THE FOURTH DIMENSION
- Dr. Roivas
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Re: THE FOURTH DIMENSION
I am not sure what you are saying. Is the above a question? And if so, do you mean mentally or visually. If visually, obviously not, no one can. If mentally, I feel I have a pretty good amateur understanding of it.
The shapes are neat too.
The shapes are neat too.
Re: THE FOURTH DIMENSION
This is neat.
I was super young when I used this forum and probably said weird or odd stuff. Dont hold me to it!
- Blade Genexis
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Re: THE FOURTH DIMENSION
I find the science behind it more interesting than the visuals.
http://en.wikipedia.org/wiki/Four-dimensional_space
http://en.wikipedia.org/wiki/Spacetime
http://en.wikipedia.org/wiki/Four-dimensional_space
http://en.wikipedia.org/wiki/Spacetime
Without change, there can be no progress.
- Pumpkinium
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Re: THE FOURTH DIMENSION
help me
Re: THE FOURTH DIMENSION
Geometrically the fourth dimension is painful to contemplate. Other than the object that is a cube in the third dimension doesn't even translate well in my mind. But when I think about the fourth dimension when looking at the boxy image I imagine the progression of time taking place in three dimensions. I far prefer spacetime to be the fourth dimension, as cool as the images are.
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Re: THE FOURTH DIMENSION
^I had a debate about that with my friend. He was thinking of the 4th dimension as that of a spacetime, while I was preferring to think of a 4th dimension spatially. Granted, this was before we understood that these were two entirely separate concepts pioneered by Mikowski and Euclidean geometry expanded, respectively. I think spacetime is ideal to easily comprehend because it is something we are exposed to, unlike a fourth spatial dimension, which anything beyond the basic concept of a tesseract eludes me.
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Re: THE FOURTH DIMENSION
I don't quite understand... nice shapes, I guess.
- Moonstalker
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Re: THE FOURTH DIMENSION
You typically aren't able to understand; the fourth dimension is not visible simply by the human eye and must be synthesized by means of visual media such as shown in the original post.
Re: THE FOURTH DIMENSION
My brain x.x it's frying my BRAIN!
I hate math...
I hate math...
- Jeffery Mewtamer
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Re: THE FOURTH DIMENSION
I comprehend the pentachoron, the tesseract, polyhedral prisms, and duoprisms.
If I was to explain them to another:
Pentachoron:
You are standing in a room that is a perfect tetrahedron(triangular pyramid).
There is a hatch in the middle of each wall, as well as one in the middle of the floor.
Each hatch leads to another room with the same layout.
There are five such rooms in total, each connected by a hatch to all of the others.
Tesseract:
You are standing in a room that is a perfect cube.
There is a hatch in the middle of each wall, as well as one in the middle of the floor and one in the floor.
Each hatch leads to another room with the same layout.
There are eight such rooms in total. Each room is connected to six adjacent rooms and one room that is non-adjacent.
To get from the starting room to the non-adjacent room, take any hatch to an adjacent room, and then take the hatch opposite the first hatch.
Traveling in a straight line will return you to where you began every fourth room.
Polyhedral Prisms:
A polyhedral prism has two rooms that are congruent polyhedra with a hatch in each face.
Corresponding faces between the two polyhedra are connected by a room that is a prism with the given faces as their bases.
The rectangular walls of the prism rooms have hatches connecting to the prism rooms that join adjacent faces of the polyhedral bases.
For example:
The tesseract is a special case of a Cubic Prism where the prisms connecting the two cubic bases are themselves cubes.
A tetrahedral prism has two tetrahedra as its bases that are connected via four triangular prisms arranged to match the faces of a tetrahedron.
A dodecahedral prism has two dodecahedra as its bases that are connect via twelve pentagonal prisms arranged to match the faces of a dodecahedron.
Duoprism:
Start with a room that is an n-gonal prism and make a stack of them n high.
Hatches in the n-gonal floor and ceiling take you to the next prism in the stack.
The hatch in the ceiling of the top prism connects to the hatch in the floor of the bottom prism.
You have second stack identical to the first, but oriented perpendicular to the first.
The hatch in the square walls of each prism connect to one of the prisms in the other stack.
Every room has a direct connection to every room in the other stack plus to two rooms in the same stack.
To makes more complicated, the same construction works with a stack of m n-gonal prism and a stack of n m-gonal prisms.
