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So I have been working on a world where space has been "cracked" by some mysterious disaster which plunged the world into chaos.

It is not immediately apparent - i.e. no giant glowing holes in the sky, but the world map no longer follows the rules of geometry;

  • The journey between two settlements may be longer one way than the other
  • Retracing your steps may not return you to your destination
  • A "pocket" that can only be reached by one specific route. i.e - travellers from the wrong direction will bypass altogether
  • Places that occupy the same location on the map, but are completely separate

The changes are large enough that they wouldn't necessarily affect travel within a settlement, but would only become a factor over a couple of days of travel.

The survivors are located in a series of villages and settlements scattered across the continent where the story takes place. Communications and trade routes are being reestablished. This is some time after the apocalypse- possibly a generation or two, so the immediate aftermath has been dealt with. There are no GPS or communications satellites, though some maps of the world world remain.

My question is - how hard would it be to discover the distortions using traditional cartography? Could you definitively prove that space has been warped, taking into account survey errors, etc etc?

EDIT: Typo and clarifications

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    $\begingroup$ When you say distortions, what exactly are the distortions you're talking about? Do you mean to say that the earth's landmass has changed due to the anomaly? $\endgroup$ – Sydney Sleeper May 16 '18 at 23:39
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    $\begingroup$ It would be trivial to find out the distortions, if humanity still has math at least as advanced as the ancient greeks'. $\endgroup$ – Renan May 16 '18 at 23:55
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    $\begingroup$ Please clarify "A "pocket" that can only be range by one specific route". $\endgroup$ – RonJohn May 17 '18 at 0:18
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    $\begingroup$ "Humanity has split into a number of settlements". We're already in a number of settlements, no? $\endgroup$ – RonJohn May 17 '18 at 0:19
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    $\begingroup$ My first thought was an exploding TARDIS. Geronimo! $\endgroup$ – pojo-guy May 17 '18 at 1:30
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Triangulation is very useful tool for navigation. Basically, you take the angle between three different landmarks and correspond that to a map. But, it relies on space being (approximately) flat such that the angle you perceive between three landmarks is unique.

Here's a crude example. Imagine you see a landscape like this:

landscape

After you determine the angles between the three landmarks, you can refer to a map and play with the map to try and find the one spot where you would perceive these landmarks with this angle between each of them:

triangulation

Notice that if space is flat, then there should always be a one-to-one correspondence with the angles you perceive landmarks making to each other and places in the world. All you would need to do to prove that some sort of extra dimensional overlapping or distortion is occurring is to find a location where three landmarks all appeared to be the same angle from each other as viewed from some other distinct location.

Here's a final mock-up. Notice that the new location has bent lines leading from it to represent the non-euclidean spacial relations, but the lines meet at the same angle:

non-euclidean example

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    $\begingroup$ That’s a beautifully simple representation of non-euclidian space. +1 $\endgroup$ – Joe Bloggs May 17 '18 at 9:55

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