Hyperbolic

Three Blind Mice 

Three blind mice, three blind mice
See how they run, see how they run
They all ran after the farmer's wife
She cut off their tails with a carving knife
Did you ever see such a sight in your life as three blind mice?

In addition to blind mice, what about Blind Men and the Elephant?

The Blind Men and the Elephant is an ancient Indian parable that has roots in Buddhist, Hindu, and Jain texts, that discussed the limits of perception, and the importance of complete context, and is a poem by John Godfrey Saxe. It is also the subject of the of illustration below.

This is the phenomena that is responsible for the flat Earth Fallacy. If you use only your own perception, the Earth looks Flat, even though the Earth is a sphere. Mathematically it would be described as being locally flat, but globally spherical. If we only use our local perception it looks flat. The issue is that we are so small compared to the radius of that sphere, that it looks flat, just as the surface of a beach ball would look flat to an ant on that beach ball.  Just like the blind men who mistook the elephant as being a spear, a snake, a rope, a fan, a tree, or wall depending on what part of the elephant they were perceiving, or as Saxe’s poem goes

So oft in theological wars,
    The disputants, I ween,
Rail on in utter ignorance
    Of what each other mean,
And prate about an Elephant
    Not one of them has seen!

What we perceive as straight lines and parabolas might both only be parts of a hyperbola. A hyperbola looks like a straight line at great distances from its vertex and looks like a parabola close to its vertex. What we perceive as straight lines and parabolas in flat space might only be different parts of the same hyperbola……IOW space might be locally flat and universally hyperbolic.

That space is hyperbolic is NOT a unique idea. It was proposed by Mabkhout (Mabkhout, 2012). He pointed out that if space is hyperbolic and the Einstein field equations are solved in hyperbolic space, the need for dark matter and dark energy goes away. This is hardly the limit of this proposal. It has implications on mathematics, physics, statistics, EVERYTHING. Don’t be blind.

Mabkhout, S. (2012). The infinite distance horizon and the hyperbolic inflation in the hyperbolic universe. Phys. Essays, 25(1), p.112.