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*eix, 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.