Wednesday, May 31, 2006

A Love Poem in Tensor Algebra

As promised, many posts ago, from Stanislaw Lem's Cyberiad.

A Love Poem in 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 ever 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 hear,
Thou’lt tell me all the constants of they love;
And s 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 scalers 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 they sigh.
Bernoulli would have been content to die,
Had he but known such a2 cos 2 f!

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