Lincoln on equality

I watched Steven Spielberg’s movie ‘Lincoln’ recently.  Lincoln is portrayed as quoting Euclid on equality: ‘Things that are equal to the same things are equal to each other’.  This is from Euclid’s book ‘Elements’ which was in common use until modern times as a mathematics textbook and is believed to have sold more copies than any other book besides the Bible.  In the movie Lincoln extends the meaning of this first of Euclid’s ten axioms from mathematics to embrace the equality of men.  Since I am teaching thermodynamics at the moment, I was struck by its similarity to the zeroth law of thermodynamics, which states that ‘two systems in thermal equilibrium with a third system  are also in thermal equilibrium with each other’.  The concept of the zeroth law is sometimes accredited to Rankine who lived in the middle of the 19th century, or more than two thousand years after Euclid (380BC – 260BC).  It is reputed to be called the zeroth law because it was only recognised as being of fundamental importance to thermodynamics after the first and second laws were well-established and to rename them would have caused confusion.  The zeroth law allows temperature and temperature scales to be defined.  It seems to me to be a special case of Euclid’s first axiom ‘Things that are equal to the same things are equal to each other’, and that it is remarkable that it took the fathers of thermodynamics so long to recognise it, especially when they were probably brought up on Euclid’s ‘Elements’ as their mathematics textbook at school.

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