March 2005

Lang Lang’s encore is Liszt’s Petrarch Sonnet No. 104, Années de pèlerinage, No. 2. The following description is copied from a program note for a Lang Lang concert on 11/23/2004 at Kimmel Center, Philadelphia.

Liszt’s three Petrarch sonnets form part of his collection Années de pèlerinage, deuxième année, Italie (Years of Pilgrimage, second year, Italy), composed between 1837 and 1849, though not published until 1858. Whereas the first book of the Années de pèlerinage (Swiss) had been concerned mainly with evocations of nature, the second book dealt with works of art—both literary and visual—that Liszt had encountered on his travels in Italy with Marie d’Agoult. His Sonetti del Petrarca were inspired by three of the best known sonnets in Petrarch’s Canzoniere: Benedetto sia ’l giorno (No. 47), Pace non trovo (No. 104), and I’vidi in terra angelici costumi (No. 123). Liszt had originally set them as songs for high tenor voice, then for piano solo, then revised them again for the Années. He even returned to them many years later, making “simpler” versions for medium tenor or baritone. Taken as a group, the various versions provide fascinating insight into Liszt’s transcription procedures. Formally the piano pieces, with some divergences from the songs, loosely follow the structure of Petrarch’s sonnets with introduction, interludes and coda. Sonnet 104 begins with an agitated ascent that introduces the main melody, which Liszt presents three times in different guises (the various versions of the piece differ significantly in form). The basically lyrical melody is subjected to occasional tempo changes and pianistic outbursts that suggest the sonnet’s images of a restless search for peace. A recitativelike passage introduces the coda, which dies away quietly.

Petrarch Sonnet No. 104

I find no peace, yet make no war;
I fear yet hope, I burn yet am ice;
I fly in the heavens, but lie on the earth;
I hold nothing, but embrace the whole world.

One imprisons me, who neither frees nor holds me;
nor keeps me for herself, nor loosens the noose;
Love does not slay me, nor unshackle me;
Love wishes me not to live, but leaves me in torment.

I see without eyes, and have no tongue but cry,
I long to perish, yet I beg for aid;
I hate myself, but love another.

I feed on sadness, yet I weeping I laugh;
death and life repel me equally.
I am in this state, Woman, because of You.

I made up my mind to read all my backlog magazines like DDJ, IEEE Spectrum, ACM Communications, etc. I read 08/04 DDJ today by not doing work for 1 hour 🙂

A very interesting article in Programming Paradigms column (need subscription) talks about digital universe, incompleteness of formal axiomatic systems, and Chaitin’s Omega.

Chaitin’s Omega is the probability that a particular Turing machine will eventully halt given an input of a truly random sequence of 0’s and 1’s.

Some interesting thoughts from the article: Math is empirical because of Gödel’s incompleteness theorem. The universe is a computation (computer + program) but there’s no other computation that’s faster, so the future is still unpredictable.

I read an abbreviated Chinese version of “Gödel, Escher, Bach: An Eternal Golden Braid” as a child and again lately and didn’t finish it either time. I should buy the English version soon.

The article also mentions that Steve Wolfram’s A New Kind of Science is available online in full text. Wish I could find time to read it…

UPDATE 03/06: March 2006’s Scientific American has an article by Gregory Chaitin himself explaining his omega. It’s based on Turing’s halting problem, stating that it’s impossible to answer generally whether a program will halt in a Turing machine. The precise definition of omega is \sum_{N=1}^{inf} \sum_{all N-bit programs that halt) (0.5^N). The binary value of omega is 0.110110001… (of course 0 and 1 are random) Omega is incompressible: you cannot use a program substantially shorter than N bits long to compute the first N bits of it. Because the binary omega is irrational, there’s an infinite number of digits that any finite-length program cannot compute. The general implication on a formal system is that it has infinite complexity, in other words to prove everything in it there must be an infinite number of axioms (irreducible principles).

UPDATE 12/09/05: I’ve bought GEB, so now I need to say “I should read the English version soon”…

UPDATE 11/23/07: From Gell-Mann’s Quark and Jaguar I learned that Chaitin was only in his late teens (17 when he started, according to his own time line) when he worked out these things. Wow.