Beyond Measure: The Hidden History of Measurement from Cubits to Quantum Constants

by James Vincent

It was the nineteenth-century British physicist William Thomson, better known as Lord Kelvin, who offered one of the most memorable summaries of the contribution of measurement to human knowledge. ‘When you can measure what you are speaking about, and express it in numbers, you know something about it,’ said Thomson, ‘but when you cannot express it in numbers, your knowledge is of a meagre and unsatisfactory kind; it may be the beginning of knowledge, but you have scarcely, in your thoughts, advanced to the stage of Science.’

Of all the units of measure we have today, the day is the only one that had meaning before there was a mind capable of comprehending it.

The science writer Robert P. Crease suggests that there are three crucial properties that units of measurement must possess: accessibility, proportionality, and consistency.

we still measure precious gems like diamonds and emeralds with the carat,37 a unit derived from the seed of the Middle Eastern carob tree (and that is now standardised as 200 milligrams).

Condorcet himself was associated with a group of economists now known as the physiocrats, who argued that agricultural productivity was the cornerstone of national prosperity. As Karl Marx explained much later in Das Kapital, ‘the Physiocrats insist that only agricultural labour is productive, since that alone, they say, yields a surplus-value’.

It’s interesting to contrast this method with older traditions of survey and ownership in the British Isles, such as the annual ritual of ‘beating the bounds’. During the beating of the bounds, residents of a town or village would gather together to carry out a foot survey of their community. Priests and elders would lead the expeditions, pointing out geographical features like streams, rocks, and walls that marked the limits of their parish. They would be followed by a gang of children armed with willow sticks, who would beat these objects to place them in their memory or, in earlier centuries, be subjected to hazing themselves to achieve the same end. One account of beating the bounds in Dorset tells how, if the boundary be a stream, one of the boys is tossed into it; if a broad ditch, the boys are offered money to jump over it, in which they, of course, fail and pitch into the mud, where they stick as firmly as if they had been rooted there for the season . . . if a wall, they are to have a race on top of it, when, in trying to pass each other, they fall over on one side, some descending perhaps into the still stygian waters of a ditch, and others thrusting ‘the human face’ divine into a bed of nettles.

As de Tocqueville observed with brutal clarity, the legal charades of property rights, treaties, and surveys allowed the United States to remove Indians from the land ‘with wonderful ease, quietly, legally, and philanthropically, without spilling blood and without violating a single one of the great principles of morality in the eyes of the world’. He was wrong about the bloodshed, but entirely right in his bitter conclusion: ‘It is impossible to destroy men with more respect to the laws of humanity.’

Galton would later coin the phrase ‘nature versus nurture’ to describe these two categories of influence, but was always clear which he thought dominant.

Galton called this phenomenon ‘regression towards mediocrity’, though today it’s known as regression to the mean. He then realised that the mathematical tools he’d used to track the difference between two expressions of height (that of parent and child) could be tweaked to measure the strength of connection between any two variables, to see if they moved in tandem or not at all. These measurements didn’t have to belong to the same scale, but could encompass any set of figures, connecting anything from temperature and suicide rate to an individual’s beard length and buoyancy. Galton named his method ‘co-relation’, though the spelling soon changed to the now familiar correlation.

The eugenics movement would not have existed without the statistical underpinning created by Galton and his disciples, but another form of measurement was equally crucial in justifying this creed: the IQ test.

The danger of this situation was demonstrated with dramatic emphasis in 1834, when the UK’s seat of parliament, the Old Palace of Westminster, burned down and took with it the country’s standard yard and pound. Ironically, the fire itself was caused by the disposal of another ancient tool of reckoning: tallies. These are short lengths of wood carved with notches to represent money owed. These staves are then split down their length into two pieces, foil and stock, which are given to the debtor and creditor respectively. The unique shape of the wood’s split ensures this record cannot be forged (and is also where the term ‘stockholder’ originates).