Non-euclidean virtual reality
ฝัง
- เผยแพร่เมื่อ 20 มี.ค. 2017
- Try at h3.hypernom.com and h2xe.hypernom.com. Controls: wasd rotates, arrow keys move, numbers change decoration, c changes colours. Also works on smartphones - touch the screen to move forwards.
If you have a Vive, you may be able to get this to work on Firefox - press v then enter to get graphics showing on the headset. No guarantees though, WebVR is a fast moving target.
This is joint work with Vi Hart, Andrea Hawksley and Sabetta Matsumoto.
Papers: archive.bridgesmathart.org/201..., archive.bridgesmathart.org/201...
Code: github.com/hawksley/hypVR, github.com/henryseg/H2xE_VR
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Who needs drugs when you have a noneucledian space
Drugs are cooler but well
@@PhillipAmthor dude no. Drugs arent cool, stay in school
@@galaxynova9276 im an adult
@@PhillipAmthor then you are a shitty one
nah, Drugs would always be better than some computer generated geometry, since fractals from lsd and shrooms are literally impossible shapes and not some mathematics, I am not saying is not cool but...
"Dormammu, I've come to bargain"
Dormammu, I've come to bargain
Dormammu, I've come to bargain
Dormammu, I've come to bargain
Dormammu I've come to bargain
Dormammu I've come to bargain
Roll for sanity check.
Atomicskull s just wondering, what dice do you use for a sanity check?
A non-euclidean die of course!
non-euclidean dice would actually be the same as euclidean dice, probably
Critical failure, the nerves linking my eyes to my brain have evaporated.
I now have the BLINDED status and take 2d6 radiant damage.
The Hounds of Tindalos live in the *angles* of time, while we live in the *curves* of time...
😲 by God I just learned what Lovecraft was referring to when he described someone falling into a corner.
What's the story??
@@Julzaa i wanna know too but i don't think we ever will
@@Pthaloblue2 The tooner was probably talking about Lovecraft's quotes about the other gods, where gazing onto them would cause you to go insane, and fall into the sky, kind of referring how it would feel to do that, as well as talking about how falling upward would be an unsettling and unrecoverable punishment. I don't know any Lovecraft quotes that talk about falling into a corner, and I doubt Lovecraft knew about non-euclidean geometry enough to use that in his books, although, I'm sure he would.
@@Julzaa The tooner was probably talking about Lovecraft's quotes about the other gods, where gazing onto them would cause you to go insane, and fall into the sky, kind of referring how it would feel to do that, as well as talking about how falling upward would be an unsettling and unrecoverable punishment. I don't know any Lovecraft quotes that talk about falling into a corner, and I doubt Lovecraft knew about non-euclidean geometry enough to use that in his books, although, I'm sure he would.
Lovecraft frequently referred to the non-euclidean nature of the constructions of the inhabitants of his mythos, most notably R'lyeh, which I believe he directly described as being non-euclidean.
If there's ever a sequel to Antichamber, it should have some rooms like these.
How would the guns work? There seems to be no natural way to build things out of small cubes in hyperbolic space :)
Well the rooms are built with cubes. You could do it so that locally within a single room, cube placement is euclidean. I was mainly thinking about he maze aspect of the game where hyperbolic space would be fun.
My HyperRogue has many hyperbolic navigation puzzles :)
Hahah David Madore has a hyperbolic maze on his site, 2D though
You can't be the guy.
An infinte prison to drive someone insane
you mean life?
KrylonGeek2 Is anyone ever really at peace? Or have they just lost their last marble...
Just give the prisoner the task to find the exit in this world and he won't ever get it😂
@Aniquin Yeah, that's right.
in particular, you will never reach the truth.
If you listen closely, you can hear my visual cortex crying out in pain.
"pathetic"
"pathetic"
@@whoneedsaquirkwhenyougotag8435 is this "pathetic" a reference to something? my cultural context cortex is crying out in confusion x)
@@nitoy12489 Noo u ruined the chain. Btw knowyourmeme.com/memes/principals-skinner-pathetic
"Pathetic"
*Non-Euclidean trypophobia.*
Imagine if spiders started crawling out of the holes
* curled in a ball, rocking and whimpering *
@Sean Wilkinson Now that sounds like a dimension I want to be stuck inside!
-If you know what I mean ; )-
@@Bubbly_Dragon Only a few species of spiders are deadly to humans. Mosquitoes kill the most of people (#not all. Some awesome mosquito species eat another while in larva stage). 2nd place goes to humans. Then theres snakes, some sort of flies and 5tht place goes to dogs. Since i have spiders on top of the hedge i have significantly less mosquitoes.
@@benq994 I'm aware of that. But more people are scared of spiders than mosquitoes. Personally, I think spiders are cute, but most of the population would be far more scared of them. Humans aren't rational, especially when it comes to phobias, so don't expect people to suddenly like spiders just because you said they aren't dangerous
He: Complicated words to explain in mathematical terms
Me: It's bigger on the inside, isn't it?
spongebob’s house is non-euclidean🤔
@@TitleGoesHere Timesponge Hypercubepants
I want to put this on, eat some acid, and crawl around on the walls for a few hours.
Connor Phebus you'd go nuts.
Using VR while on LSD doesn't feel too great, your pupils are fully dilated and you essentially have thousands of tiny light projectors pressed up against them.
