Klein bottles: you know a glass vial is metal if it manages to defy everything.

[Doomonkey]

Actually, the equations for Volume and area are v=L x W x H and a=L x W.

I use length^dimension because we don't have a name for fourth and beyond dimensional measurements, so it keeps it consistent an easier to understand. Substituting L^3 for LWH or L^4 for LWH(IV) doesn't change my point.

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[otto-san]

Too bad no one has figured out how humans can perceive the fourth dimension of matter.

probably because they can't

[TheChaosCarrier]

this isn't the fourth dimension, this is a .gif with two mesh boxes moving within themselves, it is also physically impossible because for this to happen, parts of the mesh would have to become longer and shorter. it could be done with some kind of stretchy material, but stretchy materials are not rigid enough to hold the shape well.

That is not a depiction of the 4th dimension.
That is a 4-dimensional shape moving through space.

I use length^dimension because we don't have a name for fourth and beyond dimensional measurements, so it keeps it consistent an easier to understand. Substituting L^3 for LWH or L^4 for LWH(IV) doesn't change my point.

I know, I was more-or-less adding on to what you said.
And what I said was for 2 sided or 3 sided figures, not 1 sided (whereas again, L^2 or L^3 would be appropriate for a 1-sided figure because you're only using Length. There is no width or height.).

[Dodger]

Blockland forums: Certified theoretical physicists

[Ipquarx]

Then you must be handicapped or trolling.
Or not in highschool yet.

It's Algebra to very advanced level. Of course you wouldn't understand it, simpleton.

Try me.

The Klein bottle is not four dimensional. If you don't believe me look at its Wikipedia page, where you can clearly see it constructed in 3d. If it was 4-d, there would be no way to construct it in 3d without loosing some amount of information.

Furthermore, while it is true that it technically has no area (as it intersects itself), that does not mean that it could not contain liquid or that mathematically it shouldn't be able to hold anything. This is basic physics.

[Doomonkey]

Blockland forums: Certified theoretical physicists

It is theoretical math, which is not complex at all because theoretical math (for the most part) is defined by its consistency and patterns.

[fred da kiko]

probably because they can't

we can using some sort of proxy, like a computer or some stuff. i'm not really sure how dimensions even work, but i would think we could figure out how to turn other dimensions into something we can perceive. 

[Doomonkey]

The Klein bottle is not four dimensional. If you don't believe me look at its Wikipedia page

From your beloved wikipedia:

Note that this is an "abstract" gluing in the sense that trying to realize this in three dimensions results in a self-intersecting Klein bottle. The Klein bottle, proper, does not self-intersect. Nonetheless, there is a way to visualize the Klein bottle as being contained in four dimensions.

By adding a fourth dimension to the three dimensional space, the self-intersection can be eliminated. Gently push a piece of the tube containing the intersection along the fourth dimension, out of the original three dimensional space. A useful brown townogy is to consider a self-intersecting curve on the plane; self-intersections can be eliminated by lifting one strand off the plane.

tl;dr A true Klein bottle must exist in the fourth dimension.

[TheChaosCarrier]

Try me.

Okay, kiddo.

The Klein bottle is not four dimensional. If you don't believe me look at its Wikipedia page, where you can clearly see it constructed in 3d. If it was 4-d, there would be no way to construct it in 3d without loosing some amount of information.

The Klein bottle in reality is 4th dimensional, therefore does not exist.
The representations you see on the OP and throughout this thread are simply that, fake representations. The one in the OP is simple glass work. The other pictures posted are simple models made in a 3D Modeling program.

The real, mathematical Klein bottle does not and cannot exist in our 3-dimensional plane. It is called math. Learn it.

Furthermore, while it is true that it technically has no area (as it intersects itself), that does not mean that it could not contain liquid or that mathematically it shouldn't be able to hold anything. This is basic physics.

You must be failing math or your teacher is a bloody moron.
The 4th dimension is said to completely obliterate all current laws of physics because our physics are meant for the 3rd dimension, not the 4th. In reality and in math, a real, 4-dimensional Klein bottle defies human physics because it is imperceptible.

Go back to school.

[Littledude]

If it's mathematically impossible and hasn't been created in reality then why are people saying it exists?

that's like saying that someone with nothing but richards for bodyparts, richard arms, richard hands, richard fingers, richard legs, richard feet, richard toes, richard butts exists. That person cannot scientifically exist nor does it so it doesn't exist.

[Doomonkey]

If it's mathematically impossible and hasn't been created in reality then why are people saying it exists?

It is mathematically possible. That is the whole point.

[TheChaosCarrier]

If it's mathematically impossible and hasn't been created in reality then why are people saying it exists?

that's like saying that someone with nothing but richards for bodyparts, richard arms, richard hands, richard fingers, richard legs, richard feet, richard toes, richard butts exists. That person cannot scientifically exist nor does it so it doesn't exist.

It exists in the 4th dimension.

That was a horrible brown townogy, by the way.

[Xalos]

This does not break mathematics in any way.

It merely proves that every single human who ever lived is a moron who can't get mathematics, and that's assuming you're even right about what a Klein bottle is.


Hint: It's a projection of a 4D object in 3D space. You wouldn't be able to see some part or another of the bottle otherwise.




This tesseract is a four-dimensional object. We would only see the portion of the cube which intersects our three-dimensional region, but if we project it into three-space, it looks like this. Same for Klein bottles.

[Ipquarx]

Okay, kiddo.
The Klein bottle in reality is 4th dimensional, therefore does not exist.
The representations you see on the OP and throughout this thread are simply that, fake representations. The one in the OP is simple glass work. The other pictures posted are simple models made in a 3D Modeling program.

The real, mathematical Klein bottle does not and cannot exist in our 3-dimensional plane. It is called math. Learn it.
You must be failing math or your teacher is a bloody moron.
The 4th dimension is said to completely obliterate all current laws of physics because our physics are meant for the 3rd dimension, not the 4th. In reality and in math, a real, 4-dimensional Klein bottle defies human physics because it is imperceptible.

Go back to school.

I see what you're getting at, you're saying that because in a 'proper' Klein bottle there is no self-intersection, and that that is where the fourth dimension comes in.

You see I thought you meant that it couldn't exist at all. Silly me.

[Xalos]

The 4th dimension is said to completely obliterate all current laws of physics because our physics are meant for the 3rd dimension

Just noticed this part of this post.


WRONG

All our physics still work perfectly fine in four dimensional space. A 4-sphere colliding with another 4-sphere or the gravity coming off of them can be represented with the same equations, we just have to use 4D vectors and rotation instead of 3D vectors and rotation.