Like let’s say that we start on the cape of goodwill for example and follow the coast.
Represent each 1km with 1mm for example on our map (map size isn’t a problem just for the sake of the argument). Getting the directions of drawing off a compass exactly. And just walk around all the coasts of the world.
What type of map do we end up with in this hypothetical?
In: 5
A globe happens when you keep everything to scale. You can’t represent curved surfaces correctly proportioned on a flat plane
If I’m reading you right, I think what you might end up with is something like an interrupted pseudocylindrical projection
https://en.wikipedia.org/wiki/Goode_homolosine_projection
If you accurately measure and draw everything to scale, then once you arrived “back” at the Cape of Good Hope, where you finished on the map would be wayyyyy off from where you started. You’d be sacrificing direction and orientation in favor of scale, and the only alternative would be to sacrifice scale in favor of direction/orientation.
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How would your map deal with hills or mountains?
You’d end up with a discontinuous map.
The starts and ends of continents and other large land masses wouldn’t join up, by noticeable amounts. Technically even the outlines of small islands wouldn’t join up either, just the scale would mostly hide it.
You can do this at home with an orange. Draw a simple map on half of it, peel that half off and then flatten it. It’ll split in one or more places and your map lines will be discontinuous where they cross splits.
How do you intend to transcribe your motion onto paper?
By simple angle change?
The allow me to give you a simple path that should demonstrate the problem. You start at the north pole, and follow the prime meridian south. You turn 90 degrees left at the equator, and travel a quarter of the way around the Earth. You then turn left 90 degrees again, and walk another quarter.
You’re back at the north pole, having followed a ‘triangular’ path. Each corner is 90 degrees. If you were to draw this path on flat paper, your map would have two north poles on it. Your path would look like 3 sides of a square, since each corner is 90 degrees, and each side would be 10 meters long. Your start point and end point were both the north pole, but on paper they’re a quarter world (10 meters) apart.
If you were to try and trace a country using this system, walking its border, you would walk the full length and your drawing on paper would not be a full loop; your start and end points would be in different spots on your paper despite them being in the same place on Earth.
Start at north pole. Walk 100km due south. Draw a 100mm line on your map. Turn 90 degrees left. Walk due east 100km. Draw a 100mm perpendicular to the first.
Turn 90 degrees left and walk due north again. You are now at north pole again, but the map says you are 100km from north pole.
Simply put, your method can’t work. In general, the line generated by traversing the coast of any continent wouldn’t form a closed loop on the paper when you returned to your starting point. As a simple example, imagine a three-sided continent that reaches a point at the north pole and two other points on the equator. Two of its coast lines run due-north/south and the third runs due east/west. Drawing those three lines on a flat piece of paper doesn’t make a triangle. Using the north pole is an extreme example but the same issue will occur for all the continents. And think about what would happen if you tried to do Antarctica!
I think you would just end up with a scribble.
For the sake of visualization, let’s start walking from the north pole.
– Walk all 10,000km down to the equator, then turn 90-degrees to the right.
– Now walk 10,000km along the equator, then turn 90-degree right again
– walk another 10,000km and you will arrive at the north pole, having drawn a “triangle”
On paper:
– you would draw a 1000cm line down
– then a 1000cm line to the right, forming an L shape
– then a 1000cm line up, drawing a U shape or a square with no top
– the square would also be reversed
Now imagine all the twists and turns of a coastline, left/right reversed at time, with 90-degree angles actually being 60 degree angles.
A scribble!
If you wanted to make it join up properly you’d end up having to twist around the piece of paper you were drawing it on, making it into a sphere. You’ve basically invented the globe.
To take an obvious example of what would happen if you tried to do this on a flat surface, let’s say you started at the South Pole, walked North in a random direction 5km, then walked East 5km (so a 90 degree turn), then walked South 5km (another 90 degree turn).
If you draw that on paper you would have three sides of a square. But where you end up should be the same place you started. So your 2d projection is wrong – it doesn’t join up.
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