Derrick Best you’d get lost in thought.
tyler millaway have a good ass trip sitter talking you through it, that would work pretty well
Idk turn the brightness down maybe?
Wow, I'm glad I live in euclidean space
OR DO YOU?! This is actually a pretty big question in cosmology/astrophysics. What is the overall geometry of the universe? Locally, things may appear euclidean, but the bigger picture might not be.
By the way, the surface of the earth is non-euclidean. boom
except you dont lol
Shiny Rayquazza eh, close enough, the universe is pretty flat
We don't, we live a non euclidean one
me after dmt
5:23 sick moves bro xD
That part made me laugh so hard XD
User Name hehehehe
The cord on the wall glitches when he does this
This is what R'lyeh must look like.
You can visit R'Lyeh in HyperRogue. You can find Temples of Cthulhu there, which appear to be circles within circles of columns, but they are in fact horocycles -- they are infinite and there is an infinite number of them.
Damn it you beat me to the R'Lyeh joke.
Funny that we thought of Lovecraft. This whole affair made me think of *The Dreams in the Witch House*
"Impossible angles"
Terrence McKenna would be so stoked to see this...he always talked about VR being the way to express the visual part of the DMT expierence
Yee Theres a whole chapter about in Archaic Revival goood comment
Me, after watching this video and realizing that 90% of every coding channel”s “non- Euclidean” world engines/ray-tracers/etc (looking at you, CodeParade) are just normal versions of said things, but with teleporters and multiple maps: *_T H O S E B A S T A R D S L I E D T O M E_*
Edit: now that CodeParade has announced the development of Hyperbolica, his mention in this comment is now outdated. And yes, teleporters in a space makes it technically non-Euclidean, but the properties of the space itself in such engines are still locally Euclidean; you still can only fit 4 equal squares around around a vertex even if part of one of squares is teleported somewhere else entirely.
Yeah its kind of hard to break physics even in programming lmfao. Did you really think even for a second we could simulate something we don't really understand?
GamerNot Valid
But we _do_ understand non-Euclidean geometry though, it has been a part of mathematics for decades, if not centuries.
@@declantecho1717 not to mention we simulate things we don't understand *constantly* in order to understand them better.
@@dumchican That's a fair point, however a lot of it is based off of assumptions, not absolute fact. When we get it right, great. A problem can be solved by maths. But when it comes to dimensions that we can't physically understand except in theory it all becomes guess work, we can't make a simulation and then test it against a real world example like we can in our 3d world.
We can test if a math solution would work because it's based in our reality.
Not saying you're wrong, just that a lot of the maths we use are based in our reality
@@yungcrow7992 Well, it's actually fairly easy to get a computer to simulate extra dimensions, it's just numbers to it. It is, however, impossible to render, for example, a 4D sphere in a manner we can understand, and so we have to get the computer to render a 3D 'projection' of the 4D cube.
Also, we can use real world examples to figure out extra dimensions. This video by 3Blue1Brown (th-cam.com/video/zwAD6dRSVyI/w-d-xo.html) goes over how we use examples from how 2D and 3D space works to figure out how similar concepts would work in the 4th and 5th dimensions.
This channel also plays a lot with simulating the 4th dimension and then rendering a 3D projection of it: th-cam.com/channels/NqSF-tYoFYFxa7aayp_wiA.html
I love this type of stuff. I wish someone made a game where you could stretch spacetime.
check out "a slower speed of light". It has accurate aspects of special rel.
It's called Hyperrogue!
Not exactly that, but you should check Antichamber
Very similiar aspect have a game called Everything...except everything in the game, there is also 'space' that is pretty trippy and interesting to play with
it's not exactly that but a game called the under presents added that
What happens if you live in non-euclidean VR for a year then try to walk around in real life?
Not much, since you still experience gravity as you normally would, ruining the immersion. Now if some astronaut would do this shit in space!
@@6squall9 We should propose this as a business venture to Elon Musk.
"How would you like to live in 4D vr space for a month while floating around in a massive enclosure orbiting the earth?"
@@shipwreck9146 who knows VR might be very useful in space travel and mars assuming those guys will have free time at all
@@6squall9 Well, now that we've gone to this topic of thought. One problem with long range space travel is the mental state of the people on board.
No natural sunlight, no nature, closed in with not much space to move around. VR could be a way to escape this. And with a 7-9 month travel time to Mars, the entire mission would be planned out before they launched, so during the trip they'd just be making sure everything is operating right, and then they'd drop into vr. They could even use their exercise machines in vr with it simulating that they're running in a park.
@@shipwreck9146 yeah that's exactly what i meant in my previous comment, spot on. With how lightweight VR is going to become in next decade it might just reach value/weight ratio to be considered acceptable. That said, first ones to travel to mars and beyond will probably so busy they won't have time for such luxury.
Skip to 10:15 that's the part where he peels back the gossamer veil that separates our reality from cosmic horrors beyond imagining.
At 10:59 the image feed cuts out with an electronic hiss, and he begins screaming and stumbling around the room in an apparent effort to run away from something.
At 12:02 the sound of distant flutes can be heard playing a maddening melody as he attempts to tear the viewer from his face, only to find that the metal and plastic have fused with his skin.
