Spherical Geometry Is Stranger Than Hyperbolic - Hyperbolica Devlog #2
ฝัง
- เผยแพร่เมื่อ 22 พ.ค. 2024
- A quick look at spherical geometry in 2 and 3 dimensions and why it looks so unusual. This is part 2 of my Hyperbolica Devlog series, and both geometries will be in the game. I promise I'll get to some actual game development stuff in the next video!
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A mathematician builds a fence around himself and declares that he is outside the fence, thus all the lions are contained.
He has to save people who also end up inside the fence though. It's not easy to save 7 bil people.
Mallory SF idk man, Jesus seems to be doing an okay job in that department.
@@nolan9101 Butbut... what about Keanu Reeves?! I thought...
"Here I added a fence to divide the level in half" *builds a fence circle around him*
thank you❤️😂
Imagine playing first-person shooter in this environment.
puke city
Far away opponents will be super large
if you shoot a bullet and it hits nothing itll hit you
you would never be safe from their shots
motion sickness
“But now lets go to the opposite side of the level”
**Reality starts to melt**
*Starts to see in higher dimensions*
@@thatoneguy7419 this is somewhat random but also kinda true
OKAAAAY😅🙂🙃😉😟🤢
This comment has 666 likes... makes sence.
@@rohankishibe6433 not random nor true
In an FPS :
"I'll take cover inside the house!"
"Inside? Are you sure about that?"
@Ebola you don’t get it
if you make a wall around the equator what are you trapping
@@official-obama uH
@@pogpogger9497 what? i have no memory of this
'Bro come rez me I'm inside the house.'
'Dude I'm inside the house.'
'Bro you're outside the house I see you though the window'
'...My bad'
*he promptly got shot by a camper on the opposite side of the map, it's still a mystery how he missed to see the guy when his face with covered over the screen*
pu55y5l4y3r443: lol u suck
@@official-obama you're trapping the meaning of life intself
Imagine living in a world like this and never knowing of the existence of the sky.
Maybe we do. But we have of cource no word for this 'sky', because we never have and never are going to 'see' it. Math and science could be indirect tools to experience some effects of this 'sky'.
Except we literally don't. As this video shows, living in a universe with positive spacial curvature is pretty obvious.
I think you were trying to say something profound but lost track of the fact that we can, in fact, tell the difference.
@@Cyrinil142 Living in a world with extreme positive curvature is obvious. It is not obvious, if this curvature is beyond what we can measure so far. But anyway there are lots of unsolved problems in modern physics and therefore multiple potential 'skys' that we don't know about. And of course I dont count in 'skys' that are beyond any possible physical measurements.
Just like "UFOs" arriving or popping out of their dimension into ours to our planet say "imagine these 3D people, not perceiving our heaven above, they only see the sky and stars above".
There is no sky because you cant look "outward" from your sphere. You can only look above you and see the opposite side of the sphere. That's why this looks so weird
Diverging light-rays be like "Bro, come back, I miss you"
Diverging is in hyperbolic geometry. In spherical geometry, they converge, and any two straight lines intersect exactly twice.
@@lev7509 The joke is that they start out diverging and then converge.
@@wessmall7957 Oh, that's smart.
HOW DID THIS HAPPEN?
@@lev7509 I bet someone's going to reply to you with a "r/wooooosh".
There’s something so comfortable and cozy, while eerie and terrifying about this spherical space. I can’t quite put my finger on it. It still blows my mind today.
I think becuz is an claustrophobic space geometry, if a person lives there, he could only walk around and use what is on the sphere, it cant infinitelly go an way and Never come back and explore new things becuz he is trapped inside that place, on the 3D surface of the 4D sphere
I find the way the objects get larger and smaller to be terrifying, and just the way things move in this in general.
Blursed space?
kid named finger
This is my vibe
2:37
The roof is above us,
The walls are around us,
But not in the way you'd expect.
Deep lyrics man.
r/Im14andthisisdeep
And the Impostor is among us.
