How to Draw a Four Dimensional Cube


Einstein is famous for his work in the 4 dimensions of spacetime: 3 dimensions of space plus one dimension of time. Since it's been a hundred years when Einstein first published his paper on relativity, everybody should be able to draw a 4 dimensional cube.

Einstein said,
   "It can scarcely be denied that the supreme goal of all theory is to make the irreducible basic elements as simple and as few as possible without having to surrender the adequate representation of a single datum of experience."

Or, simply restating Einstein's quote for the purpose of drawing a 4 dimensional Cube,
   "Systems should be complete and simple as possible."

Complete in that the final drawing is a 4 dimensional cube.
Simple in that the instructional steps are the fewest and simplest to follow.


Drawing Techniques

It only takes two core techniques to draw a 4 dimensional cube. Once you have master those, there are only two instructional steps to draw it.

1. The first technique is the drawing of squares because all sides of a cube are square.
This needs to be second nature when you go onto dimensions higher than 3.

2. The second technique is drawing dimensional baselines.
Sorry, you can't Google "dimensional baselines" to find the method. However, I will show you.

Draw a Square

Key points when drawing a square,

   Start by drawing the dimensional baselines.

   Opposite sides of a square are parallel to each other.

First --- Previous --- Next Draw Squares

Draw a Cube

Key points when drawing a cube,

   Start by drawing the dimensional baselines.

   All sides of a cube are square.

First --- Previous --- Next
Draw Cubes

Draw Dimensional Baselines

Key points when drawing dimensional baselines,

   The number of baselines is the same as the quantity of dimensions.

   The baselines are guidelines to draw the rest of the cube or square.

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Draw dimensional baselines


Instructional Steps to Draw a Four Dimensional Cube

If you can draw a square and a cube from their dimensional baselines, you're ready to draw a 4 dimensional cube.

   1. Draw the cube's dimensional baselines.

   2. Draw the cube's square sides using the dimensional baselines, as guidelines.

The trick of course, is how to draw the 4 dimensional baselines.

First --- Previous --- Next
Draw dimensional baselines


Tokyo's Shibuya crossing on a Saturday afternoon.


Reference

"Everything should be made as simple as possible, but no simpler."
A quote often attributed to Albert Einstein. See the Quote Investigator for further details.

If I truly have come up with the fewest, simplest steps, then people will select my instructions over others. Because others also favor the basics. Occam's razor favors the fewest. Lao-Tzu favors simplicity.

Occam's razor says,
   When presented with competing hypotheses that make the same predictions, one should select the solution with the fewest assumptions.

Lao-Tzu, the author of the Tao Te Ching, named simplicity as one of his top three virtues. Compassion and modesty being the other two.