Where would we be without units of measurement?
Admittedly, it’s kind of a strange question to ask. Measurement units are so fundamental to our understanding of a wide range of phenomena that a world without them is unimaginable. But, as we’ll see, the world of measurement units and the way they are measured are changeable and not always easily understood.
The theme for World Metrology Day 2019 is ‘The International System of Units (SI) – Fundamentally better.’ The theme reflects key changes to the definitions of the SI that are now based on quantum phenomena. Basing these definitions on the laws of physics aims to help continuous improvements in metrology and future-proof technology based on the new definitions.
Obviously, we here at Hexagon work every day to make measurement more robust, ensuring error and misunderstanding are things of the past. But even we can appreciate some of the fascinating conundrums humanity inherited due to some of the measurement practices and ‘units’ of the ancient world.
Floored by the Rings
In the Scottish archipelago of Orkney, a circle of stones has stood for some 5 000 years.
Surrounded by towering megaliths and the mysterious Comet Stone, the Ring of Brodgar is an enigma. There are numerous theories about why the rings were built: a place of ritual; a religious shrine; a site of astronomical observation; a memorial for ancestors. Nobody knows.
Another point of contention is the measurement of the stones’ perfect circle diameter (103.6 m). In the mid-twentieth century, Oxford professor Alexander Thom suggested that the builders must have understood Pythagorean mathematical theories to achieve this. An impressive feat, you might think – particularly since it would be a fair few centuries until Pythagoras developed his theorem (or was even born).
After researching some 250 megalithic sites, Thom proposed that the structures, including the Ring of Brodgar, were constructed using a Megalithic Yard, a unit of around 0.83 m.
How was this level of precision achieved? Thom suggested that astronomical observation, particularly the moon’s movements, may have been used to calibrate the unit and control its accuracy.
It’s a lovely idea, but not one that has found much favour. British Archaeoastronomer Clive Ruggles has argued that “evidence in favour of the Megalithic Yard is at best marginal. Even if it does exist, the uncertainty in our knowledge of its value is of the order of centimetres, far greater than the 1 mm claimed by Thom.”
For Ruggles, the unit used was probably measured with the length of a stride. The argument that the Megalithic Yard was used for hundreds of structures across Britain and Northern France was clearly a step too far for some.
And yet studies found that evidence for the Megalithic Yard reached statistical significance when looking at a very small collection of Scottish stone circles. Coincidence? Was too broad a tolerance used? Or was Thom on the cusp of discovering a local phenomenon and set his sights too far south?
Unfortunately, it’s a bit late to ask the builders involved how they did it, but I think we can be sure that the metrology mystery they left behind will live on for centuries to come.
A Spiritual Unit (and a Few Units of Spirit)
Of course, we pride ourselves on taking measurement very seriously at Hexagon, but archaeologists discovered that metrology can take on a whole other level of significance for some.
In the Louvre Museum in Paris, there stands a 4 000-year-old life-size sculpture of Gudea, the ruler of Girsu, an ancient city in Sumer (now Southern Iraq). For years, archaeologists were perplexed by the statue’s measuring rod and its tablet, which shows the architectural plan for a temple. When they began to unearth the remains of the temple outlined in the tablet, it was time to figure out the significance of the ruler.
It was archaeologists Sebastien Rey and Julien Chanteau who cracked the mystery. The revelation came in the early morning hours, after a long night of transcending modern man’s metric mindset and with the help of a little whiskey.
They theorised that the ruler’s measurements were constructed of fractions of a ‘sacred unit’. Looking at the plan, they realised that walls, buttresses, and gates aligned with fractions of the unit. What’s more, when they returned to the temple’s remains they tested the theory to see if they could find a gate outlined in the plan. Three weeks of excavation later, they found the foundation of the gate.
Clearly, measurement had a divine importance for Sumerian culture, but, as we’ll see, the symbolic significance of metrology in other cultures is more of a mystery.
Ask for Whom the Drum Measures
In 1889, three chalk cylinders known as the Folkton Drums were unearthed from the ancient grave of a child in a village in Yorkshire, England. The beautifully decorated Folkton Drums are all different sizes and thought to date back to at least 1 800 BCE, possibly earlier.
For over a century, the purpose and significance of these drums were unknown, but a research paper published in 2019 might have unravelled the mystery.
In 2007, two researchers identified the ‘long foot’ (equivalent to around 1.056 feet), which they argued may have been used to construct Stonehenge and other prehistoric structures. The idea needed more support, and that’s when researchers noticed that the smallest Folkton Drum has a circumference within 1% error of the long foot.
It turned out that the Folkton Drums, along with the Lavant Drum discovered a century later, form a ‘mathematical harmonic sequence’ and that rotations of each drum produce particular subdivisions of 10 long feet.
It’s thought that the drums acted as a kind prehistoric tape measure, allowing users to check the length of a rope or cord. Since wood has a low coefficient of thermal expansion, the chalk stones are probably replicas of original wooden measuring devices. But it’s unlikely these artefacts will have survived.
The ingenuity and pursuit of measurement standardisation here is remarkable, but why were the Folkton Drums included as grave goods? There are probably a number of explanations, but it seems reasonable to assume from all these stories that prehistoric people revered geometrical and mathematical principles and placed a great value on the power of measurement.
And who are we to argue! Please share this blog to help drum up enthusiasm for the importance of measurement.
Happy World Metrology Day!
Richard Law is a Global Marketing Copywriter at Hexagon Manufacturing Intelligence. He has written numerous articles and blogs across a range of industries. He holds a Bachelor of Arts in English Literature with Creative Writing and a Master of Arts in Poetry from the University of East Anglia.