Opposites, Balance

     Recently, and perhaps always, opposites have interested me.  For example, the complementary and sometimes  conflicting nuggets of advice contained in "Pinch a penny, waste a pound" and "It is best to prepare for the days of necessity."   And in  "Kindness effects more than severity" and "Spare the rod, spoil the child."   Maybe what I like best is the challenge of synthesizing opposite truths.
     Mathematics contains many pairs of entities that are, each in some different sense, opposites:

2 and -2      2 and 1/2

horizontal and vertical   differentiation and integration

And there are some arbitrary subdivisions that often are treated as if they are disconnected opposites:

pure vs. applied (creating mathematics vs. solving problems)

teaching and learning, creating vs. teaching, arts and sciences

In an ideal world, opposites exist with "Balance" -- which is the title of the following lovely and contemplative poem by Adam Zagajewski :