Finite Geometry Notes

by Steven H. Cullinane 
This page
was created Friday, August 11, 2000, in memory of Sir Alec Guinness.
"Philosophers ponder the
idea of identity: what it is to give something a name on Monday and
have it respond to that name on Friday...." "Elegant" "I too must dream of some
perfected heaven." "At the still point, there
the dance is." "We have heard much about
the
poetry of mathematics, but very little of it has as yet been sung. The
ancients had a juster notion of their poetic value than we. The most
distinct and beautiful statement of any truth must take at last the
mathematical form. We might so simplify the rules of moral philosophy,
as well as of arithmetic, that one formula would express them both." 
A Week on the Concord and Merrimack Rivers, Chapter 8
(Friday) 
The worlds of poetry and mathematics meet in a single word, "elegant," used to describe the best of each world. The New York Times paid Sir Alec Guinness a considerable, but deserved, honor by so characterizing his life's work in another world, that of the theatre. Though it is perhaps less than elegant to elaborate on the Times' verdict, a tribute to a poet and a mathematician, as well as to an actor, may serve to illustrate this nowadays illunderstood adjective. 
The Poet: 
William Shakespeare, who perfected iambic pentameter, lives on in the occasional perfect line of verse, even when that verse is disguised as prose. The line of Vikram Seth quoted above is an example. 
Shakespeare's Verse 
The Mathematician: 
Peter J. Cameron quoted Eliot's line (above) about the "still point" as the epigraph to the chapter on automorphism groups in his book Parallelisms of Complete Designs (London Mathematical Society Lecture Notes, 23, Cambridge University Press, 1976). This book may serve, along with the related web site below, as an example of elegance. The combination of Cameron's mathematics with Hopkins' aesthetics seems close to meeting the high standards (see above) of Thoreau's poetics. 
Parallelism
in the Aesthetics of Gerard Manley Hopkins 
Finally, though it is not written in iambic pentameter, and deals with mathematical rather than musical groups, the following work of P. J. Cameron is not without its relevance to the topic of this memorial. 
Classical
Groups, by Peter J. Cameron 
Related Material: 
A
Mathematician's Aesthetics 