Let's
try to assign a number to each of the sets on each face of the
cube. Let's take as an example cube #2 and establish the three
cartesian coordinates marking them with the numbers 1, 2, 3.
The three numbers indicate the three planes of the cube. Now let's
assign the number 1 to the plane that forms the two parallel faces
in front of us (direction forward and backward) the number 2 to
the lateral faces (direction left right) and the number 3 to the
upper and lower faces (direction up and down).
Now we have to decide how we have to decide how we are going to
go about assigning symbols to the single elements of each face.
One logical system would be to find an analogy between groups
of numbers and sides, angles and surfaces of the cube.
In fact the 18 numbers between 4 and 21 (we have already used
1, 2 and 3 to indicate the dimensions) are divisible in three
groups of six figures each, exactly what we need. There are six
numbers divisible by two and not by three and six prime numbers
(which can only be divided by one).
Thus
we have three sets of the parts of the cube and three sets of
numbers. How should we relate them to each other?
In effect it's not difficult to see that the angles are similar
to triangles and could be symbolized by numbers divisible by three;
the surfaces are easily divisible in equal parts and can be symbolized
by numbers divisible by 2, and the sides, which in a cube are
so difficult to divide beween one square and the bordering square,
are symbolized by the prime numbers. Let's start by assigning
the numbers 4, 5, 6 to one of the faces of the cube that are on
the plane indicated by the numbers 1,7,8,9 to the face indicated
by the number 2, 10, 11, 12 to the face indicated by the number
3 and so on for the remaining numbers.
If,
when assigning
the number, we adopt a system on naming close things before distant
things, of proceding from left to right and from up to down (as
we do in writing) we will obtain an ordered disposition of the
numbers that for each number between 4 and 21, tells us not only
if we are referring to the angles, the sides or the surfaces on
one of the faces in front of us, of one of the lateral faces,
or of one of the surfaces above or below, but also to which of
the two faces of each couple we are referring to.
The
number 17, for example, indicates the surface of the face placed
in front of us, in the second plane, while the number 17 refers
to the sides of the face of the cube that is to the right side.
The curious thing is that the numbers related to the 2 faces numbered
1 are 4, 5, 6 and 13, 14, 15; the cabalist used to simplify the
numbers composed of more than one figure by adding together the
figures of which they were composed. If we were to perform this
same operation with 13, 14, 15, they would become 4, 5, 6 and
thus the sum of the numbers on each face would be the same. And
it is the same for every couple of sides on each face of the cube.
By observing cube 2 you can spend an entire day playing these
games.
