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

[Littledude]

It is mathematically possible. That is the whole point.

then I just read something wrong I guess, carry on then.

[Ad Bot]

[TheChaosCarrier]

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.

Source?

[Doomonkey]

2d physics. Add 2d vectors (polar coordinates). [magnitude , direction]
3d physics. Add 3d vectors (spherical polar coordinates, as opposed to cylindrical). [magnitude , direction , direction]
4d physics. Add 4d vectors (hyperspherical polar coordinates, as opposed to whatever the other ones are called). [magnitude , direction , direction , direction]

[Ipquarx]

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.

Xalos, let me explain to you why you can't represent the Klein bottle in 3d, and that will also apply to why our physics would no longer work in 4-d.

The Klein bottle, a real one, has no self-intersection. If you represent it in 3d, no matter how you do it, there will always be a self-intersection.

Why? Because you can't represent an object of dimension n in any lower dimension without forming some sort of contradiction.

For example, take a 2d square. Now, take that and make it 3d. (ie coordinates 1,2 would become 1,2,0)
But, there's a contradiction!

The 3d square is infinitely thin! It has no depth! None! That's not physically possible!

See? Because of this, yes our 3-d physics equations may be right, but they cannot function properly in the next dimension without having some sort of breaking point.

[Doomonkey]

See? Because of this, yes our 3-d physics equations may be right, but they cannot function properly in the next dimension without having some sort of breaking point.

0s do not matter in physics.
[10 , 0°] + [5 , 180°] = [5 , 0°] = 5
[10, 0° , 0°] + [5 , 180° , 0°] = [5 , 0° , 0°] = [5 , 0°] = 5
[10, 0° , 0° , 0°] + [5 , 180° , 0° , 0°] = [5 , 0° , 0° , 0°] = [5 , 0° , 0°] = [5 , 0°] = 5

A diagram would be hard to draw for 4d physics but the math is the same.

[Ipquarx]

Is it possible to have a 3-d square?
No, because everything 3-d has to have physical depth, if it doesn't have depth then by definition it is 2d.

What I'm saying is, adding a zero onto the end of a vector does not add a dimension. An object can exist in only one dimension.

[Doomonkey]

Is it possible to have a 3-d square?
No, because everything 3-d has to have physical depth, if it doesn't have depth then by definition it is 2d.

What I'm saying is, adding a zero onto the end of a vector does not add a dimension. An object can exist in only one dimension.

Vectors are not objects. They are forces in directions. There is no limit to the amount of dimensions they can exist in. It is possible to do the math without 0s, but I didn't pay attention enough to make up the formula to convert 4 dimensional hyperspherical polar coordinates into 4 dimensional hyperrectantgular coordinates to add them.

[Xalos]

Squares having no depth has nothing to do with physics breaking down. Take any two-dimensional planar slice of reality.

YES I KNOW YOU CAN'T TAKE A PLANAR SLICE OF AN ATOM forget YOU JUST TAKE THE INTERSECTED PORTION OF IT ASDF

That planar slice of reality is in three dimensions and it has no depth. Therefore, since reality is made up of an infinite number of objects with no depth whatsoever, reality does not and cannot exist. Well done, you just proved reality doesn't exist. You are a nonexistant Ipquarx.

[DrenDran]

Nothing breaks down.
You pour liquid into kleine bottle.
Then you can look at water, still in kleiner bottle.
Simple as that.

What the forget is all this "physics done broke" stuff?

[Doomonkey]

Squares having no depth has nothing to do with physics breaking down. Take any two-dimensional planar slice of reality.

YES I KNOW YOU CAN'T TAKE A PLANAR SLICE OF AN ATOM forget YOU JUST TAKE THE INTERSECTED PORTION OF IT ASDF

That planar slice of reality is in three dimensions and it has no depth. Therefore, since reality is made up of an infinite number of objects with no depth whatsoever, reality does not and cannot exist. Well done, you just proved reality doesn't exist. You are a nonexistant Ipquarx.

Except you cannot divide the depth on anything into a quantity of planes because planes have a depth of 0. So you are wrong because in order for you to be correct you must divide by 0.

You could say everything is made up of an infinite amount of infinitely small stuff, but that does not pose an issue to anything because it pretty much already is.

[Ipquarx]

everything 3-d has to have physical depth, if it doesn't have depth then by definition it is 2d.

Therefore

adding a zero onto the end of a vector does not add a dimension.

Squares having no depth has nothing to do with physics breaking down. Take any two-dimensional planar slice of reality.

YES I KNOW YOU CAN'T TAKE A PLANAR SLICE OF AN ATOM forget YOU JUST TAKE THE INTERSECTED PORTION OF IT ASDF

That planar slice of reality is in three dimensions and it has no depth. Therefore, since reality is made up of an infinite number of objects with no depth whatsoever, reality does not and cannot exist. Well done, you just proved reality doesn't exist. You are a nonexistant Ipquarx.

Time is a continuous stream, it is not made of "slices"

[Xalos]

Time is a continuous stream, it is not made of "slices"

One, I was talking about SPATIAL dimensions, but since you went and handicapped up, let me correct you.

TIME IS IN FACT MADE OF SLICES. Each instant of time is a snapshot of a three-dimensional reality. Since these have no, uh, time-depth, by your logic they cannot exist. Yet they do, because time is made up of an infinite number of such instances of time. Just because each instant of time flows together in a perfect fashion does not mean they are not individual instants.

Yes, I know 'time-depth' isn't a word, but apparently we've already assigned length to a spatial dimension and I want to avoid confusion because Ipq is apparently already having trouble understanding the concept of dimensions.

[Doomonkey]

0s do not matter in physics.
[10 , 0°] + [5 , 180°] = [5 , 0°] = 5
[10, 0° , 0°] + [5 , 180° , 0°] = [5 , 0° , 0°] = [5 , 0°] = 5
[10, 0° , 0° , 0°] + [5 , 180° , 0° , 0°] = [5 , 0° , 0° , 0°] = [5 , 0° , 0°] = [5 , 0°] = 5

Let me rephrase this.

Dimensions do not matter in physics. Whether you have [5 , 2°] + [5 , 8°] or [5 , 13° , 7° , 412° , 1° , 9°] + [5 , 12° , 6° , 411° , 0.5° , 8°], both are solvable and the method for solving them is the same.

[Ipquarx]

Just because something can be broken up into an infinite number of something else does not mean that it IS; if you were to look at each "instant" in the order that happened they would all be the exact same, meaning that everything would be a single "instant" by your definition. In order for time to progress there has to be some distance between "slices" which your definition cannot provide.

[Menen]

One, I was talking about SPATIAL dimensions, but since you went and handicapped up, let me correct you.

TIME IS IN FACT MADE OF SLICES. Each instant of time is a snapshot of a three-dimensional reality. Since these have no, uh, time-depth, by your logic they cannot exist. Yet they do, because time is made up of an infinite number of such instances of time. Just because each instant of time flows together in a perfect fashion does not mean they are not individual instants.

Yes, I know 'time-depth' isn't a word, but apparently we've already assigned length to a spatial dimension and I want to avoid confusion because Ipq is apparently already having trouble understanding the concept of dimensions.

Of you put all the slices together you get a stream.