Euclidean or nonEuclidean eternity?

This is probably one of those threads seen as a useless insertion of a topic into "theology" that is outside of any such discussion-- and it may be, especially since I have not developed the thought very far and do not have much time to post.

Most of us (I think) know that Euclid wrote out the basic axioms of geometry around 300 BC, and most of his work has been utilized well over the centuries. But his Parallel Postulate has caused a lot of debating and "nonEuclidean" geometries have been developed and used, especially in the modern world at the atomic and subatomic levels. His PP stated that through a point not on a given line, one, and only one, line can be drawn that is parallel to the given line. Remembering that a point is not strictly defined in geometry, and thus 'line,' consisting of more than one point, and 'plane,' consisting of 3 or more points not in the same line, are also not definitive, we can see how a line and its points become infinitely smaller, and thus any line can be seen as intersecting the given line at some level; or else infinitely many lines can be parallel to the given line.

How does this fit into theology in any way? Well, the concept of infinity-- or eternity-- would seemingly be subject to the same logical debate. As our experience in this life is limited to less than a century, or maybe a little more, then thousands, millions, and billions of years are nothing but a concept we do not experience. If we are created with a propensity to do wrong-- the reason for the need for a savior-- do we still have such a propensity after this life, or this world, is over? After all, does God not want our worship because we choose to give it, and not because he 'pulls our strings' and forces us? I we still have a choice, then, could we go through those millions and billions of years choosing right?-- that would be, choosing wrong does not meet us-- is parallel to our possibilities as long as it's still there. And its not skew-- in a different plane-- if part of our being is facing choices (it would not then be a choice in our plane of existence).

So-- in the billions, trillions, and so on, of years, would the propensity to do our own will eventually prove not parallel to our 'progress line' after all, as the points of the past go by and become infinitely smaller? This, of course, does not take into consideration that we shall have no concept of time anyway-- but that is something to which we cannot relate at all in our current state.

I will end this with a bit of silliness... I remember as a kid a song called "Found a Peanut." Its melody was "Clementine," and it began, Found a peanut, found a peanut, found a peanut, just now!.." And it goes on to say "it looked rotten... ate it anyway... made me sick... then I died... went to heaven-- "then finally, "Said a dirty word... got transferred"--then starts over again with "Found a peanut-- threw it away!"
[I said it was silly, didn't I?]
But is the basic idea not at all a 'point' to consider? If our essence of being includes choice, while we have a propensity to put our own will first-- which is 'missing the mark'; sin-- will we always-- infinitely; eternally-- choose right, or will a single wrong choice sooner or later come about? And if not, then do we actually have "choice?"