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.
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.
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.
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.
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.
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 you have to go round _three_ times to get back to where you started.
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
No
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.