Measurement – Part 2

How government’s abuse of measurement led to historic revolutions.

It’s reasonable to expect government to set out uniform systems of measurement.  But it’s also reasonable to expect government to abuse that authority when it suits government officials. (And of course, government use of measurement can also be based simply on incorrect calculations, as occurred during the COVID pandemic when the Centers for Disease Control issued guidance on the required spacing of desks in schools. This essay shows that the careful placement of desks, using well established geometric principles, allowed for a dramatic increase from 9 to 21 in the number of socially distanced students in a typical classroom, and comparable gains in larger classrooms, after correcting a math error in official CDC guidance documents.)

The harm caused by cheating through unfair counting has been recognized as particularly bad since Biblical times, and earlier.  As James Vincent writes in his book Beyond Measure: The Hidden History of Measurement from Cubits to Quantum Constants:

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.

Early in the history of measurement, there was a perceived need for the government to prevent cheating.  As Vincent writes:

Warnings against cheating with false measures can be found in some of the earliest known legal records, such as the Code of Hammurabi, authored around 1750 BC. Among its infamous prescriptions of an “eye for an eye” justice, the code rules that wine-sellers who give customers short measures should be “thrown into the water” (a euphemism for drowned).

But government officials soon learned how to cheat with measurements, starting with the physical space occupied by grain in a bag:

[A]s anyone who uses American cups as a unit of capacity in the kitchen knows, the tricky thing with measuring dry goods by capacity is that the space they occupy can change depending on how you fill your container. Shake a cup of oats from side to side and the grains will settle, allowing more to be added. In other words: the method makes the measure. This might not sound like cause for scandal, but 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. These included ruling on whether grain should be poured from shoulder height or “dropped-arm height” (the latter allowing the substance to compact more tightly); whether the measure was to be shaken after being filled or its contents pressed down, and whether the grain was to be measured “heaped” or “striked” (that is, whether it was allowed to pile up above the top of the container or levelled off with a special stick known as a strickle). These were not minor issues, either. A heap could account for a third of a bushel’s total size when measuring wheat and rye, for example, and added as much as 50 per cent extra capacity to the units for grains like oats that pile more readily. This awareness of measurement was so ubiquitous that these acts became proverbial.

The Bible mentions methods to prevent that sort of cheating.  As Vincent writes:

[I]n the 1611 King James Bible, Jesus promises attendees at the Sermon on the Plain that whatever good they do in life will be repaid with a “good measure, pressed down, shaken together, and running over.” … In the five oldest books of the Bible, known as the Pentateuch or the Torah, advice on measurement is practical and didactic, a matter of social probity, like our earlier example of Talmudic law. Leviticus 19:35 in the King James Version states: “Ye shall do no unrighteousness in judgment, in meteyard, in weight, or in measure. Just balances, just weights, a just ephah, and a just hin, shall ye have.” (Ephahs and hins being ancient Semitic units roughly equal to 15 kilograms and 6 litres respectively.) Later, Deuteronomy 25:13-14 states: “Thou shalt not have in thy bag divers weights, a great and a small. Thou shalt not have in thine house divers measures, a great and a small.” … [T]he Bible mentions measurement more often than it does charity.

And the terms of the Magna Carta were forced on King John in part to address measurement grievances:

[F]ailure to regulate units of measurement could destabilise regimes, as illustrated in England in 1215 with the signing of Magna Carta, through which the reluctant King John made a number of concessions to his unhappy barons. These included the promise that there would be but “one measure of wine throughout our whole realm, and one measure of ale and one measure of corn [...] and one width of dyed and russet and hauberk cloths [...] And with weights, moreover, it shall be as with measures.”

Contemporaneous art from the later Middle Ages includes a series of paintings displayed in an Italian town hall in 1338 designed to remind its leaders to rule justly, by measuring fairly:

