Friday, January 14, 2011

Rather like an elephant

What is mathematics?
          These days I am outside of mathematics looking in and my views of the subject are more complex than during the days when I was a professor and mathematician. Back in my math-prof days -- when I moaned about those who held the view that mathematics is merely computation -- I tried to explain to uncompreheding friends the role of calculation within mathematics with this analogy:  computation is to mathematics as spelling is to poetry.  But those for whom computation is all of their mathematics do not accept this argument.  Indeed, I myself now have the notion that one can navigate life competently without algebra -- much as I get along without Spanish or Chinese. But I regret not knowing them -- they are, like algebra, among the world's important languages.
          Now retired from teaching, I write poetry and enjoy grandchildren and have some time to follow my curiosity -- in this time I am discovering how many different views of mathematics exist in the world. While I see mathematics as one of the arts (and the artist-mathematician as a seeker of patterns), others see it differently.  Cognitive psychologists, philosophers, sociologists, anthopologists, linguists, computer scientists,and poets -- to name a few -- see mathematics from the perspectives of their applications.  It thus seems appropriate to offer -- as poetic companion to discussion of "What is Mathematics?" -- the familiar tale, "The Blind Man and the Elephant," rendered with rhyme by John Godfrey Saxe (1816-1887) and found at this Wikisource link.

The Blindmen and the Elephant.  A Hindoo Fable    by John Godfrey Saxe

     It was six men of Indostan
        To learning much inclined,
     Who went to see the Elephant
        (Though all of them were blind),
     That each by observation
        Might satisfy his mind.

     The First approached the Elephant,
        And happening to fall
     Against his broad and sturdy side,
        At once began to bawl:
     "God bless me!-but the Elephant
        Is very like a wall!"
     The Second, feeling of the tusk,
        Cried: "Ho!-what have we here
     So very round and smooth and sharp?
        To me't is mighty clear
     This wonder of an Elephant
        Is very like a spear!"

     The Third approached the animal,
        And happening to take
     The squirming trunk within his hands,
        Thus boldly up and spake:
     "I see," quoth he, "the Elephant
        Is very like a snake!"

     The Fourth reached out his eager hand,
        And felt about the knee.
     "What most this wondrous beast is like
        Is mighty plain," quoth he;
     "Tis clear enough the Elephant
         Is very like a tree!"

     The Fifth, who chanced to touch the ear,
        Said: "E'en the blindest man
     Can tell what this resembles most;
        Deny the fact who can,
     This marvel of an Elephant
        Is very like a fan!"

     The Sixth no sooner had begun
        About the beast to grope,
     Than, seizing on the swinging tail
        That fell within his scope,
     "I see," quoth he, "the Elephant
        Is very like a rope!"

     And so these men of Indostan
        Disputed loud and long,
     Each in his own opinion
        Exceeding stiff and strong,
     Though each was partly in the right,
        And all were in the wrong!

     So, oft in theologic wars
        The disputants, I ween,
     Rail on in utter ignorance
        Of what each other mean,
     And prate about an Elephant
        Not one of them has seen!

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