Choosing what words mean . . .

     Nineteenth century writer and mathematician Lewis Carroll (1832-1898) gave his character, Humpty Dumpty, these words:  "When I use a word, it means just what I choose it to mean -- neither more nor less."  And so it is in mathematics -- where, for example, the term "rational" (used in the poem"The Disposition of Art," shown below) has a precise meaning that differs from its typical conversational usage.
     The photo below shows computer-generated art by Silver Spring artist Allen Hirsh -- and, beside it, a framed version of the poem mentioned above.  Our work was exhibited together at last summer's BRIDGES and MAA conferences.  A clearer presentation of Hirsh's art -- "An Outgrabed Mome Rath" -- is available here.  My poem is presented below, beneath the photo.  

Hirsh's painting and the poem it inspired

The Disposition of Art      by JoAnne Growney 

written in response to “An Outgrabed Mome Rath" by Allen Hirsh

my poetry teacher said everything
        connects
my physics teacher said nothing
       is a vacuum
and the Queen said sometimes
       I’ve believed
              six impossible things
                     before breakfast

the artist said if equations
       can predict the weather
then equations
       can recycle Fritos wrappers
              into paintings

it is true that Stein said a rose
       is a rose
but the windmill is tilting and Jabberwocky
       is a Looking-glass poem

‘Twas brillig Humpty Dumpty said
       And in the wabe those slithy toves
               and mome raths outgrabe
when I say a rational number can always be expressed
       as a ratio of integers
              someone always
                     doesn’t understand

Humpty Dumpty chooses what words will mean
       and will pay a word extra
              if it means a great deal

a picture means a thousand words
                                  Humpty Dumpty, open your purse.

Our Hirsh-Growney contribution to BRIDGES consisted of three painting-poem pairs.  Text for all three of the poems is available here.