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Comment by ZeroCool2u | Hacker News Reader

I still remember the first time I learned about this. I was watching the West Wing (Season 2 Episode 16[1] which explains the problem pretty quickly) for the first time in the early 2010's and was absolutely blown away that we'd never been taught about this in public school (U.S.A.). Having graduated High School and a couple of years through undergrad, and just then realizing that my entire perception of the relative size, and in some cases position(!), of the continents is basically just wrong. It was actually a generally useful thought exercise though, because it really forced me to confront the fact that I need to consistently reflect on whether my previous assumptions on even basic topics hold true.

I'm not sure it would be worthwhile to advocate for changing the default projection at this point due to the logistics, but at least teaching kids about the issue, which can be covered in no more than a few minutes and is obviously not super complex, just so they're aware of it seems totally worth it!

[1]: https://www.youtube.com/watch?v=vVX-PrBRtTY

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Oh great, the Gall-Peters projection.

The Gall-Peters projection is just as problematic as the Mercator projection. Actually, it is arguably more problematic because it doesn't have any compelling features that it does better than other world-scale maps.

The best world-scale maps are going to be along the lines of the Robinson projection, where you give up on trying to pretend that the world atlas is a rectangle. You're going to be screwed any way you go about it. Cylindrical map projections suck at large scales, because one of the directions is being stretched way too much. Conic map projections are good at intermediate scales (state-to-continent size), but when you expand the map to large sizes, the distortions at the edges become too great to bear.

The Gall-Peters projection is an equal-area map, but it goes about this in an especially annoying way. The areas near the equator are made excessively tall and skinny, and near the poles, they are excessively short and wide. And it turns out that human beings are really not good at comparing sizes of rectangles that have drastic aspect ratios in different orientations. The spaghettification of countries doesn't lend itself to a visually pleasing map, and it really obfuscates useful tidbits such as "Maine is closer to Africa than any other US state", which is pretty clear in virtually every other world map. To top it off, it was presented to a cartographic conference as the map that's better than Mercator at a time when all cartographers were already using non-Mercator maps and complaining about lay people relying on Mercator maps for world projections.

I think the Waterman butterfly projection is my favorite:

https://en.wikipedia.org/wiki/Waterman_butterfly_projection

Mine is Buckminster Fuller's dymaxion map: https://en.wikipedia.org/wiki/Dymaxion_map

Great for showing the relative sizes of continents (and also visualizing how all the continents are nearly one contiguous landmass), at the cost of chopping up the oceans.

Second favorite is the Peirce quincuncial map: https://en.wikipedia.org/wiki/Peirce_quincuncial_projection , which tiles the plane.

The Dymaxion map is very interesting, I was a bit surprised just how connected the continents actually are.

Pangea theory is much more obvious when you look at that map.

Also it is interesting that it is as if the whole "land" of the world is basically a big island in the middle of the ocean.

That looks pretty tough on New Zealand.

The parent comment never endorsed Gall-Peters.

It's unclear whether they were simply made aware of different projections through the show or if they thought Gall-Peters was the ultimate solution, as you assumed.

They did link to a video entitled Gall-Peters though, so it's clearly on topic.

>And it turns out that human beings are really not good at comparing sizes of rectangles that have drastic aspect ratios in different orientations.

I keep wondering, if there are a map like Mercator projection, as reference since everyone is familiar with it, but provide size that is relatively accurate but not 100% area accurate like Gall-Peters projection.

i.e It is a map that is not accurate by an metrics or projection in any shape or form but a better Mercator ( Normal ) Map with slightly more accurate showing of relatively size.

It is only used to provide some sort of better mental model without using the Globe. Rather than Direction And Traveling ( Mercator ), true Size, ( Gall-Peters ).

The Robinson projection is probably what you're looking for. It was explicitly created to try to balance these two extremes.

I also think that the Robinson is probably the best candidate for an accurate "default" map of the world. There are projections I prefer but the Robinson retains the recognizablity as being obviously a map of the world.

