Consider the following concept:
There are five 5-d manifolds, five 4-d manifolds, five 3-d manifolds, five 2-d manifolds, five 1-d manifolds, and 5 singular points. The five singularities, are embedded in the five basis 1-d manifolds. The five 1-d manifolds, are sub-manifolds embedded in the five 2-d manifolds. The five 2-d manifolds, are sub-manifolds embedded in the five 3-d manifolds. The five 3-d manifolds, are sub-manifolds embedded in the five 4-d manifolds, The five 4-d manifolds, are sub-manifolds embedded in the five 5-d manifolds. Now, the correspondence between all five 3-manifolds is one-to-one, and onto. All the manifolds 1-d through 5-d are smooth, and therefore differentiable. The correspondence between all the-manifolds is one-to-one, and onto. All n-manifolds are ordered in a series with the other n-manifolds, and there is a one-to-one relation and onto between each of the five singularities. More specifically, the singularities and manifolds' relationships are as follows:
The first of the five singularities, corresponds to one, and only one, singularity to it's right. The second singularity corresponds to both the first singularity to it's left, and the third singularity to it's right...the fifth singularity corresponds to one, and only one, singularity to it's left. The same goes for all the other higher n-spheres. Now, the quantifiable relationship between the first n-manifold, and the manifold to it's right, is such that it is entirely additively displaced into the content of the second n-manifold so that the content of the second n-manifold increases to (1st n-manifold+2nd n-manifold), while the first n-manifold goes to zero, such that, after the displacement, there are only four n-dimensional manifolds remaining. The second relation, is that when an n-manifold is displaced into the n-manifold to it's right or left, all other higher dimensional, and lower dimensional manifolds are displaced, correspondingly, to the next manifold over as well. Thus the singularities and manifolds can be represented by a 6X5 matrix, where the columns represent the dimensions 0,1,2,3, etc, and the rows represent the series relationship between the singularities and n-dimensional manifolds.
| 1st 0-d 2nd 0-d 3rd 0-d 4rth 0-d 5th 0-d |
| 1st 1-d 2nd 1-d 3rd 1-d 4rth 1-d 5th 1-d |
| 1st 2-d 2nd 2-d 3rd 2-d 4rth 2-d 5th 2-d | =D
| 1st 3-d 2nd 3-d 3rd 3-d 4rth 3-d 5th 3-d |
| 1st 4-d 2nd 4-d 3rd 4-d 4rth 4-d 5th 4-d |
| 1st 5-d 2nd 5-d 3rd 5-d 4rth 5-d 5th 5-d |
All columns can be added linearly left to right to make a single row. However, none of the rows can be simply added together, because all manifolds in a given column do not have the same dimensionality. All rows can be put together, but under a special operation that lifts the higher dimensional manifolds into the lower dimensional manifolds. In fact, as we shall see later in this paper, such a lift may veritably describe gravity in four space.
Here is an example of such a lift:
Consider a solid 3 centimeters x 3 centimeters two-dimensional square embedded into a 2-dimensional Cartesian coordinate system [x, y]. The perimeter of the 2-dimensional square is 9 centimeters.
Now suppose you subdivide the square into 9 smaller 1 centimeter squares, and label them as follows:
1cm square 1 1cm square 2 1cm square 3
1cm square 4 1cm square 5 1cm square 6
1cm square 7 1cm square 8 1cm square 9
This square is an example of a 1-dimensional sub-manifold embedded into a 2-dimensional manifold, where the square is the 2-dimensional manifold, and the perimeter of the square is the 1-dimensional manifold that is embedded in the 2-dimensional manifold (square).
The surface area of the 2-dimensional manifold is 9 centimeters squared 9cm^2. The surface area of the embedded 1-dimensional sub-manifold is 9 centimeters 9cm^1=9cm.
Now suppose you cut out square 2, square 4, square 6, and square 8...
1cm square 1 1cm square 3
1cm square 5
1cm square 7 1cm square 9
...like this.
The surface area of the 2-dimensional manifold is decreased by 4 centimeters squared. However, the surface area of the embedded 1-dimensional manifold has increased by 8 centimeters so that the surface area of the 1-dimensional sub-manifold is now 20 centimeters around instead of 9 centimeters around. In addition, the sub-manifold is less smooth. What we have done by cutting out the four 2-dimensional one centimeter squares is lift those 2-dimensional squares into the 1-dimensional sub-manifold resulting in a conversion of the four 2-dimensional squares into the 1-dimensional sub-manifold. By collapsing one of the diagonals of each of the four 1cm^2 squares, that we cut out, we get four 2 centimeter long line segments whose total lengths add up to 8 centimeters, which is exactly the amount of length we had added to the 1-dimensional distance around the 2-dimensional square by cutting out those square segments in the first place. Notice that, although, we cut the square itself, we have not done anything to the Cartesian coordinate system, into which, the solid 2-dimensional square was originally embedded. Now we can continue cutting out 2-dimensional sections of the remaining 5 squares up to infinity, which translates into lifting the entire 2-dimensional surface of the solid square into the 1-dimensional sub-manifold embedded into that square. At this point, the area of the solid square goes to zero, and the distance around the 1-dimensional sub-manifold goes to infinity. In addition, the 1-dimensional sub-manifold is not smooth, but rather, infinitely jagged, and therefore, is no longer a differentiable manifold. Now the 1-dimensional manifold is still embedded in the 2-dimensional Cartesian coordinate plane. Now if we collapse one of the two dimensions composing our 2-dimensional Cartesian coordinate plane, in which, our infinitely long 1-dimensional sub-manifold is embedded, our infinitely long 1-dimensional manifold, will become smooth and only 3 centimeters long.
The general idea is to apply this same technique to the white powdered gold concept, where white powdered gold is held to be a 5-dimensional hyper-spherical manifold with the embedded dimensionality mentioned above.
Let us assume that when gold is in it's ordinary metallic state, that the gold's overall gravitational, and inertial masses are occupying five singularities, five 1-dimensional spaces, five 2-dimensional spaces, five 3-dimensional spaces, five 4-dimensional spaces, and five 5-dimensional spaces. When we convert our gold to white powdered gold, 33% of it's gravitational and inertial mass is converted over to the 3-dimensional space to the right, and therefore 33% percent of all 5-dimensional components of the gold are shifted over to the parallel five dimensions. Now when the temperature is increased to a critical stage, all one hundred percent of the gold is translated from this 3-dimensional space, and to another 3-dimensional space, and it's 4-dimensional space is converted to a parallel 4-dimensional space, and so on, while it's 5-dimensional space, 4-dimensional space, 3-dimensional space, 2-dimensional space, and 1 dimensional space, in our Universe, vanishes, as do all of it's five dimensional components, after which, there is only four sets of 5-dimensional parallel spaces that the gold can transition into. With each transition, the gold's gravitational and inertial mass adds to the gravitational and inertial mass of the gold in the other parallel n-dimensions. The other four transition states would not probably be seen from our perspective, because our reference frame basically goes to zero as soon as the gold transitions completely into parallel dimensions. This is, theoretically, a reversible process that is facilitated by a change in the white powdered gold's temperature.
(Continued in next post)