Which Tool song is that?
@@avalonwillowbloom1590 such an underrated comment lmao
Just saw Tool last night too.
you say that will eat us
but I just know where your mother might find us
if we won't produce the
Euclidean geometry: Farther away objects look smaller
Hyperbolic geometry: Farther away objects look WAY smaller
Spherical geometry: Farther away objects look smaller, until they don't
it's like a straight line in Euclidean, a hyperbolical sine in Hyperbolic and a sine wave in Spherical
kinda obvious when you look at the projection matrix.
Makes sense
Yep
Fun fact: If you go to Endia 🇮🇳 you'll see lots of diirty disgusting stinky slums
When you install sketchy Minecraft shaders
where did you find these i only found 4 of these types of shaders
@@vii-ka MiningGodBruce made a few once, there were some others that are not worth mentioning but his are the best.
Wait, this makes me wonder, what would hyperbolic minecraft look like?
@@catoticneutral well for starters, there would be 5 squares at every corner instead of 4. also it would basically look like what hyperbolica looks like except with cubes.
When you build Minecraft VR in Minecraft VR in Minecraft VR
This reminds me of the Russian sci-fi novel "The Inhabited Island" (1969, a.k.a. "Prisoners of Power) by Arkady and Boris Strugatsky (who also wrote "Roadside Picnic," on which Andrei Tarkovsky's sci-fi masterpiece movie "Stalker" was based). In this book, a cosmonaut lands on a planet where atmospheric refraction of some sort (it's not explained) causes an illusion where the land bends upwards in the distance, making it so there is no horizon. The inhabitants believe they live on the inside of a hollow sphere with a "world light" at the center, and find the idea that they live on the outside of a sphere and that there are other planets to be incomprehensible. Of course, this isn't a curvature of space itself, as in this video, but in the book the metaphorical implications (of a closed society and insular ideology) are what's important.
Holy moly that’s scary
Sounds great
my understanding is that venus actually has this to a small degree. the horizon looks like it curls up a bit and you're in a shallow bowl
I just watched the movie and it's amazing. Only problem is that it's only dubbed in Russian and German, so I had to watch it with subtitles
Very interesting, thanks for the heads up! I know what to read next 😁
I'm curious on what an intelligent life form that evolved in an environment like this would react to euclidean geometry, since their brains would be structured to understand things as getting smaller then larger and reversed above them. I feel it'll be more alien to them than spherical geometry is to us.
Ofcourse that I an unfair assumption
They'd be as confused as we are Wich is to say not alot since they would have done the same math as we have ,to understand non euclidean,
To understand euclidean
Saying they'd be more confused is like saying
A Russian won't understand french aswell
As a France person would understand russain
In truth neither of them would understand eachother at all
I think that is kind of overthinking. The thing that would be interesting would be: How would they react to moving in eucledian space? Since in spherical space, objects will experience a squishing tidal force as they move through space. They would freak out since their brains would evolve to being able to tell they are moving through said tidal force, meaning that in eucledian geometry, they have no way of telling if they are moving through space or not, this would simpky be normal for un eucledian dwellers.
I see where you're coming from, but I am not sure that's the case. Actually, I think we are just missing out on non-flat space experience in our world, but Euclidean space is always there. Locally, everything is Euclidean! Curvature is a global effect only.
“No, wait, are you saying the more I go this way, I will *NOT* eventually find my home again? What is this bizzare dimension??”
Imagine how much motion sickness this would give you playing in VR.
I'm ready for it. Give me the exotic geometry induced nausea.
This needs to be made now.
Game will com to VR too :D
Btw, imagine it, walking in straight life in real life, you would be in other room when in the game you get back where you started from and just made a circle around the house :D
Something like go around the world.
This already gave me nausea just from watching it full screen...
I could barely handle watching this on my phone are you kidding
CP, I really like my brain, please take it out of the fryer.
Yes, me too please.
Also love your videos :D
Oh hey! Just found your videos like 5 hours ago. small world :)
*video ends
Thank you.
