I want to explore three statements about information theory I made in a post last week (see http://dailyimprovisation.blogspot.co.uk/2013/04/the-pattern-which-connects.html). They are:
- "abstraction is the removal of redundancy from the flow of experience"
- "learning an abstraction is a process of recreating the redundancy that was removed in the abstracting process"
- "teaching is the process of creating the conditions for the production of redundancies related to a particular abstraction"
The statements are guesses. I find them tantalising because they present the prospect of a more analytical approach to learning. Because online learning presents many measurable factors, it is particularly amenable to this kind of analytical approach (although I will stop short of saying 'quantitative' - that would be going too far!).
There is a complex relationship between abstraction and cognition. Our daily existence would be impossible were if not for the fact that we create abstractions and largely coordinate ourselves through the world with them. Sometimes we believe our abstractions more than the evidence of our own eyes, ears or hearts - and then we find ourselves in a kind of 'false consciousness'. The abstracting process, whatever it may consist of, is fundamental. In the cybernetics of the Viable System Model, abstraction in this sense is simply an attentuation process as part of an effort to maintain requisite variety.
I don't think its going too far to suggest that learning is essentially a process of engagement with abstractions. Most academic knowledge (the stuff that we go to school to learn) exists in essentially abstract forms that we call "subjects". In the process of learning, we often have to abstract from the experience of engaging with subjects - for Bateson this would be 'learning to learn'. And Bateson is probably right that the process of abstracting from the flow of experience leads to "levels" of learning. (Although I think I might prefer 'stratification')
But the question is "what's driving the show?" Could it be Ashby's (and Beer's) concept of "Variety"? In this sense, Beer's ideas of amplification of variety might amount to 'reproducing redundancy from abstractions'; attenuation is the process of abstraction. But I think this is too flat. The stratification of abstractions and the way that variety appears to get 'chunked' at the higher levels of learning do not, to my mind, get satifactorily explained by this process. Neither does the production of new abstractions to account for new experiences. Finally, the production of novelty seems poorly accounted for.
For these reason, I think looking at redundancy itself makes more sense. In Shannon's theory, redundancy seems to have at least two meanings: on the one hand there is the idea of 'excess bits' to carry messages; on the other hand, there is the simpler notion of repetition of messages. At some level, these may be the same - although they do not immediately appear to be related. But the point is that redundancy seems to do something.
If I continuously repeat a message to somebody, they are likely to get bored. What is boredom? My first inclination is to say the boredom is a response to low variety, and to say that my "variety" must be low if I am simply repeating the same message over and over again. But now I'm not so sure. Indeed, all human beings probably have very high variety (a large number of possible states) irrespective of whether they say the same thing over and over again or not. The boredom is more likely to be poor variety management - between myself and my environment. I am in oscillation - I don't know what to do because the complexity is overwhelming. I see many students like this!
But the redundancy produced in oscillation is important. The unmanaged variety in a sender that might produce the redundancy also might produce unmanaged variety in receivers. In this way it may be possible to say that the redundancy has a causal bearing in a social dynamic which increased the probability that some novelty emerges which serves to "mop up" the unmanaged variety - the mopping up is done by new concepts which change expectations within the social dynamic. Redundancy causes expectations to be attenuated in such a way that variety is unmanaged.
When expectations are attenuated because of high redundancy then it is unlikely that there is much information transfer between people. It is interesting that the idea of 'attenuated expectations' is highly compatible with the notion of absences in a metagame tree. The high redundancy produced results from the few strategies that are available for inspection - this becomes a self-perpetuatng mechanism. But eventually, there must be some 'determination' of absence. And it is at this moment that expectations are adjusted. At this moment, there is high information transfer.
Sometimes I find that I become too abstact. At that moment, it is useful to 'tell stories' (I often do this through music). What happens here is the deliberate production of redundancy. My blogging activity often has this form: most of what I write is redundant!! But through the telling of stories, through the production of redundancy there is a process by which the "deep absence" can be identified. The story itself is in itself a flow of redundancy and abstraction. Like the play within a play, this appears to be a necessary process to keep the wheels moving.
The brief retreat into a fantasy world is the move that I need to find the thing that is missing from the 'real' world. Is our response to unmanaged variety to "generate redundancy?"
But the question is "what's driving the show?" Could it be Ashby's (and Beer's) concept of "Variety"? In this sense, Beer's ideas of amplification of variety might amount to 'reproducing redundancy from abstractions'; attenuation is the process of abstraction. But I think this is too flat. The stratification of abstractions and the way that variety appears to get 'chunked' at the higher levels of learning do not, to my mind, get satifactorily explained by this process. Neither does the production of new abstractions to account for new experiences. Finally, the production of novelty seems poorly accounted for.
For these reason, I think looking at redundancy itself makes more sense. In Shannon's theory, redundancy seems to have at least two meanings: on the one hand there is the idea of 'excess bits' to carry messages; on the other hand, there is the simpler notion of repetition of messages. At some level, these may be the same - although they do not immediately appear to be related. But the point is that redundancy seems to do something.
If I continuously repeat a message to somebody, they are likely to get bored. What is boredom? My first inclination is to say the boredom is a response to low variety, and to say that my "variety" must be low if I am simply repeating the same message over and over again. But now I'm not so sure. Indeed, all human beings probably have very high variety (a large number of possible states) irrespective of whether they say the same thing over and over again or not. The boredom is more likely to be poor variety management - between myself and my environment. I am in oscillation - I don't know what to do because the complexity is overwhelming. I see many students like this!
But the redundancy produced in oscillation is important. The unmanaged variety in a sender that might produce the redundancy also might produce unmanaged variety in receivers. In this way it may be possible to say that the redundancy has a causal bearing in a social dynamic which increased the probability that some novelty emerges which serves to "mop up" the unmanaged variety - the mopping up is done by new concepts which change expectations within the social dynamic. Redundancy causes expectations to be attenuated in such a way that variety is unmanaged.
When expectations are attenuated because of high redundancy then it is unlikely that there is much information transfer between people. It is interesting that the idea of 'attenuated expectations' is highly compatible with the notion of absences in a metagame tree. The high redundancy produced results from the few strategies that are available for inspection - this becomes a self-perpetuatng mechanism. But eventually, there must be some 'determination' of absence. And it is at this moment that expectations are adjusted. At this moment, there is high information transfer.
Sometimes I find that I become too abstact. At that moment, it is useful to 'tell stories' (I often do this through music). What happens here is the deliberate production of redundancy. My blogging activity often has this form: most of what I write is redundant!! But through the telling of stories, through the production of redundancy there is a process by which the "deep absence" can be identified. The story itself is in itself a flow of redundancy and abstraction. Like the play within a play, this appears to be a necessary process to keep the wheels moving.
The brief retreat into a fantasy world is the move that I need to find the thing that is missing from the 'real' world. Is our response to unmanaged variety to "generate redundancy?"
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