#### ew0054

##### Troll Extraordinaire

If we extrude a point, which has zero dimensions, into an arbitrary direction, we now have a one-dimensional line with two end points. If we extrude this line into a new direction shifted by 90 degrees, such that the length of the new sides of the figure are equal to that of the line rotated by 90 degrees, then we have a square, which is two-dimensional and has four end points and four sides. Further, if we extrude the square into yet another dimenson altered by 90 degrees, such that its new side is equal to that of the prevoius figure, we have a 3-dimentionsal cube that contains eight end points and six sides.

Name.........Dim...Endpt....Sides

Point..........0........1..........0

Line...........1........2...........2

Square.......2........4...........4 Lines

Cube..........3........8..........6 Squares

?...............4........16.........8 Cubes

We can observe both arithmetic and geometric paterns. Thus, it follows to suggest that extruding this cube into some unknown direction would in fact produce a figure containing 16 points connected by eight cubes? This would be very difficult to imagine projected onto a 2-D plane for illustration.

However the concept of illustration warrants itself to another speculation. For beings of the 3rd dimension can easily comprehend concepts of the lower dimensions, we must recognize that perspective of 3rd dimensional objects are taking place through a 2-D eye, since the light is projected onto the retina, which although it is spherical in shape, is really a 2-D map laid out on the inner surface of the eye.

Suffice to speculate that in fact what would be required of us to view 4th dimensional objects would be a "3-D eye". This may not be too difficult to envision, since projecting 3D images onto 2D surfaces is natural. Imagine a retina in which the rods and cones are arranged in a cubical array (or any other 3-D object of your choosing) in which a section 3rd dimensional world is projected into this retina such that the viewer would be aware of every aspect of the world. That would be to say, the viewer would thereby know what is both behind and inside objects by seeing them from all angles at once.

That is my speculation, which could be one possible explanation of how viewing higher dimensions could be done. But I still cannot determine what direction the cube would have to be extruded into, and how it could physically be done in the third dimension. Any speculations?