Originally published at: https://boingboing.net/2017/12/21/watch-a-mathematician-explore.html

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…it took mathematicians over two thousand years to see an alternative to Euclid’s parallel postulate.

This amazes me, since we live on the surface of a sphere.

Watch me explore non-Euclidean geometry with a balloon and a marker pen.

We all know how well this sort of thing ends up being

sez you, round-earther! Euclid! Euclid! Euclid!

Ph’nglui mglw’nafh Cthulhu R’lyeh wgah’nagl fhtagn!

will monument valley game app go here at some point maybe… ok

This is like the training video on how to escape.

My understanding is that, at the time, the thought was that said sphere was embedded in Euclidean 3-space - where the parallel postulate works. In fact, take Wikipedia’s translation of the parallel postulate:

If a line segment intersects two straight lines forming two interior angles on the same side that sum to less than two right angles, then the two lines, if extended indefinitely, meet on that side on which the angles sum to less than two right angles.

In order to even get that to *refer* to spherical or hyperbolic geometry (let alone be false), you have to significantly generalize what you mean by straight lines because, quite obviously, geodesics aren’t straight in the classical sense. Add to that the fact that spherical geodesics intersect twice and can’t be indefinitely extended and I’m sure Ye Olde Mathematicians thought that spherical geometry was just some completely separate thing.

The best things have one looking stupid while doing them.

This has surely already been used as the premise for a horror movie or two, hasn’t it? Not quite From Beyond.

If they ever get around to creating immersive VR movies, someone should write a script based on this story and consult with the makes of this software.

Link to story: https://archive.org/stream/Astounding_v26n06_1941-02_dtsg0318-LennyS#page/n67/mode/2up

I had hoped this would be Vi Hart

You want the hounds of Tindalos chasing? because this is how you invite the hounds of Tindalos in. Keep Ryleh in Ryleh.

Yes, I understood all of that perfectly.

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