Bridges 2018 talk - Visualizing hyperbolic honeycombs

[Owen-bkfc]

This is still probably my favourite talk of all time because it shows how much is so fundamental and yet so unexplored.

I also find it mildly amusing that pqr->inf appears to fall victim to carcinization!

[DaniErik]

Hope you enjoyed my hometown of Stockholm. I really wish I could have made it to some of the open sessions, but I'm out traveling.

[timh.]

All of this rendering of tightly curved hyperbolic space makes me wonder how the coordinates are handled from the computer standpoint. I ask this because I want to make a MMO Co-Op survival videogame where the very geometry of the universe is trying to split you from your party. Obviously, highly negative spatial curvature like we see here is very disorienting and would be hard to play with, but a lighter negative curvature might work. The theory problem I keep running into is trying to represent the locations of objects in globally hyperbolic space. These honeycombs are stirring up some thoughts, though.

[henrikljungstrand]

@Henry Segerman You should check out Norman Wildberger and his Universal Hyperbolic Geometry, where he makes material sense out of hyperideal points, lines and planes etcetera, using projective vector space with an indefinite symmetric bilinear form, plus the Klein Model.

Please research the "other" Hyperbolic geometry, that one outside the ideal boundary, it has curved (Non-)Lorenzian geometry and funny topology!

[CuulX]

At 26:53 you show us "The Beast" in post, but the shirt you are wearing while taking the question is a fairly close match. Similar enough that I can't see any difference due to the limited size and blurryness of the video of you. So what schläfli symbol are you wearing on your shirt? (Edit: Guessing {6, 6, 4} after comparing with high res images)

Love this video. Going to download and look at those pictures in high res and later go through the paper and source. Amazing resource, thanks!

And the 3D simulation is fantastic!
Thank you so much :)

[Rubrickety]

I assume the Hyperbolic Catacombs are haunted by the lich who's hiding in "hyperboLICHoneycombs".

[zh]

Thank you. Absolutely fascinating and I actually understood all of it! Hyperbolic space and tilings of 3D space are both favourite topics of mine, so this video was ideal for me. I have only one question, about 14:00 - would the surface (p - 2)(r - 2) = 4 have any significance?

[br]

I thought he had a giant chin but it was his microphone lol

[Carmenifold]

this made me angrier the better i understood it, as all great math should

[veggiet]

I think I understand... I'm a little unclear on how a finite set of numbers can lead to an idealized cell shape. I'd like some further explanations, it's really not intuitive.

[ThingOfSome]

Why does the p-q-r plot not match up with the p-q plot, where r = 0?

[TomtheMagician]

I want you to be my maths teacher but we don’t learn this for ages