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.

Daughter and Father - a warm geometry . . .

     Kate Stange is a mathematician -- from the Canadian province of Ontario and now at the University of Colorado -- whose father, Ken Stange, is a visual artist and poet. I met them on the internet via our combined interests in the intersections of poetry and mathematics. Lots of years ago, Kate gathered an online anthology of mathy poems. One of her recent online ventures is the development of WIN -- Women in Number Theory.  Below I offer one of Ken Stange's poems, taken from his collection Advice to Travellers (Penumbra, 1994).

Don't Mistake Your Mirror for a Window on the World     by Ken Stange

A reflection is both a thought about the world and the image we see in the mirror. -- Hippokrites

Consider your daughter's first smile.   
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