Friday, June 21, 2019

Connecting with BRIDGES . . .

     Bridges Math-Arts Conferences have become an annual summer tradition and this year's conference is July 16-20 in Linz, Austria.  One of the participants in this year's Mathematical Poetry Program is University of British Columbia Professor Susan Gerofsky -- and I offer her "Desert Poem" below.  Gerofsky's poem was constructed using a permutation pattern called PH4 (from bell-ringing) and an explanation follows the poem.

               Desert Poem     by Susan Gerofsky

               Wings over dry land
               Over wings, land dry
               Over land, wings dry
               Land over dry wings
               Land dry over wings
               Dry land wings over
               Dry wings land over
               Wings dry over land --
               Wings over dry land.

Note: This poem is constructed using the PH4 (“Plain Hunt on Four”) permutational pattern from traditional bellringing. PH4 takes a string of four elements (here, four words, or in bellringing, four distinct bells) and swaps them pairwise (first the two outer pairs, then the one inner pair, recursively) to create eight permutations of the 4!=24 possible permutations before returning to the initial string. As shown in the following diagram:

A varied collection of applications of PH4 are found in this paper from Bridges 2018 -- coauthored by Gerofsky and three others.

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