Robinson or Winkel tripel are probably the best here. Aitoff, Mollweide, Kavrayskiy, Wagner, etc. are all decent choices here as well.

One commonality all of these projections have is that they are pseudocylindrical instead of cylindrical: lines of longitude are not depicted as straight lines but as curved lines, with the curve being more pronounced the further from the central meridian you are.

I am wondering, are globes rare where you live? They do not suffer from any distortion. Changing maps does not help, there is a theorem that no faithful planar map of a sphere exists, the video is a bit short on this.

For kids (and adults!) the LaapFrog interactive globe is superb.

Not sure how much they've retained, but when they were younger, my kids could pinpoint every country on the globe, and knew the capital of every country.

Edit: The model we had was much less sophisticated than that currently available (no screen or videos). It had, for example, fun speed games where it would name countries and you had to find them on the globe and tap them with the stylus, competing for who could find the most countries in a set time.

I was excited to buy one for my kids, but apparently they may not have improved since then :-( https://www.amazon.com/gp/customer-reviews/RJ4ZQ1SDMKLNU/

I'm guessing there's a term for products that get worse by virtue of being "enhanced".

They really should reintroduce the old model, just with updated political geography.

You can't generally see two countries next to each other on a globe. The globe itself is accurate, but a human looking at a globe sees an orthographic projection up to binocular perspective, which is only accurate near the center. So you can't compare India to Brazil for example.

Sure you can, you just rotate the globe back and forth. You can even measure and compare it roughly using your fingers.

Use two globes?

And I wonder why inflatable ball globe are not that common? Much better than globe on axis.

They are in every single classroom in the US. A lot of kids, like the parent poster, just never look at them.

Thats interesting. Here they usually are not in classrooms, but at home.

No, they really aren't. While there was a globe or two in different classrooms, most classes that needed maps of sorts had pull-down maps.

Once we reached middle and high school, most classes didn't have maps. If I were building a modern school, I might not put physical maps in any classroom equipped with modern projection tools and smart boards.

> They do not suffer from any distortion.

You must be from the northern hemisphere. Globes seem to be mounted upside down usually, Antarctica belongs on top.

Is there a truly rationale basis here (other than “magnetic north” which is equally arbitrary and has rotated)? I’d argue since the vast majority of the world’s population lives in the northern hemisphere, it generally makes sense to put that at the top, all else being equal.

On the contrary, it makes the most sense to place some point of the equator on top, so that you can rotate to look at any part of the globe you want, surely?

It's a lot easier to add the rest of the solar system if it rotates around the Earth horizontally, and you need that to explain the day/night cycle, seasons and tides.

Call me weird if you must, but I would prefer a globe rotate in the same fashion as the planet does: around the poles.

That's perfectly compatible with the poles being on the sides and the equator being on a vertical plane. In fact, many globes can be tilted to this position and the main rotation still happens around the poles.

Granted, but surely that would place "all points" on the equator "on top" rather than "some point"?

You're right, I spoke imprecisely. Some point on top to begin with, any other equatorial point you want with a quick spin.

They all do, but you can have more than one dimension of rotation.

Look at https://www.amazon.com/dp/B085K2ZPWB/ .

You're still free to spin the earth backwards, though.

Interesting, so a globe on a 90 degree axial tilt rather than a 23 degree one. I'm sure I've seen such (either fixed at 90 degees or variable from 0-90 degrees), but I can't see any after a quick browser online.

no, just most people lives on top that's all.

For one, the southern hemisphere is mostly water.

But if the majority of the population lives in the northern hemisphere, shouldn't that make it heavier and thus flip the earth, placing the south pole on the top?

I think there is, actually: The Milky Way Galaxy. South is "down" towards the center, North is "up" towards the exterior. It was a revelation to realize this after growing up looking at the Milky Way in Northern Europe, that we're somewhat stationary in relation to the galaxy.

