Tuesday, September 14, 2010

Ghosts of Departed Quantities

     Years ago in calculus class I excitedly learned that an infinite number of terms may have a finite sum.  Manipulation of infinities seems somewhat routine to me now but my early ideas of calculus enlarged me a thousand-fold.  Algebra was a language, geometry was a world-view, and calculus was a big idea.  Like any big idea, even though it had been hundreds of years in formation, it met with resistance.  In 1764 Bishop George Berkeley attacked the logical foundations of the calculus that Isaac Newton had unified.  Here, from the online mathematics magazine plus,  is a description of the attack.

Berkeley stated that the calculus involved a logical fallacy
and described derivatives thus:  "They are neither finite quantities,
nor quantities infinitely small, nor yet nothing.
May we not call them ghosts of departed quantities?"

     Below you will find Adam Dickinson's poem which takes as its title Berkeley's questioning phrase.  Dickinson teaches at Brock University in Ontario where he specializes in poetics. Although without  formal training in mathematics, he says that he has always been interested in it -- particularly in overlaps between mathematical and metaphorical thinking.  I found "The Ghosts of Departed Quantities" in The Shape of Content, Creative Writing in Mathematics (edited by Chandler Davis, Marjorie Senechal, Jan Zwicky, A K Peters, 2008)--and the poem first appeared in Problematical Recreations (Littlefishcartpess, 2008).

     The Ghosts of Departed Quantities          by Adam Dickinson

     Speak of small,
     so small
     that we differ from it
     by as little as one wish.

     But this implies motion,
     sidling up to hope.
     Are we any closer?

     Cantor's family moved from Judaism
     to Protestantism,
     from Russia to Germany.

     To prove that two set of objects are the same size,
     Cantor relieved us of counting.
     Simply put your hands together,
     no need to add the fingers.

     Relation before number;
     body to faith,

     A set of misunderstandings,
     a list of languages you never learned,
     the number of intentions two people have in common.

     all the days that have come before today.

     He put the infinite in a bag
     and shook;
     everything came out larger.

     What separates us is innumerable,
     but like applause,
     other words for the same thing,
     all our differences fit.

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