Sometime ago, when lost in Edinburgh, I came across the line in the title painted on the gable end of a building. It is a line from a poem recited by Bilbo Baggins in The Lord of Rings by JRR Tolkein. At the time, it struck a chord with me because I was lost, though not wandering, but I am an advocate of mind-wandering, which it seemed to characterize nicely [see my post entitled ‘Mind-wandering’ on September 3rd, 2014]. This week I am on leave. I will be wandering the hills, though hopefully not lost, and I am optimistic that this will induce some mind-wandering. If you don’t have the opportunity for a vacation, then at least ‘Slow down, breathe your own air‘ [see my post on December 23rd, 2015].
JRR Tolkien, The Lord of the Rings, George Allen & Unwin, London, 1954
Einstein’s famous equation, E=mc², does not influence everyday interactions of energy, E and mass, m. The speed of light, c is 299 792 458 m/s which is very big number and implies a huge amount of energy is required to create a small amount of mass. This means that energy and mass are independently conserved. For energy, this is the first law of thermodynamics while the law of conservation of mass is usually attributed to Antoine Lavoisier. On a planetary scale, the conservation of mass implies that we can assume that the quantity of matter is constant. Can we apply the second law of thermodynamics to matter as well as energy? One interpretaton of the second law is that Gibbs energy, or the energy available to do useful work, must decrease in all real processes. This also applies when matter moves through our economic system. For instance, we must do work to convert mineral ores into useful products which gradually degrade through use and natural processes, such as corrosion, until they become scrap and we must expend more resources to recycle them and make them useful again. The sun provides us with a steady supply of useful energy, so that in energy terms planet Earth can be considered an open system with energy flows in and out. Conversely in mass terms, planet Earth is effectively a closed system with negligible mass flow in or out, so that we do not have a steady supply of new matter from which to manufacture goods. However, most of us behave with open-world mindset and throw away matter (goods) that are no longer useful to us when we should be repairing and recycling [see my post entitled ‘Old is beautiful‘ on May 1st 2013]. Maybe we can’t reach the zero-waste status aimed at by people like Bea Johnson, but most of us could do better than the 2.2 kg of solid waste produced each day by each of us in OECD countries. That’s 2.1 tonnes per year for an average OECD household (2.63 people)!
In his book, ‘Economic Rules – Why economics works, when it fails and how to tell the difference‘, Dani Rodrik describes models as fables – short stories that revolve around a few principal characters who live in an unnamed generic place and whose behaviour and interaction produce an outcome that serves as a lesson of sorts. This seems to me to be a healthy perspective compared to the almost slavish belief in computational models that is common today in many quarters. However, in engineering and increasingly in precision medicine, we use computational models as reliable and detailed predictors of the performance of specific systems. Quantifying this reliability in a way that is useful to non-expert decision-makers is a current area of my research. This work originated in aerospace engineering where it is possible, though expensive, to acquire comprehensive and information-rich data from experiments and then to validate models by comparing their predictions to measurements. We have progressed to nuclear power engineering in which the extreme conditions and time-scales lead to sparse or incomplete data that make it more challenging to assess the reliability of computational models. Now, we are just starting to consider models in computational biology where the inherent variability of biological data and our inability to control the real world present even bigger challenges to establishing model reliability.
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.