Stand-up Maths - 2017-07-28
Details about Sabetta and the hyperbolic VR project (with links to code) can be found here: http://elevr.com/portfolio/hyperbolic-vr/ Madeleine Shepherd makes some great mathematical objects out of yard and fabric. http://www.madeleineshepherd.co.uk/ Check out Henry’s shapes on shapeways. https://www.shapeways.com/shops/henryseg Watch my previous video with Henry. https://www.youtube.com/watch?v=LOVzytir7bM And Henry’s written a book about Visualizing Mathematics with 3D Printing. http://www.3dprintmath.com/ Filmed with the kind support of the Summerhall in Edinburgh. https://www.summerhall.co.uk/ Sorry some of the audio is a bit sketchy. We had a corrupted card in the main audio recorder and so had to piece bits together from the back-up recordings. CORRECTIONS: None yet. Let me know if you spot anything! Thanks to my many Patreon supports! Here is a subset: Eric Sexton Malcolm Rowe Jörgen Englund David Wagner Fredrik Petrini Support my videos on Patreon: https://www.patreon.com/standupmaths Filming and editing by Trunkman Productions Music by Howard Carter Design by Simon Wright MATT PARKER: Stand-up Mathematician Website: http://standupmaths.com/ Maths book: http://makeanddo4D.com/ Nerdy maths toys: http://mathsgear.co.uk/
Matt parker does acid and maths with friends.
I want to mess around with non-Euclidian geometry in VR on acid.
Though I always find myself peering through a different geometrical lens anyway, could just be my brain recognising points of data as being connected when conventionally they are not considered to be.
People who have used DMT often report impossible geometries.
Both being 'inside' of them (like this VR here) , as well as interacting with objects that have the same property.
@Butts Butts DMT is fricking nauseating.
Honestly I just wished Matt would have stopped talking sometimes and let the guests speak but still a great video either way
Matt not talking. AAAAAAHHHAAAAHAHAHAHAHA! you funny guy!
that is his problem. he thinks he knows everything and others should know about it.
That has to do with the fact that he already knows everything they're saying because it's all scripted
i definitely wanted to hear more from Sabetta
Agree, I was looking for this comment
The amount of content Matt could fit into 20 minutes is, might I say.... hyperbolic
did you just use the word hyperbolic in a hyperbole talking about hyperbolism? WHAT HAS SCIENCE DONE?
So that's how the TARDIS works. I get it now.
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Is there a hyperbolic Parker square?
A cube
parkerbolic square....ish. more of a squaroid.
If you take 2x the integral of the infinite series for sin and cos, you get a function that is just slightly off. Could be used to make a virtual world where everything is a Parker thing
a hyperparkoid, if you will
Hi!
Nothing like hyperbolic space and crochet
To make a model of hyperbolic space, just get a 4D printer!
I love the idea of getting 'topologically ill'
Almost like walking in an Escher drawing.
PlayTheMind , you gotta be careful you don't fall up the horizontal stairs and end up where you started.
+PlayTheMind It would be interesting to try and recreate some of Escher's non-Euclidean work in VR.
That's actually very accurate. Many of Escher's drawings are hyperbolic tilings.
You can load a Escher drawing to walk on it in my HyperRogue -- or do weird things to them, like painting a hyperbolic crochet with Escher's hyperbolic tiling, or changing them to another hyperbolic/spherical/Euclidean tiling. No pics for IP reasons, but some of the tilings in the game are Escher style.
Yeah, HyperRogue has a Reptile land which is obviously a reference to Escher.
Those infinite corner polyhedrons make my brain hurt badly....
Would be ahndy to have multiplayer and see someone enter them through one triangle and exit through another... observe how it will look like from inside and outside of them...
That would end up really weird. Your friend could walk a few feet and end up miles away -- by euclidean reckoning, at least. They'd still be only a few feet away (you can just follow them through the same way they went) but if you tried to get there by going around the outside, it could take a very long time.
12:30 That is so interesting! Now, I've heard of people using goggles that invert their perception of the world (literally flipping it on their retina), and their brain adapts and they see things right-side-up again. Could the same thing happen in a hyperbolic simulation? Would our eyes begin to work independently to locate objects?
Spencer T - I've heard of that upside-down glasses experiment too but it's only half true. The subject did adapt to the upside down vision, allowing him to perform any task as skillfully as he could before. His vision never flipped to upright though, until he took the glasses off.
sounds like Hyperbollocks to me
Lewis Edmonds xD best pun of 2017!
