pia hufungua kwa ajili ya maboresho ya kuongezeka kwa njia ya crowdsourcing. Asanteni kwa kusoma. "Ninaamini kwamba kwa chapisho hili ninaweza kudai kuwa nimebadilisha ulimwengu kwa angalau idadi fulani ya watu.""" Shiriki na kuwasaidia wengine kupata maoni mapya pia! "Kama ilivyoelezwa hapo juu, ""Map ya picha ya picha ya picha ya picha ya picha ya picha ya picha ya picha ya picha ya picha ya picha ya picha ya picha ya picha ya picha ya picha ya picha ya picha ya picha ya picha ya picha ya picha ya picha ya picha ya picha ya picha ya picha ya picha ya picha ya picha ya picha ya picha ya picha ya picha ya picha ya picha ya picha ya picha ya picha ya picha ya picha ya picha ya picha ya picha ya picha ya picha ya picha ya picha ya picha ya picha ya picha ya picha ya picha ya picha ya picha ya picha." Matarajio mengine ya kumbuka - Watu kadhaa wamegundua kwamba Authagraph inawakumbusha Dymaxion. Katika maoni kadhaa nimeona watu wakisema kwamba Authograph inaonekana kuchochewa na utabiri wa Dymaxion, lakini hii haionekani kuthibitishwa na mwendeshaji rasmi wa Authograph. "Kutokana na mapepo ya ""Dymaxion"" ya dunia, dunia inaonekana kama icosahedron, ambayo ina pembe 20." Authograph ni mfano wa picha ya dunia iliyogawanywa katika pembetatu 96. Vipande hivyo vitatu vilipigwa kwenye tetrahedron, na hivyo kuwezesha kuunganisha ardhi na maji na kuunda mstatili. Bila shaka, hakuna hata mojawapo ambayo ingeweza kutumiwa kwa ajili ya kusafiri. "Hajime Narukawa, mwandishi wa kitabu cha ""Dymaxion,"" aliandika hivi: ""Kama ilivyoelezwa hapo juu, ni wazi kwamba mapu ya dunia yote ni ya aina tofauti." Kuondoa pembetatu hiyo kwa njia moja huonyesha nchi kavu iliyo karibu na nchi kavu, huku kuifuta kwa njia nyingine kuonyesha bahari zilizounganishwa na nchi kavu". "Map ya Buckminster Fuller ""Map of the World: The Innovation that Revolutionized Map Design"" (1943) ni map ya kwanza ya dunia iliyochorwa na mchoraji wa Mercator." Hapa kuna baadhi ambayo huenda ukafurahia. Nimeona mengi ya haya kwenye Reddit lakini vyanzo vya awali havijulikani. Ikiwa haipo, ninafurahi kuongeza sifa ya muundaji ikiwa chanzo kimetambuliwa. "Kutokana na ""mjadala wa Urusi na Afrika"" (Ufunguzi Aprili 17, 2023): ""Mstari mrefu unaovuka Urusi unaonyesha umbali mfupi kuliko mstari mfupi unaovuka Afrika." "Hii ni moja ambayo watu wengi wanapata vigumu kukubali na ambayo imekuwa mada ya mjadala, ikiwa ni pamoja na ""Twitter Community Notes"" na ""Encyclopedia Britannica.""" Tomas Pueyo alituma tweet kiungo cha chapisho hili la blogi na picha hii kama mfano. Twitter ina kitu kinachoitwa Community Notes ambacho kinaweza kutumiwa na wengine kuelezea makosa ya kweli. "Kama ilivyoelezwa katika taarifa ya Twitter, ""Wasomaji waliongeza muktadha ambao walidhani watu wanaweza kutaka kujua.""" Urusi ina umbali wa kilomita 5,600 kutoka mashariki hadi magharibi, na kutoka kaskazini hadi kusini ni kilomita 2,500 hadi 2,500. Afrika ni kilomita 7,400 kutoka mashariki hadi magharibi na kilomita 5,000 kutoka kaskazini hadi kusini. "Kama ilivyoelezwa hapo juu, ""Kuna uwezekano mkubwa kwamba ""mwisho wa siku"" utaonekana kuwa unaonyesha picha ya ""mwisho wa siku"" na ""mwisho wa siku"" kwa sababu ya idadi ya alama zilizopatikana katika Encyclopedia Britannica." Jambo la pili la kuzingatia ni kwamba Britannica ni kupotosha kila mtu linapokuja Urusi. Na