 we acquire the concept of &quot;coordinate-freedom&quot;
in our personal mathematical development.  We start out with courses
where coordinates are everywhere, we gradually pick up the idea that
&quot;many bases look alike&quot; in so far as their adequacy to tag the points
of a space, and then we learn to value invariants, in effect computable
from coordinates, but in essence arising whole and entire from their ashen
graphite characters, as if the true spirits of the whole mathematical corpus.
That is wha