Copydot ha
some things should not be awoken
Your time stamps don't work with a euclidean concept of linear time. You must be refering to alternative dimensions of time instead. Shame, I can't find them.
KitZunekaze You dont want to experience my worldline, trust me
You're experience of time is far to limited. You need to branch out and use imaginary numbers in your timestamps.
Raise a baby in a virtual world like this but with more stuff in it; 5-D math will become so natural to them, and they'll look at us simply 3-D folk like we'd look at a flat-lander.
this child will feel like pacman when you take that VR off after some years
Highly unethical, yet interesting, experiment.
@@pablovirus unethical? Depends to who
he can still only move around in a 3d space. virtual reality does not change the fact that we live in a 3d world and are forced to live by its rules.
@@GewelReal
What? It 100 percent does not depend on who. The kid couldn't consent. Even if the experiment resulted in nothing interesting, it would still be unethical by definition.
Im still waiting for a company to make an escape room in vr where you're locked in a room that is the same size as the room in vr so you can actually walk around it without worrying about bumping into walls
I work at such a cpmpany. Terragamecenter.com
I'm developing 1-1 scale games happening in hangars with real life walls doors and furniture
someone put their flat into VR to play around: th-cam.com/video/QNmW25ykPJY/w-d-xo.html
@Rhyen that sounds really fun...I've heard of people designing games like this with, say, a plank on the floor to walk across which in VR looks like it's between two skyscrapers :s
@@0dinah0 haha yes that's not what we do. Our zones are between 500 and 800 sq meters
@@unwisestudio6020 looks really cool, it's sad that we don't have this where I live :v
walking in euclidean, dreaming in hyperbolic
I wonder what theyre actually talking about
What a beautiful variety of perfect comments. 😥 Beautiful!
Ever play those fantasy role-playing games? This is the inside of a Bag of Holding.
They who?
Lots of random and pseudo-scientific words which translates into: "look at my trippy world I created!"
The first one is if pi was = to 3
This reminds me of dreams I've had where I'm inside this big, weird geometric house, and I can float around and squeeze myself into even the tiniest corner and hole of it.
"Non-euclidean virtual reality" a.k.a. "what would a mathematician see on DMT"
i would like to see a demo with a non-euclidean room.
like with a floor, and chairs and furniture
Something that has those shapes from initial perspective or what's the idea?
Non-euclidean furniture would be awesome, but probably headache inducing!
wouldn't every object be very distorted by every movement you make? probably the biggest problem with these projects, doesn't seem very practical.
My intuition for hyperbolic space isn't particularly great, but if the corners are infinitely far away, you could fit a lot into that room. :D If you fix your room size to say 30m² instead of infinity I bet you would get used to it quickly.
Possibly the preferred shape for a dining table would be hexagonal rather than rectangular. I imagine that having a dinner party would be pretty annoying nevertheless, as everyone is really far away and you have to speak loudly, but at the same time everyone is fighting about table space because the center table is really small.
In that regard, people sitting in the center around a circular bar or counter-type thing and facing outwards would be more practical, as you can fit 20 side dishes and 3 drinks on the table without bothering your table neighbor; and at the same time you're closer together, encouraging chatter. But then of course nobody is facing each other which is a bit awkward aswell.
Hyperbolic architecture seems pretty challenging :D
So... Slendermonkey lives in H^3.
Makes me wonder if this engine could make a cool horror game? Have something that hunts the player, moving more slowly than them but along geodesics.
Well, the game might not yet exist, but that's basically the concept behind H.P. Lovecraft's Hounds of Tindalos :) Not nearly enough is done with HPL in my opinion...
Ok. I don't know if anyone else has thought of this but what OP said reminds me of *Hunt the Wumpus*. Some one should make a version of it in positively curved space instead of negatively only for the fact that positively curved spaces are by nature finite.
I want to play that! TAKE MY MONEY!
This was nauseating thank you
weakling
YOUR WEAKENED LIFEFORM STATE ASTOUNDS ME...
Imagine wearing the VR. Now THAT'S nauseating. And I've never even used one of those.
i only have one problem: as a non-matematician, i sometimes wondered whether the things you explained were only due to this program or due to how such a space would necessarily behave (the head-spinning stuff, especially.)
The head-spinning effects (parallel transport and holonomy) are a result of the mismatch between the euclidean space we live in and the curvature of the simulated space. One could write a program that doesn't have these strange effects, but doing so would necessarily introduce other strange effects. I think that the way we did it is the most natural way to do things.
thanks for the fast answer
I'm thinking of it like Infrared and Ultraviolet. We have to have a machine that understands it translate it back into what we know
@@cyanimation1605 I assume it's something like this too, but I have no idea. I'm guessing it's something like when astronomers record data from the sun and then pitch-shift the "recording" into audible frequencies so we can hear it as "music." There is no "sound of the sun" per se, it's data converted into audio *_we can perceive_* as sound. Those "conversions" likely wouldn't even sound very cohesive to animals with different hearing capabilities, like a cat, dog, or bat. The frequencies would be in odd places for their hearing range.
If you move your head in a certain way and the floor is now on the ceiling, then you haven't moved the floor, you have moved your head. The floor now appears to be on the ceiling because your head is now upside down.
