Following on from yesterday's post, what does a logic of multiple expectations in music look like?
We have rhythm, harmony, tonality, melody, motif, structure, etc. Each is itself social, and the expectations with each in themselves is a social function. In the mutual redundancy of expectation generation within the social domain for each phenomenon, there is the hyper-incursive routine which creates a new generative system. Across all phenomena, there is mutual redundancy across these expectations. In that small domain of mutual redundancy across the social anticipations at all levels, there is generation of something new, some new system: some meaningful moment.
Such moments are contrived by artists by constructing events within a musical work which at certain points bring together the mutual redundancies of different dimensions: melody and rhythm and tonality combine at moments of climax.
We can analyse these moments by simply looking at the content: we have many ways of looking at the musical work, and through each lens (rhythmic, harmonic, structural, motivic, etc) we can identify the redundancies and we can identify the mutual redundancies. To do this is to get some picture of human experience in a normative context. Could we do the same with learning?
I have also thought about this in terms of absence. To what extent is the same diagram above representable as this:
The idea behind this diagram, which was based on Nigel Howard's metagame idea, was the concept that absence is causal on decision (which in turn depends on expectation): what we think is caused by what we can't think. Within absences - what can't be thought - are the seeds of new recursive principles - recursive principles which can reshape the metagame tree and (sometimes) aid decision-making. A recursive principle is nothing more than 'the system which generates the system'. Beer's Viable System Model concepts are a perfect example of recursive principles that generate the system; although most cybernetic concepts fall into this category.
There is a distinction to be made between incursive and hyperincursive anticipation. The metagame is an incursive idea: future states are based on present states. The seeding of new principles is a hyperincursive idea: the generation of the generating system - of the present from the future. How does this relate to redundancy?
Redundancy is constraint on what can be expressed. Redundancies of anticipations constrain what can be anticipated because they shape the 'grammar' of anticipation - some things become more likely than others; other things are forgotten. The blanks in the diagram are caused by the multiple occurrences elsewhere. Overlapping expectations are redundant expectations which will cause blanking elseswhere in the metagame. The constraining effect of the overlapping is also catalytic in the identification of the system that gives rise to the system. Large scale overlapping means massive redundancy = massive absence. The system that gives rise to the system in this case will be highly meaningful.
A while ago I thought about climaxes in music as being related to attachments: we struggle to maintain attachments in the flow of experience, but approaching a climax we struggle harder and harder to hold on. Until eventually, finally, we have to let go. Attachments are expectations. Holding on to an attachment means maintaining the system that generates its expectations. It get harder and harder when there is more redundancy amongst the expectations. As the redundancy increases, so the autocatalytic processes generate a new generating system.
And the world begins again.