Tuesday 14 May 2013

Mutual Redundancies and Entropy in Online Discussion and Music

There is a problem when analysing information transfer insofar as a particular 'item' of information that is to be transferred must be identified first. This might then be used as an index of the success of failure of a particular communication network. However, when we communicate, it may not be the transfer of particular items of information which is the best measure, but rather the coordination around shared redundancy. Where shared redundancy can be measured, then this might provide a better way in which expectations are managed.

Measuring redundancy is easy enough. We can look at the maximal lossless ecoding of a message and compare it to its uncompressed version to see those things which are most redundant. In a Huffman code, the lowest value items (which occupy the least number of bits) will be the most redundant. Where the redundancy relation between two speakers online is a set pattern, then we might say there is no information transfer. However, there are moments when the redundancies change. What's important in this process is the process of chunking sections to find those section where the redundancies change. These are the most significant moments.

When redundancies change, it is a sign that something new has been discovered. There is a sign that there is a restructuring of expectations. I think this is because there is a relationship between expectations and  redundancy. Basically, I think redundancy serves to prolong (or retain) expectations. Expectation is not only a synchronic feature (a structured set of probabilities); it is a living diachronic  process. The thing that keeps the diachronic aspect of expectation alive is redundancy.

As with any new idea like this, I think "what does this mean in music?" Basically, I am talking about the relationship between a melody (which can be thought of as a set of expectations) and its accompaniment. The accompaniment serves to prolong the melody. Most accompaniments generate redundancy (think of the Alberti bass). The redundancies punctuate the expectations of the melody to keep it alive (see below)

What about in a dialogue? How might we spot the melody? How might we spot the accompaniment? Redundancies are easier to spot than expectations. In fact, if we can see the redundancies, then what isn't redundant can be seen to be prolonged. At a very simple level, text analysis tools like http://www.wikisummarizer.com/ illustrate the point nicely. By using a simple entropy calculation on Wikipedia text, wikisummarizer is able to pick out passages that are of key importance. Everything else punctuates it...

Now the key question is whether such techniques can tell us something about online discussion list communication (or even, large-scale discussion within MOOC forums). The key issue is where expectations change. This might occur where a particular set of expectations entertained by one person and prolonged by one set of redundancies, becomes transformed as a set of similar expectations prolonged by the redundancies of another person.

How could we test for this? Well, identifying the redundancies of an individual's utterances is fairly easy. Guessing the set of expectations might be possible by looking for common patterns. But what is most important is examining the relationship between the set of expectations and the set of redundancies. Where these is  a common pattern, where the pattern changes for each person, these are (I think) the moments we should look for in the data.

In order to think about this clearly we need some sort of concrete example to play with. Music fits the bill most effectively. It appears that different aspects of redundancy (motif, rhythm, harmony, tonality, dynamics, articulation, etc) create different prolongational and expectation structures. It is through the interplay of these that expectations shift. As they shift, so we can talk about 'information transfer'. In an online discussion, the lack of redundancy means that expectations shift  less easily. New redundancies have to be generated by individuals consciously. If no new redundancies are created, there is effectively no communication. There is more redundancy in face-to-face communication, much of it unconscious.

But it will take another post to look at this in more detail....

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