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

by James Vincent

measurement, like speech and play, is a cornerstone of cognition. It encourages us to pay attention to the boundaries of the world, to notice where the line ends and the scales tip. It requires that we compare one portion of reality to another and describe the differences, creating a scaffold for knowledge.

Every weight in the world (even the non-metric ones) could be traced back to this single standard, to the kilogram, or Le Grand K as it was known to its keepers.

To measure is to choose; to focus your attention on a single attribute and exclude all others.

Measurement is not an intrinsic feature of the world but a practice invented and imposed by humanity.

In the case of the Wolf Bone, its incisions are divided into groups of five, a common boundary in many numeral systems. Cultures from around the world tend to count by marking one, two, three, four, and then striking, slashing, or hooking a line for five. Psychological studies suggest this is something close to an innate cognitive limit – a natural partition in human thought, though one that is far from impermeable.

I'm curious about cultures that don't use base ten or base 5 now

At some point, though, evolutionary forces nudged a group of our ancestors into trading their souped-up memory for other cognitive aptitudes, including, we think, the ability to process language; to socialise and learn from one another. These were the cognitive tools that would allow measurement to flourish, helping to construct the systems that now sustain so much of modern life.

‘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.’

Science™. So Lord Kelvin was an early advocate of scientism

By most accounts Brahe was an eccentric, possessed of a huge fortune (his uncle Jørgen Brahe was one of the wealthiest men in the country), a metal nose (he lost the original in a duel), and a pet elk (which allegedly died after drinking too much beer and falling down the stairs of one of his castles).

Consider the old Finnish unit of length known as the peninkulma, which was originally measured as the distance at which a dog’s bark could be heard13 (around 6 kilometres).

An absence of standardised measures created a power vacuum that was easy to exploit.

As the historian Eric Hobsbawm has noted, metric units are in some ways ‘the most lasting and universal consequence of the French revolution’.17 By helping transform measurement from something particular to a specific time and place to something indiscriminately applicable, it allowed for organisation, analysis, and control on a scale undreamt of by our ancestors.

Measurement is unquestionably a tool of control and, as a result, has been used throughout history to manipulate, persecute, and oppress.

Measurement is a tool that reinforces what we find important in life, what we think is worth paying attention to. The question, then, of who gets to make those choices is of the utmost importance.

The floodwaters themselves were deified in the form of Hapi: an androgynous god depicted with a full belly and swollen breasts to signify the abundance he brought to the world.2 It was the inscrutable will of Hapi that offered the best explanation for the Nile’s largesse, and it was thought he released its waters each year from hidden caverns in the mountains.

Hell yeah nonbinary deities

A brief sketch of the origin of writing goes like this: in the beginning there was the Thing, and the Thing needed counting. What the Thing was doesn’t matter much.

Some scholars argue that the splitting of noun and number on clay tablets didn’t just allow kings to better track their taxes but was tantamount to a cognitive revolution: a leap forward that allowed humans to abstract and categorise the world around them like never before. Lists may not seem like cognitive dynamite, but their proliferation appears to have helped develop new modes of thought in early societies, encouraging us to think analytically about the world. ‘The list relies on discontinuity rather than continuity,’ writes anthropologist Jack Goody. ‘[I]t encourages the ordering of the items, by number, by initial sound, by category, etc. And the existence of boundaries, external and internal, brings greater visibility to categories, at the same time as making them more abstract.’

As Goody argues, the process of constructing a thematic list ‘leads to increments of knowledge, to the organisation of experience’.15 It is a precursor to organised philosophical systems, and, eventually, to science. Centuries later, in the fourth century BC, Aristotle would turn the list format into the bedrock of his thinking by divvying up all of reality in his great work, the Categories.

The ability to categorize is a prerequisite of cognition, in Kantian terms.