Me: I'm perfectly being fine
Also me: fine
-please don’t call him CP-
The way I thing about it is spherical geometry is the inside of a sphere, not the outside. While it is not a perfect explanation it helps me wrap my mind around the space.
But really it is neither, just the surface. It is not the inside of the sphere above him, just the "north pole" of the hyper sphere. Below him is the "south pole", so he could not escape by digging, and by going straight down he'd end up on the opposite side just as if going upwards.
In the released game there is a well you can jump in to show that effect.
It kind of has that visual effect due to there being no sky. But I think what it really is is that you're confined to the surface of a 4d ball
What a mind-blowing effect
haha first under a verified youtuber
check mark = likes
What a casual response to this video
More like, what a stupid effect utterly annoying
@@Anudorini-Talah ?
literally my mind even hurt a little
"Yeah this whole place Is like a circle. But not like a normal circle, more like a freaky circle"
You are not on the circle, you are the circle
Piss off, ghost!
I understood that reference
@@theninjascientist689 Did you mean: *_ectoplasm_** off*
"
3:23
imagine the tutorial being:
"now to complete the tutorial, please get out of this fence"
“I’ve been playing this game for 5 hours and still haven’t gotten past the tutorial”
Hmm
Aaaaaand game over
RIP game journalists
just climb on top of the fence then
Ah, yes, my horrific abstract nightmares as a kid simulator, would play 10/10
1:48 For some reason, seeing you walk around this area with this music gives me nostalgic feeling. Especially at 2:43 with the illusion of the reverse house with concave floor and a massive area. I just don’t know why
FPS game using spherical geometry: headshotting the farthest player
Noscope players be like:
Oh wow, you're right! It would be so friggin' easy!
if you crouch they'd be an even bigger target, but there'd be a smaller window they'd have to be in to be zoomed in like that.
Keep in mind that aiming in and of itself is a headache to think about. Just imagine how weapon spread would work, when your bullets get bigger the farther away they are, however are still actually the same size.
Oh my gosh I didn't even think about that! The bullet would get bigger as it approaches the face of the guy you shot at that already takes a lot of space in the sky
“Are you fenced in or fenced out?”
We should build a fence across the equator just for this reason
You'd be fenced inside one hemisphere and fenced outside the other one.
@Lotfi Adam bro...
There is a comic strip
where people built a fence to protect them from wildlife and as their city grew it eventually became a fence to protect the wildlife from them.
@@absolutehuman951 I'm 14, and this is deep
@@conservativedemocracyenjoyer False.
"divide the level in half"
looks at the fence on the map.
The fence:
C I R C L E
Yes, usually you use circles to divide spheres in half. The equator divides earth in half and if you looked from the north pole, it’d also be a circle.
I challenge you to cut a sphere in half without using a circle.
@@bramvanduijn8086 The map isn't portraying a sphere. The whole point of the demo is that it's showcasing a "flat" plane (Flatland) but in a spherical reference frame. The fence isn't a circle either, it's a straight line.
I know that it's like an inside out sphere
@@qaasi95 Not quite, the issue is defining shapes in weird coordinate systems.
'The formal definition of a circle is "The locus of all points equidistant from a fixed point called the center." To translate, that means all points (an infinite number) that are the same distance from the center.' (credit to google) Looking at the map, you can absolutely identify a point that is at the exact center of the fence (where the fence is about halfway up the wall all around). Thus, it is a circle.
However, it is undeniably straight within the coordinate system, making it a line, so you aren't wrong there.
But the Equator is also a line if you look straight down it as well as a circle centered on, well, the center of the earth, so there's no reason that I can see that it can't be both a line and a circle. (Although technically it would be a line segment at most because it does not extend infinitely, as evidenced by the fact that if you were to make a marking and follow the fence, you would eventually return to the marked spot and the fence is thereby not infinitely long)
this is how mario feels after eating all them shrooms
This game would probably be a neat educational tool, especially for encouraging people to studay maths at university
Or independent study, perhaps under a mentor who knows a lot already.