Can you explain this more? I do not understand this

The galactic center roughly aligns with the constellation Sagittarius, which is considered a southern constellation.

If you try to do milky way astrophotography in the northern hemisphere you quickly find out you are limited to the late spring / early summer, because you want to be seeing the southern sky at night. Most of the year the sun is too close to Sagittarius during daylight hours, making viewing impossible.

On what basis do you pick a definition for a globe being "upside down"?

certainly not the right-hand rule.

right hand rule for orital motion instead (or am i as usual getting this wrong)

it was mostly a joke, since the right-hand rule is itself an arbitrary convention.

I think you are right though; "up" and "down" are defined by applying the right-hand rule to the orbits of the planets around the sun, not their rotation about their own axes. this is why we consider venus to spin "backwards" as opposed to being "upside down". this does lead to an odd conundrum in the case of uranus, whose axial tilt is almost a right angle. which of uranus's poles is north?

> the right-hand rule is itself an arbitrary convention

This may not be true - if magnetic monopoles exist, choice of handedness becomes linked to choice of magnetic sign convention.

The claim there is no distortion all depends on one’s perspective. Top, bottom and, obviously, size have been chosen.

Distortion shares a root with torsion, twisting.

Scaling something evenly is not distortion, nor is placing it upside down, or otherwise changing its orientation.

There is no sense or perspective in which the orientation of a globe can be said to distort the shape of its features.

I believe the other commenter is referring to a distortion of mental perspective, not geometry, and honestly I’m buying it. It’s so strange to look at a globe upside down, even though there’s nothing unnatural about it.

I honestly thought I must have missed something big until I got to your comment... It seemed painfully incongruous in my mind to equate the demonstrably geometric ‘distortion’ artifacts directly resulting from a lower dimensional representation of a sphere ... to the mathematically unrelated notion of orienting the observational frame of reference. 2D maps literally distort and misrepresent the spatial arrangement of our planet’s surface in a metaphysical sense. Globes do not suffer from this distortion of space in their spherical approximate representation of the planet. The latter seems to be the the most salient point of the thread given whether you use an actual globe or a virtual one such a Google Earth... both of which are ubiquitously common and available ... it seems practically irrelevant (if nevertheless interesting) to consider the distortion of a 2D map as an actual “problem”. And whether or not one agrees with that, it’s wholly unrelated to whether you choose to hold your 2D map or 3D globe upside and any other orientation relative to your observational frame of reference—the former remains geometrically distorted in an egregious manner and the latter not.

Hahaha. I was wondering if I shd mention this. Of course north is up (like on any map :-)). On a more serious not this is probably really a political bias, but a lot of globes can be taken out and rotated in the frame (maybe with tooling). So one shd check before buying if the north bias can be cured.

But then you need to stand on your hands to read the labels

Sports is good, isnt it

That would be cruel. The turtles would be unable to right themselves and could possibly die.

I've had a globe since I was a young boy. I have an illuminated one in my study now. How better to explain "Great Circle" air travel?

No projection is accurate. Cartographers generally recommend against rectangular map projections. The Mercator is better at local shapes, because it's conformal, which is a not-often-mentioned advantage. Conformal maps have the property that accuracy consistently improves as you zoom in at every point. The tradeoff is that the discrepancy between regions separated by large distances can be much worse. Because the Mercator both works locally and supports loxodromic navigation it has remained popular.

One alternative I like is using a conformal projection divided into hemispheres. You can get much less distortion at the cost of a single interruption. Eg:

https://postimg.cc/N5nZ18CF

I taught this in 6th grade social studies in Ohio (a state in the USA) two years ago.

A reasonable interpretation of the standards should see this being taught in all 6th grade social studies classes across Ohio.

SPATIAL THINKING AND SKILLS

Content Statements:

3. Geographic tools can be used to gather, process and report information about people, places and environments. Cartographers decide which information to include and how it is displayed[0]

There were a number of videos explaining this concept. I remember this one from Vox [1] in particular resonating with the students.

