All things being equal

firstsixbooksofe00eucl_0007Some of the greatest insights and inventions are obvious once they have been pointed out to you and you wonder how you could not have spotted them yourself. Is it luck or genius that allows someone to be the first to have a great idea? The quest for more efficient engines to power the industrial revolution led the likes of Sadi Carnot, Rudolf Clausius, William Rankine, William Thomson and James Watt to experiment and think deeply about thermodynamics or what might be called energy science or energy engineering. They established the First Law of thermodynamics (energy is always conserved) and Second Law of thermodynamics (entropy increases in all processes) of thermodynamics but initially missed the more fundamental, and arguably simpler, Zeroth Law (two systems in thermal equilibrium with a third must also be in thermal equilibrium each other). Rankine, working around 1850, is often attributed with identifying the Zeroth Law but probably the credit should go to Euclid (380-260 BC) who appears to have got there first in the fifth of his series of six books, ‘Elements’ [see my post entitled ‘Lincoln on equality‘ on February 6th, 2013).

The first English translation of ‘Elements’ is believed to have been by Sir Henry Billingsley in 1570.  A later version by Oliver Byrne was published in 1847 and you can read it on-line.  Go to page 173 to find a version of the Zeroth Law which can be paraphrased as ‘Things that are equal to the same things are equal to each other’.

Oliver Byrne, was Surveyor of Her Majesty’s Settlements in the Falkland Islands which presumably left him plenty of time to be the ‘author of numerous mathematical works’ as the title page to his book states.  The title page also tells us that ‘coloured diagrams and symbols are used instead of letters for the greater ease of learners’.  The bold primary colours and straight lines remind me of the paintings in the recent Mondrian exhibition at the Tate Liverpool. Maybe Piet Mondrian (1872 – 1944) was inspired by Oliver Byrne’s beautiful book, which was an early example of innovative graphic design and as well as an attempt to make mathematical concepts more accessible – something many writers of modern textbooks make little serious effort to do!



    1. Thank you for bringing this recent journal article to my attention. I don’t suppose that I was the first to observe the connection between Euclid’s first axiom and the Zeroth Law of Thermodynamics but clearly I am will not be the last. Maybe the obviousness of the connection is the reason that it was not identified as a law of thermodynamics until after the first and second laws. It certainly does not warrant a paper in a reputatable journal since there is nothing original in identifying the link.

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