Thousands of years later, in an essay published in 1942, the writer Jorge Luis Borges captured the absurdity and scope of list-making with his own fictional taxonomy, supposedly found in an ancient Chinese encyclopedia titled Celestial Emporium of Benevolent Knowledge. In it, an unknown scribe orders all the animals of the world into fourteen categories. These include ‘those that belong to the emperor’; ‘trained ones’; ‘suckling pigs’; ‘mermaids’; ‘those included in this classification’; and, my personal favourite, ‘those that tremble as if they were mad’.

Tag yourself I'm those included in this classification

The fundamental unit of time is, of course, a day: the 24-hour period it takes the Earth to complete one rotation on its axis. As the Book of Genesis says: ‘There was evening and there was morning, one day.’ The value of this unit is nothing more than an accident of our planet’s rate of spin, set when the Earth first coalesced from a cloud of gas and dust (and slowing down minutely ever since). But it’s also a measure that is written into our biology, hard-coded in our DNA as circadian rhythms. This pattern of physiological events coordinates each of our bodies to the spin of the planet that is our home.

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.

Except in the most southern latitudes, the Pleiades first become visible in autumn at dawn (an event known as heliacal rising), appearing higher in the sky each day until they reverse course in midwinter and disappear before the start of spring. For the ancient Greeks, these stars were the seven daughters of the Titan Atlas running from the hunter Orion while their father was occupied holding up the heavens. But they were also a signal to labourers: when the stars disappeared, it meant that the sailing season had ended and they must return to their fields.

Perhaps inspired by the repeating patterns of the natural world, these cultures framed time itself as a grand cycle – a ‘cosmic odometer’27 – that ticked over once every 1,872,000 days (5,125 years), resetting the universe in the process. This calendar has fascinated Western observers, especially as the most recent cycle was estimated to have started on 11 August 3114 BC and ended on 21 December 2012.28 The flurry of excitement, paranoia, and opportunistic doomsaying that preceded this date was not echoed in contemporary Mayan communities, however. The ancient Maya were never particularly clear on what a reset of the Great Count meant, but it seems to have been more concerned with renewal than destruction. True enough, those hoping for the world to end in 2012 found that the sun came up once more on the morning of December 22nd.

These changes in the moon’s appearance would be announced by star-gazing priests, a practice from which we get the word ‘calendar’, derived from the Latin verb calare, meaning ‘to call out’.

Ancient civilisations dealt with these problems in different ways. Some added extra months to their calendars at the discretion of priests or astronomers, while others kept multiple calendars: a lunar calendar for religious rites and a calendar based on the solar year for civic purposes.

The calendar may be a human creation, an attempt to derive structure from the natural world, but like all measurement it creates its own realities too. Metrology helps to organise our lives, and as a result we imbue these systems with gravity and power, making it all the more important to understand the influence they have.

Gilgamesh – a superhuman Sumerian king who is two-thirds god and one-third man

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 barleycorn, for example, has a long history in Great Britain as a unit of length. It’s equal to a third of an inch, or around 0.8 centimetres, and has been associated with length at least since the early fourteenth century, when King Edward II declared that ‘three grains of barley, dry and round make an inch’. This definition later became standardised in the imperial system of measurement, and is still in use today as an increment in UK and US shoe sizes. The difference between sizes is equivalent to a third of an inch, which shoemakers call a barleycorn.

A bowshot, a stone’s throw, and an axe-throw are all common measures of length in early civilisations, as are units based on sound, such as the distance from which you can hear someone shout or a dog bark.

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.

The piss distance lol

The coordination of labour and resources needed to create the Great Pyramid is as awe-inspiring as the thing itself. Tens of thousands of workers toiled over decades to create the bigger pyramids, setting up towns just to support themselves, with bakeries and kitchens to feed the craftsmen, dormitories for sleeping, and graveyards to bury them in.43 The American historian and sociologist Lewis Mumford has argued that it’s this sort of mass organisation that actually sets humanity apart from other species, not individual displays of intelligence or mastery of any particular tool.