@@SonGoku-iw4zk which is arguably the far superior option.
Nah its just a way to get nausea
Baiting kids into university level math with some fancy trippy games. This just sounds cruel.
Bump
Imagine trying to play billiards in this world.
I guess it wouldn't be that different, since you have to get close up to the table to play. Unless you had really extreme curvature.
Imagine golf
I think it might actually be easier, because your shots would be more accurate.
There is actually a VR game "non-Euclidean billiards" by Jeff Weeks. It is quite cool, but I am not sure whether it is already publicly available. There is a paper in Bridges conference about it.
@@8bitMushroom it would be hard for us but to someone used to this kinda world it probably wouldn't be that hard
This NEEDS to be VR
Having binocular depth perception would be absolutely fascinating watching our brains truly try to understand these worlds
There's at least the "4D toys" or whatever it's called, not about perspective but about the 4th Dimension
vomit vomit blargh blargh blegh
The reverse perspective part along with the background music, is all like some dream I had a long time ago as a kid and it always makes me feel nostalgic.
I love the idea of seeing non-euclidean geometry like this. "Non-euclidean" is so often misused for locally euclidean spaces, but this is something truly alien. This is what HP Lovecraft was so terrified of.
Yeah, the title of his "Non-Euclidean Worlds Engine" video bothers me a lot because it's really just Euclidean space but with weird doorways and tunnels that put you in different places than you'd expect. But this? This is just something else.
No kidding. This is so freaky, so alien, it's the stuff of nightmares. I remember seeing distortions like this when looking through the curved glass of tanks at the aquarium and how unsettling it was. Also, much more recently, when playing Psychonauts, there's a small part when fighting the lungfish where if you go up to the edge of the battle area (the wall of water), the water hands appear to keep you from going outside the boundary. However, when you move away, they too move away--but instead of getting smaller, they get _bigger._ I don't think it was meant to be creepy, but somehow, the idea of something getting bigger as it gets farther just freaks me out. No wonder Lovecraft referred to strange geometries so much.
That, and miscegenation
The world we live on is by definition non-Euclidean all parallel straight lines eventually converge
In Euclidean space triangles always have an interior angle of 180° and only one corner can be 90° or more
On earth starting from the equator heading north to the north pole turning 90° going back down towards the equator and returning to your point of origin you have created a triangle with three 90° angles
@@deangeloenriquez1603 The world is a sphere, but it exists in Euclidean space. It is not spherical space. This is why when we travel in a "straight line" on the earth, we're actually curving around the surface, and it is visibly a curve. In true spherical space, you could travel in a straight line, but then if you moved perpendicular to it, it would appear curved--even though it would actually be straight.
This could be the scene for such a great short story/game.
Imagine someone wakes up one day, stuck in this world with one house, a pond, and a small grove of trees. Any direction they go they end up back where they started, not only that if they try to leave some area behind it only looms over them. Tired of the house? Even if they walked to the other side it weighs down on them from above like the demons of the characters past.
There’s so many themes you could explore and I’m so excited to see where you take it in the game!
In Hitchhiker's Guide to the Galaxy part 4, there's a guy named Wonko the Sane who comes to the conclusion that the entire world has gone mad and he's the only one with his head screwed on right. So, he does what any sane person would do, and builds an inside-out asylum, with the entire world on the "inside" and his home on the "outside." The book describes it as hadd to wrap your head around, but i imagine it would look some like 2:33
So, when the outside of the house seemed to contain us, I immediately imagined this is what the outside of the asylum looked like in Douglas Adams' so long and thanks for all the fish.
things I'd like to see:
- jetpacking into the sky to the other side of the map (you'd have to flip halfway?)
- a pole from one side to the other
- no floor, just an "asteroid field" like situation (you would see yourself massively?)
