One Idea May Hide Another . . .

     One of the excitements I find in both mathematics and poetry is the continuing discovery of new meaning.  A first reading discovers something but subsequent readings discover more and more.  A poem by Kenneth Koch (1925-2002), "One Train May Hide Another," opens with "In a poem, one line may hide another line" -- focusing also on the idea that one thought may obscure another.

     Koch's poem is one that I first met lots of years ago when I was working with middle school students in a poetry class at a newly established Children's Museum in Bloomsburg, Pennsylvania.  At the time, the poem excited me by bringing back memories of traveling through western Pennsylvania as a child when my parents' car often needed to obey flashing red lights and stop while a train crossed our highway.  And sometimes there were parallel sets of tracks and the possibility that two trains might be passing our intersection in opposite directions at the same time. 

     I offer below the opening lines of the poem and a link to the complete poem; I post it with the hope that you also will enjoy it -- and will reflect on the ways that (in mathematics and elsewhere) one idea may hide -- or lead to -- another.   

One Train May Hide Another     by Kenneth Koch

     (sign at a railroad crossing in Kenya)

In a poem, one line may hide another line,
As at a crossing, one train may hide another train.
That is, if you are waiting to cross
The tracks, wait to do it for one moment at
Least after the first train is gone. And so when you read
Wait until you have read the next line—
Then it is safe to go on reading.
In a family one sister may conceal another,
So, when you are courting, it's best to have them all in view
Otherwise in coming to find one you may love another.
One father or one brother may hide the man,
If you are a woman, whom you have been waiting to love.
So always standing in front of something the other
As words stand in front of objects, feelings, and ideas.
One wish may hide another. And one person's reputation may hide
The reputation of another.  . . .   

Koch's complete poem is available here at PoetryFoundation.org.