Following on from last week’s theme of machines, we have a poem with a mathematical theme by Stanisław Lem which is generally known as “Love and Tensor Algebra” (don’t all run off at once).
Ellipse of bliss, converge, O lips divine!
Stanisław Lem (1921—2006), translated by Michael Kandel (1941—)
The product of our scalars is defined!
Cyberiad draws nigh, and the skew mind
Cuts capers like a happy haversine.
Poem 349. 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 a2cos 2Φ!
This is one of my favourite poems, despite being a lot of nonsense mathematically. I think it is really ingenious in its use of mathematical terms to express love.
Between 1964 and 1979 the Polish writer Stanisław Lem wrote a series of science fiction short stories that satirised authoritarian regimes and commented on the search for happiness and the undesired consequences of using technology in that search. The stories generally chronicle the exploits of the robotic constructors Trurl and Klapaucius “who could kindle or extinguish suns as easily as shelling peas” and whose friendship and rivalry constitute the bulk of the stories which were collected as The Cyberiad and translated by Michael Kandel.
One such story is “Trurl’s Electronic Bard” where Trurl attempts to silence his friend’s mockery by “building a machine that could write poetry.” This he eventually does and invites Klapaucius to the inaugural performance. After a few false starts, and just as Klapaucius is laughing hardest, the machine produces this:
The Petty and the Small
Are overcome with gall
When Genius, having faltered, fails to fall.
Klapaucius too, I ween,
Will turn the deepest green
To hear such flawless verse from Trurl’s machine.
Klapaucius dismisses this as a pre-prepared calumny and this nettles Trurl, who tells him to ask it for something else. After some thought, he demands a poem about a haircut. “But lofty, noble, tragic, timeless, full of love, treachery, retribution, quiet heroism in the face of certain doom! Six lines, cleverly rhymed, and every word beginning with the letter s!!”
The machine complies:
Seduced, shaggy Samson snored.
She scissored short. Sorely shorn,
Soon shackled slave, Samson sighed,
Silently scheming,
Sightlessly seeking
Some savage, spectacular suicide.
Klapaucius immediately asks for another “Now all in g!” but Trurl prevents the machine from going any further: “How dare you waste a great talent on such drivel?” He tells his rival to “Just give it a topic, any topic, as difficult as you like…”
Klapaucius thinks for a while and then, “Let’s have 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.”
This is rather like telling one of our artificial intelligences to write a poem (see Dimitri Papaioannou’s “ChatGPT vs. Trurl’s Electronic Bard” for an example), but the machine duly complies with “Love and Tensor Algebra.”
Now I have done mathematics as part of an electronic engineering degree but that was a long time ago and I know little or nothing about tensor algebra, but the translation by Michael Kandel of Lem’s original is, I think, just brilliant. It uses the language of pure mathematics to express the sentiments of love in a unique way and it seems as if you don’t need deep knowledge of the esoteric abstrusities of tensor algebra to understand and enjoy the poem.
I particularly like “We shall encounter, counting, face to face” and “Ellipse of bliss, converge, O lips divine!/The product of our scalars is defined!” but it seems invidious to pick out particular lines as the whole thing is certainly “with feeling…and in the cybernetic spirit.”
Each stanza rhymes the first line with the last line and the middle lines together (ABBA) and there’s a lot of clever work here: Venn (as in the overlapping circle diagrams) with “one to n” (a sequence of numbers of indefinite length starting at 1), matrices with breeze, Euler with ruler (although Euler is actually pronounced OY-LER) and in the last stanza, eye rhymes with the closing formula which is read “a squared coz two phi”.
In the story, the poetic competition comes to an abrupt halt as Klapaucius leaves, apparently chagrined by the machine’s excellence; his story is that he does not wish to give Trurl more cause to boast. The story which is available online (here) continues and I’d encourage you to read it and perhaps get a copy of The Cyberiad which details the further adventures of the intrepid constructors.
I like it because it is unique, clever, and a love poem.
There are only two performances of this poem online which is a shame in my opinion. One performance is by the Polish industrial metal band Cruentus and the other is spoken with a musical background by David Ball, and was apparently an engagement gift to a couple of former students.