@@Painketsu if light can travel across, so can you
@securitycountercheck if the self is solid, that "objects at infinity" thing will be irrelevant, because all light will be blocked by one's own body
@securitycountercheck you can deal with the singularity (which is more accurately referred to as the "north pole" not the "center", thinking of the 2d example) by just having the gravity decrease to zero as you get closer to it (which is what would actually happen in such a universe) Of course the camera might need to flip abruptly, but you can solve that by having the camera be free when the gravity is low enough
@securitycountercheck @securitycountercheck if there is no ground, you could look in any direction to see the other pole. also you would see past it and see your own pole again, with you projected massively on it (inside-out in every visible direction). even weirder is that, ignoring the gravity generated by the floor, every point on the map IS a "pole" and has a corresponding opposite pole.
an interesting thought experiment would be to imagine the floor as a translucent membrane. at the gravitational poles (on both sides), the floor looks like a sphere. at the floor itself, it looks like a plane. now imagine it with two such membranes crossing each other perpendicularly... at the point they cross, both are planes, but there is also a point where one is a sphere and one is a plane.
@@LCTesla Maybe you could add the correct amount of fog. Vision will depend on the ratio "radius of the sphere" / "light dispersion"
This video makes me feel claustrophobic
There's no sky
Well, it is quite literally smaller than euclidean space.
@@durnsidh6483 but... the fact that there *is* sky but you can't see it .... odd
Well, it's a small world after all.
Me too, I felt really uncomfortable!
This is what flat earthers think a globe earth looks like.
I don't think so. It's more that they don't think... anythinf at all.
So... The sky does exist but person from this point of view can not um "experience" it? This is so cool and mind-blowing
𝓈𝓅𝒽𝑒𝓇𝑒 𝓌𝒾𝓈𝒹𝑜𝓂𝓈:
>running from your problems eventually makes them bigger.
>don't 𝓋𝑜𝓂𝒾𝓉 in sphere land, it is an enclosed space.
that is a good wisdom
ba ba ba
>switching to your pistol is always faster than reloading.
"100π-th" person to like your comment!
Well, approximately "100π-th" since
100π ≈ 314.1592 ≈ 314-th like
(Man, I just realized that I will take advantage of every opportunity I spot to utilize the new Math symbols locked to my clipboard. I can just paste without copying like "what!!") 🤓
And now we wait...
I just have to be patient,
I got this.
It's just a matter of time before the
"square root" of "something" comes up naturally in a conversation & I can be ready like:
"Ohhhhhhh, you mean √x right? I have no idea what 'sq rt' stood for; I was like 'is he trying to spell 'squirt?' Yeah, I get it, but now it's clear," (thanks to me.)
Omg I would sound like a major d**k wad.
(I'm doing it.)
Oh, wow... look at that: my new symbol got used; that was so unexpected and natural. 😀
(I recently broke up with my girlfriend; pasting that √ with 1 click was the high point in my day. She was such a foul mouthed little slut... I'm going to miss that the most.)😔
Sorry guys, I need a moment.☝️😖
😫→😭→😙💨 whew... oκ 🤧 I'll be oκ.
(these→ arrows are also new.)
edit :
"I sound like a major d**k-wad"
&
"(these→ arrows are also new.)"
@@Pete-Logos Yeah bro sometimes I just open my clipboard and all the
↑⇐←↦ℒℳℂℕℚℝℤ½¼∕⊥∥≪≫~ΓΔΛΞΠΣΦΨΩαβγδεζηθκλμνξπρστυφχψω⇒→⇔↔∈∉⊂⊆⊄⊈⊃∪∩∖∅∏∑¬∨∧⊕∀∃−±·×÷²³√∛≠≈≡≝≤≥°∠
fall out and I'm just like... W̶h̶i̶c̶h̶ ̶o̶n̶e̶ ̶w̶i̶l̶l̶ ̶g̶e̶t̶ ̶m̶e̶ ̶b̶i̶t̶c̶h̶e̶s̶ ̶t̶o̶d̶a̶y̶?̶?̶?̶?̶?̶?̶? Where's that one I need to comment on the paper I'm grading?
