If you can do this to a 2d object in 3d space, what can you do

> what can you do to a 3d object in 4d space?
flip it horizontally

>>8796543
Turn it inside out essentually.

>>8796549

Could you turn a person so their right hand is on their left side?

>>8796543
But you're flipping it in 2d space?
>>8796559
yeah look at a mirror?
The mirror space is a three dimensional representation of you.

>>8796543
Well, just think about what you are really doing.

What you are doing to that 2D object isn't really a 3D transformation. It is a 2D transformation. A flip. But what you are probably imagining is the way you can picture that motion in 3D. In particular:

You take that 2D object, fix its left (or right) edge in the plane it is, then take it by the other edge and pull that edge into other planes (basically 3D space), then you keep doing this until you can only see a 1 dimensional cross section of the 2D object, and then you keep pulling it until the object is completely back into its original plane, but now flipped.

So now simply change the dimensions:


You take that 3D object, fix one of its faces in the space it is, then take it by the opposite face and pull that face into other spaces 3D spaces along the 4th dimension (basically 4D space), then you keep doing this until you can only see a 2 dimensional cross section of the 3D object (a single face), and then you keep pulling it until the object is completely back into its original space, but now flipped.

>>8796545
The point he's making is this flip is only possible in 3d.

A 2d object in 2d space cannot be made to flip.

>>8796590
>What you are doing to that 2D object isn't really a 3D transformation. It is a 2D transformation.

It's impossible to *continuously move* the beginning state into the ending state in 2D. Things generally don't just magically appear in new positions in real life.

>>8796543
you can do the exact same to a 4D object in 6D space

File: 8d7a28523ae7878fce9e3b8d24946df2.jpg (91KB, 600x595px) Image search: [Google]

91KB, 600x595px

>>8796543
If a shadow is a 2D object, cast by a 3D object then that means a 3D object is the shadow of a 4D object. What does the 4D object look like?

>>8797253
If a goat is like a dog, but can chew every thing. What is a cat then?

>>8797295
>What is a cat then?

An asshole.

File: figure-02-03-06.jpg (61KB, 680x362px) Image search: [Google]

61KB, 680x362px

Not exactly sure of this, but essentially what happens in the 2d flip is that the asymmetric parts of the image get mirror reversed, so I'd imagine that a similar flip in 4d would have the same effects. Coming from a chemistry background, I'd imagine such a flip would be like producing the other enantiomer of a chiral molecule. You're just reversing the asymmetry. mathfags please confirm

>>8796543
mirror the object

>>8797230
>A 2d object in 2d space cannot be made to flip.
Mathematically? Sure it can.
Physically? Only when we invent a material which can move through itself without losing structural integrity.

>>8797253

Light in 4d probably works totally differently

Snell's law/lambert's cosine law only work in 2d and 3d

>>8796543
Turn in inside out.

>>8797875
>Mathematically? Sure it can.
no
they are not talking about homeomorphism induced by the group transformations, they're talking about isotopy between those two

>>8797373
the OP did a C2 rotation which lead to the reflection. since the two operations are different I wouldn't assume that it would be always true