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 12^{th}, 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 19^{th} 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 17^{th} 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 18^{th} 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 29^{th}, 2017] but far fewer understand it [see ‘Two cultures’ on March 5^{th}, 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 2^{nd}, 2016]. This concept caused problems to 19^{th} 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’.

Tony PateyDear Prof Patterson,

Always look forward to your emails – always interesting and thought-provoking!

One of your points sparked my thoughts on an issue which has intrigued me for decades – the “invention” of the calculus.

I initially perceived the calculus in the 50s as some obscure (arcane!) study only highly intelligent and highly skilled mathematicians could approach – thankfully WW Sawyer in Mathematician’s Delight later saved me in that respect (it was his 110th birthday recently by the way; a fact no-one seemed to be interested in.)

It was, of course, the fault of my schoolmasters, and, I hate to say, the textbooks available at the time (I used Durell and Robson’s Elementary Calculus to teach myself – ah! I’ve still got them, but I’d recommend them to only very keen students.)

Only years afterwards – after a career in Fleet Street and training as a teacher at the age of 40 in 1987 – was I able to say with confidence to students that calculus is “just the maths of change, get over it.”

Again as a youngster, I’d used National Certificate Mathematics by Mahon and Abbott (still the best for introductory maths; I’ve secretly used them in class for exercises), and during lockdown I’ve combed the web for them as completely revised by WE Fisher.

In vol 3, page 96, Fisher says: “A distinguished physicist [Lighthill on Shock Waves] recently referred in a public lecture to the ‘special language invented by Newton and Leibniz, called calculus.’ That language was not invented and subsequently applied to the solutions to Newton’s problems: it is the expression of the way in which these problems had been (italics) attacked and solved. The calculus is not just a discipline invented by professors of mathematics but a method of expression which takes the place of arithmetic when it is necessary to deal with quantities which are changing – whether with time, or position, or anything else.”

That sums it up for me.

(Also during lockdown I’ve been delving into medieval maths, logic and metaphysics – the Oxford Calculators in the 1300s and later the pre-Newton scientific clubs and societies here and in Italy and France were nibbling at the idea of change/flux. Perhaps, if it had not been for the Black Death and Wycliffe, Merton/Oxford would have been the axis for the advance in science and not Newton/Trinity/Cambridge!

How the concepts attached to “impetus” developed from the Greeks onwards I find fascinating.)

Thoroughly enjoyed your superstructure MOOC by the way.

Tony Patey (Bristol. Retired.)

Memoirs of a MoustacheAwesome topic and great blog. Where would you place “Karl Popper” in the mix of understanding thermodynamics?