Rotations

 

Twist and Shout

Well, shake it up, baby, now
Twist and shout
Come on, come on, come, come on, baby, now
Come on and work it on out

Is life twisted?

The surface, with a coefficient of the imaginary axis=0 and a rotation of that imaginary axis of π, passes through the origin of a two-sheeted hyperboloid where those two sheets intersect at that origin. This surface in complex Cartesian coordinates can be described as -r +0*i.  where r is the real radius and i is the imaginary number, √-1.  But in doing so there is the need for a hyperbolic trigonometric function, the hyperbolic cosine, on that surface to be rotated, twisted, by π.  This is because of the nature of that function, which is undefined, and undefinable, for negative numbers.   In order to not allow negative  numbers, the hyperbolic cosine must be twisted, rotated, by π, in order to pass from one sheet of that two-sheeted hyperboloid to the other sheet through that origin.  It must also be translated at a point which is equal to the variance of that sheet, when the value of that hyperbolic cosine is equal to the variance of that sheet.

This sounds complicated but it is not.   A fluid in a pipe or channel passes from a laminar, calm, domain to a turbulent, white water, domain, when the flow in that pipe, or channel approaches its capacity.  Flow in traffic passes between a congested and an uncongested domain when the volume of traffic on a road is equal to the capacity.  When passing between these domains the fluid flow and traffic volume appear to follow a hyperbolic cosine.  

The variance of the surface is always a multiple of .5²*π²/3, in other words n*.25*π²/3.  This has a minimum value of 0.822467...., when n=1. 

This means that the hyperbolic cosine on the surface which includes our universe has both a mean/median locational position and a non-negative variance.  Since it has both parameters, that makes it a random function.  While that mean/median location can take on many values, if the variance was zero, it would be flat-lined, i.e. dead, not alive. By having a non-zero vaviance and twisting, it is alive and able to shout.