The map you see is the Mercator projection.

But unlike a standard Mercator projection, you can substitute any point on earth as the "pole". (The initial view shows Boston as the pole point)

Furthermore, this map cuts off much, much closer to the poles than normal, allowing you to see many more orders of magnitude of distortion.

Because this yields a map several times taller than it is wide, it is shown sideways from its usual orientation.

The Mercator projection is infamous for its distortion at high latitudes. This distortion gets exponentially worse as you approach the poles. It is in fact impossible to show the poles on a Mercator map — they are infinitely far away.

Any Mercator map you've ever seen must cut off the top/bottom edges at some arbitrary point. The map usually stops hundreds, if not thousands of miles short of the poles.

But I've often wondered what lies beyond those cut-offs... to make a map that didn't cut off but simply kept going. As the distortion progresses towards infinity, you would eventually reach the scale of cities, houses, insects, atoms...

But of course that'd all be on a featureless expanse of ice.

To make things actually interesting, we must artifically shift the pole of the projection to a more interesting place. Imagine the earth encased by a rigid cage of latitude and longitude lines. We rotate the earth while leaving the cage fixed until a new point of interest has taken the place of the North Pole.

This is called an oblique Mercator, and is normally used to shift an area of interest onto the equator of the map to avoid distortion. But whereas others avoid the distortion, we embrace it.

Note how strange the oblique Mercator looks even without the increased cutoffs. The standard Mercator is so ingrained in the public consciousness that we perceive it as 'normal'. But once you shift the pole its pervasive distortion is shockingly apparent.

Lastly, increasing the cutoffs produces a map much taller than it is wide. So it is presented sideways here for easier viewing (set the pole to the North/South Pole like usual to see this most clearly). You can also switch back to "normal" orientation via the button.

Let's take a moment to digest what we have here. Namely:

• a single map projection
• …showing the entire surface of the earth
• …while traversing all the way from the human scale, to the global scale

It really creates this "center of the universe" feeling. Basically a mathematical embodiment of the sentiment in this famous New Yorker cover. (Mercator: Extreme version)

Keep these principles in mind to best navigate around the map:

• Horizontal lines on the map ("meridians") represent straight lines radiating out from the pole point in all directions. Lines one half of a map-width apart from each other represent opposite directions. The properties of the meridians are best seen with a central plaza like the Arc de Triomphe.
• Vertical lines ("parallels") show rings of constant distance from the pole point. This can visualize encircledness or remoteness. The nearest landfall from St. Helena in any direction can be found by a vertical line sweeping towards the left.

You may find yourself trying to get 'behind' or 'to the other side of' the pole point. There is no such thing! All directions away from the pole point proceed towards the left. The pole itself exists at all points along the right-hand edge (technically, infinitely far to the right).

If at any time you get disoriented, I strongly recommend using the companion map to see the correspondence to a normal map which makes these navigational principles clear.

Now knowing that horizontal and vertical lines represent distance and bearing, if we center the pole on a major city, we can visualize its transportation network in a whole new way. Beltways and ring roads become vertical frontiers, while highways become a dendritic network branching off to destinations in all directions. We can see all of Atlanta's highway links in a single view, including the special few that make it as far as New York, St. Louis, Dallas, and Miami.

Closely related, the extreme Mercator is an excellent way to visualize long-distance driving routes. Think about how when you drive such a route, you start on some local/residential roads, then make your way to bigger arteries, and eventually to a highway. Here, even as smaller roads fade into nothing, the next road of your route always seems to still be visible. Size in this map is proportional to distance, so the extreme Mercator ends up normalizing scale in a very human-accessible way. The only cost is you have to turn your mind inside-out a bit.

Lastly, the extreme Mercator is an excellent way to visualize antipodes — points that are on the complete opposite sides of the earth from each other. So far we haven't touched the left-side cutoff, namely because the antipode is usually in the middle of the ocean. But this is not always the case. Here we find two buildings exactly opposite the planet from each other. Where one is day, the other is always night.

I hope you enjoy this novel way of viewing our world.

Icons from flaticon by Daniel Bruce, Icomoon, SimpleIcon, Icons8, Smashicons, Freepik: CC BY 3.0.

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