Tag Archives: knowledge sphere

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

Out and about

butterfly-with-branched-scrolls-vaseI have been away from Liverpool a lot in the last few weeks. Teaching in Manchester and London but also visiting Taiwan. In the capital, Taipei they have yellow cabs and a succession of black limos pick up visitors from the airport. I even saw a baseball pro shop but despite the strong American influence, the culture is definitely Chinese so ordering meals and buying train tickets is a challenge if you don’t speak or read Mandarin. I am a Visiting Professor at the National Tsing Hua University and was there to meet with some PhD students and participate in a research workshop on computational modelling [see my post on Can you trust your digital twins?on November 22nd, 2016]. It wasn’t my first trip to Taiwan [see my post entitled ‘Crash in Taipei: an engineer’s travelogue?’ on November 19th, 2014] but I visited a high school for the first time. I spent half a day meeting teachers and pupils at the Taipei European School. I gave a talk based on my post entitled ‘Happenstance, not engineering?’ [see my post on November 9th, 2016] to several groups of science pupils in an attempt to explain what engineers do. The reception was enthusiastic and we had some good question and answer sessions. It was a first for me to do this in any school and the first time in the memory of the teachers that a professional engineer had visited the school. A while ago I wrote about nurturing the spirit through the exchange of gifts in the form of knowledge [see my post entitled ‘Knowledge spheres’ on March 9th, 2016]. My spirits were lifted by talking to the pupils and maybe one or two of them will have been persuaded to think about becoming an engineer. We also exchanged material gifts so that I have a beautiful vase to stand on my shelf and remind me of an enjoyable visit and hopefully prompt me to go again. Lots of young people have no idea what engineers do and are looking for a career that will allow them to contribute to society, so they are surprised and excited when they realise engineering offers that opportunity. So, we should get out more and tell them about it.

Knowledge spheres

Out-of-focus image from optical microscope of 10 micron diameter polystrene spheres in water

10 micron diameter polystyrene spheres in water (see Holes in fluids)

There is a well-known quote from Blaise Pascal: ‘Knowledge is like a sphere, the greater its volume, the larger its contact with the unknown’.  Presumably, Pascal was eloquently observing that the more we know, the more we realise how much we don’t know and the more questions that we have.  Perhaps this is also a test of whether we have acquired knowledge and understanding or only information; because the acquisition of knowledge and understanding will lead to further questions, whereas information tends simply to overwhelm us.  We need to process information into some form of ordered structure in order to gain understanding and render it more useful.  Of course, as in any process that involves increasing order and reducing entropy, this involves an expenditure of available energy or effort.  What makes it interesting and stimulating when mentoring learners on a MOOC is that very many more of them are prepared to make that effort than in a class of undergraduate students.  Some of their questions, including (or perhaps especially) the tangential ones, cause me to think about concepts in a new way and this increases my own knowledge sphere.  Lewis Hyde remarks in his book, The Gift, that ‘ideas might be treated as gifts in science’ and ‘a circulation of gifts nourishes [a] part of our spirit’. I would like to think this is happening in a MOOC, both between the educator and learners and between learners.  In my experience, it is a culture that has been lost from the undergraduate classroom, which is to the detriment of both educator and student.