what's my line

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.

roger joseph boscovich sj