Knots to Narnia – Bill Thurston (1992) [video]

This is a lovely lecture by the legendary topologist Bill Thurston, in which he illustrates the cyclic branched cover of a knot by interpreting the knot as a portal to other universes.

I don’t think the idea has ever been used in a real video game, but there have been a few demos: the most impressive is the VR demo [0], which is described in detail with lots of background in [1].

There’s also a pretty comprehensive thread on Twitter [2], where @RAnachro collects a lot of videos and demos of knotted portals.

[0] https://www.imaginary.org/program/knotportal

[1] https://link.springer.com/article/10.1007/s00283-020-10028-8

[2] https://twitter.com/RAnachro/status/1362478176874754050

Thurston was very active on mathoverflow snd a lovely character. His answer on "What's a mathematitian to do?" [1] is fairly famous by now. It's been already on HN a couple of times [2]

His geometrization conjecture is at the backbone of Perelman's proof of Poincaré hypothesis.

[1] https://mathoverflow.net/questions/43690/whats-a-mathematici...

[2] https://news.ycombinator.com/item?id=23461983

I understand how going through a portal (let's say an un-knot to keep it simple) and then back through it in the opposite direction takes you back where you came from; it's like passing a piece of string through a ring and then back out the inside again, the ring falls off.

But what I don't understand is how going through a portal, then back around the outside and through it again, takes you to the same place. If you run a string through a ring, then around the outside and back through the middle again in the same direction, the ring is stuck on the string.

Loved this. I did want to see it keep going beyond the trefoil! This is tempting me to figure out a VR setup so I can try the VR demo.

Is this anything to do with the CS Lewis books? I’m re-reading them now