Y e s . I t s h a l l a l l o w A u s t r a l i a n s o n l y t o a p p r o a c h i t

Ha

...why?

@@ninjacat230 uluru is a big rock in the middle of Australia

@@pantheraviva yus

Yeah, his animations about how walking a path in a different order leads you to different locations, or how moving can add unexpected rotation, really grounded the abstract rules of the gyrovectors in a neat way.

I think a great teacher should make the student actually understand the topics, not "feel they understand". (While it is of course impossible to explain non-Euclidean rendering to a 5yo in five minutes, gyrovectors are not the simplest way to do it.)

i had the exact same reaction

haha I don’t know what any of that means

@@tosterm "Not commutative" - the order of things matters. "A, then B" is not the same as "B, then A". Inconvenient, but manageable. "Not associative" - the grouping of things matters. "A, then "B, then C"" is not the same as ""A, then B", _then_ C". Fuck that.

@@tosterm Commutative means you can change the order of the things you want to transform without changing the result, like 5 + 8 = 8 + 5 = 13, while associative means you can change the order of the operations themselves, like (7*2)*5 = 14*5 = 70 = 7*10 = 7*(2*5). Associativity is more fundamental than commutativity, so hearing that associativity stops working feels weird. (Sorry by any wrong words, English is a second Language to me)

@@lonestarr1490 But he's using them to model translations in hyperbolic space. Translations are functions => their compositions is associative. But gyrovector addition is not associative, so something doesn't add up.

It's this and teardown, my wallet will suffer…

Check out HyperRogue. It's a similar geometric concept, but the gameplay itself is kinda shit (in my opinion. I just don't like roguelikes.)

Me too (if I can)

And Meigakure as well...

same but kinda terrifying

Once you have mastered thinking with portals... you must try... thinking without them?

Yup, I've been making a hyperbolic game as well. Something that trips me out as I'm programming is how messed the coordinate system is haha. I miss left, right, up and down, but they don't mean anything in this space!

yeah, this is the real big boy leagues

Are you telling me that you can walk forwards 19 meters.... without portals???

@@raconvid6521 at least its meters, I know those. it doesn't matter its a gyrovector made of 2 quaternions and 1 "thing" that's a complex number

I just watch it because it's trippy especially the spherical geometry one

only people that focused in school can understand this big brain stuff

*"And, though it was perhaps unsurprising that Cameron should be unenthusiastic about Juncker's candidacy, the vehemence of his opposition was extraordinary."*

I'm a mathematician, and when he started talking about Gyrovectors, my brain told me to go look that up. The Operation that's described in the paper he puts on screen is a fucking monster, as well. Although, it kind-of sounds like he's describing Quarternions, so "gyrovector" could just be a generalized term for the algebraic structure that quarternions operate in. Although, the non-associativity is definitely *not* something that Quarternions do, _and_ it presents a major problem for anyone who wants to do algebra with them, since inverse operations are difficult at best.

C'mon calculus is fun :)

If you want to hate it even less - I'd like to recommend you the channel called Insights into Mathematics or the playlist of algebraic calculus on another channel of him.

@@sillygoose210_6 for me math is fun once i understand it, but getting there is a real pain in the ass.

I love algebra and league ❤️.. calculus just a little 🤭

There is such a thing as "Tensor Calculus" :-P :-) and apparently tensors often contain a nested structure of lesser tensors rather than just being of scalars/reals/complex.

It is at 4th now

i'm so confused on all of this stuff.....

it really does explain a lot, in fact for me it actually kinda made me feel stupid about myself because the answer is so... SOO simple, just makes me think on how i didnt think of it of course its been in develpment for over 10 years, go ahead and tell me a game engine that can run 4 dimensions

oh, well i'm actually relatively new to all of this stuff so it makes sense i'm confused. i like the videos though, they're cool(at least, the parts i can understand)

Noticed the Minecraft pig in your picture. Thought I should let you know I'm working on a hyperbolic minecraft game :)

@@kayturs Ayo??

We just need F and B to finish out the set

3d hyperbolic space let's go but seriously, if you can map the "coordinate" of a 3d hyperbolic space onto any rubik's cube scramble, how close does that make them to being in the same group/set? (Sorry if I'm using the wrong terminology I'm not good with group theory yet) Edit: Thinking about it, rubik's cube moves are also (I believe) not commutative or associative, the only hole would be inverse moves but if you re-wrote them into 3 normal moves it could totally get mapped to a hyperbolic space

HYPERBOLIC RUBIK'S CUBE

@@Supertimegamingify Oh god I wonder what THAT would look like

@@OrangeC7 What's tricky about this is there's no good way to add points on hyperbolic space together. In order to think of scrambles as points in hyperbolic space, you'd need points associated to 2 different scrambles to "sum" to a new point which corresponds to the composition of the 2 scrambles. That would mean the structure of the scrambles and their corresponding points would be the same. Unfortunately, there's no structure on hyperbolic space. What you CAN do is map each scramble to a *transformation* of a hyperbolic space. These could be rotations, scalings, etc. Composing two transformations gives you a new transformation, just like composing two scrambles gives you a new scramble! However, To fully capture all the different ways to scramble a Rubiks cube, you'd probably need to consider hyperbolic spaces with more than 3 dimensions. A similar line of thinking (mapping groups onto transformations of euclidian space) constitutes a whole field of math called "representation theory", which surprisingly enough is a vital part of modern physics!

big epic

Hyperbolica*

Yes. Keep it coming. Please. I beg you!

