Blood, dirt and nonograms

Sometimes one stumbles across a piece of ostensibly academic research that glows with sense, vitality and fresh insight. It may be because I’m relatively speaking an outsider to the history of science that I often find that it’s in this field one gets the most delightful surprises.

Thomas Hankins’ lecture entitled ‘Blood, Dirt, and Nomograms’ gives the history of graphs, culminating in L.J. Henderson’s ‘nomogram’ representing the complex systems of the blood in a single graph.

It’s a story that starts around the end of the eighteenth century, with the likes of William Playfair’s graph of the British national debt from 1699 to 1800. Playfair, we are told, ‘went to Paris as agent to the Scioto Ohio Land Company; there he assisted in defrauding large numbers of French citizens and, according to tradition, helped storm the Bastille.‘

Graphs were already being considered in France as a means of providing easy conversion tables for the new metric system. These met with limited success, and real progress was made only when graphs suggested a descriptive geometry suitable for engineering drawing, initially to solve the military engineering problem of defilade. (In brief, defilade presents the problem of moving the minimum amount of earth the shortest distance such that no point of the fortification is overlooked by neighbouring ground.)

Defilade problems naturally led to the calculations required for laying out the new railways across France. Here we learn why the French railway is so fundamentally efficient: it was laid out with enormous concern for earthworks, so that curves were as gentle as possible, and gradients never exceeded five millimetres per metre.

From here we move rapidly through the first topographical map, isotherms, isobars, iso-everything, ‘the best statistical graphic ever drawn’ (representing Napoleon’s march on Moscow), the much feared log tables, and eventually to nomograms.

The beauty of nomograms is that one can lay a straight line (or, as is suggested, a piece of string) from a value on one side to a value on the other, and read off the result from the graph. Henderson clearly found this beauty suggestive, as he ended up speculating teleologically; that just as creatures displayed ‘fitness’ to their environment, so the environment displayed an elegant fitness to its creatures. This - further evidence why it is dangerous to let scientists make philosophical speculations - is the sort of thing that Charles Sanders Peirce used to propose even though he ought to have known better. It’s no surprise that Peirce manages to get a mention in the essay, albeit for other matters.

And so, finally, back to Henderson’s nomogram of the blood, which was hailed for integrating no fewer than 105 different relationships into one unifying picture.

If I’ve engaged in an enthusiastically extended description, it’s because every paragraph of Hankins’ lecture offers something to distract and entrance. Good on him, and good on all the other academics who still believe that the best way to communicate their learning is through communicating their delight.