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  #1  
Old 12-01-2005, 04:00 AM
mr_whomp mr_whomp is offline
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Default 2D, 3D and 4D Man

Would like others thoughts on this.

2Dimensional man comes accross a circle with a dot inside it. He cant get to the dot because it is impossible for him to get past the circle (we are ignoring the fact that 2D man would fall in half because his digestive tract splits him in two).

3D man comes along, sees a dot inside a circle and just reaches overtop the circle and touches/grabs the dot. To 2D man, this is a miracle.

Now where it gets interesting...

3D man comes accross a ball surrounded by a sphere. He cannot touch/grab the ball since it is impossible for him to get past the sphere.

Along comes 4D man. He sees the ball inside the sphere and takes it. The sphere is no more barrier to him than the circle was to 3D man. To 3D man this is a miracle.

Now 4D man comes accross a sphere surronded by the 4D equivilent of a dot/circle/sphere. To him he cant touch/grab the sphere. But 5D man can easily take the sphere, there is no barrier for him. To 4D man this is a miracle.

Soooo...Is god 4D man?
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  #2  
Old 12-01-2005, 04:19 AM
MelchyBeau MelchyBeau is offline
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Default Re: 2D, 3D and 4D Man

I think you should read Flatland by Abbott. The story is about a 2d character trying to understand a 3d object.

Melch
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  #3  
Old 12-01-2005, 04:29 AM
mr_whomp mr_whomp is offline
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Default Re: 2D, 3D and 4D Man

thanks will check it out, my post was based on what i read by stephen hawking.
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  #4  
Old 12-01-2005, 09:25 AM
hmkpoker hmkpoker is offline
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Default Re: 2D, 3D and 4D Man

Does 4D man have infinite power wihtin the 3-D realm?
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  #5  
Old 12-01-2005, 12:45 PM
mr_whomp mr_whomp is offline
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Default Re: 2D, 3D and 4D Man

Do you have infinite power in the 2D realm?
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  #6  
Old 12-01-2005, 02:29 PM
Ringo Ringo is offline
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Default Re: 2D, 3D and 4D Man

An interesting point of this is that 2d man is able to see a shadow of a 3d object - say a cube. He can see the shadow of this cube in his 2d world, but is unable to comprehend what it is.

If you have a 1 dimensional world (ie, a line), and the only movement is "Left-Right" - then the way to turn that 1D line into a 2d square is to project the sides into the 2nd dimension and join the points. Now you have a 2d square.

Doing that again, you can make this 2d square into a 3d cube, again by projecting the corners into the 3rd dimension , and violla, a cube.

Now - we live in a 3D universe. To make a 4D object, all we do is project the corners of the cube into the 4th dimension (which we understand as much as the 2D Flatland man understands the concept of a 3D cube). BUT..

..in the same way the 3D man can see the shadow projected by a 3D cube, so us 3D citizens can see the "shadow" projected by the 4D equivelent - and it's called a "tesseract" I think, and it's as real a shape as the cube is to the 2D man. Here is what the shadow of a 4D object in 3D space looks like.. http://www.logic-alphabet.net/tesseract.htm

I'm sure someone can do a better job of explaining the 3D/4D type stuff, but it's very interesting if you get into it.

Ringo
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  #7  
Old 12-01-2005, 04:17 PM
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Default Re: 2D, 3D and 4D Man

In Flatland, 3D man has the ability to move up and down vertically, so can literally move into the 2D man. Likewise, 2D man can move horizontally along the 1D man's plane. The 1D man's plane allows for more than one existing entity - the 0D man is a singular entity point, aware only of its own existence, where all others are posited to be the thoughts of another.

The opportunity of another to have more powers than ourselves (i.e. to have another dimension to themselves) is something we might consider as akin to "Godliness". However, the problem exists that if our 3D world is superceeded by a 4D world, then there are theoretical 5D, 6D, 7D... etc worlds. Thus there is a continual sense of "Godliness" until we reach an "InfinityD" world, where every possible dimension of existence is present in each entity.

Ergo, a 4D man may be a 3D man's god, but we would both deify a 5D man, and so on.

Edit - But we would struggle to understand anything with more dimensions than we contain.
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  #8  
Old 12-01-2005, 05:33 PM
DoomSlice DoomSlice is offline
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Default Re: 2D, 3D and 4D Man

There are infinite dimensions!

If I take a trillion integrals over a line, I'm going to get a number, right?
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Old 12-02-2005, 04:03 AM
Brom Brom is offline
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Default Re: 2D, 3D and 4D Man

Don't we live in a 4D world with the 4th dimension being time? We need 4 co-ordinates to describe the position of something (its traditional x,y,z co-ordinates and a fourth co-ordinate to say what time it occupied that state).

Sorry to be nittish but I've only started reading in this forum and have noticed the 3D world reference a lot and wanted to clarify.
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  #10  
Old 12-02-2005, 04:27 AM
baumer baumer is offline
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Default Re: 2D, 3D and 4D Man

[ QUOTE ]
the way to turn that 1D line into a 2d square is to project the sides into the 2nd dimension and join the points.
Doing that again, you can make this 2d square into a 3d cube, again by projecting the corners into the 3rd dimension , and violla, a cube.

Now - we live in a 3D universe. To make a 4D object, all we do is project the corners of the cube into the 4th dimension

Ringo

[/ QUOTE ]

Check this out if you want to read about N-dimensional cubes.
Hypercubes
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