Books

A superb history of measurement reveals the strange and inventive ways we have quantified the world around us, says Tom Whipple.

Afingerprint has a weight. You don’t think about it, but it does. The residue left behind when you touch a surface, the telltale undulations of oil from your skin, has a barely quantifiable mass. In 1988 the weight of a fingerprint caused a crisis in metrology, the science of measurement. Because, scientists realised, the Kilogram (“the”, not “a”) was a fingerprint’s-weight out: 50 micrograms.

In a vault in Paris there is a lump of metal called Le Grand K and, in 1988, it defined mass for the world.

“Like the Holy Ghost, the [Kilogram] is singular but its presence is multiple,” James Vincent writes in Beyond Measure: The Hidden History of Measurement, his superb history of measurement. “Whether you are measuring flour for bread, lifting weights in the gym or buying timber by the tonne, it is Le Grand K that sits, invisible, on the other side of the scales.” Every other weight in the world, from a bag of sugar to (close your ears, Nigel Farage) the imperial pound, only made sense in relation to Le Grand K.

Now something was wrong. To be clear, nothing so ephemeral and grubby as a finger had been allowed to touch Le Grand K. Yet, for reasons we don’t understand, by comparing it with other identical kilograms minted at the same time and stored in the same way, scientists realised its mass had changed. Or it would have changed its mass if doing so was not philosophically impossible. “By global agreement,” Vincent writes, whatever Le Grand K weighs “is a kilogram”. “That means it can’t lose weight – everything else in the universe just gets a tiny bit heavier instead.”

So began a grand scientific project: to find a way of defining the kilogram that didn’t put us all at risk of suddenly and arbitrarily getting heavier if someone accidentally dropped it and knocked a bit off.

The history of human civilisation is also a history of measurement. As far back as we look we measured things – often in ways that speak of how we used them. There is a Finnish unit of distance, the peninkulma, defined by how far a dog’s bark can be heard (about 10km). Head north, and the Sámi measured length using the poronkusema, the distance a reindeer can walk before urinating (about 7.5km).

Travel west and you find the Ojibwe of Canada, who described distance over water in terms of the number of pipes smoked in your canoe. The residents of the Nicobar Islands displayed different priorities but alighted on a conceptually similar measure of voyage length: in the heat of the Indian Ocean they judged distance by coconuts drunk. Throughout medieval Europe land was measured by the area that could be ploughed in a day – a value that changed according to terrain.

These units mattered. In the Code of Hammurabi (c 1750BC), the penalty for wine sellers who gave short measures was drowning. In the Holy Roman Empire, in the 13th century, regulations were more lenient: first offence was a whipping, second a hand chopped off, third a hanging.

To enforce a standard, though, you needed to know what it was. Slowly conformity came. Villages needed to trade with villages, Sámi needed to travel in places where reindeer never micturated. We needed a way to make measures that travelled too.

The obvious way of doing so was to use the body itself – to measure in terms of feet, hands, fingers, and other parts too. Isaac Newton once toyed with defining temperature using the “greatest heat of a bath which a man can bear”.

The downsides of the scheme are obvious. Which man? Whose body? What if they really like baths? In Ethiopia folk wisdom had it that you sent a friend with long arms to the market to get a better deal in any goods measured by the arm. In Scotland in the 11th century an attempt was made to confound long-armed friends by defining a standard inch as the average thumb length of “a mekill [large] man, and a man of messurabel statur, and of a lytell man”. But it was unsatisfactory.

Then, in the late 18th century, the quest for conformity reached its natural conclusion. The French Revolution had swept away the old and a new, rational order was to be built in its stead. No longer should big, small and medium men have their thumb length averaged out: Napoleonic France was to create a system of units so logical, so sensible, that, declared Napoleon, “conquests will come and go but this work will endure”.

The conquests did, as he found, go. The metric units forged (sometimes literally) in those tumultuous years did not. Or not exactly.

Along with the other units we now call the International System of Units (SI), the scientific architecture that underpins these weights and measures has undergone many revolutions.

The metre was first defined as one tenmillionth of the distance from the Equator to the North Pole. It is now the same length, but defined using the wavelength of light. The second was once 1/86,400 of a day, but after discovering the length of a day is quite changeable it is now set to the oscillation of a caesium atom. The kilogram, though, held out.

For Bill Phillips, a Nobel prizewinning metrologist, this was manifestly absurd. “Think about this: today in the 21st century, the unit of mass is an artefact, a piece of metal.” Standing in a hall in Versailles in 2018, he made a face of mock horror at his audience. “This scandalous situation must be fixed!” And he knew how.

After three decades of work, the world’s metrologists, many in front of him, had at last found a way to define mass without needing a mass. They did so in terms of a fundamental constant – known as Planck’s constant – and using apparatus so sensitive it not only could weigh a fingerprint, you needed to adjust it to take account of the gravitational pull of the moon.

Now, he told them, the definition had reached the requisite level of accuracy, and Le Grand K was not a scientific artefact but a museum one. The kilogram was dead, Vincent writes, long live the kilogram.

Telling the story of metrology is not easy. It requires blending philosophy, science and history ultimately to explain how a human desire to quantify the world resulted in the world we see around us. Does Vincent do justice to the sweep of this tale?

If I had written this book I would have done it differently. I would have spent longer on the surprising geopolitical ramifications of having an atomic clock define time better than the Earth’s spin. I would have devoted more space to how Avogadro’s constant –a number relating the amount of a substance to the number of molecules in it – is also used to define the kilogram.

These are not my idle musings. I know exactly how I would have written Vincent’s book, because it is what I planned to do. In 2018 I spent months researching the history of measurement. I visited Le Grand K. I joined the world’s Time Lords (as they, occasionally, call themselves) at conferences on the future of the second. I prepared a pitch for a publisher. Then my agent emailed to say that a journalist I’d never heard of called James Vincent had had the same book accepted for publication – and all my work was for naught.

So what do I think of the result? Personally, I stick to my prejudice that Vincent is a filthy upstart weasel, and I look forward to watching his book, career and, ideally, life fail.

Professionally, very grudgingly, I fear that may not happen. To my great regret Vincent is equal to the task. He has a deft eye for the telling anecdote, but can also pull back elegantly from the minutiae to place that anecdote in the sweep of human progress. It is, in fact, my sad duty to inform you that this book is extremely good. Please don’t buy it.

As far back as we look we measured things - often in ways that speak of how we used them. There is a Finnish unit of distance, the peninkulma, defined by how far a dog’s bark can be heard (about 10km).