Wednesday, July 9, 2014


Googling Flatland turned up this Wikipedia entry, of which I quote part of the opening sentence: "Flatland: A Romance of Many Dimensions is an 1884 satirical novella by the English schoolmaster Edwin Abbott Abbott. Writing pseudonymously as 'A Square'." 

This should be required reading for anyone concerned with... well, just about anything.  It is about as thought-provoking as anything I have ever read, its imagery applicable to all kinds of disciplines, not just mathematics.

Take music theory, for example.  According to music theory, there is such a thing as a pitch class, by virtue of which an A is in the same pitch class as all other As.  But what if it isn't?   

How could it not be?  If some composer uses A in a way that robs it of all its ordinary characteristics it is, strictly speaking, no longer a member of a class but an event unto itself.  

  • Recalling some specific instances of this:  The G minor triad on the piano with which Debussy opens the Violin/Piano Sonata

  • The opening unison G of the Mozart G minor Piano Quartet
  • The famous B# on the cello C string in Mendelssohn's D minor Piano Trio - don't let anyone ever tell you that B# and C are the same.
Never have I experienced the mystery of pitch specificity more intensely than in the Brahms Horn Trio with natural horn and violin.  And I am extremely fortunate to have two partners who notice this also.