I love me some good science fiction so I’ve been actively working on reading the classics of the genre over the past decade, and it’s always stuck in my craw that I haven’t read anything by the Polish writer Stanislaw Lem. I finally got around to reading his short story collection The Cyberiad last week and thought it was magnificent, especially Trurl’s Electronic Bard, in which the constructor Trurl creates a machine that writes poetry. His friend and rival, the constructor Klaupacius, envious of what Trurl has done, tries to confound it by requesting it write “a love poem, lyrical, pastoral, and expressed in the language of pure mathematics. Tensor algebra mainly, with a little topology and higher calculus, if need be. But with feeling, you understand, and in the cybernetic spirit.”
I loved the resulting poem, but my undergraduate degree is in creative writing—my knowledge of mathematics is almost entirely forgotten from high school and just enough for me to broadly get the jokes within. I decided that wasn’t good enough, set myself a-googling (I learned more about math this past hour googling than I did in college) and came up with the annotated version of the poem you see below. I didn’t bother to define some terms (I figured if I knew what they meant most everybody else interested would) and others I likely didn’t pick the best definition because I didn’t know any better, so please feel free to point out my mistakes and suggest better links in the comments. Otherwise, enjoy the annotated Electronic Bard’s poem of love and tensor algebra:

Come, let us hasten to a higher plane
Where dyads tread the fairy fields of Venn,
Their indices bedecked from one to n
Commingled in an endless Markov chain!

Come, every frustum longs to be a cone
And every vector dreams of matrices.
Hark to the gentle gradient of the breeze:
It whispers of a more ergodic zone.

In Riemann, Hilbert or in Banach space
Let superscripts and subscripts go their ways.
Our asymptotes no longer out of phase,
We shall encounter, counting, face to face.

I’ll grant thee random access to my heart,
Thou’lt tell me all the constants of thy love;
And so we two shall all love’s lemmas prove,
And in our bound partition never part.

For what did Cauchy know, or Christoffel,
Or Fourier, or any Boole or Euler,
Wielding their compasses, their pens and rulers,
Of thy supernal sinusoidal spell?

Cancel me not – for what then shall remain?
Abscissas some mantissas, modules, modes,
A root or two, a torus and a node:
The inverse of my verse, a null domain.

Ellipse of bliss, converge, O lips divine!
The product of our scalars is defined!
Cyberiad draws nigh, and the skew mind
Cuts capers like a happy haversine.

I see the eigenvalue in thine eye,
I hear the tender tensor in thy sigh.
Bernoulli would have been content to die,
Had he but known such a² cos 2 ψ!

More about Stanislaw Lem: official site, Wikipedia entry, great article from The Modern Word. If you don’t read science fiction and Lem’s name sounds familiar it’s probably because his novel Solaris has been adaptated for the silver screen twice, most recently in 2002, directed by Steven Soderburgh and starring George Clooney.
Thanks to Ranjit for lending me the book out of his excellent personal library!