I would love to see DLC called Sphericala cause spherical looks so interesting
If I remember correctly, spherical geometry will be in the main game.
if you look closely in the trailer, you can see some stuff is spherical instead of hyperbolic. I suspect Hyperbolica just sounded cooler.
@@tobybug779. I imagine there are different worlds or something. Some of them are inside out, and some arent
@@tobybug779 I couldn't find it, timestamp?
Take a look at 0:08 this s spherical x and y with a euclidian z, which is the correct spherical counterpart to the H2xE space most of the game takes place in. They use H2xE because gravity in hyperbolic space is freaking weird, and might not even work
spheric geometry looking like those dreams in which you climb an impossibly steep road
This is beautiful, I was always curious about this idea but was never knew how to visualize it, like _really_ visualize it. You've both quenched my curiosity and stirred it up more. Thank you
This is like 360 fov but less tripping...
imagine spherical geometry with 360 fov
@@andrasfogarasi5014 either it looks like euclidian geometry or it becomes a monster
@@zuzka9061 If you just look up you effectively have 360° Vision across the surface.
Exactly xD
@@zuzka9061 would just be a moving map with you looking down
Me: watches a CodeParade video
My brain cells: *Adios*
Loved it
Underrate
Desde Chiquito de la Calzada se dice: "Hasta luego Lucas!". "No puido, no puido,.... cobbardee... "
"Are you fenced in or out?"
Yes!
Woah this is trippy. Well done on creating an actual interactive, 3d visualisation, looks super cool!! Had to subscribe!!
"are you fenced in or are you fenced out?"
idk, but the grass looks greener on that side :)))
nice. reminds me of Sir Ben Kingsley in Lucky Number Slevin: "I am a good man who does bad things. I live on both sides of the fence; my grass is always green."
0,255,0
@@tristenarctician6910 green?
@@SpaceMissile :)
@@tristenarctician6910 #00FF00
2:20 "Now lets go to the opposite side of the level" Spacetime folds in on itself, you pray to whatever the god is of this twisted world that your death will be brief
Death will be swift*
A brief death would have you die for a moment, then bought back again to continue experience the wild dimension!
@@deadgonk1 no it wouldn't
life is good! Brief would imply something happened only for a little while
@@marielikes2502 ah damn, you're right lol... It just sounded so wrong the first time
I'm so in love with this geometry. I think a multiplayer shooter in this kind of space would be extremely fun and interesting
I find this geometry extremely scary for some reason. It was actually kind of hard to watch this video all the way through because I felt so scared looking at the scary nightmare world
Ikr, I tend to be Carsick but the 3D Spherical Geometry World was way worse on the “Making me Dizzy to the Point I feel like Throwing up” Scale
Yeah, I have a fear of voids, and this is terrifying.
maybe claustrophobia but isnt a close space, in reality is a close space but not like inside a box, its much more like a tiny world that has limited space, but u only thinks is infinity becuz when u see at a side, u could see ur back
@@georgiangelov13 Yeah, it was strange my mind periodically said:
This is natural, but you're sick, throw up now!, and then
So if light goes this way this is actually simple to understand!
Then when it got tired
QUICKLY! PUKE NOW!
IMO its super claustrophobic, there is no escape and there is no sky
Me after eating the sugar I found under my uncle's bed:
🤣🤣🤣🤣🤣👍👍
Yeah, a sweet, yet _strange_ tooth. 😂
Personaly, my brain interprites this as being inside a concave sphere.
Is that not what it is?
@@RubelliteFae Not really. If it was a concave sphere in euclidean space, objects on the other side would look smaller rather than larger. Also if he were to dig straight down, he would end up in the surface at the opposite side, while in a concave sphere he would end up outside of the sphere.
@@thethievingmonkey Oh, I see. ty
@@thethievingmonkey
That what I think, except to I feel like there is a magnifying glass in the sky. Like a sphere.
