# What’s the length of a coastline?

6 february 2024

How long is the Belgian coastline? When searching for an answer, there’s no conclusive number to be found.

The Belgian government website claims it’s 65 kilometers, while Visit Flanders says 67 kilometers. The English Wikipedia page on the “Geography of Belgium” says 66,5 kilometers, the Dutch version 72,3 kilometers. Why is this so? ​​The variation in reported lengths of the Belgian coastline may arise from different methods of measurement and the inclusion or exclusion of certain features. Coastlines can be measured using different approaches, and the results may vary based on factors such as the level of detail considered, the inclusion of bays and inlets, and the measurement scale.

When asked "How long is the Belgian coastline?", the answer may as well be “How long do you need it to be?". When you start tracing a coastline through the grains of sand or into the molecular structure, then what happens to the length?

The Richardson effect

Lewis Fry Richardson was a mathematician and a Quaker who, later in life, turned his mathematical and pacifist mind to the topic of war. In researching the possible effect of border lengths between states on the probability of war, Richardson discovered what is now termed the "Richardson effect": the more accurately you try to measure some things, the more complex they become.

Suppose the coast of Britain is measured using a 200 km ruler, specifying that both ends of the ruler must touch the coast. Now cut the ruler in half and repeat the measurement, then repeat. What you see is that the smaller the ruler becomes, the longer the measured coastline will be. One might suppose that these values would converge to a finite number representing the true length of the coastline. However, Richardson demonstrated that this is not the case: the measured length of coastlines, as well as other natural features, increases without limit as the unit of measurement is made smaller.

By Tveness- Own work,CC0

Instead of resolving into order and clarity, ever-closer examination reveals only more and more detail and variation. The truth is always stranger, more lively and more expansive than anything we can compute.

In practice

These problems are more theoretical, rather than practical considerations for planners. It's not practical to make a map at the scale of reality (1:1). Maps are just models of reality and are inherently inaccurate. Of course modern technology and better data can improve our measurements. But the ultimate goal isn't just more precision; it's providing insights that are relevant and actionable.

At Nazka Mapps we are helping people use maps for decision making. Sometimes that means not always giving them the most detailed data, information, or tool. It’s hard to back away from the most accurate, highest resolution, but often that is the most useful position to take.

Nazka's Boundaries-API

An example of weighing accuracy against usefulness can be found in our Boundaries-API. For many of the applications that we build at Nazka Mapps we are reliant on boundary information. The data we need for this comes from different sources with different levels of accuracy.

The Open Maps for Europe project is created for 1:250 000 scale and provides information from country to municipality level. For Belgium, we wanted a more detailed dataset as we have many projects focusing on municipality or sub-municipality level. That's why we opted for the FOD Financiën (AAPD), which maintains a dataset for a more detailed 1:10 000 scale.

On these datasets we did a lot of post-processing, and on top of that processed data we created a REST API where the end-user has the final say on what level of detail polygons are served:

• level 0 = bounding box
• level 1 = a simplified dataset with 10% of vertices of the Eurogeographics data
• level 2 = a simplified dataset with 50% of vertices of the Eurogeographics data
• level 3 = the original dataset by Eurogeographics (1:250 000)
• level 4 = the more detailed dataset for Belgium only (1:10 000)

Our Boundaries-API is openly available for map application builders who need boundary information in a performant and reliable way — without the need to grapple with complex concepts like the Richardson effect.