kwamba umbali ulioonyeshwa katika picha ni kweli sahihi. Ilinibidi nichunguze hii kwenye Google Earth ili kuthibitisha kwamba ni sahihi. Ndio, ni hivyo! "Alichukua hatua ya kuelezea jinsi ya ""kuchunguza"" Urusi kwa njia ya mtiririko wa kilomita 9,000."" Maingiliano yangu ya kwanza na Maelezo ya Jumuiya... na ni makosa! "Kama ilivyoelezwa katika makala ya ""Kaliningrad"" na ""Kaliningrad"" na ""Kaliningrad"" na ""Kaliningrad"" na ""Kaliningrad"" na ""Kaliningrad"" na ""Kaliningrad"" na ""Kaliningrad"" na ""Kaliningrad"" na ""Kaliningrad"" na ""Kaliningrad"" na ""Kaliningrad"" na ""Kaliningrad"" na ""Kaliningrad"" na ""Kaliningrad"" na ""Kaliningrad"" na ""Kaliningrad"" na ""Kaliningrad"" na ""Kaliningrad"" na ""Kaliningrad"" na ""Kaliningrad"" na ""Kuril"" na ""Kuril"" na ""Kuril"" na ""Kuril"" na ""Kuril"" na ""Kuril"" na ""Kuril"" na ""Kuril"" na ""Kuril"" na ""Kuril"" na ""Kuril"" na ""Kuril"" na ""Kuril"" na ""Kuril"" na ""Kuril"" na ""Kuril""." "Kama ilivyoelezwa hapo juu, ""Maelezo ya Jumuiya"" kwenye Twitter ni hatari zaidi kuliko kusaidia katika kusema kitu ni uwongo wakati ni kweli." "Scafidi aliuliza jinsi kipimo cha Britannica cha Urusi kinavyoweza kuwa kibaya sana na kuonyesha kwamba ""Afrika inayoambatana ni pana kuliko Urusi inayoambatana"" na kuonyesha kwamba itakuwa hivyo ikiwa tungetumia viwango sawa vya kipimo kwa Afrika: Njia pekee ya kupima Urusi kama pana kuliko Afrika ni kuanza kipimo katika Kaliningrad na kuvuka bahari (au Bahari ya Okhotsk au Bahari ya Japani)." "Kama sheria mpya, Afrika itakuwa na upana wa kilomita 10,500 kuanzia Cabo Verde na kumaliza katika kisiwa cha Rodrigues, ""kimsingi mashariki mwa Afrika.""" <unk> Kama utakavyoelewa sasa, ukubwa wa Afrika bila shaka umepunguzwa mara kwa mara. Mfano wa Mercator una jukumu kubwa katika kutofautisha. Pia: huwezi daima kuamini Britannica, au Maelezo ya Jumuiya ya Twitter. Kwa kweli, hii ni moja ya picha za kuvutia zaidi za Afrika, na kwa sababu ya kuvutia sana, hii ni moja ya picha za kuvutia zaidi za XKCD. "Stephen Will, Julai 20, 2023: ""Kuhusu mfano wa mstari wa moja kwa moja, umbo la sinusoidal linanikumbusha jinsi mizunguko ya satelaiti ya mviringo inavyoonekana wakati wa kupigwa kwenye ramani ya Mercator." Na ni vigumu kubishana kwamba hizo si "sawa". "Mapema mwaka wa 2023 ""Mercator projection"" ilitumiwa na wakoloni wengi wa Marekani kwa sababu walipeleka ramani za nchi zao." Katika Poland, makadirio ya Mercator yanaonyeshwa tu kama mfano wa ramani ya equiangular, wakati ramani ya ulimwengu ya "kiwango" inayotumiwa katika madarasa na atlas za shule hutumia makadirio ya hyperelliptical ya eneo sawa. "Kwanza, ""Nashukuru kwa muhtasari huu, ninaendelea kurudi kwake kujikumbusha ukubwa wa kweli wa nchi, ikiwa ni pamoja na Canada, ambayo si kubwa kama inavyoonekana." "Lewin Heitmeier, ""Hii ni moja ya makala bora zaidi nilizowahi kusoma.""" "Thom Sulphur, mwandishi wa ""The Economist,"" alisema kuwa ""kuhifadhi ramani ambayo inabadilisha ukubwa wa nchi ni njama ya Ulaya dhidi ya nchi za ikweta, ilitengenezwa na Peters wakati wa kushinikiza makadirio yake ya eneo sawa katika miaka ya 1970 na 1980.""" "Hii ni hoja ya kupendeza, ingawa, kwa kuwa, pamoja na kuwa wazi kuwa sio nia ya awali, watu hawafanyi hitimisho kwamba Greenland ni nchi yenye nguvu, Marekani ni chini ya Canada na Mashariki ya Kati ni