Question..

[Nick]

I'm going to try and sail off the corner...

[Solfius]

d be interested to know what happens, do you vanish into the cantr abyss? or is ut just impossible to sail off the corner? (very boring in my opinino)

[Sho]

It's been mentioned that it's a torus...

It can't be a torus. It exists only in two dimensions.

Take a sheet of paper and try to make a torus...

Just take a cylinder and bend it.

Sure. Easy. A nice, smooth torus, no folds or overlapping sections.

Go ahead and try it, before you open your trap. Punk.

You can't do it with actual paper without folding. Doesn't mean 2-tori don't exist. Or Klein bottles, for that matter. The Cantr map is connected like a torus, but that has nothing to do with any "three-dimensional" representation of the world.

[Abu Amaal]

I'll try to explain this but let me start in one dimension.

1.
A line segment becomes a circle if you put the two sides together.
In the real world, whether you can do this depends on how rigid the line is.
You can do it with string but not with a pencil.
But you need TWO dimensions to do it.


2.
A square becomes a torus if you put each side together with the opposite side (left/right and top/bottom)
You can't do this with tin.
You can do it with stretchable wire mesh in three dimensions.
With paper - well, with paper you can't do it inside 3 dimensions but you actually can inside 4 dimensions. You just have to fold in both the extra dimensions.

For more information, Google "flat torus".

3. A cube becomes a 3-torus but it probably takes 6 dimensions to do it unless you stretch it a bit. Even with stretching you would need four.

In the real world according to string theory there are 11 spatial dimensions so in theory it could be done, but 8 of them are really tiny.

[Spiritus]

Correct me if i'm wrong but wouldnt simply linking the top coordinates to connect to the bottom and the right coordinates to link to the left and vise versa make it a torus? it wouldnt be a sphere... I guess it might not be a true torus but it seems to me like it acts just like one I didn't even know what a torus was tho before this post so thats just me.

[BarbaricAvatar]

You all have too much time on your hands.

[Abu Amaal]

Correct me if i'm wrong but wouldnt simply linking the top coordinates to connect to the bottom and the right coordinates to link to the left and vise versa make it a torus? it wouldnt be a sphere... I guess it might not be a true torus but it seems to me like it acts just like one I didn't even know what a torus was tho before this post so thats just me.

Yes.

And there is are real differences between maps on a sphere and maps on a torus. You can have 7 countries with a common boundary on a torus and only 4 on a sphere. This means that in principle the complexity of political relationships might depend on the shape of the map.
Example

(Practically speaking this would only affect relationships between very large regions, at least the size of continents.)

[SekoETC]

The only problem in wrapping something first in one way and then the other is that the inside would be shorter than the outside due to stretching. But that really isn't the case.

[Nick]

If you're all hung on the torus thing, then it's a flat square with transportation portals at each side.

[sem]

The only problem in wrapping something first in one way and then the other is that the inside would be shorter than the outside due to stretching. But that really isn't the case.

Maybe this would explain why distances between locations on the English islands are larger than on the newer ones?

[Nick]

The only problem in wrapping something first in one way and then the other is that the inside would be shorter than the outside due to stretching. But that really isn't the case.

btw...

Post 5000!

Congratulations. Or not.

[kroner]

as a math major, i'm sort of obligated to comment on this thread.
you can have a torus with locally 2D euclidean geometry even though any torus you embed in 3-space isn't going to be shaped like that. fortunately for us no one has to build a scale model of the cantr world in real life.

as people have said, simply imagine a rectangle with wrapping. in other words when you go off one edge you come out on the opposite edge. think pac man, or any of those old space games, or star fox 64 multiplayer.

[Sekar]

You all have too much time on your hands.

I totally agree. I don't even understand half of what they are saying.