Sigil Ciy of Doors (Topology of a Torus) - MATHS

[MoppyDragon]

Just reading the new 4E Manual of the Planes. Came across this:

"Sigil is a recursive demiplane. The city fills the interior of a torus, so a traveler can’t help but circle back to where he started by continuing in a straight line."

So they are saying that if I were to walk in a straight line across the inside of a torus, I would return to my point of origin? I can see this happening if you walk directly around the doughnut or directly across the tube, but for other angles? I would spiral around the the inside, but ... I am not a mathematician so I don't understand the topology of torii. Some on here is be qualified to comment/explain?

 

[kenmarable]

I haven't looked up the exact mathematical definition of a torus in a long time, but as for the layout of Sigil, what they say is correct in a general sense. If you look at the pictures of it, the center section isn't closed off (that's not a cut away).

So you are not walking inside a closed tube. Think of it instead as a car tire without the inner tube and metal wheel section - just the rubber tire. You are on the inside and, just to assign arbitrary directions, north and south are along the big loop. So if you start walking directly north, you will wind up making a big loop and come back to where you started.

However, if you head east or west, you will only be able to go a short distance before coming to the edge. (Haven't read 4e Sigil, but back in 2e it's all backs of buildings without windows, so you can't "lean over the edge" if I recall. Even if you did and fell, you would fall into the Astral or something.

So, you are correct that you only wind up back where you are if you walk the long way around the inside of the doughnut/tire. Since it is not a closed tube, you can't walk all the way around the short way (unless of course, in 4e they changed that, but from the pictures it sure doesn't look like it). You will come to an end of an alley or back wall without windows inside a building.

My interpretation is just that it explains the "walk the long way around the inside of the doughnut/tire" rather than any other special property of a torus. You can walk in other directions and wind up hitting an edge.

Does that make any sense or just confuse it more? And someone correct me if they changed the 4e version of Sigil.

 

[Dire Bare]

So, you are correct that you only wind up back where you are if you walk the long way around the inside of the doughnut/tire. Since it is not a closed tube, you can't walk all the way around the short way (unless of course, in 4e they changed that, but from the pictures it sure doesn't look like it). You will come to an end of an alley or back wall without windows inside a building.

Yeah, that's pretty much it right there. Although in the Downer comic that ran in Dungeon pre-digital, there was a building/train that ran along at least one of Sigil's edges. Neat idea, IMO.

 

[Shemeska]

You could look "outside" of Sigil if you looked to either side when flying directly across the ring of the city from one side to the other. And there was one spot called "Suicide Alley" where the edge was low enough and not blocked by any architecture so that people could climb and look over the edge, and it was often used as a method of just what its name suggested. However no one that ever jumped over the side was ever heard from again, so the Fraternity of Order had a standing offer to pay money for the dark of just what happened/was there if anyone did jump the side and eventually came back to tell them.

Of course looking over the edge to see something, you saw nothing. Not a void, not darkness, not empty sky, not clouds, not even the Infinite Spire - just something disconcerting and indescribable except to call it nothingness. However some of the details on that last bit may have been of my creation in some of the stuff I've written, so if you're a fiend for printed canon, check on the precise bits of that.

I believe 3e had you getting bumped to a random spot on a random plane if you jumped the edge, but I prefer to keep it undefined.

 

[Lord Xtheth]

I haven't read thing 1 about Sigil in a very long time. When I read the 4E description I also thought it was a fully enclosed city. Makes me wish I could still hunt down the original Planescape material.

 

[Rel]

Just reading the new 4E Manual of the Planes. Came across this:

"Sigil is a recursive demiplane. The city fills the interior of a torus, so a traveler can’t help but circle back to where he started by continuing in a straight line."

So they are saying that if I were to walk in a straight line across the inside of a torus, I would return to my point of origin? I can see this happening if you walk directly around the doughnut or directly across the tube, but for other angles? I would spiral around the the inside, but ... I am not a mathematician so I don't understand the topology of torii. Some on here is be qualified to comment/explain?

A torus is, by definition, a hollow "donut" (I believe that if it is solid then it's called a "toroid"). In terms of coming back to where you started from, I'd say that if you went in a "cardinal direction" then that's true. If not then it might eventually be true depending on the angle.

In practical terms, if Sigil has streets laid out on the diagonal, it would be a LONG walk around the city but you'd eventually arrive at least close to where you started from.

 

[Ktulu]

In our recent 4e planescape game, we used the "tire" explanation and the waxing/waning of day night was explained as sigil being the epicenter of the Astral Sea and the Elemental chaos. as day approached, the fires of the elemental chaos erupted pouring upward between the ringed city, lighting the streets. As evening came, the Astral Sea emptied into the same column, cooling the fires and the sparkles of a "starry" night could be seen that way.

We enjoyed the idea.

 

[MoppyDragon]

From your answers I can see that you haven't seen that Sigil has changed in 4E. I am asking about the 4E version of it. In the 4E Planes book page 25 "The city is built on the inside of gigantic hollow ring that has no outside". Picture on page 27 shows the city wrapping around the inside of the ring so there is no sky (well it might have an interior sky, but if you look up from your roof you will see air, then the top of the buildings on the other side, assuming you can see that far and it doesnt have internal clouds). Take a pipe. Bend it into a circle. Coat the entire inside with buildings. That's what the picture shows. Although I suspect some 4E adventure will change that soon, they never were that hot on consistency .... Anyway, still hoping someone can answer the original question

 

[Fallen Seraph]

There is an open section of 4e Sigil. If you look at the map, you will notice on the inside edge of the ring you can see it is open the whole way around that side.
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[Tequila Sunrise]

So Sigil is now built on the inside of a snow tube? And you want to know if someone walked straight in a random direction, whether they would find their way to their original location? Why exactly does it matter?

I'm no mathematician, but I'm willing to bet that yes, the person would eventually get back to their original location. They'd probably have to crisscross the city a few hundred times first, but it'd happen. But again, what does it matter? Unless the gamers you play with are mathematicians, they won't know either and therefore the in-game reality can be whatever the plot needs it to be.

TS