We have created
a world of rectilinearity. The rooms we inhabit, the skyscrapers
we work in, the grid-like arrangement of our streets, the shelves
on which we store our possessions, and the freeways we cruise on
our daily commute speak to us in straight lines. But what exactly
is a straight line? And how do such “objects” relate
to one another?
This question, so seemingly trivial, lies at the heart of a conundrum
that dates back to the dawn of the Western mathematical tradition.
Though seemingly obvious, the property of “straightness”
turns out to be a subtle and surprisingly fecund concept. Understanding
this quality ultimately led mathematicians to discover a radical
new kind of space that had hitherto seemed abhorrent and impossible.