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More 4-Dimension Objects: The Klein Bottle

Hits: 8331 | Rating: (1.7) | Category: Science | Added by: MacGuffin
Page: 1 2 Next >   Jump to: Bottom    Last Post
doug1963aaa
Male, 40-49, Southern US
 347 Posts
Sunday, July 22, 2012 6:54:29 PM
@MacGuffin: I have written software that allows one to visualise true 4-d objects in 3-d using 3-d glasses. I have spent a good amount of time over the last 30 years working on it, and I have gained a solid understanding of 4-d geometry in the process.

MacGuffin
Female, 30-39, Europe
 2597 Posts
Saturday, July 21, 2012 1:37:13 PM

>>>@MacGuffin: I don't know why you keep insisting that Klein bottles are 4D objects when they are clearly NOT.

...

Hell, you can *buy* Klein bottles!
http://www.kleinbottle.com/ <<<


Well, if you can *buy* 3D projections of the real thing on the internet and everything, that *must* prove that the 4D object that said 3D projection is a projection of can't exist.

Read this, then realise how mistaken you are. To quote:

"While the Möbius strip can be embedded in three-dimensional Euclidean space R3, the Klein bottle cannot. It can be embedded in R4, however."

As I said, this *is* a 3D projection of such an embedding in R4 - that's how the object is shown to pass through itself. That only happens in 4D.

MacGuffin
Female, 30-39, Europe
 2597 Posts
Saturday, July 21, 2012 1:26:05 PM

@MacGuffin--a 4-d Klein Surface would not show an intersection and would rotate without any flattening.

This is a matter of some expertise for me.


Again, this is a *3D projection* of a 4D Klein Bottle. Nobody is saying that it is the 4D object itself. If it was, we'd be unable to perceive it, since we live in 3D.

I guess it's not that much of an area of expertise for you, or you'd be able to understand that simple concept.

HiEv
Male, 40-49, Eastern US
 598 Posts
Saturday, July 21, 2012 4:17:13 AM
@MacGuffin: I don't know why you keep insisting that Klein bottles are 4D objects when they are clearly NOT.

Seriously, no part of a Klein bottle needs to project into the 4th dimension for it to be a Klein bottle, therefore it is, by definition, *not* a 4D object.

Hell, you can *buy* Klein bottles!
http://www.kleinbottle.com/

Since we cannot build 4D objects, doesn't that prove to you that they're *not* 4D?!?

(Or do you have some strange definition of 4D that most of us don't use?)

Squrlz4Sale
Male, 40-49, Eastern US
 6018 Posts
Thursday, July 19, 2012 11:14:49 PM
Yeah, I uhhh... have *no* idea what's going on here.

~looks for this thread's exit~

doug1963aaa
Male, 40-49, Southern US
 347 Posts
Thursday, July 19, 2012 3:41:24 PM
@MacGuffin--a 4-d Klein Surface would not show an intersection and would rotate without any flattening.

This is a matter of some expertise for me.

keith2
Male, 18-29, Midwest US
 2565 Posts
Thursday, July 19, 2012 2:52:25 PM
Up, down, left, right, forward, backwards... in, out.

keith2
Male, 18-29, Midwest US
 2565 Posts
Thursday, July 19, 2012 2:51:49 PM
When I imagine a 4th dimension to space, I've imagined myself sprinting in one direction, looking as if I've stayed in the same position in 3d space but becoming ever smaller as if I've ran a 1/4 mile away.

MacGuffin
Female, 30-39, Europe
 2597 Posts
Thursday, July 19, 2012 10:40:59 AM

What you are seeing is a 3-d Klein Bottle being rotated in 4-space and being projected into 2-space. The tell-tale is when the object appears to flatten itself during rotation.

That's incorrect. It's a 3D projection of a 4D Klein Bottle. If you look at the video carefully you'll see that the bottle never completely "flattens". Only parts of it appear to as those parts briefly sit at right angles to two or more of the three dimensions that make up 3D space. Those parts which appear flat at any one time, are actually sitting at 90 degrees perpendicular to at least two of the axes that make up 3D space at those points. We get the same view at those moments as a 2D being would get of a flat square seen edge-on.

MacGuffin
Female, 30-39, Europe
 2597 Posts
Thursday, July 19, 2012 10:40:48 AM

This is not a 4-d representation.

Nobody said that it was. It's a 3D projection of a 4D object.

