A complex plane exists between any two neighbouring spatial dimensions.
This suggests to me that distances in the complex plane are not linear (see below: Hyper Dimensional Space). Distances in 3D and 4D are linear but if complex space between these dimensions follows
a general path of y = 1/x then there should be some distortion. Fortunately that distortion is regular and described by y = 1/x.
To mesh completely with complex space the complex plane needs distances that vary logarithmically. If we draw a graph for y = ln x this tends to follow a
corner of a square and a circle near x = 1 (in the most vague terms).
The work done under the curve y = 1/x is given by ln x. This is from the mathematical rule that:
The integral under the curve y = f'(x)/f'(x) is equal to ln (f(x)) +C.
This itself implies that any function along the ztar will translate onto the complex plane without any difficulty. It also implies the reverse: that a wave along the complex plane has enough energy to do the work necessary to translate into 3D but only according to it's function value.
Normally the complex plane can be considered flat but when there is a connection between 3D (or 4D) and the complex plane then the complex plane will fold.
The easiest way to see this is with the use of a linear number line for 3D and a logarithmic number line for the complex plane.
For both number lines to line up exactly the complex plane must fold. This is called "Complex Folding" and is described fully in my Analytic Complex Number Theory.
The extent of this folding will depend upon the forces being present and acting between these planes.
The Geometry of Hyper Dimensional Space
I define the geometry of Hyper Dimensional Space as being hyper-spherical for odd numbered dimensions and polygonal for even odd numbered dimensions.
This is cosistent with a spherical geometry for 3D and 5D while for 4D and 6D we have a square or cube representing 4D and a pentagram representing 6D.
Normally we would not expect pentagrams to fit seamlessly together when constructed in six dimensions and to some degree this is a matter of faith since we can only visualise three dimensions.