So while we might have been short changed (I grew up in Ohio), the curriculum is improving.

[0] http://education.ohio.gov/getattachment/Topics/Learning-in-O...

[1] https://www.youtube.com/watch?v=kIID5FDi2JQ

In our case (VA), it was the 5th grade curriculum where we discussed map projection shortcomings, as part of world history. (For timing, this would have been about 2000).

5th grade for me too, with lots of memorizing features, drawing our own maps, learning different map projections... This was the early 90s, NJ

One thing that could be done is for schools to actually teach geography.

It’s extraordinarily relevant to history and current affairs. It gets a bad reputation because there is of necessity a significant amount of memorization. Knowing rivers, cities, mountain ranges, climates, the relative size and population of cities and countries really enhances your understanding of both historic and current events.

And I really hate to be one of those the-US-is-really-terrible-at-this guys, but it’s been my experience that the US is really terrible at this.

I never learned much about mapping or map projections until university, I still think it's one of the most valuable things I learned there and one of the things I learned actually worth the money.

We had a couple courses on manual mapping, surveying, geography, compass reading triangulation, all that stuff. How to draw a map by hand based on compass and survey data.

By far some of the most awesome stuff i've learned. I agree, more stuff like this should be touched on in high school. Mapping is such a large yet underappreciated part of society.

When I went through high school (in Australia) the memorisation parts of geography had long since gone out of fashion, and what had replaced them was a series of "case studies" where you learned about the lifestyles of some obscure group of people elsewhere on the planet for a few months before forgetting about them entirely.

At least memorising the capital cities of every country on Earth gives you some kind of big picture knowledge that you can build on in later life.

I'm almost 50, and we did a geography project in grade 5 on Brazil. I still remember a lot about that project, despite a lot of that information being completely out of date now (My instinct is to still say cruziero as the currency of Brazil even though it's wrong). I've never been to the country and probably never will just out of lack of interest, but it's funny how some things stick with you.

I'm confused at the "didn't learn it in school!" comments. I went to an average public school in lower-middle class area in the US and remember learning lots of geography. Memorizing rivers, mountains, major cities, national parks etc., and yes multiple forms of map projections. 5th grade in particular really hammered it home. We even had to draw maps. This was the early 90's.

Being old I have noticed that a lot of people swear they didn't learn this or that in school. Even though they were to the same school as me. I think it's down to selective memory, it was just not registered because there was something more interesting at the time. Youth only being humans after all.

I think it comes down to what interests you. Nuggets like how different map projections impact size and shape of the earth is the kind of thing I would never forget.

Other kids could discuss specific goals, matches, titles and football players; sometimes from foreign leagues. Even though I vaguely enjoy watching the odd match, the details would instantly be lost to the ether.

Was this the entire world, or just the US?

My public school matches everything on your list except map projections, but it is possible I just did not pay attention to that...

I was taught world geography, just have no memory of different map projections

> It gets a bad reputation because there is of necessity a significant amount of memorization.

Ah, the joys of having to memorize all the counties and then all 50 states and their capitals. Never again.

> And I really hate to be one of those the-US-is-really-terrible-at-this guys, but it’s been my experience that the US is really terrible at this.

We could do better but it's not like we don't learn geography. We learn state and national geography. I supposed world geography could be emphasized more.

I had high hopes for geography at secondary school but dropped it at the first available opportunity.

As a small child I spent a lot of time memorising the atlas, not just the maps with the towns/rivers/capitals but also the pages that went before that about what countries exported what, what countries imported what, how the continents had changed over millions of years, the flora and fauna as well as the volcanoes stuff.

At school there was no teaching of the towns/cities/countries it was just about how volcanoes and tectonic plates worked. Which was far too boring for me.

