Many people take a week’s holiday at this time in the UK because Monday was the Spring Bank Holiday. We went walking in the Clwydian hills which we can see from our house to the south-west across the rivers Mersey and Dee. However, despite the walking on the wild side [see ‘Take a walk on the wild side‘ on August 26th, 2015], I did not feel particularly creative when I sat down to write this week’s blog post. Together with most of my academic colleagues, I am in the midst of reviewing student dissertations and marking end of year assessments. I have written in the past about the process of marking examinations and the tens of thousands of decisions involved in marking a large pile of scripts [see ‘Depressed by exams‘ on January 31st, 2018]. However, the constraints imposed by the pandemic have changed this process for students and examiners because the whole exercise is conducted on-line. I have set an open-book examination in thermodynamics which the students completed online in a specified time period and submitted electronically. Their scripts were checked automatically for plagiarism during the submission process and now I have to mark about 250 scripts online. At the moment, marking online is a slower process than for hardcopy scripts but perhaps that’s a lack of skill and experience on my part. However, it seems to have same impact on my creativity by using up my mental bandwidth and impeding my ability to write an interesting blog post [see ‘Depressed by exams‘ on January 31st, 2018]!
The economists John Kay and Mervyn King assert in their book ‘Radical Uncertainty – decision-making beyond numbers‘ that ‘economic forecasting is necessarily harder than weather forecasting’ because the world of economics is non-stationary whereas the weather is governed by unchanging laws of nature. Kay and King observe that both central banks and meteorological offices have ‘to convey inescapable uncertainty to people who crave unavailable certainty’. In other words, the necessary assumptions and idealisations combined with the inaccuracies of the input data of both economic and meteorological models produce inevitable uncertainty in the predictions. However, people seeking to make decisions based on the predictions want certainty because it is very difficult to make choices when faced with uncertainty – it raises our psychological entropy [see ‘Psychological entropy increased by ineffective leaders‘ on February 10th, 2021]. Engineers face similar difficulties providing systems with inescapable uncertainties to people desiring unavailable certainty in terms of the reliability. The second law of thermodynamics ensures that perfection is unattainable [see ‘Impossible perfection‘ on June 5th, 2013] and there will always be flaws of some description present in a system [see ‘Scattering electrons reveal dislocations in material structure‘ on November 11th, 2020]. Of course, we can expend more resources to eliminate flaws and increase the reliability of a system but the second law will always limit our success. Consequently, to finish where I started with a quote from Kay and King, ‘certainty is unattainable and the price of near-certainty unaffordable’ in both economics and engineering.
I am teaching thermodynamics to first year undergraduate students at the moment and in most previous years this experience has stimulated me to blog about thermodynamics [for example: ‘Isolated systems in nature?’ on February 12th, 2020]. However, this year I am more than half-way through the module and this is the first post on the topic. Perhaps that is an impact of teaching on-line via live broadcasts rather than the performance involved in lecturing to hundreds of students in a lecture theatre. Last week I introduced the second law of thermodynamics and explained its origins in efforts to improve the efficiency of steam engines by 19th century engineers and physicists, including Rudolf Clausius (1822 – 1888), William Thomson (1827 – 1907) and Ludwig Boltzmann (1844 – 1906). The second law of thermodynamics states that the entropy of the universe increases during all real processes, where entropy can be described as the degree of disorder. The traditional narrative is that thermodynamics was developed by the Victorians; however, I think that the ancient Greeks had a pretty good understanding of it without calling it thermodynamics. Heraclitus (c. 535 BCE – c. 475 BCE) understood that everything is in flux and nothing is at rest so that the world is one colossal process. This concept comes close to the modern interpretation of the second of law of thermodynamics in which the entropy in the universe is constantly increasing leading to continuous change. Heraclitus just did not state the direction of flux. Unfortunately, Plato (c. 429 BCE – c. 347 BCE) did not agree with Heraclitus, but thought that some divine intervention had imposed order on pre-existing chaos to create an ordered universe, which precludes a constant flux and probably set back Western thought for a couple of millennia. However, it seems likely that in the 17th century, Newton (1643 – 1727) and Leibniz (1646 – 1716), when they independently invented calculus, had more than an inkling about everything being in flux. In the 18th century, the pioneering geologist James Hutton (1726 – 1797), while examining the tilted layers of the cliff at Siccar Point in Berwickshire, realised that the Earth was not simply created but instead is in a state of constant flux. His ideas were spurned at the time and he was accused of atheism. Boltzmann also had to vigorously defend his ideas to such an extent that his mental health deteriorated and he committed suicide while on vacation with his wife and daughter. Today, it is widely accepted that the second law of thermodynamics governs all natural and synthetic processes, and many people have heard of entropy [see ‘Entropy on the brain’ on November 29th, 2017] but far fewer understand it [see ‘Two cultures’ on March 5th, 2013]. It is perhaps still controversial to talk about the theoretical long-term consequence of the second law, which is cosmic heat death corresponding to an equilibrium state of maximum entropy and uniform temperature across the universe such that nothing happens and life cannot exist [see ‘Will it all be over soon?’ on November 2nd, 2016]. This concept caused problems to 19th century thinkers, particular James Clerk Maxwell (1831 – 1979), and even perhaps to Plato who theorised two worlds in his theory of forms, one unchanging and the other in constant change, maybe in an effort to dodge the potential implications of degeneration of the universe into chaos.
Image: decaying ruins of Fountains Abbey beside the River Skell. Heraclitus is reported to have said ‘no man ever steps twice into the same river; for it’s not the same river and he’s not the same man’.
Puzzles and mysteries are a pair of words that have taken on a whole new meaning for me since reading John Kay’s and Mervyn King’s book called ‘Radical uncertainty: decision-making for an unknowable future‘ during the summer vacation [see ‘Where is AI on the hype curve?‘ on August 12th, 2020]. They describe puzzles as well-defined problems with knowable solutions; whereas mysteries are ill-defined problems, that have no objectively correct solution and are imbued with vagueness and indeterminacy. I have written before about engineers being creative problems-solvers [see ‘Learning problem-solving skills‘ on October 24th, 2018] which leads to the question of whether we specialise in solving puzzles or mysteries, or perhaps both types of problems. The problems that I set for students to solve for homework to refine and evaluate their knowledge of thermodynamics [see ‘Problem-solving in thermodynamics‘ on May 6th, 2015] clearly fall into the puzzle category because they are well-defined and there is a worked solution available. Although for many students these problems might appear to be mysteries, the intention is that with greater knowledge and understanding the mysteries will be transformed into mere puzzles. It is also true that many real-world mysteries can be transformed into puzzles by research that advances the collective knowledge and understanding of society. Part of the purpose of an engineering education is to equip students with the skills to make this transformation from mysteries to puzzles. At an undergraduate level we use problems that are mysteries only to the students so that success is achievable; however, at the post-graduate level we use problems that are perceived as mysteries to both the student and the professor with the intention that the professor can guide the student towards a solution. Of course, some mysteries are intractable often because we do not know enough to define the problem sufficiently that we can even start to think about possible solutions. These are tricky to tackle because it is unreasonable to expect a research student to solve them in limited timeframe and it is risky to offer to solve them in exchange for a research grant because you are likely to damage your reputation and prospects of future funding when you fail. On the other hand, they are what makes research interesting and exciting.
Image: Extract from abstract by Zahrah Resh.