How did your head get upside down if you didn't rotate it? It has to do with navigation, thusly:
If you walk forward into the cube in front of you, then shuffle to your left, then you haven't changed the direction you are facing in, you have changed your direction of travel (90° anticlockwise)
change it again and walk backwards into the cube behind you,
then again and shuffle to your right into the cube that is there. If you were in Euclidean space, then by now, you would be back where you started and still facing in the same direction as when you started, but you still have two more cubes to go.
Walk forwards into the cube in front of you.
Shuffle to the left into the cube to your left. NOW, you are back where you started, but you are facing in the opposite direction to the one you were facing in when you started.
Similarly, if you could climb up into the cube above you,
then shuffle to the left into the cube to the left,
then lower yourself down to the cube below that,
then shuffle to the right into the cube that is there, then you would not be back where you started.
Then climb up into the cube above you,
then shuffle to your left into the cube that is to your left. NOW you are back in the cube you started in, but you are upside-down.
This is the journey your eyes would go on, if you were to observe someone in front of you, making such a journey.
And that is how your head ends up upside down.
Instead of VR, a platformer game in such a space would be funny to try.
There aren't a lot of non-euclidian games out there. Most commonly used game engines can't render true non-euclidian space. ( although obviously this one can lol )
Monument Valley is a good example. It's basically MC Escher style puzzle mazes. Impossible shapes and all that.
funny its an understatement
Imagine Game Grumps playing that game, and having an existential crisis
MY BRAIN
IT TREMBLES!
Said your brain
oh damn. i could only really understand what's going on when you move your head like that when trying it for myself in the web version you guys put out. i thought it was a VR calibration thing you guys were doing to move space, but apparently your heading depends on your position inside a cube. two perfectly parallel lines diverge with distance from the source while still being parallel. this is so fascinating.
"Where is the bathroom?"
"Just take 5 turns to the left one u get past that door"
"what the ####"
But the room 5 cubes to your left is also the cube that's behind you, so it would be better to simply turn around and walk forward
@@maxxcastillo9347 that's the joke..
r/woooosh
That head-rotating mechanic looks trippy from the inside and hilarious from the outside.
Just tried this on the Vive and it is pretty interesting.
You can have a whole cube that looks like it is close enough and small enough that you can grab it, but the closer you get the further and bigger it appears until it is big enough to be a room.
Also, maintaining my balance while walking around was pretty hard. I constantly felt like I was tripping on air.
I think it would be pretty interesting to have a mode with different shapes of different sizes at varying distances which would make this much harder for your mind to comprehend the space..
Watching you walk deep into the corner, I suddenly realized how a Hound of Tindalos works.
I know right?! I immediately thought of that as well. As soon as he zoomed into that corner and then popped out into the corner of another Cube. Makes me wonder how Lovecraft and contemporaries came up with this crap. I know absolutely nothing about mathematics and or geometry/whatever the hell this is..?¿
obnoxiouspriest The human mind has a sort of intuitive grasp of these kind of things. It is just never nurtured.
He's trapped in the 90s screensaver dimension.
5:24 - And here you see the Segerman in its natural habitat performing a mating ritual through a hyperbolic transmission
This video is infinitely more entertaining if you only see the left side.
Thank you for this incredible visualization!
I did not realise all these highly varied videos I've seen were all by you! I saw your scissor NOT Gate video just yesterday, I didn't know you made this video too!
10/10 would seizurely puke again.
Because of your mind blowing videos, I have an appreciation for geometry that I did not. Thank you
Oh nice to hear About Vi Hart being on the collaboration. I miss her videos.
Wow such cool visualizations! Thanks for sharing!
I think the true art of this video can be found in the amazing display of intelligence involved in making this disorienting VR demo contrasted by the appalling lack of intelligence involved in demonstrating it next to a glass wall 10 stories up with no railings.
That's computer nerds for you: We're really good at making computers do things, but we have to free up some space and most of us end up deleting CommonSense.cpp from our hard drives.
That was great! Thanks for sharing
Really incredible work! Thank you for sharing.
pretty cool. I could see some amazing games and learning materials made out of this in the future
Good stuff as usual Henry. Should get together and make some cool VR experiences sometime.
What would it feel like to be in such a space? Would you feel some sort of anti-gravity pulling you apart in every direction or something of the sort? And what would happen if you tried those parallel transport movements with a real body instead of a floating camera, with your feet attached to some solid part of the structure? Would you feel a torque on your head? Assuming some sort of gravity-like force aligned with the "floor" of each cell, would a human be able to walk in there without tripping or would the parallel transport keep twisting the feet too much on each step? Would our balance sense even work right with these movement induced torques?
There would be a noticeable effect, depending on your size relative to the curvature. As you walk forwards, your head and your feet move along geodesics that diverge, so you would feel an effective force pulling them apart.
Hm, I hadn't thought about it that way; so all motions would cause a stretching force on objects? Would that make solid objects spring back to a fixed position, or would it just produce a drag effect even in a vacuum? What about the behavior of liquids?
*Caution:* do not try to enter any non-euclidean space in real life. You would die.
No rigid object can transition between spaces of different curvature and survive intact, since the ratio between volume and surface area would be forced to change. To visualize what would happen to your rigid sub-parts (aka "bones") if the curvature of the space you're in were to decrease to make it hyperbolic, think about what happens if you take a hemisphere (a 2d object with positive curvature) and force it to become flat (zero curvature).
