Sagar Behere

I doubt, therefore I might be

Love and tensor algebra

'The Cyberiad' by Polish author Stanislaw Lem is a brilliant set of short stories. Its translation from Polish to English is an astounding achievement in itself, faithfully preserving the wonder of the original.

In the book, the 'Constructor' Trurl creates an 'Electronic Bard', a machine that can create poetry. Trurl's envious rival, Klaupacius, then attempts to confuse the Bard by asking it to 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."__

The Bard obligingly spits out (annontated version taken from http://lliiaa.com/2005/08/18/lem_love_tensor_algebra.php ) :

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 2ψ!