Perception

 

If They Could See Her Through My Eyes

Yet when we're walking together
They sneer if I'm holding her hand
But if they could see her through my eyes
Maybe they'd all understand

Let’s not forget that there is a difference between your and my eyes.

Perception, what you see through your eyes, is important.

If you think that you are the only thing that matters, the surface of the Earth may appear flat. You would be wrong, the earth is a sphere, NOT flat, and you can circumnavigate that sphere, globe.

If you think that you are the center of the universe, then the sun may appear to  revolve around you. You be wrong, the Earth revolves around the sun, and this has been known since Copernicus. 

If you may think that everyone sees the same stars as you, you would be wrong. Many of the stars visible in Perth, Australia are different from those visible in New York City.

Thus it is not surprising that our human perception of the absolute may NOT be the absolute’s perception of itself.  Einstein showed that perspective matters when viewing an absolute.  That is the basis of his Theory of Relativity which deals which different frames of reference by observers of the absolute speed of light.

However Einstein solved his equations assuming that space was Euclidean, flat.  If space is instead hyperbolic, that also makes a difference. What may be assumed to have imaginary solutions, for faster than light speeds, might instead only be a difference in perception. Instead, two solutions with NO imaginary solutions, may only be different solutions on sheets of the same surface. (A hyperbolic surface has two sheets, with opposite signs).

On a flat space, transformation of a complex number from polar coordinates, r*e^ix, to complex coordinates is r*cos(x) + r*sin(x)*i, where r is r=cos^-1(cos(cos²(x) * cos(sin²(x))) which because of the circular identity cos²+sin²=1 is identical to r=√(r²*(cos²(x)+sin²(x))) or r=r.  But this does not consider that r² can be either (r)² or (-r)². By contrast on a hyperbolic surface, the solution  is always                     r=cosh^-1(cosh(r*cos(x))*cosh(r*sin(x))). Because of:

1) the hyperbolic identity, cosh²-sinh²=1, 

2) the inverse of the function cosh, cosh^‑1(u),  which has two solutions, ln(u±√(u²-1)), and

 3) the sin(0) is equal to 0, 

if the coefficient of the imaginary axis is 0,  then the solution is

r=ln(cosh(√(a²+b²)) ± sinh(√(a²+b²))), where √(a²+b²) is the real coefficient, r.

If the absolute is an infinite number of triangular waves, just one of its waves might be perceived by an observer on a hyperbolic surface as a normal logistics distribution with s=.5 and μ=π/2 and there would be no solution on the other hyperbolic sheet which is only the negative (e.g. π to 2π ) portion of that wave which can not be perceived. This means that Pythagoras’ Theorem, which is also the CDF of a triangular wave from 0 to π, is only a matter of perception, as are hypotenuse of any triangle. Thus a logistic distribution, and all sum of squares, may only be the perception of a single wave of the absolute as a logistics distribution from an observer on one sheet of a surface with two hyperbolic sheets.

PDF of Triangular wave versus Logistics Distribution on hyperbolic surface.

CDF of Triangular wave versus Logistics Distribution on a hyperbolic surface.

The absolute may feature straight lines and sharp corners, discontinuities, but from the perspective of an observer on a hyperbolic surface, these might look like curved lines and smooth corners.  Know your place.