In the republic of Siena in Tuscany … weights and measures feature centrally in The Allegory of Good and Bad Government, a series of fresco panels created in 1338–9 in the commune’s Palazzo Pubblico, or town hall. They are a remarkable artefact: rare secular paintings in an era of devotional art, and perhaps unrivalled in their didactic and allegorical ambition. These huge illustrations cover three of the walls in the Sala dei Nove, or Salon of Nine, where Siena’s executive magistrates met to rule on city business, and any magistrate gazing about him during a long meeting would have been reminded of the power he wielded. On one side the fresco shows the effects of bad government, with farms burning in the countryside and violence in the cities. On the other side are the riches of good governance: farmers gathering abundant crops in their fields and transporting them to a bustling urban market where women dance in the streets. In the centre of the fresco is the huge figure of Justice, enthroned beneath the angel of Wisdom, who gently adjusts a set of scales. In the left pan is a figure representing Distributive Justice, who is busily beheading a criminal with one hand and crowning an honest man with the other. And in the right is Commutative Justice, who is handing down a trio of objects to a pair of waiting merchants. These objects are Siena’s standards of measurement: the staio, or bushel, a unit of dry capacity; and the passetto and canna, two units of linear measure used for industry and construction. Two woven cords lead down from these scales to be gathered in the hand of Concordia, or “harmony,” who holds them with the help of a group of Sienese citizenry. It is a striking image that is both metaphorical and literal, didactic and utopian. Not only are standards of measurement given equal precedence to more traditional acts of justice (like beheading criminals), but merchants and citizens are shown as having an equal duty in their maintenance. Like the Sienese republic itself, reliable measurement required communal effort and cooperation. It bound people together, and in doing so ensured their mutual prosperity. Nearby on the wall, the text reads: “Turn your eyes to behold her, you who are governing, who is portrayed here [Justice], crowned on account of her excellence, who always renders to everyone his due.”

The duty of citizens to measure fairly was also enforced in a practical way through stone carvings in Padua, Italy, in 1277:

A set of standards on Padua’s Palazzo della Ragione from 1277 include a standard-sized brick, roof tile, and loaf of bread. The latter appears as a circle with a cross through the middle, like an oversized communion wafer. Paduans buying bread in the market could presumably hold up their purchase to the standard to check that it was the proper size. It is a symbol of good governance to rival that of the frescoes in Siena, with the local government literally certifying citizens’ daily bread.

Measurement corruption in government was also a cause of the French Revolution:

[T]he Cahiers de doléances [was] an eighteenth-century survey of complaints and grievances collected in the run-up to the French Revolution. Issues of measurement figure heavily in the complaints of the peasantry, who demand that their lords be stripped of authority over weights and measures … A statistical analysis of these documents found that metrological standardisation is the fourteenth most common complaint of fifty mentioned, sandwiched between taxes and issues of “personal liberties,” and repeated throughout the Cahiers are calls for “one King, one law, one weight, and one measure.” As with Xun Xu’s manipulations, measurement here is not only a practical matter, but symbolic of higher injustices and social order. The peasants were fed up with being short-changed by their feudal masters and wanted their due … [I]n 1789, when the Estates General of France were called during the prelude to the Revolution, a demand to standardise weights and measures was high on the agenda. In the huge survey of national grievances intended to guide reform, known as the Cahiers de doléances, the issue is mentioned by members of the Third Estate more frequently than complaints about courts or infringement of personal liberties.

The result was the imposition of the new metric system in France, a system of measurement thought to be a more scientific approach to measuring, championed by the Marquis de Condorcet:

Condorcet, a mathematician, economist, and philosopher … argued that only the sciences could fulfil the promise of “the indefinite perfectibility of mankind.” …

Condorcet advocated for one, universal language, and also one universal system of measurement, namely the metric system:

Condorcet never had the chance to complete his universal language, but he did see the metric system as an important precursor. Metric units spoke in one tongue, equally capable of conversing with lace from Calais and cheese from the Auvergne. In time, it would be embraced not just by France or Europe, but by the whole world, thought Condorcet … Equipped with decimal measures, housewives would be better able to manage their accounts, farmers to survey their lands more accurately, and merchants to tally and trade their goods. Decimalisation would make people “self-sufficient in calculations related to their interests,” said Condorcet, “without which they cannot be really equal in rights […] nor really free.”

As Vincent writes, defenders of the new metric system claimed the older, traditional units of measurement in France had “no other right to be a standard than [it has] certain marks upon it and a certain name given to it,” while the meter and kilogram were “perfect,” “true,” and “objective.”  But as Vincent points out, even the metric system, which claimed to be based on immutable physical laws defining its base units, didn’t rest on such a solid foundation itself:

The inconsistencies in this argument [of the metric system’s defenders] can be seen whenever we dig into the practical work of actually defining and realising these new [metric] units. To realise the kilogram (originally known as the grave), for example, you had to weigh the mass of one cubic decimetre of water, a process that sounds natural enough. But scientists soon found that not just any water could be used for this task, as water sourced from the sea, lakes, or mountain streams varied in its composition, altering the kilogram’s final weight. Only purified water could be used, which could only be sourced from a laboratory. Similarly, the temperature of this water had to be fixed using newly improved thermometers, while the weighing process had to take place in a vacuum, an environment as natural for the Earth as a forest on the moon.

In the next essay in this series, we’ll explore how every system of measurement has inherent limitations, and how those limitations, if unrecognized, can give misleading impressions overall.