What shape is the Earth?

The extraordinary challenge of determining the true shape of Earth reveals the deep value of measurement to scientific progress

by Miguel Ohnesorge  BIO

Surveyors on the Bæskades plateau near Alta, northern Norway, 1900. Photo courtesy the Norwegian Mapping Authority Museum, Hønefoss/Kartverket

is assistant professor of philosophy at Boston University in the US, where he teaches and researches the history and philosophy of science. His book Newton’s Open Problem: Earth’s Shape and Universal Gravitation is under contract with Oxford University Press.

Edited byRichard Fisher

Sometime in 1852, the Swedish astronomer Nils Haqvin Selander travelled northward past the Arctic circle to oversee the completion of one of the largest projects in precision measurement in human history. Over the previous 40 years, he and his predecessors – most notably Friedrich Wilhelm von Struve – had been occupied by a seemingly simple problem in physical geodesy: what is the shape of the Earth?

By the 1850s, scientists knew that Earth is not a sphere and its surface flattens closer to the poles: Selander wanted to find out by how much. To do so, he measured the length of several sections along an arc of meridian – a line of longitude – stretching from the Black Sea to the Arctic Sea. The arc covered more than 20 degrees in latitude or, by their estimate, 2,821.833 km.

It required a mindboggling amount of work. To measure such a long distance exactly, the meridian was split up into 258 interconnected triangles, whose internal angles were measured repeatedly by sending light signals and recording them with small telescopes mounted on so-called theodolites. In each measurement, they needed to know their exact altitude over sea level based on a large network of continuous measurements with spirit levels and barometers. Ten sides of their triangles had to be measured by manually concatenating standardised rods hundreds of times using specialised apparatus. I won’t even start listing all the calculations and statistical exercises involved in aggregating all that data. And Selander and Struve were not alone; over the course of the 19th century, similar measurements would be completed in most of Central and Western Europe, North America, Great Britain, Japan and British India.

An 1860 map of Finland. The Struve arc is a later addition. Courtesy the National Land Survey of Finland

Why would anyone invest so much effort into measuring Earth’s shape? There were many economic and political incentives for constructing precise maps, but this cannot be the entire story. Geodesy wasn’t the first time scientists had sought extremely precise measurements of apparently obscure details of the world, nor would it be the last. Think, for example, of measurements of the magnetic muons in the Large Hadron Collider or astronomical measurements of the precise angular momentum of our galaxy. What justifies the enormous value scientists attribute to pursuing precise quantitative measurement?

The quest to measure Earth’s shape offers an exemplar that helps us understand why precise measurement is valuable. That value is not exhausted by the economic value of precise data. Neither is measurement’s value merely instrumental: a tool for confirming our scientific theories. Measuring matters for deeper reasons than are immediately apparent.

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Before we turn to the story of Earth’s shape, a few words on what quantitative measurement is. We hear about quantities all the time: in science journals, political debates, educational assessment, and wellness apps. Despite being so familiar with quantitative concepts, we rarely ask what exactly we mean by them. It’s commonly known what sustainability scores, global warming targets, or earthquake magnitudes are, but the incremental differences on each of these scales are less understood. These incremental differences, however, are the defining features of quantities. Most people could tell the difference between a minor tremor and city-destroying quake, but what about a magnitude 7.0 and 7.2? What properties of earthquakes do such differences correspond to?

To play such a strange language game, we need to make sure we know its rules. More precisely, any useful quantity needs rules of measurement. In an homage to one early device used as a rule of measurement, we tend to refer to such rules as ‘scales’. Scales spell out how to assign magnitudes to objects. As a first approximation, it is helpful to think of measurement simply as the art of building scales. Scales can be physical devices, like a fulcrum balance or a thermometer, from which we read off magnitudes. They can also be cognitive devices, such as the scales for measuring reading comprehension. Such scales take your answers to specific questions about a text and compute a reading comprehension score with the help of statistical regression and some ideas about what usually makes texts difficult to read (the number of words, their familiarity, etc). Usually, scales are a mix of both: a physical device and many cognitive devices that we use to correct, read, and calibrate it (models, theories, rules of thumb, etc).

So much for quantitative concepts and the careful art of measurement that makes them meaningful. But why go through the ordeal of building scales? Why measure at all? Modern science teaches us that building good scales can take centuries, involve many hiccups, and require hard physical and intellectual labour. It is perfectly legitimate to ask why measurement is worth that effort.

History vindicates the importance of asking that question. For a long........

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