A coastline has no single true length, because the finer you measure it the longer it gets

the gist

A coastline has no single true length, because the closer you measure it the longer it becomes. Coastlines are jagged at every scale, from hundreds of kilometres down to fractions of a millimetre, so there is no smallest feature that should count. A ruler measuring a metal bar gets closer to the true answer as its precision improves, but a shorter ruler on a coast just traces more bays and pebbles and keeps adding length. Lewis Fry Richardson first studied the effect systematically, and Benoit Mandelbrot later showed that the mathematics of fractals explains it. The true length is therefore undefined, not just unknown.

how it works

Measuring a coast means laying a line of fixed step length along it. A small step follows every inlet and headland, adding length that a larger step would skip. Because coastlines are fractal, the number of new details keeps growing as the step shrinks, so the total grows without limit rather than converging to one value.

so what

The paradox shows that some everyday measurements are only meaningful once you specify a scale, which matters for mapping borders, coastal planning and science. It is also a foundational idea behind fractal geometry, which describes many natural shapes such as clouds, rivers and lungs.

fun fact

Mandelbrot's 1967 paper 'How Long Is the Coast of Britain?' was published in the journal Science.

Hampi was once one of the world's largest cities, until its Vijayanagara capital was destroyed in 1565

the gist

Hampi is a UNESCO World Heritage Site in Karnataka, India, with more than 1,600 surviving remains spread over 4,100 hectares. It was the capital of the Vijayanagara Empire from 1336 to 1565. Travellers from Persia and Portugal described it as a prosperous, wealthy and grand city with temples, markets and farms along the Tungabhadra River. By 1500 it was estimated to be the world's second-largest city after Beijing, and probably India's richest at the time. In 1565 a coalition of Muslim sultanates defeated the Vijayanagara Empire, its capital was conquered and destroyed, and the city was left in ruins. Hampi remains a religious centre, with the active Virupaksha Temple at its heart.

how it works

The city was built around a fortified core with temples, markets and water structures along the river, supplied by an extensive network of roads and waterworks. When the empire fell, the city was not rebuilt, so its stone monuments were left standing.

so what

Hampi shows how quickly a great city can vanish after a military defeat, and how a ruined capital can remain sacred. Its ruins give historians a view of medieval South Asia that few other sites can match.

fun fact

The name Hampi comes from Pampa, an old name for the Tungabhadra River.

From Wikipedia, the free encyclopedia · text CC BY-SA 4.0

Image: Wikimedia Commons

source: Wikipedia ↗

2 min

politicsshortCNA2:01

False allegations about Singapore’s hand in Indonesia’s markets and a made-up meeting

from CNA

CNA Verify has found close to 400 posts pushing falsehoods tying Singapore to Indonesia’s stock market rout and to a secret meeting that never took place. Together, they drew nearly 12 million views, and some were circulated by accounts that appeared to be working in concert, across multiple social media platforms.

Here’s how the disinformation campaign targeting Singapore was uncovered.

on YouTube: CNA ↗