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

37 points by robinhouston 4y ago

robinhouston 4y ago
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 https://www.imaginary.org/program/knotportal [1] https://link.springer.com/article/10.1007/s00283-020-10028-8 https://link.springer.com/article/10.1007/s00283-020-10028-8 [2] https://twitter.com/RAnachro/status/1362478176874754050 https://twitter.com/RAnachro/status/1362478176874754050
throwaway378037 4y ago
Is this anything to do with the CS Lewis books? I’m re-reading them now
- martzy13 4y ago
  No
- NateEag 4y ago
  I think only at the level that in the books Narnia is reached from our world via magical portals, so it's a reasonable reference to make when discussing portals.
deleted 4y ago
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nhatcher 4y ago
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-mathematician-to-do/ https://mathoverflow.net/questions/43690/whats-a-mathematici... [2] https://news.ycombinator.com/item?id=23461983 https://news.ycombinator.com/item?id=23461983
whatrocks 4y ago
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.
deleted 4y ago
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raldi 4y ago
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.
- robinhouston 4y ago
  It doesn't have to, that's just the simplest way to set it up. There are other possibilities. For example, in https://youtu.be/eb2DhCcGH7U https://youtu.be/eb2DhCcGH7U you have to go round _three_ times to get back to where you started.

37 points by robinhouston 4y ago

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 https://www.imaginary.org/program/knotportal [1] https://link.springer.com/article/10.1007/s00283-020-10028-8 https://link.springer.com/article/10.1007/s00283-020-10028-8 [2] https://twitter.com/RAnachro/status/1362478176874754050 https://twitter.com/RAnachro/status/1362478176874754050

throwaway378037 4y ago

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

martzy13 4y ago
No
NateEag 4y ago
I think only at the level that in the books Narnia is reached from our world via magical portals, so it's a reasonable reference to make when discussing portals.

deleted 4y ago

[deleted]

nhatcher 4y ago

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-mathematician-to-do/ https://mathoverflow.net/questions/43690/whats-a-mathematici... [2] https://news.ycombinator.com/item?id=23461983 https://news.ycombinator.com/item?id=23461983

whatrocks 4y ago

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.

deleted 4y ago

[deleted]

raldi 4y ago

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.

robinhouston 4y ago
It doesn't have to, that's just the simplest way to set it up. There are other possibilities. For example, in https://youtu.be/eb2DhCcGH7U https://youtu.be/eb2DhCcGH7U you have to go round _three_ times to get back to where you started.