“But if some mind very different from ours were to look upon some property of some curved line as we do on the evenness of a straight line, he would not recognize as such the evenness of a straight line; nor would he arrange the elements of his geometry according to that very different system, and would investigate quite other relationships as I have suggested in my notes. We fashion our geometry on the properties of a straight line because that seems to us to be the simplest of all. But really all lines that are continuous and of a uniform nature are just as simple as one another. Another kind of mind which might form an equally clear mental perception of some property of any one of these curves, as we do of the congruence of a straight line, might believe these curves to be the simplest of all, and from that property of these curves build up the elements of a very different geometry, referring all other curves to that one, just as we compare them to a straight line. Indeed, these minds, if they noticed and formed an extremely clear perception of some property of, say, the parabola, would not seek, as our geometers do, to rectify the parabola, they would endeavor, if one may coin the expression, to parabolify the straight line.”

“Straight is the line of Duty, Curved is the line of Beauty, Follow the straight line, thou shall see. The curved line ever follow thee.”

“For the elements have the property of moving back to their place in a straight line, but they have no properties which would cause them to remain where they are, or to move other-wise than in a straight line, These rectilinear motions of these four elements when returning to their original place are are of two kinds, either centrifugal,vziz.>the motion of the air and the fire; or centripedal,viz.> the motion of the earth, and the water; and when the elements have reached their original place, they remain at rest.”

“Straight lines go too quickly to appreciate the pleasures of the journey. They rush straight to their target and then die in the very moment of their triumph without having thought, loved, suffered or enjoyed themselves. Broken lines do not know what they want. With their caprices they cut time up, abuse routes, slash the joyous flowers and split the peaceful fruits with their corners. It is another story with curved lines. The song of the curved line is called happiness.”

“If the old man looked at straight lines to keep his act together, I was going to stare at curved lines and go down in flames.”

“But actually time isn't a straight line. It doesn't ave a shape. In all senses of the term, it doesn't have any form. But since we can't picture something without form in our minds, for the sake of convenience we understand it as a straight line. At this point, humans are the only ones who can make that sort of conceptual substitution.”