A Nickel, a Dime, a Dollar . . .

    In childhood -- and later also -- rhymes help us to remember.  I recall reciting, in early years. "Pme, two, buckle my shoe; three, four, shut the door . . ."  Here -- at the website, Empowered Parents -- are a number of counting songs and rhymes.

    Recently I found among the poems of one of my favorite poets -- Harlem Renaissance poet Langston Hughes (1902-1967) -- a delightful counting poem entitled "Brass Spittoons."  Here are some of its lines:

A counting rhyme, a riddle

     During the summer I had lots of activities with grandchildren -- they all love to read and one of the books we enjoyed together was Counting Rhymes (selected by Shona McKellar, a Dorling Kindersley book, 1993).  Here are a rhyme and a riddle from that collection.

Let's Send a Rocket     by Kit Patrickson

TEN, NINE, EIGHT,                                 We're counting each second,
SEVEN, SIX, FIVE . . .                             And soon it will boom!

We'll send up a rocket,                         Get ready for . . . TWO;
And it will be LIVE .                              Get ready to go . . .
        
FIVE, FOUR, THREE . . .                          It's TWO--and it's--ONE!  
It's ready to zoom!                                We're OFF!  It's ZERO!

                                    RIDDLE -- What animal do these clues describe?

                                    Four stiff-standers,
                                    Four dilly-danders,
                                    Two lookers,
                                    Two crookers,
                                    And a wig-wag.

Echoes of childhood rhymes

For those of us who live and breathe mathematics, there is much of it that affects us deeply.  Even those of us whose mathematics is mostly arithmetic have a literature of number that we hold close .  And does anything affect us more than the counting rhymes of our childhood?  Washington, DC poet Rosemary Winslow uses emotionally-charged repetition of nursery-rhyme numbers to help us know incest in "Four Five Six." 

Counting rhymes -- Catalan, Bell numbers

     In mathematics, the Catalan numbers (named for Belgian mathematician Eugène Charles Catalan, 1814–1894, and beginning with 1, 1, 2, 5, 14, 42, 132, 429, . . . ) and the Bell numbers (named for the Scottish mathematician Eric Temple Bell, 1883-1960, and beginning with 1, 1, 2, 5, 15, 52, 203, 877,  . . . ),  provide answers to a variety of mathematical counting-problems, including counting the number of rhyme schemes for stanzas of poetry.  In English, earliest classification of rhyme schemes dates back to George Puttenham and his treatise, The Arte of English Poesie (published around 1590).