Dimensions






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"Flatland, A Romance of Many Dimensions" indeed flatland, although focusing on the two dimension world did describe those of us in the 3rd dimension, as well as those in 1st (line land) and no dimension (point land) worlds. It even went as far as discussing the 4th dimension and beyond, these however lie uncomprehendible to our current understanding. 

Below I will attempt to compare the dimensione by picturing how an observer from each would see the "same" objects.

3d.gif (31730 bytes)
First we're starting with a view of objects in a way we are used to seing them, with length height and breadth. Represented here are some basic figures, prisms, pyramids and speres. A horizon line an grid are also left in for perspective purposes.

On page 69 in the book, the sphere attempts to describe a cube such as the one pictured at left. "Behold this multitude of of movable square cards. See, I put one on another, not as you supposed, Northward of the other, but on another. Now a second, now a third. See, I am building up a solid by a multitude of squares parallel to one another. Now the solid is complete, being as high as it is broad, and we call it a Cube."
 
 

2d.gif (18690 bytes)
This was of course very difficult to comprehend for the flatland inhabitants, as for in flatland things appeared much like they do in the picture at right. You may notice it is the exact same image, transfered to two dimensions. Note however that if you were indeed a flatlander, looking from the corret perpective you would notice no more than a line, provided you weren't excersising sight recognition. 

As described by the sphere, "what you style Flatland is the vast level surface of what I may call fluid"