Meta-knowledge: knowledge about knowledge

As engineers, we like to draw simple diagrams of the systems that we are attempting to analyse because most of us are pictorial problem-solvers and recording the key elements of a problem in a sketch helps us to identify the important issues and select an appropriate solution procedure [see ‘Meta-representational competence’ on May 13th, 2015].  Of course, these simple representations can be misleading if we omit parameters or features that dominate the behaviour of the system; so, there is considerable skill in idealising a system so that the analysis is tractable, i.e. can be solved.  Students find it especially difficult to acquire these skills [see ‘Learning problem-solving skills‘ on October 24th, 2018] and many appear to avoid drawing a meaningful sketch even when examinations marks are allocated to it [see ‘Depressed by exams‘ on January 31st, 2018].  Of course, in thermodynamics it is complicated by the entropy of the system being reduced when we omit parameters in order to idealise the system; because with fewer parameters to describe the system there are fewer microstates in which the system can exist and, hence according to Boltzmann, the entropy will be lower [see ‘Entropy on the brain‘ on November 29th, 2017].  Perhaps this is the inverse of realising that we understand less as we know more.  In other words, as our knowledge grows it reveals to us that there is more to know and understand than we can ever hope to comprehend [see ‘Expanding universe‘ on February 7th, 2018]. Is that the second law of thermodynamics at work again, creating more disorder to counter the small amount of order achieved in your brain?

Image: Sketch made during an example class

4 thoughts on “Meta-knowledge: knowledge about knowledge

    1. Eann Patterson Post author

      Yes, entropy is an illusive and immeasurable quantity. I have written about it frequently see in the this blog: ‘Entropy in poetry‘ on June 1st, 2016; ‘Entropy management for bees and flights‘ on November 5th, 2014; ‘More on white dwarfs and existentialism‘ on November 16th, 2016; and ‘Entropy on the brain’ on November 29th, 2017. I also wrote a book about it with Bob Handscombe about fifteen years ago. You can probably still find a second handcopy if you are interested. It was called ‘The Entropy Vector’.

      Reply

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