Matthijs van Duin, how do you explain humans being able to move from the curvature at the surface of Earth, to the curvature of orbital altitudes, and then to the curvature at the surface of the Moon, and all the way back to Earth?
I had to think a moment what on earth you were talking about, but then I realized you're talking about the curvature of spaceTIME. I don't know enough about general relativity to say much about this topic, so I'm not even sure whether the metric when restricted to a spatial slice (in, for example, the frame of reference of someone standing on earth) even has non-zero curvature at all. To the extent that it does, it is negligible on the scale on humans. The world we experience is flat, not curved.
That was a very well done presentation, thank you.
dude this is like a virtual reality dmt trip just very tuned down. Very cool stuff
This is why we need time travel: to show VR to Classical Greek mathematicians
could somebody explain what the actual fuck is going on here? its like... 3.5d or something
You're almost going in the right direction, guessing at "3.5d". Imagine drawing two straight parallel lines on a piece of flat paper. As long as the lines started parallel, you could extend them out forever and they would _stay_ parallel - never crossing or moving apart. But if you tried drawing two straight parallel lines on a sphere, you wouldn't be able to - the lines would eventually cross over each other. A sphere is like a 2D surface "curved" through a third dimension. On a sphere, some of the rules of "flat" geometry don't apply, or work differently - like how parallel lines behave, or how the angles of a triangle add up to _more_ than 180° depending on how big the triangle is. You can also have a 2D surface that looks kind of like a saddle, that curves "opposite" to how a sphere curves - initially parallel lines will veer _away_ from each other instead of crossing like they do on a sphere, and triangles will add up to _less_ than 180°.
These VR demos look and behave so weird because they show a 3D space "curved" through a _fourth_ dimension. Specifically, these are "hyperbolic" spaces - 3D spaces that "curve" the same way a 2D saddle "curves". Similar rules apply - such as parallel lines veering away from each other, despite being perfectly straight all along their length. This leads to things like being able to stick more than four 90° angles around a point (how many depends on how _much_ the space is curved), so you can walk through more than four cubes going around a single vertical axis (as shown).
Another way to think about it visually, from the inside, is that "horizontal" distances in hyperbolic space are "bigger" the further away from you you look. If you made a circle and measured the radius vs. the circumference, you would notice that the circumference was _larger_ than 2 * pi * radius. In essence, "pi" is not constant, but _increases_ as the circle's radius increases. This is why things look "squished" or smaller than expected as they get further away - the angle of the chunk of space you're looking at is getting bigger with increasing distance, making everything in that space look smaller compared to how it would look in the "flat" 3D space you're used to.
Fantastic explanation... Thanks!
HaloInverse that doesn't make sense. Non-euclidean space has nothing to do with 4d; it is still 3 dimensional; the inherent properties of a non-euclidean space differ from euclidean space; that doesn't magically mean another dimension is in any way involved; it simply means that thing behave differently as the properties that make up the space are different; it is still 3 dimensional...
And what's with the 2d saddle comparison? You're better off saying it's a 3d saddle, since there is obviously depth involved.
Technically, you're right - non-euclidean space is not necessarily 4D, or any particular dimension other than "at least one more than the space itself". It'd just easier to describe non-euclidean spaces simply with visual metaphors, rather than breaking down the math of manifold classifications and Lie groups. If someone can do _that_ in a brief TH-cam comment, more power to 'em.
Yes, the space _itself,_ and the objects in it, is/are still completely three-dimensional. The properties of geometry within that space can be defined by the curvature of that space _through_ an additional dimension.
There is no "magical" involvement of higher dimensions, any more so than how words have certain meanings is "magical". The higher dimensions are used as part of the _definition_ of the properties of the space.
A saddle-shape is indeed three-dimensional, as you say, but the surface _of_ that saddle is two-dimensional, like paper. It's just bent in a way that normal flat paper _isn't._ Describing how that 2D surface bends is easiest in 3D.
+hans wurst Confusing wording, maybe - but I don't think _wrong._ Have another look at your globe - the lines you're referring to (parallel to the equator = lines of latitude) are actually not straight at all. If you look at a _small_ section of one line of latitude, it may _look_ straight, but if you try to roll a ruler (or cylinder) along a latitude line (without sliding it!), you'll find that you have to keep _turning_ the ruler to stay matched up with the line. The closer to the poles you get, the more obviously the latitude lines curve. The only "straight" line of _latitude_ is the equator itself. (The lines of _longitude_ are all perfectly straight - but they all cross at both poles, so they're not "parallel".)
Another way to test this is with some string. Remember that a straight line connecting two points is the _shortest_ path between them. If you lay a string between two points on a line of latitude (other than the equator!), then pull the string _tight_ across the surface of the globe between those points, you'll see the string "bend" away from the line of latitude. In fact, you'll be pulling the string _straight_ relative to the surface, and showing that the line of latitude (which follows a longer path than the tightened string) is _not_ straight by comparison.
This is also related to why long-distance airplane routes often show up as "curved" on maps - the actual path is usually as straight as possible (gotta save fuel to maximize profits!), but when you "unfold" the globe onto most flat-projection types of map (with straight and parallel/perpendicular latitude/longitude lines), the airplane's apparent path is "bent" into a curve on the map by distorting the lines of latitude into straight lines.
