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

by James Vincent

Capturing this abundance required ingenuity, and Salima is taking me to see one of the tools used for this task: an artefact of ancient measurement that is testimony to metrology’s role as the kindling of civilisation. It is a nilometer: a measuring tool used by the ancient Egyptians to gauge the depths of the Nile’s floodwaters each year. These readings were vital, as the depth of flooding determined whether the year’s harvest would be slim or bountiful, an insight that powered the operations of the state like the mainspring of a clock. If the nilometers said a famine was coming, then food would need to be set aside to sustain the people and stem unrest. If they predicted the harvest would be plentiful, then appropriate taxes could be levied in the form of crops, labour, and land. These resources then supported the business of the nation, contributing towards trade for silver or copper, rations for the army, and construction projects like the society-warping pyramids. Most importantly, the bounty of a good harvest would be used to fill the granaries that would feed the people in leaner years. But for all those decisions to be made, measurements had to be taken.4

Units like these seem exotic or fantastical to us now, artefacts of a time when the world thrummed with variety and there were truly authentic ways to be. But these sorts of ad hoc estimations have never gone away. 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. We improvise new units, too, estimating our walk to work in podcasts, or telling ourselves that a flight is only three movies long. Such measurements are useful because they transfer information from an objective realm of distance to a subjective one of experience.

This acceptance of the primacy of nature in marking the hours of our days is also present still in civil contexts in the form of daylight saving. The practice of shifting the clock backwards and forwards one hour is maintained in most of the northern hemisphere, and though it’s decried by many as an outdated concession to older methods of work, it’s a reminder that the world doesn’t always run on human time. Measurement may be the tool by which we impose structure on reality, but it still requires accommodation and concession in some domains.

These devices were also viewed as public utilities that benefited citizens by encouraging industriousness. A petition to the Town Council of Lyon in 1481 says that the town ‘sorely felt the need for a great clock whose strokes could be heard by all citizens’,50 while the inscription next to a clock installed in Caen in 1314 reads: ‘I shall give the hours voice / To make the common folk rejoice.’51 How the ‘common folk’ actually felt isn’t clear, as the records we have from this period capture mostly the thoughts and feelings of the rich and powerful. But it seems that timekeeping inspired the same mixture of emotion it does today, with some welcoming their newfound sense of order and efficiency, while others resented the clock’s restrictions and surveillance.

10 chains by 10 chains square).

Should be 1 x 10. Or 10 acres.

The text starts as a dry overview of the geography and resources of Jefferson’s home state, but, like the lord of the manor admiring his plat, Jefferson is enthralled by the idea of the land and begins to rhapsodise over America’s natural bounty and its potential to nurture a particular sort of liberty. The latter, he thought, would be achieved through the development of the land, an activity that Jefferson elevated to the status of religious virtue. ‘Those who labour in the earth are the chosen people of God,’ he writes, ‘if ever he had a chosen people, whose breasts he has made his peculiar deposit for substantial and genuine virtue.’16 Europe could keep its dirty metropolises and crowded workshops, thought Jefferson; America would till the soil, cultivating in its ‘immensity of land’ a vigorous, moral, and independent citizenry. These men – these white men – would own the land they stood on, making them impervious to bribery, debt, or other economic threats.

The survey ensured ‘perfect security of title and certainty of boundary,

Surprised not to see some mention in this chapter about adjustment for earth's curvature.

Although the original Northwest Ordinances only covered a portion of the continental US, the survey system would be reproduced in future legislation throughout the nineteenth century. As the United States expanded west through bloodshed, treaty, and commercial dealings (including the 1803 Louisiana Purchase from France of land to the west of the Mississippi, a cherished ambition of Jefferson’s that almost doubled the size of the country overnight), the grid was repeated with methodical intent. Over the next two centuries, it would come to encompass more than 1.8 billion acres of land, covering three-quarters of the total area of the continental US, including thirty new states. There are still significant tracts that the survey has yet to reach, mostly in the depths of Alaska,31 but to date, some 1.3 billion acres of rectangular plots have been sold off, with the rest kept for federal and state use.32

Colonisers often justified their acquisitions by arguing that the Indians wasted the resources that America offered. The flexible ecology of Native Americans, which balanced static farming with mobile activities like hunting and fishing, was derided as unproductive.

Even without this trickery, the imposition of strict systems of land ownership and boundaries undermined the way of life for some Native Americans. Indians in the Great Plains region, for example, relied on nomadic movement across vast tracts of land to hunt, following the migratory paths of bison. But in tracing these routes, they would now find themselves unknowingly trespassing on territory claimed by colonisers – the surveyor’s grid transformed into tripwires strung invisibly across their home.

In our time, the concept of the average is most likely to be seen as an insult, as an indictment of mediocrity. But for Quetelet, to be average was to be perfect. He saw the average statistics in his biometric data as the proper outcome of natural laws; an indication that the subject was free of all abnormality.

Why should intelligence be heritable in humans just because horses can be bred to run slightly faster – are these qualities really equivalent?

