Compared to
What
Slaughterhouse is
killin' hogs
Twisted children killin' frogs
Poor dumb rednecks rollin' logs
Tired old lady kissin' dogs
I hate the human love of that stinking mutt (I can't use it!)
Try to make it real, compared to what? C'mon baby now!
Making it real
might be accepting that reality is hyperbolic.
If the shape is always flat, then Euclidean geometry would apply
in all places. It does appear to apply locally but fails to produce reasonable results
when traversing the globe, when the distance between two points is significant compared
to the radius of the spherical Earth. When the distance is large, spherical
non-Euclidean geometry, not Euclidean geometry, applies and its Great Circle distance
is used, rather than the shortest distance between two points in flat space.
Similarly if the universe is flat, then Euclidean geometry
would apply in all places. As above, it does appear to apply locally but, given
the above, it is reasonable to question if it applies globally. If the universe is hyperbolic,
rather than flat, then non-Euclidean geometry, i.e. hyperbolic trigonometric functions,
should apply and not the shortest distance between two points in Euclidean
geometry.
If only the shortest distance were involved, this would
not be as significant. However this is really the relationship between numbers,
where any number, c, can be defined by two other numbers, a and b.
c = a * b
c = a + b
While these relationships are true in any geometry, the relationship
between the sum of squares depends on the geometric system being used.
c2 = a2
+ b2
has different solutions
depending on the geometric system.
·
In a flat Euclidean space, the solution is
c=√(a2+b2),
but this only has answers for c in the real plane if a2+b2
is greater than zero. If it is less than zero, i.e. negative, then the solution
for c is a complex number which requires the use of imaginary numbers.
·
In a spherical non-Euclidean space, the solution
is
c=1/R*cos-1(cos(a/R) *cos (b/R))
but this also assumes that this solution is on a sphere which
is a closed space which has a Radius, R.
·
In hyperbolic non-Euclidean space, the solution
is
c=cosh-1(½*cosh(a+b)+½*cosh(a-b)),
which
is on an open hyperbolic plane with no fixed Radius, R.
This relationship does not merely impact the shortest distance
between two points. It impacts every solution that involves the square of two
numbers. For example, the Lorentz transform, used in time and length dilation,
and mass expansion, which varies based on the ratio of the velocity to the speed
of light, in flat Euclidean space is √ (1-(v/c)2), which
requires the use of imaginary number if v/c is greater than zero.
However if globally space is non-Euclidean
and hyperbolic, then the Lorentz transform is 1+ln(cosh(v/c)±sinh(v/c)), and does not imply the use of imaginary
numbers when v/c is greater than zero. It simply becomes
undefined ( the natural logarithm of a negative number is undefined). It is
suggested that all physical equations, for example those in electrical engineering
involving alternating current, which involve
the square of two values should not use the Euclidean solution, but should use
the hyperbolic solution. This will prevent the creation of imaginary or complex
number solutions which are only a result of assuming that space is flat.
Further, if the universe, space, is hyperbolic, as proposed by Mabkhout [1], the implication is that dark
energy and dark matter, are not needed to deal with cosmic inflation and expansion, the size of the
observable universe is consistent with its age, and the Planck length is consistent
with the Planck energy, etc..
Additionally if the universe is random and hyperbolic, it must be tolerant and there is no rationale for superstition, scapegoating, or
intolerance which are only an attempt to find deterministic reasons for random
events.
[1] Mabkhout,
S.A., 2012. The infinite distance horizon and the hyperbolic inflation in the
hyperbolic universe. Phys. Essays, 25(1), p.112. https://www.researchgate.net/profile/Salah-Mabkhout/publication/302521692_The_Infinite_Distance_Horizon_and_the_Hyperbolic_Inflation_in_the_Hyperbolic_Universe/links/5730e0cf08ae6cca19a1f675/The-Infinite-Distance-Horizon-and-the-Hyperbolic-Inflation-in-the-Hyperbolic-Universe.pdf