The Hole Problem

Originally posted by Mindship
I cut a strip of paper, punched a hole in it, then twisted it Mobiusly.

The hole was still circular (it was never cone shaped), and yes it was a hole (I could put my pencil tip through it).

The hole would go from one location on the one side of the true Mobuis strip to another location on that same side. It would be more like a warm hole then a normal hole.

Originally posted by Shakyamunison
It would be more like a warm hole then a normal hole.

The hole would go from one location on the one side of the true Mobuis strip to another location on that same side.

Originally posted by Grand_Moff_Gav
But the hole goes from one end of the strip to the other...weird..

A 2D object, such as a rectangle, has only one (planar) surface (let's call it surface A). A 2D hole can not lead from surface A to surface B because there is no surface B. But it's still a hole because it is a discontinuity.

Therefore, topologically speaking, I don't think there is a difference between a rectangle with a hole in it and a Mobius strip with a hole in it (just like in 3D topology, there is no difference between a donut and a coffee mug). Both 2D figures contain a single discontinuity which, in 2D, does not have to lead anywhere to still be a hole.

Originally posted by Mindship
A warm hole, huh.
I could not have looked at myself in the mirror had I let that one go. 😉

As 3D beings, it's normal for us to think in 3D, even when considering 2D objects, though that's when we get into trouble because we're not used to thinking in 2D.

A 2D object, such as a rectangle, has only one (planar) surface (let's call it surface A). A 2D hole can not lead from surface A to surface B because there is no surface B. But it's still a hole because it is a discontinuity.

Therefore, topologically speaking, I don't think there is a difference between a rectangle with a hole in it and a Mobius strip with a hole in it (just like in 3D topology, there is no difference between a donut and a coffee mug). Both 2D figures contain a single discontinuity which, in 2D, does not have to lead anywhere to still be a hole.

First: I'm not the best speller. 🙄 😛

Second: So, a 2D being can't go into a hole anyway? What about the 2D serface inside the hole?

Originally posted by Shakyamunison
So, a 2D being can't go into a hole anyway? What about the 2D serface inside the hole?

http://www.flatlandthemovie.com/
...as an intro (and keep in mind this depicts not so much a genuine 2D world, as a 2D world depicted by 3D beings).

Originally posted by Mindship
To a Flatlander, a "hole" is a gap in a line; a line is a wall; and any closed 2D figure = closed room.

http://www.flatlandthemovie.com/
...as an intro.

I have the book, and have read it. A hole would be a place they can't go for some unknown reason. However, the inside of the hole could have a completely different population of flatlanders that would not know about the other flatlanders. It would be like people living in different dimensions to them.

Originally posted by Shakyamunison
I have the book, and have read it.

Originally posted by Mindship
😕
I thought so, but I wasn't sure.

I think it should be mandatory reading for and science class having to do with space and time.

Originally posted by Mindship
To a Flatlander, a "hole" is a gap in a line; a line is a wall; and any closed 2D figure = closed room.

http://www.flatlandthemovie.com/
...as an intro (and keep in mind this depicts not so much a genuine 2D world, as a 2D world depicted by 3D beings).

Hey I just got it.

From a 2D perspective traveling though the hole in the MobiusStrip would be exactly the same as us traveling through a worm hole like Shaky suggested.

As the 2D person goes into the "hole" it warps into another dimension and then descends back to normal 2D as it comes out the other side. Though it would imply that even traveling though the most stable possible wormhole would be either extremely awkward or lethal.

It's also a clever way of using hyperspace even though it's far more complex than a wormhole.

So...where does this leave a Klein Bottle? 😈

http://en.wikipedia.org/wiki/Klein_bottle

Originally posted by Mindship
So...where does this leave a Klein Bottle? 😈

http://en.wikipedia.org/wiki/Klein_bottle

When ever I pore anything into my Klein Bottle, it spills onto the floor. 😐

😂

We may have to wormhole that sucka, too.

Originally posted by Mindship
😂

We may have to wormhole that sucka, too.

Sense the outside and the inside are the same side, where would a hole go? 😕

Originally posted by Shakyamunison
Sense the outside and the inside are the same side, where would a hole go? 😕

Originally posted by Mindship
To the spot on the floor where stuff spilling out of the Klein bottle lands, of course; the ultimate in recycling.

🙄

Im still somewhat confused as to the problem, but why cant there be a hole in a mobius strip or whatever it is? It might be a little bent, but the thing is still a hole, semi-cylindrical (contorted because of the way the paper is bent)

As to it only having one side...for the entire object that is true, but not for any individual segment. At the point of the hole, there are still two sides, just that those sides switch as you go further around the object. so the hole is still essentially doing the exact same thing.

Originally posted by The Black Ghost
As to it only having one side...for the entire object that is true, but not for any individual segment. At the point of the hole, there are still two sides, just that those sides switch as you go further around the object. so the hole is still essentially doing the exact same thing.

if you mean a whole the entire length of the loop that is in the centre of the loop then you end up with a double length loop with 2 full twists in it

Originally posted by jaden101
if you mean a whole the entire length of the loop that is in the centre of the loop then you end up with a double length loop with 2 full twists in it

A hole would be perpendicular to the surface. If it is parallel, it is call a cut.