Autocatalysis in Music, Nature and Britten's "O Waly, Waly"

If there's a central idea which has united the development of information theory and systems thinking in the last 10 years or so, it is the concept of autocatalysis. Autocatalysis is often characterised as 'positive' feedback, which is opposed to the 'negative' feedback which is associated with the concept of information. Ulanowicz points out that one of the reasons for positive feedback not being more seriously considered until this point is the fact that in simulation, positive feedback quickly produces an out-of-control situation, whilst negative feedback produces a homeostatic state. It's with the work of Stuart Kauffman, Ulanowicz himself and Terry Deacon that autocatalytic mechanisms have begun to be considered more seriously, particularly in the exploration of evolutionary, and co-evolutionary systems.

The central problem evolutionists have is in trying to explain co-evolution. The Spencerian nonsense of the 'survival of the fittest' is deficient in many ways (Bateson points out that the recent human history of the 20th century demonstrates that survival of the fittest leads to destruction of the environment), and in particular it is poor at interpreting the closely interconnected relationships between what appear to be distinct organisms. Ulanowicz argues that Darwin's intention was not to atomise species, but yet somehow a kind of atomistic Platonism overtook evolutionary theory which resulted in a discourse that privileged (and further atomised) processes at work within individual organisms. What is important is to get a grasp of is the relationality and ecology that binds things together.

Autocatalysis helps because its mechanism over-produces capacity which any individual organism cannot absorb. (It is because it cannot absorb it that the simulations run out of control) I'm struck by how similar the idea of production of over-capacity resonates with George Bataille's idea of individual organisms having "surplus energy" which they have to expend in some form through 'wasteful behaviour': Bataille, in thinking about basic facts of human existence (sex, ritual, sacrifice, taboo), seems to get very close to the mark. What's interesting is what happen when the wasteful (autocatalytic) behaviour of one organism interacts with the wasteful behaviour of another. Is this where the sticky beak of the humming bird comes from to transport pollen from one flower to another? Surely a sticky beak is not essential to the humming bird - it is an excess; but it is very useful to the flower; or the hairy legs of bumble bees... or the ant fungus which infects the brains of ants which then causes them to find a place to die which is particular suitable to the growth of the fungus and the further infection of ants; or the relationship between Toxoplasma gondii, cats and mice. We tend to find these accounts of inter-relationships amazing; we ask "how does the toxoplasma know?". But the more we look at nature, the more we see this kind of thing. We ought to be amazed that we are amazed!

Thinking about the basic things is always the best way forwards. Music is pretty basic, so I have been thinking how autocatalysis could apply there. The most immediate thing to look at are the redundancies: those aspects of repetition. I accompanied my daughter the other day in some Britten folk-song arrangements. These are wonderful, partly because the accompaniments are so minimalistic. We did the beautiful 'O Waly, Waly'. The accompaniment to this is a simple cadential rocking motion. Here's Britten and Pears doing it (with subtitles in italian! - Pears's posture and diction seem very weird now looking back!!)

Where are the redundancies here? Well, if we just look at the accompaniment, there is a simple rhythmic redundancy which might be notated as: ᴗ ᴗ _ (it's a kind of slow anapest) - the rowing of a boat.

Then there is a redundancy around the tonality, and the fact that for a few scalic and chromatic variations in the accompaniment, what is prolonged is the key of A major - each rocking is a kind of I-V-I motion.

There is also redundancy in both the rhythm of the melody, and in its scalic shape - with patterns of rising and falling, and a process of gradual rising through each verse before falling at the end of each. This pattern of rising and falling is also mirrored in the accompaniment - at least until the last verse (which is where Britten shows his genius by avoiding this pattern and asserting a different redundancy in keeping the I-V-I rocking rooted in A with the addition of dominant 7th note to highlight the poignancy of the words: "O love is sweet and love is kind /The sweetest flow'r when first it's new /but love grows old and waxes cold /And fades away like the morning dew."

Now what if we see the redundancies as autocatalytic? Then we might have a situation like this:

What I'm suggesting here is that each level of redundancy creates excess: the excess of redundancy of the rhythm (that anapestic rhythm could go on forever!), the excess of tonality (when will A major stop? when will it modulate? - that was Percy Grainger's complaint about folk songs - you couldn't develop them), finally the excess of scalic motion - again - where does it lead? Why does it stop? Why should it stop?

Each level of autocatalysis (represented by the + arrows) is complemented by some negative feedback - the 'musical information' that is presented. This, I think forms Z. However, the set between the elements is not stable (which it would be if the negative feedback dominated). It is inherently unstable. It needs a new idea. 

The 'bigger chords' of the second verse pursue the deeper logic. They too have their redundancies - they are related to the original autocatalytic set. But now there is much more tonal wandering to heighten the tension. This sets up a process whereby the instability of the autocatalytic set Z is transformed to a meta-set X.

Thus a tension is established between Z and X. Repeating the cycle by going back to Z reinforces this, but it leaves a question as to how to absorb the autocatalysis - the excess energy of the meta-set X. 

What Britten does is to reinforce the redundancy in the accompaniment, and to play down the tension and exploration, and the scalic motion in the accompaniment. So effectively this redundancy in the accompaniment becomes the one counterbalancing source of autocatalysis (or at least the other sources of autocatalysis are reduced). The moment where this becomes apparent - the words "but love grows old and waxes cold" is the key moment of the whole piece. It is the moment where some balance is achieved between the different autocatalytic mechanisms. The point reached is Y. 

Whatever the merits of this particular (rather hasty) analysis, I'm intrigued that there might be something to explore in matching musical redundancies to auocatalytic processes and their relation to negative informational processes. The moment Y - where the heart of the thing is revealed - is also the moment of realisation of meaning. There's much more to say about this - some kind of transformation of expectations has occurred. But it only occurs because there is a 'pregnancy' created in what goes on before.

When we find meaning in the world, is it because we somehow manage to generate sufficient flexibility so as to absorb all the potential that has built up around us? I'd rather like to think that was true!