Reality

 

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