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First discovered by the Italian mathematician Giuseppe Peano in 1890, a space-filling curve can theoretically expand endlessly without its path ever crossing itself to fill an infinite space. In a computer display, space-filling curves are limited by the number of pixels on a screen, but watching these fractal constructions extend isn’t just hypnotic – it’s also a helpful (if somewhat imperfect) demonstration of the enigmatic concept of infinity. To learn more about the mathematics of space-filling curves, watch Hilbert’s Curve, and the Usefulness of Infinite Results in a Finite World, also by 3Blue1Brown.
Video by 3Blue1Brown
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History of science
Meet the Quaker pacifist who shattered British science’s highest glass ceilings
14 minutes
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Language and linguistics
Do button-pushing dogs have something new to say about language?
9 minutes
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History of science
Ideas ‘of pure genius’ – how astronomers have measured the Universe across history
29 minutes
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Computing and artificial intelligence
Why large language models are mysterious – even to their creators
8 minutes
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Ethics
Plato saw little value in privacy. How do his ideas hold up in the information age?
5 minutes
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Information and communication
‘Astonished and somewhat terrified’ – Victorians’ reactions to the phonograph
36 minutes
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Physics
To change the way you see the Moon, view it from the Sun’s perspective
5 minutes
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Space exploration
The rarely told story of the fruit flies, primates and canines that preceded us in space
12 minutes
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Information and communication
Coverage of the ‘balloon boy’ hoax forms a withering indictment of for-profit news
17 minutes