You got to work with vi Hart omgggg lucky dog…I wish I saw more of her nowadays but it seems she’s kept busy!!!
This reminds me of Hyperbolica, a game in H2xE. Cool to see other TH-cam channels talking about it
I wonder how the following system would work to solve the problems with floors in H3: take some plane P in H3, and make the real "down" direction always perpendicular to P. This way, if your eye level in the real world is fixed, you will move on an surface equidistant to P in the simulation; if you crouch, you will move on another equidistant surface; if you crouch. move 1 meter, get back up, and move 1 meter back, you will end up in a slightly different location, contrary to H2xE . The world will appear to spin as you move (this effect appears in the Ivory Tower in HyperRogue which is based on a similar assumption about gravity)-- but this could be explained by the weird gravity, or minimized by assuming that the "natural" eye level corresponds to P itself.
Alternatively, horospheres could be used instead of planes and equidistant surfaces. This way, the simulation would be uniform in all directions (strange in all of them rather than less strange closer to the plane), and a quite regular tesselation consistent with gravity could be used (for example, use the shapes represented by cubes in the upper half-space model, with each cube adjacent to four cubes on its sides, 1/4 cube on the lower level and four cubes on the upper level).
We have thought about this kind of trick for fixing certain things. It's a bit of a cheat - the effects of movement will not be really "correct". But for some applications, e.g. tracking your hand controller relative to the headset, we will have to do something like this.
Well, I would say that using H2xR is a bit of a cheat too :) We have to cheat in some way to get gravity consistent between the two worlds.
Imagine the Little Prince walking on a great circle around his tiny planet, his head would obviously rotate and so will the stars in his vision, but he would not feel it because it will be always at the same angle to gravity* -- I think the feeling in H3 VR based on this idea would be quite similar.
* Not sure whether this is physically/physiologically correct, but it seems at least a bit reasonable.
corner turns out to be infinity
I'm in love with this! So cool!
this would make an amazing video game concept, VR or not, honestly.
Nobody:
August of 2020:
"Allow us non-Euclidian planes to introduce ourselves."
MY HEAD HURTS
they seem like they would be very fun to be around love it
That's really cool.
I like how VR enables better demonstration of extra-dimensional stuff.
What fresh hell
I have enough scientific acumen to appreciate the mathematical and programming genius behind this; but near zero spatial reasoning, which means I still have barely a clue what is going on... XD
Fledhyris Proudhon take a differential geometry course (or just audit one lol) and it will be more clear to you. I just finished taking a General Relativity course and besides being able to do the math, I have near zero comprehension on how to envision these. Personally, I’m really more concerned with how to take a metric and find length, volume, ..., all the way up to the Einstein tensor so that I can attempt to solve the non-linear partial differential equations but it’d also be nice to have some image in my head to guide me.
My problem is that I can envision all of it, but when it comes to solving it, my mind bounces around with so many visual simulations, that the math just doesn't make sense.
I think the lack of focus is due to ADHD, which I was just prescribed Adderall for. Hopefully next semester works out better now.
Just imagine a world where the cubes are actually trapazoids widening as depth furthers and light travels in a funnel as it returns to the viewer but they viewer assumes light returns in a straight path.
The weight of the funnel effect is dependent on distance from a point and forward velocity is directly proportional to funnel effect.
As with most of these theories they cannot work in standard 3d solid space and are more just fancy math.
Throw it in the string theory basket, It may get you a doctorate but really its all based on niche ideals and assumed states. When queried provides a paradox and as such cannot be a true theory.
edit: addition
You could assume a niche scenario as a voyager traveling through space with gravity distorting light allowing a view similar to this effect however, as the view sees this result his view is distorted, in reality these objects are placed as the basic laws of 3d space define.
Opposite problem xD
Very interesting video. It was also funny watching your weird moves on the left 😂
Thank you so much TH-cam for recommending this 3 years after it was uploaded.
Could you use these techniques to pack a larger VR environment into room scale VR?
There is more space near to you than there is in an ordinary euclidean environment, but the geometry is fundamentally different - whatever environment you want to explore would have to be designed for this geometry.
The virtual floorspace that you can actually walk on, is one and a half times larger than the physical floorspace.
You could achieve greater virtual floorspace by teleporting to places that you can see outside the windows, portals, and having sections of the floor slowly drift like rafts. Not fast enough for you to feel the movement.
Or stand still and have a giant conveyer belt, bring you rooms to step into.
Is it possible to represent the cubes as though euclidean, even when far away?
The effect, in my mind, would be that you couldn't see the 6 cubes at 8:15. The 'pale blue' and 'salmon' cubes would look like the same cube, and the white one would be completely invisible, until you moved into either of the adjacent cubes. Going inside vertices seems like it wouldn't work anymore, and you wouldn't be able to hide the edges (as they would show the change between distant space, but it may also be much easier for new people to understand it.
P.S. Vi Hart brought me here
You're describing something else - there's no choice in how the geometry is displayed here, once we have decided that we are in H^2 x E, that light rays travel along geodesics, and that the tiling is {4,6} in the H^2 direction.
Oh, I hadn't considered that the reason it looks the way it does is literally because the light rays move like that, as though through a space-warping lens. Thinking in this new way also helps me understand why things can warp the way they do without actually changing.
