## Friday, February 10, 2012

### Recursion

A mathematician may face a dilemma over the meaning of an ordinary term -- for words like "group" and "identity" and "random" (to name a few) have precise mathematical definitions that differ from their common meanings. Canadian poet Peter Norman's title, "Recursion," however, uses the term as it is used mathematically.  While a definition of "recursion" is widely available in mathematics texts, it was missing in my several English dictionaries -- and I found it only in the OED (though, even there,  noted as now rare or Obs.) : "a backward movement, return."   The term "return" indicates previous forward motion. In mathematical recursion (illustrated below by the Fibonacci sequence) as in Norman's poem, going backward is possible only because forward motion is known. (Interested readers will find an introduction to mathematical recursion following the poem.)

Recursion    by Peter Norman

I fall awake alone. Outside,
nocturnal rain ascends.

Alarms rage, summoning a thief
who hurries to the store,
unpacks his duffel sack,
replaces items on the shelf.

Morning. The plane dispenses you.
We enfold each other,
Tears scroll up our cheeks,
nestle into ducts.

Last night we wake
sweat-soaked and sated,
breathe flame to candlewick
and fuse, hips coaxing sheets
to smoothness.

Years ago, our meeting is unmade.
My life hurries back into ignorance,
days spent unrolling snowballs,
being chased by the ice cream truck,
beside a cool lake.

We will never disentangle
at the baggage check.
You won’t be tugged from me
by announcements,
gates, corridors, customs.

I am three years old.

I urge spilled milk into a jug,
right it on the table.
My mother’s alarmed eyes
flash calm.

Outside, a robin
feeds worms
to the hungry soil

"Recursion" is from Norman's collection, At the Gates of the Theme Park (Mansfield Press, 2010).

In mathematics and computer science, the term recursion describes a process of defining something in terms of itself.   For example, Fibonacci numbers are calculated from Fibonacci numbers.

A collection of objects exhibits recursion when its members can be constructed from two properties:
1. A simple base case (or cases), and
2. A rule (or rules) that relates all other cases backward toward the base case(s).

For example, there are the Fibonacci numbers, for which the first and second each have value 1 (these being the simple base cases), and each succeeding Fibonacci number is the sum of the two preceding (this being the rule that relates other cases backward toward the base cases)  -- so that the sequence becomes 1, 1, 2, 3, 5, 8, 13, and so on.   If we wish to calculate the 10th Fibonacci number can look backward in the sequence; we know that it will be the sum of the 8th and the 9th.  The 8th is the sum of the 6th and 7th -- hence (from the list above) is 21.  The 9th is then the sum of 13 and 21, or 34.  The 10th is thus 55.

Randall Munroe's webcomic site xkcd.com considers recursion in #372 and #387Wikipedia and WolframAlpha are among websites that offer detailed explanation.

#### 1 comment:

1. I just finished writing a heroic crown of sonnets in which the last line of each sonnet becomes the first line of the next. In a sense, the output of one sonnet becomes the input for the next.