Friday, September 12, 2008

Six: being a modular G-gram in 14 lines

With the unwarranted assistance of modern technology (on-line word lists and a bit of deft Mathematica programming), I've managed to complete my first nontrivial (G,φ)-gram, Six, printed below.

Six is a (Z26,φ)-gram, where φ(A)=1, φ(B)=2, ..., φ(Z)=0. Every line l of the poem satisfies φ(l)=6, except for the title, which lies in the kernel of φ: strangely enough, φ(SIX)=0. Thus, as there are 14 lines to the poem P, φ(P)=6 as well, since the order of 6 in G=Z26 is 13. (Since the title lies in the kernel, the φ-value of the poem does not depend on whether or not you include the title!) To summarize: the title, although mathematically in the kernel of the defining homomorphism, literally gives the image under that homomorphism both of each line and of the poem all told, with or without the title.

I couldn't resist retaining some classical rhyming conventions, as you'll see in reading the poem below. And the bulk of the poem is iambic, so there's some regular cadence there as well. I'll leave it to the poets among you to scan it properly.

What's next, mathematically speaking? I'd like to challenge myself with a non-cyclic group, perhaps even a non-abelian one...something small to start with, like D4. I fear that the Mathematica code I've now written to help me search for fitting words in the abelian case will be useless when faced with even such a simple group!

Enough! enjoy! And have a wonderful weekend, all!


Are we so free that we must build
tight cages out of self-wrought bars?,
that, every barrier of old o'erperched,
bold walls we must before us raise
to repress our over-anxious powers?

Dreary now is Spenser's sonnetry,
and empty are Keats's odes:
a crowd of words must measure more
than the essence it encodes.

So vowing, to this priesthood
I, in metered ciphered characters,
make an offer of my novice oath,
though a cheap and clumsy canticle,
in a passionately davened prayer.

1 comment:

Darien Gould said...

I've enjoyed your reviews on the Smart Bitches website, and was intrigued by your integration of poetry in teaching mathematics. Lucky students!!

In my misspent youth studying physics I 'discovered' Stanislaw Lem's Cyberiad. If you aren't familiar with his poem "Love and Tensor Algebra" I'm sure you'll get a kick out of it!

With the magic of the internet you can view the entire text at the link