Euclid Alone Has Looked On Beauty Bare -- Edna St Vincent Millay

Thanks to Sunil Iyengar for suggesting today's poem

(Poem #604) Euclid Alone Has Looked On Beauty Bare Euclid alone has looked on Beauty bare. Let all who prate of Beauty hold their peace, And lay them prone upon the earth and cease To ponder on themselves, the while they stare At nothing, intricately drawn nowhere In shapes of shifting lineage; let geese Gabble and hiss, but heroes seek release From dusty bondage into luminous air. O blinding hour, O holy, terrible day, When first the shaft into his vision shone Of light anatomized! Euclid alone Has looked on Beauty bare. Fortunate they Who, though once only and then but far away, Have heard her massive sandal set on stone. -- Edna St Vincent Millay

I'm afraid that this is not one of my favourite Millay poems - much as I
usually love her work, I feel that she has failed to do the subject justice
(or, perhaps, that the matter doesn't really suit her style; either way, it
lacks the feel of her really great pieces).

However, it does fit very neatly into the theme, and is worth a read, if as
much for its symbolism as for the actual poem. The comparison of
mathematical insight to a divine revelation, for instance, is a rather
standard image, but one that springs naturally to mind, for reasons not too
hard to see - most of the universe can be explained using a judicious
combination of mathematics and religion :).

Also very interesting is the parallel drawn between the transcendence into
beauty and the transition from sound to light. Mathematics seems to have
associated with it a certain abstract purity that finds its closest
reflection in our images of space and light, or perhaps light comes closest
to the geometric ideal of a straight line (one of the cornerstones of
practically all mathematics, and certainly one of the key tools in its
development). And of course, there is the obvious reference back to the
light/revelation image,

The basic form is Petrarchan, with a slightly unusual rhyme scheme in the
sestet (though see http://www.sonnets.org/basicforms.htm - the sestet had a
pretty flexible rhyme scheme). Notable is the fairly heavy use of
alliteration, which adds to the poem's somewhat 'weighty' feel.

As an afterthought, this heaviness is probably my main objection to the poem
- Millay has tried to capture both the majesty and the ethereal nature of
mathematics, but has associated with the former a weight that is quite at
variance with the latter.

Note:

Euclid is probably one of the most famous, and certainly one of the most
influential mathematicians of all time; his 'Elements', a massive
compilation of the mathematical knowledge of time time revolutionised the
field, setting the standard for rigour that even now characterises
mathematics.

  Almost from the time of its writing and lasting almost to the present, the
  Elements has exerted a continuous and major influence on human affairs. It
  was the primary source of geometric reasoning, theorems, and methods at
  least until the advent of non-Euclidean geometry in the 19th century. It
  is sometimes said that, next to the Bible, the Elements may be the most
  translated, published, and studied of all the books produced in the
  Western world. Euclid may not have been a first-class mathematician. He
  certainly was, however, a first-class teacher of mathematics, inasmuch as
  his textbook has remained in use practically unchanged for more than 2,000
  years.
        -- EB

I could go on about Euclid for several pages; however, inasmuch as this is a
poetry list I'll leave you to explore the several excellent books and
webpages about him and his work yourselves <g>.

Links:

Here's a biography of Millay: poem #34

And two of Euclid:
[broken link] http://www.treasure-troves.com/bios/Euclid.html
http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Euclid.html

And here is one of his more celebrated theorems - 'beauty bare' indeed!
[broken link] http://www.math.umd.edu/~krc/numbers/infitude.html

-martin