Yet this assumption is not entirely faulty.

Today, the mathematical principles of statistics have been mostly strained from this historical hotchpotch, and the discipline now stands as an adjunct to numerous fields, eager to direct and assist investigation. But we still struggle with the dual nature of the figures it creates; with their part-invented, part-discovered character. Statistics about education, income, and IQ are used to make sweeping judgements about whole nations and races,

Like the last chapter, it is stopping with the worst examples of oppression and glossing over recent uses of the same tools for opposing purposes.

And the grievance had remained, even though the European Union relented on the issue. In 2007, in fact, the EU had told the UK it could keep using imperial measures wherever it liked. As Günter Verheugen, EU industry commissioner, said at the time: ‘I want to bring to an end a bitter, bitter battle that has lasted for decades and which in my view is completely pointless.’8 Today the UK is almost entirely metric, but retains dual units on some food packaging and imperial measures in areas of life too culturally embedded to suffer change. There are still miles, yards, and feet on road signs; most people measure their height in feet and inches, and many use stones, pounds, and ounces to track their weight. And no one would contemplate getting rid of pints in pubs. It’s in these measures – close to the heart and the body – that imperial units are securely moored.

The most common of these arguments is the perceived appropriateness of imperial units. They are measures that have developed slowly over time and have become shaped, like a familiar tool, to the user’s grip. Practically speaking, the biggest difference is that these measures are not decimalised. In decimal systems one relies on multiples of 10, making it easy to convert between units and calculate with large numbers. But US customary measures and British imperial measures use either 12 or 16 as their base (for example, 12 inches in a foot and 16 ounces in a pound), which is easier for dividing things into thirds and quarters. It’s this feature that makes these systems more appropriate to market bartering and other quick calculations. Think of it like slicing up a pizza. You can quickly divide it into quarters or eighths, but how would you cut it into ten slices? As well as the lack of decimalisation, anti-metric campaigners argued then, as now, that imperial measures are superior because they correspond to the human body. Our bodies are our first template for units of measurements – accessible, proportional, and consistent – and in nineteenth-century America and Britain, anyone who wanted to know how long an inch, foot, or span was could estimate from the width of their thumb, the length of their foot, and the spread of their arms. Such measures weren’t precise, but they were always at hand. It’s hard to quite imagine the utility these units provided more than a century ag...

The following year, opinion polls showed that the majority of Americans were opposed to the adoption of the metric units, and the project was happily scrapped by President Ronald Reagan, another scalp in his administration’s programme of budget cuts. Despite this official rebuff, the US is definitely much more metric than it first appears. After all, the federal government has relied on metric units to define feet, pounds, and ounces since 1893,52 judging metric standards to be the product of an unimpeachably rigorous scientific process. Many commercial products in the US list measurements in both metric and customary units, the better to appeal to international markets; numerous industries are metric, like automaking and pharmaceuticals; and the US military is mostly metric, to better work alongside international forces. Nevertheless, since the 1970s any legislative attempts to go metric have failed conclusively, and it’s clear that cultural objections are as potent as ever.

I’ve found myself beguiled by the arguments of these traditionalists; by the satisfying historical and cultural density of older measures, and the admirable desire to retain their legacy in an increasingly abstracted world. But although these units once embodied important realities of everyday life, these aspects of their use are increasingly irrelevant. For example, although it’s true that base-12 and base-16 divisions of imperial units make dividing goods by halves, thirds, and quarters easier, of what relevance is that in a world of pre-packaged groceries? And while we praise older units for being built on a more ‘human’ scale, is there anything more human than reaching beyond our grasp? To do so is a defining characteristic of the modern world, which encompasses spans beyond the individual’s comprehension. As anti-metric advocates love to point out, what ultimately determines the ‘right’ measurement is familiarity and tradition. But tradition is not immune to change, and if imperial measures are abandoned because they’re no longer useful, then that is natural too.

Peirce argues that the ‘method of science’ is the only secure path to knowledge in the world. This may seem like arrogance, but he qualifies it in a number of ways.

The only thing that produces reliable data, he thought, was experiment and observation. For although Peirce was at home in the abstractions of logic and mathematics, he was adamant that truth was something produced with the hands and the eyes. He praised scientists like Lavoisier, who, in disproving the existence of phlogiston through careful measurement, had turned scales and alembics into ‘instruments of thought’. In doing so, Lavoisier created a ‘new conception of reasoning as something which was to be done with one’s eyes open, by manipulating real things instead of words and fancies’, said Peirce.30 Notably, he also stressed that such work only succeeds if verified by others. ‘[O]ne man’s experience is nothing if it stands alone,’ he wrote. ‘If he sees what others cannot see, we call it a hallucination.’ It was only by working as part of a group, by collating and comparing results, that one is able to ‘grind off the arbitrary and the individualistic character of thought’.