The Klein Bottle is a surface that only appears to not intersect itself in 4-space.

It doesn't just appear not to self-intersect. It really doesn't intersect itself in 4D. Just as the squares that comprise the 2D projection of a 3D cube I showed below really are clearly separated once you can see the object they represent in full 3D.

...

MacGuffin
Female, 30-39, Europe
 2597 Posts
Thursday, July 19, 2012 10:20:45 AM

MacGuffin: I disagree. That only works, again, because our brains work in a 'three dimensional world', but the cube representing a 3D object on a 2D plane isn't '3D' either, and so if you have someone who doesn't understand the third dimension, that is not going to be sufficient to teach it.

Whether you "disagree" or not isn't relevant. I wasn't trying to convince you of anything, I was merely stating a mathematical fact that exists whether you're aware of it and recognise it or not. It's not a matter of opinion.

You can project a 3D object onto a 2D surface, and you can project a 4D object into 3D space. Whether you understand/agree with these undisputed concepts or not is immaterial. You might as well disagree with gravity.

ssalty
Male, 60-69, Western US
 192 Posts
Thursday, July 19, 2012 8:41:51 AM
BZZZT! but thanks for playing. Now go away.

doug1963aaa
Male, 40-49, Southern US
 347 Posts
Thursday, July 19, 2012 8:02:55 AM
This is not a 4-d representation. The Klein Bottle is a surface that only appears to not intersect itself in 4-space. What you are seeing is a 3-d Klein Bottle being rotated in 4-space and being projected into 2-space. The tell-tale is when the object appears to flatten itself during rotation.

kingdomCome
Male, 18-29, Europe
 336 Posts
Thursday, July 19, 2012 5:46:49 AM
So many people confusing a concept with a nice glass trinket for keeping wine badly

taylor_stone
Male, 30-39, Eastern US
 2692 Posts
Thursday, July 19, 2012 3:14:37 AM
Someone has a failed interpretation of what 4D means... This is a 3D object that doubles back the envelopes itself on one end... As previously stated, it's nothing more than a 3D version of a Möbius Strip.

robosnitz
Male, 40-49, Eastern US
 2752 Posts
Thursday, July 19, 2012 12:13:49 AM
Looks like a failed attempt at a bong.

OldOllie
Male, 60-69, Midwest US
 14378 Posts
Wednesday, July 18, 2012 10:35:40 PM
I still count the hole in the side as an edge.

JaLacaob
Male, 18-29, Midwest US
 1793 Posts
Wednesday, July 18, 2012 6:54:00 PM
MacGuffin: I disagree. That only works, again, because our brains work in a 'three dimensional world', but the cube representing a 3D object on a 2D plane isn't '3D' either, and so if you have someone who doesn't understand the third dimension, that is not going to be sufficient to teach it.

HiEv
Male, 40-49, Eastern US
 598 Posts
Wednesday, July 18, 2012 4:43:00 PM
Ugh. No. Just... no.

A Klein bottle is *not* 4D, it's a 3D object with a single contiguous surface and no edges. Basically, it's the 3D equivalent of a Möbius strip.

They're quite interesting in and of themselves, you don't need to make up stuff about them being 4D somehow.

Wikipedia: Klein bottle

TheGuySmiley
Male, 18-29, Canada
 1222 Posts
Wednesday, July 18, 2012 3:46:17 PM
where can we get the 4d glasses?

mamba
Male, 18-29, Europe
 618 Posts
Wednesday, July 18, 2012 11:26:53 AM
Most certainly a very awesome shape, although not very interesting if you don't know much about maths.

Draculya
Male, 40-49, Asia
 12320 Posts
Wednesday, July 18, 2012 10:49:18 AM
They're a biatch to use. You get an air-lock that prevents the wine from pouring.

Mikeoxsbiggg
Male, 30-39, Canada
 1229 Posts
Wednesday, July 18, 2012 10:26:15 AM
You can accually buy one. It's glass and 3d. Looks good on my mantle. Here. Acme Klein

MacGuffin
Female, 30-39, Europe
 2597 Posts
Wednesday, July 18, 2012 10:04:52 AM

It gets interesting when you consider that the Universe itself is also an object that (from our 3D perspective at least) has only one surface and no known boundary.

madduck
Female, 50-59, Europe
 5790 Posts
Wednesday, July 18, 2012 9:58:36 AM
FFS - I am honestly not an idiot- but I think visually and this gives me a headache!!

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