Me At 47 Trying To Explain My Magic Ghost Number Cube's Inner/Outer Ghost Numbers To My 1994 Self

Magic Ghost Number Cubes, as fancy and spooky as it sounds, is really basically built up from the commutative property of algebra, and as fancy and mathematical as that name sounds, it simply means 1 plus 3 equals 4, the same as 3 plus 1 equals 4. It's really that simple, but the things it produces just boggles the mind!!!

I've called my cubes by several names, before settling on Magic Ghost Number Cubes. I got that name because I considered the true corners of the true cube to be " floating corners" and the numbers that I guessed at being at those corners, I called the " ghost numbers". It was since 1994, when I invented them that I guessed at the ghost numbers, but never really attempted to find them, because I thought it was a delusion. I admit, I also think the name is kewl!!!

My Magic Squares

Addition Square

It starts simple enough. And the operations thru-out are very simple. It's basically the commutative property thru the entire process from square to cube, but I'll start with the simplest square first.

Choose any four random numbers. I chose 1, 2, 3 and 4 to go around all four sides of the square. There are some instances where it doesn't work, such as placing two like numbers next to each other or, I think, at opposite sides. but I'm a little foggy in that respect.

The first four numbers around the square are what I call the primary numbers of the square.

Next, add up to the first inner layer's corners of the soon-to-be double-layer square.

Now, using the commutative property of algebra, sum the horizontal and vertical pairs of terms on opposite sides of the square.

Now, add those numbers up to the corners of the square's outer layer.

That's all you have to do! But if you look, you'll notice ( in the bottom three square, an orange X, showing that those numbers equal the sum at all four corners.

Then you'll notice the red circled terms. This doesn't really go no where, but it does in the multiplication square below it. It does give off an apparent half-opened interval expression which always seems to be true. In this instance, 3 is < than or = to 7.

The yellow-circled two 5's are a property of addition squares only and are not found in the multiplication squares.

Multiplication Square

You follow the same procedure as you did with the addition square, but using multiplication. Now, look at the red-circled terms. Their proportions to the uncircled term on each line are the same, horizontal and vertical and also produce an apparent half-opened interval expression that is always true. In this case, 2 is < or = to 12.

Magic Ghost Number Cubes

This example uses a 1,2,3 and 4 twice around the two vertical axis, crossing each other. Again, the number choices can be random. I simply chose to use the six primary numbers 1,1,2,3,3 and 4, when added together gives the inner ghost number ( I figured this out at the end of last year. I found the outer ghost numbers first at the beginning of last year).

Now, you are working in three square planes intersecting each other.

Since this is an addition cube, you follow the same procedures as you would for a single addition square, but with the added extra two primary numbers creating a tri-plane cube.

The purple-circled inner-layer numbers at the two spatial-diagonal ends of one of the four spatial-diagonals are circled. Those added together separately and then added altogether at each end of the the spatial-diagonal gives the red-colored outer ghost numbers of 42 at each of the true corners of the tri-plane intersected cube, which happens to be the inner ghost number multiplied by 3. A multiplication cube would be a cube of the number as seen in the sequences of the numbers ranging from 1234 to 2468 to 3579 done below this one. I only did one spatial-diagonal pair, the diagram directly below, to keep it from becoming confusing and messy.

Adding, in the case of addition cubes, the outer cubical numbers ( circled in red) also gives the outer ghost numbers around the cube.

Multiplying the outer numbers of a multiplication cube, would give those outer ghost numbers, too!

There is an angle of preferred incidence of the ( brown and yellow-circled terms) spatial-diagonals of the pairs of terms at each end, one kind of preference solely the for the addition and the multiplication cubes.

The Apparent Transmission of Secondary Numbers and Ghost Numbers Thru A Cube

Faces, Edges and Corners of A Cube: Numerical Invisibility

Addition Cube

Multiplication Cube

?

Why are there outer and inner ghost numbers and why do they relate in the ways they do?