Recently I’ve had occasion to think of this old post of mine, which I’ve rewritten here for you. Never mind why, just enjoy.

In geometry, a *point *is a zero-dimension object, having no extension in any direction.

A *line *is a one-dimensional object defined by two points (that is, for any two points, there is one and only one line that can be drawn through both). A segment of a line is bounded by two points – the endpoints.

A *square *is a two-dimensional object that is bounded by (or defined by) four lines.

Finally, a *cube *is a three-dimensional object bounded by six squares.

Notice how each object is defined by an object of one lower dimension: the cube by the squares, the square by the lines, the line by the points. Also notice the progression: two points make a line, four lines make a square, six squares make a cube.

I therefore posit a four-dimensional object that is defined by eight three-dimensional cubes.

We’ve all seen a representation of a cube drawn in two dimensions, right? [There, now you have.] Therefore we should be able to create a representation of a four dimensional ‘something’ in three dimensions. Here, however, is where I run up against the cognitive limitations of my species.

Any ideas?

Here’s another progression that I’ve been

~~medicating~~meditating upon: From muck and mire there is an exponential evolutionary leap to the pterodactyl. With another exponential leap you have the troglodyte. Then the great chasm is bridged to the Grandpa Steve and civilization. But here, however, is where I run up against the cognitive limitations of my species.Sounds like a job for the electric kool-aid acid test to me, Dr. Leary.

Sounds like you’ve already been dipping into the electric kool-aid, if you know what I mean.

Maybe a flashback or two.

“Therefore we should be able to create a representation of a four dimensional ‘something’ in three dimensions. ”

What you are looking for is called a Tesseract. It is the four-dimensional analog of the cube; and is to the cube as the cube is to the square. Just as the surface of the cube consists of 6 square faces, the hypersurface of the tesseract consists of 8 cubes.

It is also called a hypercube.

Tesseracts! I forgot all about those.

Thanks for the reminder. Now, if I could only find one on Ebay…