Tuesday, May 18, 2010

Glances at Infinity

Counter-intuitive notions are among my favorite parts of mathematics and, in considerations of infinity, these are numerous.  Recalling Zeno's paradox, we capture the infinite finitely in this summation:

     1 + 1/2 + 1/4 + 1/23 + . . . + 1/2n +   . . .    =  1

In the sum I've written above, the equal sign is slightly mis-used.  What may be said about the left side of the equation is that, as the number of terms increases, the sum of the series gets closer and closer to 1 (within 0.0001 or any small number we might choose) and it never exceeds 1.

In work by poets Frank Dux and Lucille Lang Day, offered below, we find poetic contemplations of the infinite. From Lucy Day I have learned that her poem was inspired by the discovery by Georg Cantor (1845-1918) of an infinite hierarchy of infinite sets.  My own first best introduction to infinite speculations came in the 1960s from a book (Infinity, Paul Dry books)  by mathematician Lillian Lieber.  Although Lieber said that her work (which contained illustrations by her husband, Hugh) was not poetry, its charm and clarity make Infinity an outstanding and poetic introduction to the details of her subject.  In Lieber's words:

     This is not intended to be
     free verse.
     Writing each phrase on a separate line
     facilitates rapid reading,
     and everyone
     is in a hurry

Thank you, Lillian Lieber, for one of my all-time favorite math books.  Here, below, is another special thing -- Frank Dux's untitled poem, reflicting on our places in an infinite universe:

     If the universe is infinite,
     Then I am its centre,
     And so are you.
     And this holds true
     Wherever we go.
     We cannot escape
     Our significance.

British poet Frank Dux is  also an  actor, playwright, and  antique dealer.

Californian Lucille Lang Day's poem, "Infinities," is the title poem of one of her eight poetry collections.  Day has written extensively, in prose as well as poetry, in the areas of mathematics and science.  Her work also includes a co-authored textbook, How to Encourage Girls in Math and Science.


The infinitesimal infinity dances—
a speck of force
at the edge of a petal, where
electrons are leprechauns
that always slip away
and have no quarks.

The hand-sized infinity opens—
an ivory rose
unfolding in the fifth
through tenth dimensions.

I keep it in a vase
on a lace-covered table
in the family-sized infinity
whose rooms collect dust
galaxies composed
of mites and minute
particles of skin.

Set theory says there is
an infinite number
of infinities of different sizes,
but as each leaf curls
and one by one
the petals let go,
I wonder if omega
might equal one
and the stars might slow
and dim like fireflies.

No! Let the universe
shrink to a pinhead,
then explode in flames
where possibilities bloom
endlessly again
among blue-striped roses
in new time and space.

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