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 :

Ah, you are a mathematician

Thanks to Arturo Sangalli of the Writer's Union of Canada -- and fellow-participant in a recent Banff creativity conference --  who reminded me of this poem.  And thanks to Bill Dunham who has spread it widely by including it in The Mathematical Universe  (Wiley, 1997).  These brief stanzas were written in the early 1990s  when many of us kept our financial facts in checkbooks rather than online; still current, however, is the mistaken image of mathematicians as those whose task it is to keep numbers clean and orderly.

          Misunderstanding     by JoAnne Growney

          Ah, you are a mathematician,
              they say with admiration
              or scorn.    

Averaging . . . geometry of the center

Perhaps partly due to his experience as an Air Force pilot during World War II,  Harold Nemerov (1920 - 1991) uses geometry with deft precision as he describes phenomena around him.  Here is a poem inspired by a 1986 news item.

Found Poem     by Howard Nemerov 

           after information received in The St. Louis Post-Dispatch, 4 v 86

The population center of the USA
Has shifted to Potosi, in Missouri.

The calculation employed by authorities
In arriving at this dislocation assumes

That the country is a geometric plane,
Perfectly flat, and that every citizen,

A square-root of dead weight . . .

     A poet  I love (Seamus Heaney, 1939-2013, 1995 Nobelist) has died. The NYTimes obituary for Heaney quotes one of my favorites of his poems, "Digging" -- also available at poetryfoundation.org.  Part of what I like about this Irishman's poetry is its design.  Not only do his poems offer musicality of language but they feel carefully constructed -- modeling real world phenomena as mathematical models do -- built with careful attention to structure and detail until varied factors have been erected into in integrated whole.  "Digging" ties together the physical activity of Heaney's father shoveling in the peat bogs of Ireland to his own probing with a pen for words. 

Balancing an Equation

     I grew up on a farm and spent my middle life in a small town and now live in a city.  A sort of immigrant.  A farm girl who became a professor.  A balancing act.
     Some years back, one of my math department colleagues posted on his office door a quote from George Bernard Shaw (1856-1950) :   

     The reasonable man adapts himself to the world: the unreasonable one persists 
     in trying to adapt the world to himself. Therefore all progress depends 
     on the unreasonable man.

At one time I much agreed with the Shaw quote.  Now (perhaps because I am older or because I now live near to Washington, DC and contentious party politics) I am more admiring of balance than unreasonableness.  Here is a lovely poem by Caroline Caddy about balance and numbers.