Oh my - is that an Infinite Monkey Cage I see??
Someone tell Brian Cox!!
We were actually up in Scotland filming with Robin and Brian at the same time but couldn't get the timings to line up to do this, but we're working on it!
Would love to hear them talk about it in an episode - hyperbolic space would be a great topic :)
Haha I thought the exact same thing!
Matt has been in the cage before as well :P Surprised he didn't make a reference.
+Hamstah We told him all about it. As Trent has commented: we almost managed to line everyone's schedules up so he could have a go in the infinite monkey cage but it didn't quite work.
8:42 - 9:07 is basically Antichamber
Yeah basically. Antichamber features some puzzles that behave a lot like hyperbolic space. I sort of felt "at home" in hyperbolic space since I'd been through something like it before. :)
Antichamber mostly uses euclidian geometry with a few portals here and there that make it seem non-euclidian. It's definitely not hyperbolic.
Yes, Antichamber is mostly euclidean as you would have to recode a lot of the fundamental engine stuff to really do hyperbolic, but it definitely has quite a bit of 'weird' spaces in the experience.. places where turning 360 degrees doesn't put you back where you started, etc.
There's a game called HyperRogue that actually does use hyperbolic geometry, and it has some similar situations. There are places where you can keep turning right forever and never get back to where you started.
I can't really grasp the 3D hyperbolic space yet... I mean i understand it but its just so hard to imagine
pasch013 ph'nglui mglw'nafh cthulhu r'lyeh wgah'nagl fhtagn
It's one of the "serious" applications where VR will be amazing, I think. Allowing math/physics folks to get a much more intuitive understanding of some of these extremely different environments. There's already several things out there for non-euclidean spaces and a few for exploring relativistic effects on time/space.
Hyperbolic language.
aron craig THIS
I want to see what happens if you point a line from where you are.
What if there were two people in the same simulation?
They'd both be tripping balls
Movement in 3D space of the person does not correspond 1 to 1 with movement in the simulation, so you could have them be very close to each other irl and very far apart in the simulation or viceversa.
NotaWalrus True, and if one person stood still and the other walked in a straight line irl, it would look like they were moving in weird ways to the stationary one
+Flobbled That would be very strange. You'd lose each other very quickly. And because of the way hyperbolic space does not match normal reality you could not be in the same room wearing the VR kit. Or you'd unexpected collide in the real world.
HyperRogue has a two-player mode, best played in its real-time ("shmup" mode). It does not let the players to get too far away form each other (to avoid the problem of losing each other mentioned by Matt, although even Euclidean games do this). No VR effects, but hitting your friend because you did not correctly predict the missile's trajectory in the Poincaré model is still possible :)
HOW COULD ANYONE THUMBSDOWN HYPERBOLIC VR :00000000
Hyperbolic space has no parallax.
Also the fabrics shown at the beginning have natural counterparts and can be seen in structures where surface area is important, such as on coral reefs and in a lot of plants.
If hyperbolic space didn’t have any parallax that would mean that the view from the goggle wouldn’t depend on translational movement at all. But the view changes as you move from cube to cube, so that can’t be the case.
Awesome. MATT! You should try the game HyperRogue!
Does this work on Google Cardboard?
Why did you bring the sofas with you in the first place, Matt?
More Sabetta videos!
Get James May on sometime, would love to see that conversation.
shibby Henlo FREN, you did a good idea. 10/10 good boi
+shibby I did a series of videos on a channel with James May many years ago. Lovely guy. We never managed to appear in the same video though!
“So i could get very easily lost.”
“YOU could get very easily lost”
Lol 😂
Matt I love your vids and everything you do but it gets to be really hard to follow what's going on when you keep cutting people off. I understand you know what they are saying but we don't always.
Reminds me of this 4d toys game.
3:30 LET HER HOLD THEM, OH MY GOD.
Has anyone else had success getting this to work with WebVR? I have a "Dream Vision" VR set and I was trying to get the web app to work with this, I can open the web page that has 360 vision and tap the screen to go deeper, but it won't go split screen which means I can't actually use a headset for this. If my eyes are seeing different things I can't use a headset lol, does anyone have any advice?
The 'corners' had 6 triangles around a vertex so they do tile a euclidean plane. It's hard to think about how there's a whole plane in a corner though.
EDIT: I can see it like a projection from the plane to the sphere like a sterographic projection. I think that works.
