John 18:38, What is Truth?
Pilate saith unto him, What is truth?
//When I was in 6th grade, my teacher sent me home with an assignment to prove that parallel lines never meet. I’ve never forgiven him.
When I came back to school the next morning, the best I could say was “I believe they never meet … but I can’t prove it.” After all, what architect could feed his or her family if parallel lines DID meet?
But I was believing something that was not necessarily true. Maybe parallel lines do meet; there was no way to know for sure, except in my gut. This gut feeling, for lack of being able to objectively prove it, I called belief. After I was done proving things to be true, the leftovers in my personal worldview I labeled beliefs.
It turns out that a whole world exists where space bends and parallel lines do meet. Triangles don’t have 180 degrees. Architects would starve. Ask Einstein about this world. For this reason, we Euclidean Geometrists add an axiom to our rules: Parallel lines never meet. We just make up a rule and believe it. We do this so we can ignore Einstein and pass Geometry class. This is not something we can prove, or something that is necessarily true; it is just a rule we make use of to explain our world. Much as Einstein makes use of the rule that parallel lines do meet in order to make sense of his world where space does bend.
So is “believing” good or bad? Most of us have a worldview, half of which we can justify objectively and half of which we take on faith. You might say atheists prefer straight lines that make sense in their rigid world, while believers prefer bendy lines that open up new possibilities. But there are a few oddballs like myself …agnostics … who simply prefer sitting on the fence. We like both worlds, and don’t let the two interfere with each other. Lines can be straight or bendy, depending upon which world we are talking about. If you want to talk about science, or history, or archaeology, keep those lines straight, please. If you want to talk about religion, where God lives outside the rules, then lets bend the lines a little to explain the inexplicable. Both lines are “true” in their own world.
When Pilate asked Jesus about truth, Jesus gave no answer. Maybe Jesus was an agnostic.
Parallel lines do meet in spherical geometry. Great Circles are lines in spherical geometry, and longitude lines are all parallel at the equator, but all longitudes meet at both north and south poles. Further the longitude lines are also intersected by the equator, so any two longitude lines and the equator create a triangle with interior angles larger than 180 degrees.