Peirce’s experiences with imprecision in measurement only consolidated this view: that the world was full of inaccuracies, and that even our best attempts to establish a solid foundation for truth were fragile and liable to fail. ‘We never can be absolutely sure of anything, nor can we with any probability ascertain the exact value of any measure,’ he laments in one unpublished manuscript.34 This attitude – combining an urgent desire for facts with an acceptance of their fallibility – makes Peirce something close to a patron saint of metrology; someone whose character and work captures the deep antagonism at the heart of the subject. The fact is that the more we measure, the more mistakes we find; the harder we try to bear down on the truth, the more we reveal the inadequacies of our assumptions. We push and push on the knowledge and equipment we have until finally – snap! – the pencil breaks, the glass cracks, the line tears, and we are sent spinning into the void again, hoping to rebuild what we know from scratch with our own hands and eyes.

Einstein commented later that it was this result and its subsequent analysis that laid the foundations for his revolution in relativity: ‘If the Michelson–Morley experiment had not brought us into serious embarrassment, no one would have regarded the relativity theory as a (halfway) redemption.’40 The story of twentieth-century science often means that Michelson’s comments about the future of physics residing in the sixth decimal place are seen as hubris, sometimes even mocked for their lack of foresight. But he wasn’t exactly wrong. The future of physics was found in the decimals, it just wasn’t the future anyone expected, with an experiment that involved measuring the speed of light preparing the ground for the greatest scientific re-evaluation of our universe since Galileo.

Think of it like this. The speed of light defines the universe at its largest spans. It is reality’s speed limit: you cannot travel faster than the speed of light, and so you cannot transmit information beyond its reach. In other words: it cannot be exceeded. Planck’s constant, on the other hand, helps define the lower boundaries of reality by describing the smallest action possible for elementary particles. It cannot be subceeded. If the speed of light rules supreme among galaxies, black holes, and the spaces between stars, then Planck’s constant has for its domain atoms, electrons, and the pocketable abyss of the subatomic world.

The contemporary philosopher Bruno Latour refers to this process as ‘blackboxing’ – the method by which ‘scientific and technical work is made invisible by its own success’. When scientific knowledge becomes a black box, it means we discard the context of its creation. We ignore the human errors, alternative theories, and invisible bodges that are just part and parcel of experimentation, and strip away these uncertainties until only the input and output of the work remain.44 Everything else is hidden by the black box. This process enhances the authority of science, removing the mess and contingency of research so that results seem singular and objective. It also obscures criticism of the scientific process, hiding controversial or arbitrary decisions. Think about debates about climate change, for example, and how they’ve stressed the need to limit increases in global temperature to less than 2ºC of warming. This is obviously a somewhat arbitrary figure, and the projected outcomes associated with it are far from certain. Things could go a little better or they could go a lot worse. Blackboxing this process creates a clear goal for policymakers and public discussions, but it also gives ammo to conspiracy theorists and ‘sceptics’ who believe some wonderful truth about the Earth’s future is being hidden.

Perhaps one fair way to judge the situation is with Peirce’s philosophy of pragmatism, which he once suggested was only a restating of Jesus’s wisdom: ‘Ye shall know them by their fruits.’45 In this case, the fruits of modern measurement are the fruits of the modern world, for better or for worse. In Versailles, the vote in the auditorium is approved, as everyone expected, and the official definition of the kilogram is changed the following year. As the metrologists hoped, nobody who missed the news noticed. Theirs is an invisible discipline, their work hidden from the public view, tucked away at the end of a string of decimal places. Yet on these precarious digits hangs the world of modern measurement, and with it, the frontier of human understanding.

Most items are mundane: concrete and iron samples for the construction trade; slurried spinach and powdered cocoa for food manufacturers. But others seem like ingredients lifted from God’s pantry: ingots of purified elements and pressurised canisters of gases, available in finely graded blends and mixtures. Some are just whimsical, as if they were the creation of an overly zealous bureaucracy determined to standardise even the most unique substances available. Think domestic sludge, whale blubber, and powdered radioactive human lung, available as SRMs #2781, #1945, and #4351.

In my own early career as a journalist, the value of my work was judged primarily by a pair of key statistics: the number of articles I wrote per day and the page views these attracted. My peers and I – mostly recent university graduates, badly paid and overworked – were taught to value quantity over quality, learning that what the machine of online journalism demanded was a constant churn of clickable headlines. Adapting to this pressure is something the industry as a whole still struggles with, and I personally had to unlearn many of the lessons taught by these particular metrics.

The German sociologist Hartmut Rosa suggests that our experience of life in the twenty-first century is increasingly shaped by our desire to control the world; to structure it through empirical observation, rendering it as a series of challenges to overcome. ‘Everything that appears to us must be known, mastered, conquered, made useful,’ writes Rosa. He says this is most obviously apparent in our constant tracking of our own bodies, but that the same framing increasingly structures how we encounter the world outside ourselves. ‘Mountains have to be scaled, tests passed, career ladders climbed, lovers conquered, places visited and photographed (“You have to see it!”), books read, films watched, and so on,’ he writes. ‘More and more, for the average late modern subject in the “developed” western world, everyday life revolves around and amounts to nothing more than tackling an ever-growing to-do list.’