Its because they are much larger than they appear, they just look small because of the way our line of sight bends away from the surface. The back side of the shape is actually infinitely far away! https://en.wikipedia.org/wiki/Horosphere
10:58 like a real life TARDIS OMG XD
It is still infinitely big on the inside. If you look through the comments, you will find a link to a helpful wikipedia page
Incredible!
Here is one correction for you: "I think Madeleine Shepherd makes some great mathematical objects out of YARN and fabric" and not yard and fabric.
Saying that this stuff is amazing is not... hyperbole!
I didn't really understand any of this, but it was trippy and I loved it.
this is so amazing
Imagine being on acid whilst doing this
When science and art combine into science
That VR sim was frikkin nuts, dude. I think I'm starting to understand this stuff a little better.
This should be a 360° video! I'd love to see it on my VR headset.
That looks very exciting, can't wait to try it on my Vive! Also it was a bit frustrating when Matt kept talking over his guests.
Oh man my mind is blown. I would sometimes daydream about stuff like this but had no idea it was a thing let alone something that was studied by very smart people. BTW, that hyperbolic space would make a very cool map for a FPS game or even a game of tag! I'm so happy I discovered you Matt and all your math friends a year or so ago. I'm 36 and always learning something new. I ordered your books and look forward to reading them.
Matt reminds me of Rimmer from Red Dwarf for some reason. 😂
10:33 "Am i looking into the hyperbolic abyss"
I've watched a few videos with this particular demonstration, and one thing I've never gotten was an explanation of how those infinite vertices. I kinda get an intuitive understanding that it's somehow a logical consequence of how Hyperbole works in 3D space, however an intuitive understanding is not as satisfying for me. I would like a mathematical understanding of what is going on here. Why is one point of hyperbolic space any different than any other point? That's what doesn't make sense to me. And why is that space suddenly not hyperbolic?
This looks like the lost woods from The Legend of Zelda on LSD
When if first watched this I had no idea what was going on.
Now I understand some, but not all. I am happy with this progress.
I have an oculus, how would one get it running with my hardware? This looks like so much fun! I was just trying to explain hyperbolic space to my mother the other day... but this would be the way to do it.
Be interesting to see this with some furniture rendered in the rooms.
Earthbjorn Nahkaimurrao - 2017-07-28
This is pretty cool, but I think I would find it more interesting if you could render something more familiar like a house with furniture but in hyperbolic space and see how that looks. Also, if you could have some kind of controller to allow you to move without having to walk.
Kaiveran Lugheidh - 2020-06-15
@nin10dorox yeah, that last is what I meant
nin10dorox - 2020-06-15
@Kaiveran Lugheidh I think CodeParade's Hyperbolica is similar. It looks like it has 6 squares around a point instead of 4 pentagons, but it has reasonably real-looking stuff in spherical and hyperbolic space.
The only downside is that it looks like its 2d hyperbolic space with the vertical axis being euclidean, rather than true 3d hyperbolic space.
I'd like a fully hyperbolic one, but the whole "moving in circles makes you rotate" thing means that there can't really be a "down" direction.
Kaiveran Lugheidh - 2020-06-15
nin10dorox That's called H2xR geometry, and it does simplify things a fair bit.
In H3 you could always artificially make gravity point toward a "flat" plane (i.e one that matches the curvature of the space), but as different height levels sit on equidistants, this has some weird effects.
If you've played HyperRogue, there's an area called Ivory Tower that does something similar in (highly-curved) 2D, making gravity point towards a geodesic. Not only do higher floors have more room than lower ones, but activate azimuthal equidistant projection (which is something similar to what an eye would see) and go high enough, and you'll find ladders leading "up" with respect to gravity appearing to point slightly _downwards_.
nin10dorox - 2020-06-15
@Kaiveran Lugheidh Sweet, I'll check it out. I've thought of making gravity point to a geodesic (or a hyperbolic plane in 3d) but the fact that it would be different ad different heights doesn't seem super nice to me. You'd need a curved surface to seem "flat" anywhere but at the geodesic that gravity points to.
I've never heard of HyperRogue, but I'll definitely check it out!
It's also kind of nice to hear someone actually acknowledge the azimuthal equidistant projection! The poincare disk model gets all the love, but the azimuthal equidistant projection is more intuitive (for me anyway). Also (you probably already know this) the Beltrami-Klien model is great, because that's what hyperbolic planes actually look like in H3
Kaiveran Lugheidh - 2020-06-28
@nin10dorox yes, I have witnessed native perspective views of H3! It's funny to me how lines always look straight, but planes still seem to curve away from you with distance. It's almost like every hyperbolic plane is a hemisphere model of itself.