Beyond Measure: The Hidden History of Measurement

by James Vincent

Studies like this suggest not only that measurement is a skill we acquire with age, but that a key component of this practice is our ability to abstract. It’s not enough to simply compare one tower to another or use a measuring tool the same height as the target. We must instead create an intermediary: a unit of measure that represents nothing but its own value and provides a convenient medium for transferring information from one domain to another.

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.’

The calculations of Kepler are sometimes thought of as the first ‘natural laws’ of science, in that they are unchanging, precise, and verifiable. Their authority is a product of their universality: their predictions are applicable not just to this planet at this time but to all planets across time and space. In other words, they are generalised, abstract rules – qualities essential to the development of measurement. Indeed, if you were to summarise the history of measurement in a single sentence, it would be as a history of increasing abstraction. Measurement begins life rooted in the particulars of human experience but over time has become increasingly detached from our life and labour. Just as with Kepler’s laws, the result is that it has attained authority over an ever-expanding domain.

The old Irish unit of the collop, for example, was defined as the amount of land needed to graze a single cow. Here is a unit that adapts to the practicalities of life, meaning lush, energy-dense pasture would be measured in smaller collops than the same area of barren hillside.

Many of the age’s greatest intellects contributed to what would be a seven-year project to measure the planet and define the new unit of length, the metre. This would eventually be standardised as one ten-millionth of the distance from the North Pole to the equator, with the accompanying mass standard, the kilogram, equal to the weight of a cubic decimetre of water (that’s a cube with sides one-tenth of a metre in length).

Spiritual ritual and bureaucratic rigour were therefore both needed to maintain prosperity, and the nilometers themselves were usually built inside temple complexes. The same priests who read these scales would oversee the religious festivals that celebrated the floods. ‘The flooding of the Nile and fertility of the land were linked directly to the pharaoh’s rule,’ says Salima. ‘So, if you get lots of bad floods, that means the gods are pissed off with the pharaoh, and, by extension, with all of Egypt.’ In these circumstances, measuring the depth of the Nile seems more than a practical chore: it’s a rite that gauges the favour of the gods.

Throughout the course of the third millennium bc, the pictographs on the bullae would morph into increasingly abstract signs: series of wedges pressed into clay using cut reeds that represented syllables and consonants, not just objects. This is the script we know as cuneiform, meaning ‘wedge-shaped’, which was used by all the major Mesopotamian civilisations, including the Sumerians and their successors, the Babylonians and Assyrians.11 By 2500 bc, this writing system had become ‘sufficiently plastic and flexible to express without difficulty the most complicated historical and literary compositions’,12 but from this very early period we’ve recovered only a handful of literary texts. Instead, the overwhelming majority of unearthed writing tablets – some tens of thousands – are administrative in purpose.

The library they created is one of receipts, contracts, shopping lists, tax returns, deeds of sale, inventories, wage slips, and wills. Over time, narrative writing like royal announcements and records of wars were added to the mix, but even these retain something of the catalogue format, listing provinces conquered, offspring born, and temples consecrated and desecrated.

If your records and observational skills are good enough, you could ignore the moon altogether and base your calendar on the sun, replacing the period between phases of the moon with the period between equinoxes. But this also generates problems, as the average length of a year is 365.2422 days, meaning even if you add a leap day every four years, over the centuries your calendar will still go out of sync. Whatever method you pick, you’re going to have to periodically add extra days to pad out the difference.

The science writer Robert P. Crease suggests that there are three crucial properties that units of measurement must possess: accessibility, proportionality, and consistency.35 Accessibility is needed because you can’t measure something if you can’t find your measuring standard. Proportionality is necessary because no one wants to measure mountains with matchsticks. And consistency is perhaps the most important attribute, as a unit of measurement that varies unexpectedly simply can’t do its job (though one that flexes with intention can be useful).

The difference between sizes is equivalent to a third of an inch, which shoemakers call a barleycorn.

The Saami cultures of northern Europe have a unit of distance known as the poronkusema that’s equal to around 6 miles. It means, roughly speaking, ‘reindeer’s piss’, and measures the distance a reindeer can walk before urinating.

Still today we gauge distance through contextual measures of time and activity. We explain to a friend that the next pub is just a five-minute bike ride away, or that the beach is just an hour’s drive.

The bull even refers specifically to the tools of musical measurement as responsible for this unwanted change, explaining that ‘the measured dividing of the tempora [periods, the basic unit of duration in music]’ has allowed notes of ‘small value’ to proliferate, which choke and starve the ‘modest rise and temperate descents of plainsong’ like weeds in a well-ordered garden.43

I fear that the mathematicians, who have not yet troubled the world, will trouble it at last; their turn has come. —louis-sébastien mercier, the new paris, 18001