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December 1 - December 17, 2022
The earliest evidence for what we might describe as measurement comes in the form of animal bones carved with notches. These metrological relics include the Ishango Bone, a baboon fibula between 18,000 and 20,000 years old, and the Wolf Bone, older still at roughly 33,000 years in age.1 Reading their meaning is like any augury, indefinite and intuitive, but archaeologists think the ordering of marks on these bones might make them tally sticks: the first formal measuring tools.
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.
the cubit (the length from the elbow to the fingertip) and fathom (the span of your outstretched arms).
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.
All rock, no collop.
the metre. This would eventually be standardised as one ten-millionth of the distance from the North Pole to the equator,
kilogram, equal to the weight of a cubic decimetre of water (that’s a cube with sides one-tenth of a metre in length).
the length of the lunar month varies by more than half a day, with an average length of 29 days, 12 hours, 44 minutes, and 2.8 seconds.
The ancient Egyptians were among those to maintain a dual-calendar system, with their civic calendar comprising the three 120-day seasons based on the flooding of the Nile. This only gives a total of 360 days for a year, so an additional five ‘epagomenal’ days were added after the twelfth month to bring the total up to 36529 – a practice copied in a number of cultures.
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.36
The grain has long been the smallest unit of weight for various English measures based on the pound (it’s since been standardised as 64.79891 milligrams), and 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).
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.
In England, we can see how units emerge from other practicalities of work. 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). Originally, an acre had a rectangular shape,
And in 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’.20 In other words: unlike those tight-fisted lords, God is generous with the grain, offering heavenly rewards in abundance rather than making you fight for scraps.
The compression was specific, i.e.fair
(The division of the hour into 60 minutes and the minute into 60 seconds comes from the Babylonians, who used a base-60, or sexagecimal, system of counting for their astronomy.
Noon was originally none, and
In England, measurement disputes in markets were settled by a special tribunal known as the ‘court of piepowder’ – ‘the lowest and at the same time the most expeditious court of justice known to the law of England’,
Sounds like a frat thing
and in his 1440 book De docta ignorantia (‘On learned ignorance’) he
This refraction of knowledge – the idea that the world as we experience it is somehow second-hand – is most famously illustrated in Plato’s ‘Allegory of the Cave’. In this story from The Republic, human existence is compared to a person chained inside a cavern, with a flickering fire behind them and restraints that stop them turning around. As objects pass in front of the fire, their shadows are projected on to the wall in front of the chained person. These shadows are all they can see – not the objects creating them. The objects represent the immaterial forms that comprise reality, while the
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an atom of caesium-133, which shudders back and forth an astounding 9,192,631,770 times to measure the duration of a single second.
Think of the difference like this: a customer survey that asks you to rate your happiness from one to five is an ordinal scale because you are ranking your response. But it’s not an interval scale because the exact levels of happiness are subjective and vaguely defined; they cannot be added or subtracted from one another. There’s no way to know if your five isn’t your neighbour’s three.
If heat was a factor of atomic motion, then surely that meant there could be such a thing as total absence of motion, of energy, and of heat. Thomson described this as ‘absolute zero’ – the point at which, well, nothing happens. He formulated his new measure of temperature as degrees Kelvin, which has since become the standard unit for much scientific and high-precision work. On this scale, absolute zero is defined as 0K, or –273.15°C, or –459.67
Take, for example, the introduction of surnames in Europe towards the end of the Middle Ages. Until at least the fourteenth century, writes Scott, the majority of Europeans did not have permanent patronymics, with individuals often adopting new names when starting a new job or moving to a new area.
In the UK itself, the length of the chain is encoded in one of the country’s cultural cornerstones: the cricket pitch.
Jefferson was critical in setting the manner of this expansion, and helped form a trio of laws passed in 1784, 1785, and 1787 and collectively known as the Northwest Ordinances. Along with the Declaration of Independence and US Constitution, these are among the most important documents in the founding of the United States – not because they contain impassioned cries for democracy, but because they describe, simply and plainly, how its land would be divided, sold, and governed.
The main subdivision of the grid was the ‘township’ – a 6-mile by 6-mile square (the decimally minded Jefferson had argued for 10 by 10) that contained thirty-six subdivisions of a square mile each.23 The base unit of measurement would be Gunter’s chain, 66 feet long, with its subdivisions of a hundred links. As a square mile contained 640 acres, the chain was a perfect unit for division, with each 40-acre plot (the smallest area of land that could be purchased) measured out in 20 chains’ length.
He dubbed his approach ‘the combination of observations’, a phrase that was used to refer to statistical methods in general throughout the nineteenth century,
This analogy would be the founding ethos of his new science: a discipline he dubbed social physics.
Stats.
‘It is better for all the world,’ wrote Justice Oliver Wendell Holmes Jr. in the court’s majority decision, ‘if instead of waiting to execute degenerate offspring for crime, or to let them starve for their imbecility, society can prevent those who are manifestly unfit from continuing their kind.’ Holmes, often venerated as one of America’s greatest legal minds, concluded with a brutal judgement on the Buck family: ‘Three generations of imbeciles are enough.’
Jefferson’s own interest in the subject went beyond the political, and the man seems to have had a keen personal interest in the quantified life. One of his fancies was buying custom-made odometers for his carriages that measured how far the vehicle travelled as he criss-crossed the country on government errands. The odometers fitted into the spokes of the carriage wheel and counted each rotation, letting Jefferson calculate the distance travelled from measurements of the wheel.
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?
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). The British government had been using tally sticks in its accounting since the medieval era, but had finally decided to get rid of these old records. Two
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fallibilism meant that there are no facts in life that are beyond doubt. Everything we believe exists with the possibility that it will be proven wrong, from the base evidence of our senses to the most elaborate, rigorously tested, and apparently flawless scientific theories.
if you measure the energy of photons, then your results fall into discrete categories, like rungs on a ladder, rather than being infinitely variable, as if they existed on a continuum. Planck’s constant is what defines the distance between those rungs.