Big epic by hurting my brain xD

,

I have a feeling that, considering motion sickness with just normal VR is a problem, our brains/inner ears would not be very happy in a VR setting viewing hyperbolic space

@@netsch20That is a valid concern, but I don't think it would be a big issue. While a small percentage of people will never get used to VR and always feel sick a little, most of VR users get used to smooth locomotion and have 0 issues after some exposure. Me personally, I had 0 issues with smooth locomotion games right from the getgo. And there already are some demos of 4D space and I haven't heard complains. I think it's at least worth a try, I'm sure some (if not most) would be able to enjoy it. And like I said, I think even standing in spherical spaces would be mind blowing. Don't forget you actually see how far things are. I really think it would be an otherworldly experience. Something you literally cannot see otherwise.

@@netsch20 I have a feeling that that entirely depends on the person; some people get motion sickness on a hair trigger, some effectively don't get it at all

@@rarebeeph1783 Yes exactly. But most people get used to it. Only very few are unable to get used it.

I would totally love to see a VR mode, though possibly later in development. Once all the important stuff is out of the way, it would be a fun experiment to try and probably turn out better than expected! :D

he knows too much

@@rehehehehehe4525 yes

How are you so wise with your scientific ways?

lol

maybe its because its very expensive? or maybe he just wanted to make a system from scratch lol could be anything. either way its really cool

In order to get the components of the metric tensor you still need a coordinate system, and a poor choice of coordinates will make the metric tensor components very complicated, so this doesn't avoid the coordinate system issue. By the way, I think the game also has curvature up and down.

big brain man

YOU'RE A LIFESAVER, i've been trying to make my own hyperbolic game but i wanted to use a coordinate system. Couldn't find anything on google and this was the last place i had a chance of finding a way.

@@gigaprofisi You're going to want to research things like Riemannian manifolds, geodesics, and stuff like that. Also, the tile method used in the video would probably be described as using charts in GR. Essentially, you can carve up the manifold into chunks so that they have their own coordinate systems and if you walk off a chart, you walk onto a different chart. The benefit of that method is it allows you to define points in that region(like in a mesh) independently of how warped that region is in the full coordinate system. If you had a region which was highly distorted(like near the edge of the disc), then you wouldn't be able to precisely represent points there. You could apply a coordinate transformation such that the determinant of the metric tensor(volume element) was constant. This would let you represent points with equal precision everywhere, though they may be more or less precise along different axes. I'm currently taking a GR course BTW, so I'm not an expert. Feel free to ask more questions and good luck!

me too. thought you'd just do some trickery with the output view

We need to start a petition

What about .4do

Ok?

*L U L*

Left Up Left

I'd call that a DULL RUUL, obviously any combination exists

omegalul

Have you also taken a look at what he made open-source from the game after it's release?

I believe the technical term is "smoosh".

@@OriginalPiMan Fusion is just a cheap tactic to make weak matrices stronger

yay

I deeply congratulate you on that useless achievement

"hace un día"

oh sh-

The idea of using spirals may not be hyperbolic geometry. However, that sounds like an interesting idea! I would go with something else. What about... circular? From a different persons perspective, you will be walking in a circle. Inside VR, you are going straight, and not coming back to where you started.

Lev Peslyak The reason I said spiral is because a circle would map to an infinite straight line, but some kind of spiraling curve would eventually terminate against the boundary of the play space

@@syzygy6 I realised that what I described could be a horocycle in-game, mapped to a circle IRL. If we include changing the radius of the circle you are walking along, you could explore an infinite corridor: limited width, but infinite length. Either way, the width is limited while length can be made infinite. Or do you know a way that allows both axis to be unlimited in a limited play-space?

I think you are confusing some things here. You can indeed use portals to simulate huge worlds in a relatively compact space. This has been suggested in an older video by CodeParade, and is currently used by some VR games, e.g., Tea for God. However, these are *portals*, which are sometimes incorrectly called "non-Euclidean geometry", but do not actually have anything to do with actual non-Euclidean geometry (or hyperbolic geometry in particular). Actually, this trick no longer works if you are trying to simulate a non-Euclidean geometry, at least if you are copying the movements exactly. This is because, in a non-Euclidean simulation, you can move your head in a circle, and your real head will stay in place, but your virtual head will spin (because of the differences between the two geometries). So you can just move your head to make the orientation of your real and virtual head completely independent, so avoiding virtual walls will no longer guarantee that you won't hit a real wall.

ZenoTheRogue Portals are not “incorrectly” called non-euclidean. Portal geometry is every bit as non-euclidean as hyperbolic or spherical geometries, it’s just constructed in a more ad-hoc fashion. As long as it does not obey Euclid’s five postulates, it counts. I’m mostly speculating on possibilities, and I suspect that a useful solution will rely on a combination of techniques. Fitting an open game world into a compact play space is currently an unsolved problem. Developing hyperbolic engines will probably bring us closer to a solution.

I'm pretty sure the 4D game is being developed by someone else, but same

@@robhillen8007 oh.. I didn't know that, but the point still stands

@@robhillen8007 Correct. marctenbosch.com/news/

@SArpnt You are right but 3D non-euclidean should be isomorphic to some surface in 4D.

It will do both :)

The 4d game has taken 10 years. This guy is doing a completely separate project, but he brought them up because both projects face similar issues. This project will hopefully be much quicker for the reasons mentioned in this video.

Your monitol is still 2D tho

@@Ascyt no mine is ULURU