7/27/2019 057 Dimension

1/1

THE FOURTH DIMENSION SIMPLY EXPLAINED

Get any book for free on: www.Abika.com

57

lines from the original square, four lines in the final square, and four lines traced by the movements of the fourpoints of the original square, or twelve lines in all, meeting at eight points; four points from the original square and

four points from the final square.

Let us assemble the above facts for convenience in comparing them and add to the table thecorresponding properties of an imaginary fourth dimensional figure, these being determined asfollows:

As the line, the first dimension, is formed from a moving point, so a square, a typical seconddimension figure, is formed from a moving line, making a figure bounded by four lines, and as acube having a third dimension is similarly formed by a plane moving into

Page 113

Number of

dimensions in

figure

Number of

points in

figure

Number of lines

bounding figure Number of planes

bounding figure Number of cubes

bounding figure

Point 0 1 0 0 0

Line 1 2 0 0 0

Square 2 4 4 0 0

Cube 3 8 12 6 0

Corresponding figure

of four dimensions 4 16 32 24 8

the third dimension, making a figure bounded by six planes, does it not follow that a

corresponding fourth dimensional figure is formed by the movement of a cube into the fourthdirection and will be bounded by cubes?

If this is the case and the line derives from the point two points, and the square derives fromthe line four lines and four points; and if the cube derives from the square eight points, twelvelines and six planes, does it not follow that the moving figure gives to the corresponding fourth

dimensional figure the following qualities?

The cube at rest has eight points in space, at the end of its movement it has eight new points inspace, its movement into the fourth dimension has created the fourth dimensional figure;therefore, the figure should have sixteen points. The cube has at rest twelve lines or edges and

has at the end of its movement twelve additional lines, and each of its eight points has traced anew line, making thirty-two lines or edges in all for a corresponding fourth dimensional figure.

Similarly, as the cube has six planes at the beginning and has six new planes at the ending of its

movement, and as its twelve lines will in moving

Page 114

trace twelve new planes, there will be twenty-four planes in the fourth dimensional figure. Now, as a cube is

generated from a moving square, when the cube moves to generate a figure of the fourth dimension, the new figure

will have a cube at the beginning of the movement and another cube at the end, and in addition each of the six

squares bounding the original cube will by their movement trace a new cube, thus adding six new cubes to the two

already mentioned, or eight cubes in all to bound the new fourth-dimensional figure.