Symbols shape our thoughts

     In mathematics -- as in spoken languages -- we have learned to use symbols to shape our thoughts.  Pioneering artist Marcel Duchamp (1887-1968) carefully expresses this important idea in terms of chess. 
  
     “The chess pieces are the block alphabet
     which shapes thoughts; and these thoughts, although
     making a visual design on the chess-board,
     express their beauty abstractly, like a poem...

     I have come to the personal conclusion
     that while all artists are not chess players,
     all chess players are artists.”

―Marcel Duchamp

This and other stimulating statements from Duchamp are available here.

During these days of celebration of the life of Muhammad Ali (1942-2016) I have refreshed my memory of his notable quotes (many of which are found here).  Here is one with some numbers:

     A man who views the world 

the same at 50 

     as he did at 20 

has wasted 30 years of his life.

It is clear that . . .

     "If I stand"     by Inger Christensen  (Denmark, 1935-2009)

               If I stand
               alone in the snow
               it is clear
               that I am a clock

               how else would eternity
               find its way around                

Translated from the Danish by Susannah Nied

Poems with Fibonacci number patterns

In 21st century poetry, there are a variety of non-rhyming forms--and several of them have derived from the Fibonacci numbers.*  The Danish poet, Inger Christensen (1935-2009), wrote a book-length poem, alphabet (New Directions, 2000) in which the numbers of lines in stanzas followed the sequence of Fibonacci numbers.  "Fibonacci," shown below, by Judith Baumel is a shorter example of this form.