backwater ndogo na isiyo na maana kutoka kwa makadirio ya ramani, na ikiwa watu walipima nguvu na utajiri kutoka kwa makadirio ya ramani, makadirio ya Mercator yangepunguza nguvu halisi ya uwiano na ushawishi wa Ulaya Magharibi. """ Zaidi ya hayo, bila shaka, Mercator makadirio bado ni bora kwa ajili ya urambazaji wa ndani hata hivyo kwa sababu si kikamilifu kuwakilishwa katika makala hii. Mwandishi hata haelewi vizuri sababu kwa nini Mercator ni bora kwa ajili ya urambazaji: mistari ya mara kwa mara. Kuweka kozi yako na utapata marudio yako bila haja ya kurekebisha (mzunguko mkubwa inahitaji marekebisho ya mara kwa mara). "Mimi naomba msaada wako, Thom.""" Ndiyo, sidhani mimi mwenyewe ningesema kwamba makadirio ya Mercator ni'mshirika wa Ulaya'. Badala yake, ninapotaja 'upendeleo wa kikoloni' mawazo yangu ni kwamba vitendo (au ukosefu wa vitendo) mara nyingi ni matokeo ya upendeleo na kutokuwa na ufahamu, na kutotaka kubadilisha kile kinachofanya kazi vizuri kutosha kuunga mkono maslahi ya mtu mwenyewe. Kwa hiyo, huenda madhara yakawa yamesababishwa na ukosefu wa uangalifu badala ya nia ya hila. Kwa kweli kuna mambo mengi sana ambayo yatatawala maoni ya mtu yeyote ya miundo ya nguvu ya kijiografia, mbali zaidi ya makadirio ya ramani. Lakini naamini ingekuwa kosa kuondoa ramani ya ramani ya kuenea kama isiyo na maana. Hii pia ni sehemu ndogo sana ya hatua kuu ya makala, kuhamasisha tafakari ngumu zaidi na uchambuzi wa kwa nini baadhi ya mifano inashinda na wengine ni kutupwa, na nadhani pointi hizi ni halali kwa hoja hiyo - hata kama hitimisho ni kwamba ramani hazisumbui utambuzi wa upendeleo. "Nimeongeza mfano wa ramani ya dunia ya China ili kuonyesha wazo kwamba nchi tofauti zitachagua mifano tofauti ya jambo moja, na mara nyingi zile ambazo zinafanana na picha ya kibinafsi. """ "John Yesberg, mwandishi wa ""The New York Times,"" alielezea mstari huo wa kilomita 32,000 kama ""mstari wa moja kwa moja,"" kama kwamba mstari kwenye uso wa dunia unaweza kuwa moja kwa moja." (Kwa mimi, mstari wa moja kwa moja inaweza kuwa tangent kwa uso katika hatua moja, au kuvuka uso katika pointi mbili.) Nadhani hii itakuwa nafasi kubwa ya kuzungumza juu ya duru kubwa, rhumb mistari, na makadirio mengine ya mistari sawa juu ya geometrics iliyosemwa. "Hata hivyo, kwa sababu ya hali ya sasa ya ""kuelezea"" hii, ni muhimu sana kugundua kile kinachohusika na makala hii, na kwa hivyo, ni muhimu sana kuifahamu." Ni katika hatua gani mstari wa moja kwa moja ni moja kwa moja kweli? "Ikiwa tunachukua kipande cha karatasi na kuchora mstari ""mwenye umbo la moja kwa moja"" kwa kutumia mstari, je, hiyo si mstari ulio sawa kwa sababu karatasi yenyewe si tambarare kabisa bali imejaa kasoro?" Ikiwa nitakuomba utembee kwa mstari wa moja kwa moja kwenye nyasi yangu, je, hilo linawezekana? Inaonekana kwamba mistari iliyo sawa ipo tu katika hisabati, na si kweli katika ulimwengu halisi. Linapokuja suala la kusafiri kwa meli kwa mstari wa moja kwa moja, mara nyingi uzoefu wa kibinadamu huruhusu usemi huu wa 'kibaya'. "Sebastian Lange, mwanzilishi wa video ya ""Kupeleka Pakiti Ulimwenguni kote"" ameandika: ""Ninafurahi kuwa na video hii." Hii ni jaribio nzuri na njia ya kupendeza ya kuchukua changamoto ya ramani ya dunia. Nilishangazwa hasa na safu za milima zilizo chini ya bahari. Sijaandika mengi kuhusu topografia ya ulimwengu.