If you know towns, cities and countries at the atlas level then it is knowledge learned by rote. If you find yourself living in a cosmopolitan city such as London where you meet people from all over the world then you can find this information useful. Even if you have never been there yourself you once knew a place well enough to remember the name so there is genuine interest in finding out what it is like to live there.

I wish they taught this geography of place names as a subject because it could be the one subject that kids who like memorising stuff could do well at.

This is very good, explaining much better than I could possible do. Thank you.

Also, I remember reading about AuthaGraph World Map[1] from the architect Hajime Narukawa[2] which won The Good Design Grand Award[3] back then, creating a new world map displayin each contry, including Antarctica and the North Pole shown in its entirety.[4]

[1] https://totravelistolive.co/authagraph-world-map/ [2] https://en.wikipedia.org/wiki/Hajime_Narukawa/ [3] https://www.g-mark.org/ [4] http://www.authagraph.com/top/?lang=en

If it makes you feel any better, I remember both explicitly learning about this in middle school and being blown away when I first saw a visualization of the effect 10 years later.

At school it was just something you know and regurgitate as fact. After a visualization like this, you understand what you learned.

American here. My underfunded school taught us this in 6th grade. We even cut orange peels to learn the different projections.

That was the 90s. Public schools have really gotten shitty.

Had a mid-sized globe at home growing up. It wasn't attached to anything so you could pick it up and rotate it any direction. This gave me a pretty could sense of how big any o the continents and countries were, more than anything.

Totally with you -- and I have a rant on this that expresses your same indignation![1] Sadly, the alternatives are also bad, albeit for different reasons; damn this cursed sphere!

[1] https://www.youtube.com/watch?v=F5jCXdTYJYc#t=30m35s

You know if we could all just agree on the flat earth thing it would be quit a bit easier. Gravity wouldn't make a whole lot of sense though.

Bah easy, the flat earth is accelerating through space at 9.8m/s/s ;)

That's much too fast, the turtles underneath can't walk that fast, and there's a whole lot of them

You could have just looked at a globe!

I have a globe and it does not do as good a job as this site or other visual tools that the OP was referring to. These new tools are way better at showing the difference in actual sizes.

Tools like this one might be better at highlighting the flaws of map projections, but I don't see how anything could be better than a globe at showing the true relative sizes and shapes of countries, since it shows them as they actually are. In what way do you feel the globe doesn't show the differences between countries well?

In what way does a globe not do a good job showing the true size of countries?

The biggest problem with a globe is that it is round.

In this case, that means you can’t see all of it at once, which means you’re relying on your visual memory unless you actually pull out calipers.

Seems like this could be easily fixed. Make the countries on the globe removable (magnetic?). Then they could be moved over other countries to get a direct relative comparison in the same field of view. Similar to what the OP web site is enabling.

Or have a conventional printed globe but that has a clear "shell" with an engraved map that can be freely positioned to overlay any part of the "shell map" atop any part of the conventional globe surface.

I have no idea how the mechanism allowing this globe within a globe would work.

As flexible screens get better maybe a globe whose entire surface is a touch-sensitive display that allows gesture control of the map content?

A possible issue with this is that due to the spacing between the two concentric globes the countries on the external one will appear bigger than the ones on the internal one.

Perhaps the engraving on the outer shell would need to be done on the inner surface?

> Make the countries on the globe removable (magnetic?

Countries as jigsaw puzzles pieces, made with soft Silicone, should work as well

yes, you're very clever ;). https://xkcd.com/977/

Thank you for sharing this. I'm ashamed that in all my years on this planet I thought that Greenland was nearly as big as the whole of Africa.

I think I'd over compensated - I was surprised to find that Greenland is nearly as big as India.

Oddly, in my US elementary education we spent a lot of time in 4th and 5th grade learning about different kinds of maps and their trade offs. Perhaps my classes were anomalous?

In Europe everyone has a word atlas for geography class, and the various projections are explained literally on the first page.

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