Let *G* be a group, and let φ assign to each element of {*A*,*B*,...,*Z*} an element of *G*. Extend φ homomorphically.

We say that the poem *P* is a (*G*,φ)-*gram* if there exists a fixed *g* in *G* such that for every line *l* in *P*, φ(*l*)=*g*.**Theorem.** Every poem is a ({1},ι)-gram, where ι represents the trivial homomorphism.**Exercise.** Construct nontrivial (*G*,φ)-grams. In particular, construct *gematriyists'* (*G*,φ)-*grams*, in which *G* = *Z*_{26} and φ(*A*) = 0, ..., φ(*Z*) = 25.

This assignment is due whenever you feel like turning it in. Spelling counts. Pagination is optional.

## Wednesday, September 10, 2008

### Ars Poetica

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## 1 comment:

Here it is...the non-trivial line

wait for it as I try and find where each point will land on itself.

There was a moment of beauty in the harmonic series this afternoon, that is before it blew off into infinite

and, oh ya, even without class--I noticed that groups and vector spaces have the same qualities...pretty ingenious way to confine the possibilities!

oh ya, and the moon was bright and fine in the sky. thanks for the poem

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