Now, to anyone who comprehended what I just wrote, it should to obvious that such structures cannot be built in 3-space without distorting the shape of every room, but in four space, every room would be undistorted, and this is what traveling inside the four-dimensional object would look like to a three-dimension being, similar to how a two-dimensional being would perceive a polyhedron as a series of connected polygons that should not be possible.
Now, if I could just figure out the 16-cell, 24-cell, 120-cell, and 600-cell. Honestly, I think these shapes would make interesting floor plans for a dungeon in a video game, especially if only a select few of the hatches I mentioned where available.
If I was to explain them to another:
Pentachoron:
You are standing in a room that is a perfect tetrahedron(triangular pyramid).
There is a hatch in the middle of each wall, as well as one in the middle of the floor.
Each hatch leads to another room with the same layout.
There are five such rooms in total, each connected by a hatch to all of the others.
Tesseract:
You are standing in a room that is a perfect cube.
There is a hatch in the middle of each wall, as well as one in the middle of the floor and one in the floor.
Each hatch leads to another room with the same layout.
There are eight such rooms in total. Each room is connected to six adjacent rooms and one room that is non-adjacent.
To get from the starting room to the non-adjacent room, take any hatch to an adjacent room, and then take the hatch opposite the first hatch.
Traveling in a straight line will return you to where you began every fourth room.
Polyhedral Prisms:
A polyhedral prism has two rooms that are congruent polyhedra with a hatch in each face.
Corresponding faces between the two polyhedra are connected by a room that is a prism with the given faces as their bases.
The rectangular walls of the prism rooms have hatches connecting to the prism rooms that join adjacent faces of the polyhedral bases.
For example:
The tesseract is a special case of a Cubic Prism where the prisms connecting the two cubic bases are themselves cubes.
A tetrahedral prism has two tetrahedra as its bases that are connected via four triangular prisms arranged to match the faces of a tetrahedron.
A dodecahedral prism has two dodecahedra as its bases that are connect via twelve pentagonal prisms arranged to match the faces of a dodecahedron.
Duoprism:
Start with a room that is an n-gonal prism and make a stack of them n high.
Hatches in the n-gonal floor and ceiling take you to the next prism in the stack.
The hatch in the ceiling of the top prism connects to the hatch in the floor of the bottom prism.
You have second stack identical to the first, but oriented perpendicular to the first.
The hatch in the square walls of each prism connect to one of the prisms in the other stack.
Every room has a direct connection to every room in the other stack plus to two rooms in the same stack.
To makes more complicated, the same construction works with a stack of m n-gonal prism and a stack of n m-gonal prisms.
Now, to anyone who comprehended what I just wrote, it should to obvious that such structures cannot be built in 3-space without distorting the shape of every room, but in four space, every room would be undistorted, and this is what traveling inside the four-dimensional object would look like to a three-dimension being, similar to how a two-dimensional being would perceive a polyhedron as a series of connected polygons that should not be possible.
Now, if I could just figure out the 16-cell, 24-cell, 120-cell, and 600-cell. Honestly, I think these shapes would make interesting floor plans for a dungeon in a video game, especially if only a select few of the hatches I mentioned where available.
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- Shining Chaos Chao
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Re: THE FOURTH DIMENSION
The fourth dimension has horrible lighting.
Otherwise: http://www.youtube.com/watch?v=9DoSqeJN ... re=related
Otherwise: http://www.youtube.com/watch?v=9DoSqeJN ... re=related
- Jeffery Mewtamer
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- Yzarro
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Re: THE FOURTH DIMENSION
THEY'RE LIKE MIND-****ING BUBBLES IN SHAPES. *V*
(18:10:19) shadow_is_BEAST: WHO GAVE Y'ALL THE RIGHT TO LICK OTHER PEOPLE OUT
- Tobi
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Re: THE FOURTH DIMENSION
To me it just looks like lines in a certain figure that spins about, and thanks to the dimension, it looks like it's inside of it one time, and sticks out the other time.
Quote removed because SOMEONE had to bug like 3 mods at a time over a signature.
- Enzo03
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Re: THE FOURTH DIMENSION
If we were meant to see in 4D, then:
1) all 3D would look flat.
2) we would see 4D in a way similar to 3D.
1) all 3D would look flat.
2) we would see 4D in a way similar to 3D.
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