You do say, though, that the assumption is that light rays travel along geodesics. Is that assumption able to be broken? I imagine you would lose the infinite regression to the vertices, but you would still be unable to walk around it.
I think my issue is that I don't understand why light doesn't travel straight through, obeying the 90-degree turns, but rather seems to arc, causing that extra-fast convergence at a distance (re. the parallax at 10:05).
It's not through a space warping lens. Space itself is "warped" relative to ordinary euclidean space.
If you remove the assumption that light rays travel along geodesics, you have to replace it with something. If the camera is at some point in space facing some direction, you have to tell it what it sees. Light rays traveling along geodesics is a natural choice, but there are others. See arxiv.org/pdf/1702.04004 for details.
Thank you for the link! I'll go read through that. I really appreciate your quick responses, and I can't wait to see what else is in store!
@@henryseg i think the thing he talked about is like, if exist a geometry that appears that he is using those seamless portals between the cubes when it is actually the space that is curved
I was always worried he would trip on the chord. Awesome video
I didn't know that the corners of each cube are euclidian planes in H3. This is mind blowing!
The floor problem wouldn't actually be there in hyperbolic space with gravity and floor, since it would just induce a force on the body and the body would balance that, thereby constantly realigning to stay upright.
I need to do this while on DMT
this is a tame version of DMT, i always believed it shows you higher dimesions
I don't know about you, but my vision is more or less completely gone while I'm breaking through on smoked/vaporized DMT. It's basically what we're seeing in this VR except vastly and infinitely more detailed and complex, along with a faded or completely absent sense of self, not to mention literally every other sense is replaced with the visual, audio and tactile hallucinations, completely. What would be the point of trying to put on a VR headset when you can't see what's actually going on a foot in front of you? I doubt this VR could make much of a difference to a full on DMT trip.
I feel like this would be most gratifying on something that doesn't completely destroy lucidity and sense of self like DMT does. A phenothylamine or low(ish) doses of LSD. Something like 25i-nBOMe would actually be really cool in this kind of VR, because on that drug you're still aware of where you are and what you're doing, except a massive amount of visuals are projected onto what you already see, at least that's been my experience. So on that drug this VR would just be seriously enhanced and it would be neat to be able to analyze and understand how your psychedelic influenced brain interprets the VR visual reality. A high dose of pure MDMA or 2C-B would be fun as well, mostly because as with most phenothylamines (again, this is just my experience), you retain a certain amount of awareness and lucidity that you would need to actually appreciate what's going on with this VR, but those drugs interact particularly well when witnessing bright and diverse colors - in general I get the feeling that pheno hallucinations mostly have to do with greatly enhancing and warping the bright colours that you see, whereas tryptamines have less to do with the actual external stimuli and more to do with what's happening in your head. Hell, even a heady, THC rich cannabis would be a good fit in terms of making a fun VR/drug trip experience. But DMT totally and utterly shatters your world, sense of self, and every bit of genuine, physical visual stimuli just gets crowded out by the drug. I don't think I could even be aware of the fact I'm wearing a headset during a DMT trip, let alone use the VR to walk around and explore. The great part about tryptamines is that they turn the mundane regular world into a very crowded and intense hallucinogenic landscape, that is if you haven't taken enough to be totally turned inwards and unaware of anything outside of the trip in your head. I've always found that vast open spaces provoke more beautiful visuals and trips in general during a tryptamine high than confusing colors on a screen. The more tiny details your brain has to work with, the more it's able to conjure up detailed hallucinations. Sharp, simple shapes and colors on a screen couldn't really compare to an open field IMO.
I know I'm taking this comment way too seriously, but it's often that I see people say things like "imagine this on DMT" and it makes me wonder if they've ever really broken through or smoked DMT at all, because when you're in a full on DMT trip, there's literally nothing else you can do other than be in the trip, and it's plenty exciting/terrifying/complex, so much so that even a seasoned regular DMT user wouldn't or couldn't really be looking for external ways to stimulate an already off-the-charts stimulating trip.
I already do this, and so much more, on DMT, without more technology than the DMT. This might be cool on the comedown, but it would really be better for LSD.
Why tho? You get the most out of dmt when your eyes are closed.
I don't think he means 'enhance' this experience with DMT, but rather 'recreate' the experience during a DMT trip.
I'm less concerned about the infinite cubes and whatnot and more concerned that he is using VR that close to a floor-to-ceiling window in a high rise apartment.
Lose your balance once and you fall to your death.
I'm sure the window is fairly strong
@@n1ghtblur Would you bet your life on that?
@@nerfzinet gimme the manufacturer's spec sheet and I probably would
You're definitely overthinking the possibility of that happening. He'd need a decent sprint just to smash through the window (any window really) to break completely through for his body to tumble out.
Basically it won't happen to any normal human being that has a fraction of awareness, I have a VR setup like this, it's pretty easy to remember your walls.
@@Tjerty Yeah like, it's like people don't know light isn't the only thing we use as guidance to move around.
Really cool concept
Cool, can't wait for the first VR game with this!
But is this space continuous? Can we avoid using boxes, and just have a room where you can turn around 540 degrees and look into the same spot?
