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 four scalars it defines!
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 a^2 cos 2 phi!
Commentary
(translated by Michael Kandel)
Above is a poem taken from Stanislaw Lem’s book ‘Cyberiad’. It is what you are given when you ask Electronic Bard (an ultimate poem writing machine) 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’. It is the only known to me example of using mathematical language in literature, especially to express love.
And even without understanding most words one can feel their intended meaning, which is a great achievement of Michael Kandel, the translator of the poem (and most books of Lem). I happen to be Polish, and in Polish writes Stanislaw Lem, so I know the poem much better in original. And I must admit that translation is great - even if mathematical expressions used are completely different it doesn’t matter, because the feeling I get while reading it in English remains the same. It has something to do with futuristic poems from 20’s, in which more important from the meaning was how the words sounded and ‘felt like’.
As for Lem’s books in general, he is a science fiction writer, but it would be more appropriate to name what he writes a ‘philosophical fiction’. In none of his books (save some very early ones, perhaps) is the technology a main subject - it only serves as a background to create moral or philosophical problems. ‘Cyberiad’ is a very good example for this. By creating a world of robots and machines (which, by the way, is not a result of a ‘machine rebellion’, it just is so) Lem describes, among many other things, how virtues known to us like Good, Justice etc. don’t change despite of the surrounding world. Yet it is not given to the reader in a “Star Wars” way, black and white, there are no Good Rebels and Evil Empire, everything is relative. And, besides, written with brilliant sense of humour.
You might have seen ‘Solaris’ in cinema recently - it is based on a book by Lem, but don’t rely on the film - it doesn’t have that much to do with the book, at least from my point of view. I liked the book very much and was very bored while watching the film - unfortunately Steven Soderbergh eliminated almost everything valuable from the book, leaving only the love story and changing the ending completely (killing the meaning of the book). If you haven’t seen the film and haven’t read the book yet - rather read the book. It is not the funny part of Lem’s writing, but rather sad and depressing, yet wonderful.
— Jedrek
Martin adds
If you haven’t read Lem’s magnificently quirky ‘Cyberiad’, I would like to strongly second Jedrek’s recommendation. The only thing I’ve read that comes close to it in spirit is St. Exupery’s “The Little Prince” (another unmissable classic).
r = a^2 cos(2.phi) is, disappointingly, not a cardioid (a heart-shaped curve) - I was expecting the pun. It seems instead to be a rather pretty four-petalled flower shape - think two figure-8s at right angles to each other, sharing a central point (I guess you could call it a variant on the lemniscate - is there a more specific term for this particular curve? I have
the feeling I’m missing some clever mathematical pun here).
Euler/ruler is an eye rhyme, of course (‘Euler’ is properly pronounced ‘Oiler’),
but nevermind :)
— Martin
Links
Biography
http://www.kirjasto.sci.fi/slem.htm
We ran a brief theme on the poetry of mathematics a while ago:
Poem #599, Poem #601 and Poem #604
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From the Wondering Minstrels mailing list, 1999–2008.
Steve Chernicoff · 24 March 2003
Come, every frustrum longs to be a cone
^^^^^^^^
The word is “frustum,” not “frustrum”: the portion of a cone or pyramid that remains if you lop off its point. This is a common error, probably influenced by the more common English word “frustrate.”
Thou’lt tell me all the constants of thy love; : And so we two shall all love’s lemmas prove,
An allusion to Christopher Marlowe’s “The Passionate Shepherd to His Love”:
For what did Cauchy know, or Christoffel,
^^^^^ ^^^^^
“Bools” appears to be a typo or misspelling for George Boole, the nineteenth-century English mathematician who invented a system of “logical algebra” for manipulating propositional truth values (still referred to in modern computer science as “Boolean values”).
the product o four scalars is defines!
^ ^^
Obviously a typo for “the product of four scalars it defines.”
It is the only known to me example of using mathematical language in : literature….
I offer the following original effort of my own, which I composed many years ago. The names of the letters psi, phi, and xi are, of course, intended to be given their proper Greek pronunciations (rhyming with English “tree” rather than “try”). With apologies to Joyce Kilmer (Minstrels #146):
Psi’s
I think that I shall never see
A letter lovely as a psi,
Which thrusts its base below the line
And lifts its pitchfork for a sign.
A psi that may at some times wear
A bar or tilde in its hair–
That bears exponents gracefully
And intimately lives with phi.
Psi’s can be writ by fools like me,
But only Greeks can make a xi.
Cheers–
–Steve
Raj · 24 March 2003
Just saw the old ‘Solaris’ movie (Russian, 1972, by Andrei Tarkovsky) this Sunday. It starts out being a bit slow, but then, you can’t help being gripped by the moral and philosophical questions being discussed and which the film throws up. What is life? How do we define an alien life? Are we really ready for the Contact? How does a Reality and identity get generated? One of the most beautiful SF movies I have seen.
Unfortunately, this category of superlative films, which I term as ‘serious contemplative SF’ gets very little exposure. They are dismissed by ‘normal’ movie audiences as sci-fi, and by sci-fi fans as being too serious. Some others which are my favorites include AI and Gattaca.
Raj
Jedrek Burakiewicz · 24 March 2003
1. a^2 cos 2 phi does not appear in original version of poem, there are no functions in it at all. But it is possible that Kandel might have added something. But I couldn’t find anything either (note for people not knowing mathematical computer notation: a^2 means ‘a square’).
2. Lem said that he hates Tarkovsky’s version and never saw the whole of it, accusing the director of completely misunderstanding him. I haven’t seen it by myself, so I can’t say anything except that you have to read the book to know.
3. There is a very good official Lem website, also in English, www.lem.pl Apart form many information on Lem himself you can find there parts of his books, including a part of ‘Cyberiad’ ‘How the World was Saved’.
4. Other Lem’s books especially worth reading: ‘Fiasco’ (caution: extremely depressing), ‘His Master’s Voice’, ‘Star Diaries’.
Martin DeMello · 31 March 2003
Excellent point - and the Bernoulli reference is, as you say, a very suggestive hint.
martin
Liana · 31 March 2003
If it is, in fact, intended to be a LEMniscate, the obvious-to-me pun might have to do with the author, rather than the subject matter. And it would certainly explain the mention of Bernoulli in the line just above it. (Bernoulli’s lemniscate is, of course, 2-petaled, being r^2=a^2cos(2theta). But I suppose phi rhymes better than theta…).
Liana