Take, for example, the ancient use of mass standards: stones carved into regular shapes like spools, cubes, and ovals that were placed in balance pans to weigh goods. These can be found buried deep in the archaeological record, appearing from around 3000 BC onwards. This is centuries before the first descriptions of ‘royal’ standards appear, suggesting rulers co-opted as much as they created consistent standards of measure. Despite the lack of any central regulation, these ancient mass standards are incredibly consistent in their values.

Heck yeah

However, just because measurement can be regulated without centralised authority doesn’t mean rulers have ignored the potential of these systems. As the historian Emanuele Lugli has noted, units of measurement are, for the powerful, ‘sly tools of subjugation’. Each time they’re deployed, they turn the world ‘into a place that continues to make sense as long as the power that legitimises the measurements rests in place’.5 In other words: measurement does not only benefit from authority – it creates it too.

Most petty crimes affect only individuals, but false measures can spread distrust through an entire community. Talmudic law recognises this by noting that while many crimes can be repented for, no one can fully repent for cheating with measures as they can never account for the full impact of their actions. As soon as the crime is committed, it spreads like slander, eroding trust and fomenting suspicion. ‘The punishment for unjust measures is more severe than the punishment for immorality, for the latter is a sin against God only, the former against one’s fellow man,’ says the Mishneh Torah.9 Measurement is a covenant that binds communities together and is therefore impossible to fully account for at the level of the individual.

Without direct political oversight, small towns and villages could still enforce fair dealings in measurement through communal censure, says Kula, but the most notable quality of the units themselves was their elasticity. Many measures changed in value depending on how and where they were applied, reflecting the needs of the people and society that used them.

There’s the furlong, for example, derived from the Old English for furrow, furh, and long, lang, which measures length, not area, and refers to the distance that could be covered by a team of oxen before they needed to rest (and which is now standardised as 201 metres or 660 feet). Furlongs were used to calculate the day-work unit of the aker, from the Old English aecer, meaning ‘open field’ (and from which we get the modern acre of 4,047 square metres or 43,560 square feet).

As Kula notes, many historical studies of medieval metrology refer to the ‘primitivism’ and ‘crudity’ of elastic units, but in reality they are well fitted to the needs of the people who used them, embodying the relationship of humans to the land and capturing the necessities of their work.

imagine for a moment that you’re a peasant in the Middle Ages. The grain you get from your farm is needed not only to feed your family, but also to pay your feudal dues and barter for goods at the market. When you take it to be sold, you are watching someone measure out not only months of labour, but, potentially, the future of your family. In lean years, shaking or striking the container to let the seeds settle could be the difference between survival and starvation. As a result, the activity of measuring grain is one of the most intricately controlled aspects of metrology in this period, with countless laws passed to regulate its measurement.

However, with sunset and sunrise changing throughout the year, this meant the hour had to move with the seasons, expanding in summer and contracting in winter. These so-called temporal hours were inherited by Europeans in the Middle Ages and meant that the length of the hour in London, for example, could vary from 38 to 82 minutes.28 This fact was not so much unnoticed in this period as much as it was an observation that would simply have made no sense. Thinking of the hour as a consistent measure was not a familiar concept for most people, while the minute and second didn’t exist as common units.

This unusual coexistence of temporal hours and mechanical horology is memorialised by some of the most beautiful clocks in existence: circular timepieces with hour markers positioned on rails that move about their perimeter like tiny train carriages, sliding back and forth to adjust the length of each hour so that it matches the changes of the seasons.

The pietre di paragone got the same treatment, with units of length carved as stone incisions into the walls of churches and markets. Officials could then check their standards by inserting them into these spaces. Using these hollows to verify units was a simple and clever way to avoid tampering, as they could not be shortened and lengthening could be stopped with the use of metal end caps. As Lugli notes: ‘While an object can be manipulated, a void is incorruptible.’