Philip Polkovnikov Yes the space is continuous. The cubes are just decorations - they could be replaced by anything. But note that I’m not just turning on the spot by 540 degrees. The motion forwards is necessary. A better way to think about what happened is that I walked around a right-angles hexagon.
But how small that hexagon could be? Wouldn't it work with a hexagon of infinitesimally small side?
Edit: Oh, you mean it is locally continuous, but it doesn't preserve topology over scaling?
Edit 2: I had a dream where I've been in a room with 8 right angles more than 10 years ago. When I woke up, I tried to find any good axiomatisation for such a space and failed horribly. You show that at least something similar is possible, but I'm very confused at how such a space behaves. Even when I imagine a curved space as a surface of hyperboloid.
Philip Polkovnikov Unlike euclidean space, hyperbolic space has no scaling transformations. You can’t make a right angled hexagon smaller without changing the angles. Having said that, there is a choice in this simulation of the relative scale between movement in euclidean real life and movement in the hyperbolic simulation. That choice determines how big a square I need to walk around in real life to trace out a hyperbolic right angled hexagon.
Oh, the bigger the "radius" of the room, the bigger is the sum of angles of its corners. Now I understand it. Thanks!
Philip Polkovnikov I think it’s the other way around actually. The hyperbolic triangle with the biggest possible area is area pi, and all of its internal angles are zero. As you make triangles with bigger angles, the areas of them decrease, until you approach angle sum of pi (ie a euclidean triangle) as the area goes to zero. This is consistent with hyperbolic space feeling the same as euclidean space if you don’t make any large movements.
Why would you ever want a floor?
To leave a breadcrumb trail to get out...
To _put_ things on, you philistine.
This h3 hyper whatever is the coolest app ever!
Beautiful!!!
So this would be a truncation of the paracompact tiling {4,3,6} then?
Yes.
What does that mean? Is that how curved the space is or what?
Schläfli symbol
Ah so I looked that up, cool system, so does the three numbers instead of two mean they were walking around on the 3d surface of a 4d object?
More or less, yes. I would say that the three numbers mean its a 3D tiling, using 3D tiles. There's no need to bring in a 4D thing that it's the boundary of.
I have a question: In normal space, we have a 3 Axis of rotation. In higher dimentions, do you have more than 3 axis of rotation? I can still only imagine turning around in 3 axis, even in this higher dimentional space shown here.
This is still 3D, not 4D, but with different geometry from ordinary euclidean 3D space. But to answer your question: rotations are better thought of being in a 2D plane, rather than around an axis. In 3D (x,y,z) space, there are three choices of planes to rotate in: (x,y), (x,z) and (y,z). In 4D (x,y,z,w) space, there are six choices of planes to rotate in: (x,y), (x,z), (x,w), (y,z), (y,w) and (z,w).
So 5D would be 10 and 6D would be 15?
Hextator Yes, precisely, it’s “n choose 2”.
This is incredible!
Wow, great program!!
Fun fact: non-Euclidean geometry is geometry on a curved surface.
Bonus: as one of the other commenters mentioned: this simulation is made out of teleporters and multiple maps
no, this isn't codeparade's thing
So the first space is {4,3,6} and the second one is {4,6}*{}?
ComputerCat Yes.
That was incredible!
The possibilities are rather profound.
Bigger on the inside?
Smaller on the outside
equal-er in the middle?
Can you write non-euclidean music?
Non-real time signature.
This is why VR has my interest. He is literally demonstrating higher dimensions with this program.
Its still only 3D. No higher dimensions involved.
This isn't much different from any other 3D representation, it's just wrapped around your field of view
I can imagine the cube rooms that branch into more cubes in every direction being a cool visual representation of the infinte parallel universes theory.
How did you not vomit everywhere?
It’s surprisingly non-vomit inducing. If you move your head just a little, everything feels like standard euclidean space, so it’s no worse than other VR experiences. And my reptilian hind-brain doesn’t seem to care about the larger scale distortions.
He vomited inside the 4th dimension you just cant perceive it.
I think the better question is, "How the fuck were you even able to keep up an active narration while in that space?" Wouldn't even just a simulation of that kind of space have some sort of harmful sensation effect on your mind? Are you sure your brain isn't starting to rot from being in a literally inconceivable space like that?
I think that as such immersive experiences like this become more and more widely available for people, there will be people who lose their sanity. VR games like these will have the fifth dimension version of jump scares. I can't imagine what it will do to people.
either all that or everyone will be fine and games like these won't on a scale any worse than a bad acid trip, but I sure do hope that it's the former.
wow, what a load of bull, paulo
seriouslyWeird it does kinda look sorta r/iamverysmart, doesn't it?
My brain hurts
Fantastic! Magical! I want this program! Thanks for sharing, very nice video... That is the illustration of pure MATHS, the elegant universal language that connects all of us! 🙏🏾 📖🕊
The vfx artist must have been scratching his head after receiving a video from this madman rolling around on the floor talking jibberish, well done on making bim look sane lol
*Doctor Strange.*
I don't understand.
04:20 the dynamic of correcting the camera rotation resembles how a cycloidal gear works.
You could create a pretty decent simulation of the universe crudely depicting all known space's appearance. Especially with infinitely defined vertexes. Closest representation of it's expansion, most devine perspective, best tool to better comprehend the void.