Tuesday 14 March 2017

Relative Entropy in Risk Analysis and Education

Sometimes patients die in hospital when they shouldn't have done. When this happens, there is an elaborate process of inquiry which examines all the different causal factors which might have produced the accident. The point of this process is to attempt to mitigate the risk of future incidents.

I've been reading through a number of these reports. The level of detail and the richness of description of different levels of the problem is impressive. I'm left wondering "Where is this level of description in education?". It's simply not there - apart from in fiction. In education, we move from from year to year, with various unfortunate (but rarely deadly) incidents occurring - but no rich description of what happens. We often console ourselves that "Nobody dies in education": but it is probably because nobody dies that there is no serious study of what happens; and it is not true that nobody dies - it's just that nobody dies quickly.

However, a second issue arises from thinking about adverse incidents in healthcare: despite the richness of the description, and the analytical probing of the investigating team and the identification of "root causes" - mitigation of error does not occur. In many cases, serious incidents keep on happening. There appears to be little organisational learning.

In education, a lack of organisational learning is endemic. But whilst this is rarely seen to be a problem at high levels of educational management, there appears to be a greater chance of it being taken seriously in healthcare. The problem lies in ways of thinking about the problem - and I think, if it can be addressed in health, we can use the same techniques in education.

Accidents happen because a system's model of the world is wrong. In ordinary life, when we trip up, or fail to kick a ball in the right direction, we recalibrate our system to correct the error. This is systemic learning. What changes results not from an analysis of all the different components of our knowledge, but of the relations between the different components of our knowledge. Recalibration is a shifting of relations: facts or procedures may change as a result of this, but they are not the thing which is directly changed.

How to measure relations? Shannon entropy gives some way of measuring the surprise in a particular description of the world, but not of its relations to other descriptions. Shannon's "mutual information" is more relational in the sense that it measures the common ground between two descriptions. Right now I'm most interested in the idea of "relational entropy". This measures the distance between two probability distributions. Over time, the distance between two different descriptions can be assessed: sometimes one description will change in pretty much the same way as another - it might be taken as an index for the other. In such a case, the distance between the distributions is very small. At other times the distribution of entropy is large - the two descriptions work independently.

These relations can characterise a situation where one description strongly constrains another - for example, a description of drug administration as against the health of the patient (if the drug is effective). Equally, two descriptions might be independent with the distribution of one having no effect on the other. However, even in this case, each of those descriptions might have constraining factors which connect the two descriptions at a deeper level.

I'm intrigued as to whether management might look at the relational entropy of an organisation as a way of being able to reconfigure the relational entropy, and so recalibrate the organisation in the light of an accident. Health is a good place to explore (and I'm in a good position to do it). If it works, however, it presents new possibilities for thinking about the way educational management should operate.

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