A universal hotness manifold

Slothful thermometers.

I'm working on a column for Nature Chemistry about temperature, prompted by the incredible collection of early thermometers and thermoscopes at the Museo Galileo in Florence.  (Can't get to Florence and visit it and the amazing gelato spot Perché no! — they have an incredible online virtual tour of the exhibitions.)

The question of how one can be assured that two objects, well separated in space and/or time, would be in thermal equilibrium with each other should they be brought into contact — that is, can you be sure that two objects are at the same temperature —  is not quite as simple as it sounds.

First you need a measuring device, then you need to agree on a way to quantify the output of the device.  And it would be nice if your colleague who lives across an ocean could set up her apparatus in such a way as these quantities are the same.  In another words, you need a calibrated thermometer.

There's a wild and wonderful history to figuring out how to create this basic piece of lab equipment, including what you mean by zero, how big should degrees be, and how to to tell if water is really boiling.  But my favorite find is in a paper by mathematician James Serrin, in which he defines a thermometer by formally stating the zeroth law of thermodynamics [1]:

Manifolds, M, marked in with L, hotness levels (the black enamel dots).  Or,17th century Florentine degree thermometers.

"There exists a topological line M which serves as a coordinate manifold of material behaviour. The points L of the manifold M are called 'hotness levels', and M is called the 'universal hotness manifold'."

I'm trying to imagine standing up in front of a classroom of students and talking about hotness levels.

And those slothful thermometers?  They tell the temperature by little balls that float or sink...slowly, very slowly.  Lazily, you might say.

Just reading the paper brought back memories, the collection of conference papers this quote is pulled from are reproduced from typed (double-spaced, with a typewriter!) manuscripts, complete with the typos you might expect before word processors and spell check arrived on the scene ("physcis").  In the late 1970's this was one way to inexpensively and rapidly get proceedings and reviews into print.

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1.  "The concepts of thermodynamics" in Contemporary Developments in Continuum Mechanics and Partial Differential Equations. Proceedings of the International Symposium on Continuum Mechanics and Partial Differential Equations, Rio de Janeiro, August 1977, edited by G.M. de La Penha, L.A.J. Medeiros, North-Holland, Amsterdam, p. 416.