You don't have to take Alamo-Girl's word for it. Einstein said it. Parallel lines will eventually intersect because the universe is curved.
From a first-up on google...
Parallel lines also behave differently on a plane and on a sphere. Two lines moving in the same direction on a plane will never meet at a finite set of coordinates. However, suppose that two people start at the Equator and head north. They are traveling in the same direction, but since they are on a sphere, they do meet! First they meet at the North Pole, and if they keep going long enough, they will meet at the South Pole as well...The behavior of parallel lines led to one of the most important developments in mathematics, the introduction of non-Euclidean geometry. In Euclidean geometry, a plane is like a tabletop or piece of paper, a flat object that extends forever in all directions. Using the axioms of Euclid, useful theorems can be proved like "the sum of angles in a triangle is equal to 180 degrees". However, this is only true on a plane. If you draw a triangle on a sphere (like a globe), you can measure the angles and show that they always sum to more than 180 degrees!
Interestingly, the geographic pole is also used to explain that there is no time before the beginning of time - which is to say, there is nothing "south" of the South Pole.
What the North Pole will be for us Christians in a metaphor - i.e. the new heaven and earth in Revelation - is an open question. It could be like the geographic model you use here, time without end (expanding or not expanding) - or it could be something we cannot even imagine. We'll see.
His Name is I AM.
To God be the glory!
Dr. E: You don't have to take Alamo-Girl's word for it. Einstein said it. Parallel lines will eventually intersect because the universe is curved....Two lines moving in the same direction on a plane will never meet at a finite set of coordinates. However, suppose that two people start at the Equator and head north. They are traveling in the same direction, but since they are on a sphere, they do meet!
You guys are killing me with your definitions and unfortunately misleading occasional lurkers.
First, two parallel lines moving in the same direction along the equator or any point in the east-west direction will remain parallel and will never meet even though they move on a curved surface.
Moving in the north-south direction, two parallel lines also always parallel unless you introduce convergence at a specific point (i.e. a pole).
Einstein's theory is presuming that the lines are converging towards a pole (which is not a absolute condition, for one can slice a sphere into parallel slices; convergence exists only if there is a presumption of a meeting point—a pole. Once you have a single point of convergence the lines are no longer parallel, by definition: parallel means equidistant, and equidistant is mutually exclusive with respect to convergent. Once you introduce convergence, the lines are no longer parallel (their point of convergence can be assessed theoretically as a tangent of the angle of convergence if the separaton at the starting point is known).
Alamo-Girl and you are introducing a special case where lines are converging towards a pole, by introducing curvature and polarity into space. Neither of these conditions is necessarily true of absolute. But under your conditions the lines are converging and not parallel (i.e. equidistant over distance). They can be equidistant only at a given point.
What Alamo-Girl didn't tell us is that Einstien basically said that parallel lines were only a relative observer's phenomenon and that, in space, there are no true parallel lines; only convergent ones. In other words, Einstein postulated that parallel is a mathematical (ideal) condition that doesn't exist , except in Eucledian geometry. He postulated that the reality is not "flat" but curved and polar (i.e. that there is a common center to the universe towards all object will eventually fall).
Most recent cosmological evidence suggests that Einstein was wrong (in fact, all cosmological theories are wrong—because they are all man-made working models). The universe is actually expanding and not contracting or even slowing down. So, chances are that the universe is not polar (i.e. without a gravitational "center"), and therefore all lines defining the space are not necessarily convergent.