Why did I feel hypnotized and my brain went all "fainting-goat" as my eyes got heavy and I almost fell asleep. I don't think I was ready.
An equivalent perspective, and one that's much more intuitive, is to think of spherical geometry as if you're on the inside of the spherical shell instead of the outside which is shown in the video.
Ohhh!
how?
Ehh, not really. It _kinda_ looks like that, but it's not really the same thing at all.
that's not how it works, if you were inside a spherical shell then it would just be normal euclidean geometry
and if you looked up you'd see the sky but that's obviously not the case
Meanwhile is parallel universe with spherical geometry : Euclidean geometry is so weird !!
Honestly, it wouldn't be so extremely weird. Euclidean geometry is just what spherical geometry looks like on a small scale relative to the size of the "universe", so it would just seem like you've been shrunk by some amount. And if the size of your perception relative to the size of the spherical universe was small enough to begin with, you wouldn't even notice a difference. It's entirely within conception that our universe actually is spherical...just very, very large (although cosmological evidence points against it currently).
Meanwhile in that same world: who’s Euclid?!
I'm just imagining a team combat game in a spherical geometry world... how could combat and strategy work when everyone is visible at all times? Could you get used to this projection? Very cool stuff.
Finite bullet speed or obstacles can make things more strategic, otherwise yeah you could shoot from anywhere to anywhere.
@SArpnt then people could shoot you from above, from across the level. i mean i guess that could easily be countered with rooves.
A battle royale where instead of the arena shrinking, space does.
@@WaterDroplet02 Though you could easily hide from a specific player by hiding behind nearby objects
more interesting is if you made a big enough space the mid distance from you would be too small to see but the farthest players from you would be very visible.
well assuming you did this style of ground/gravity set up.
when I first watched this, I was like "how badly could you get sick from this" and "isn't this is just walking around the inside of a sphere...?" but then I played that farm level in hyperbolica and after many migraines & hours of motion sickness later🤢 I realized that spherical geometry is still just another "flat" plane one travels on; it just didn't click until I experienced it.
Also, the wells and their interaction with each other blows my mind.
Menwhile, in a parallel universe with sferical geometry:
A man sees a video called: ecludian geometry is very strange
The man: what is this mess?
i've never had so much desire to play around in mobius-land, or kleinbottle-land.
Holy shit that would be like taking 5 acid tabs and taking a bath
That's a pretty neat idea actually. Imagine like a wraparound toroidal map but you got to walk through the same area on a different "side" before coming back to where you come from
Elliptic projective space works as well. It also has only one side, and you can move along a straight line to mirror invert the landscape and its inhabitants (or equivalently inverting yourself). At least it works for the elliptic 2d plane, in elliptic 3d space, i suppose things are merely flipped upside down when you return.
@Electro_blob I would say 8 forms of LOCALLY EUCLIDEAN isotropic 3 dimensional geometry, using universal covers only. There are various forms of LOCALLY MINKOWSKY curved isotropic geometries also, in 2 and 3 dimensions. Like the 2d plane i like to call the Dual Hyperbolic plane, of indefinite signature and constant negative curvature, shaped like a torus. Or its quotient space with the topology of a Moebius band, which is in perfect 1 to 1 correspondence with the Hyperbolic plane, when interchanging points and lines, and interchanging squared distances, and squared sines of angles with each other.
Going to higher dimensions than 3, there are more "flat" base geometries than Euclidean and Minkowsky.
The second I got this notification I stopped everything I was doing (eating lunch) and went straight here. This is the most hyped I’ve ever been for a game and I actually cannot wait until it comes out! Keep up the good work
I may end up late for work, but who cares when there's spherical geometry and Hyperbolica news!
Why would you need to stop eating to watch a video?
Henrix98 so I could watch it as soon as possible and then finish my lunch that I was eating at 3:00
I got confused for a bit because currently it's 11pm in my country.
I share the hype, beware not to burn out yourself still.
I would be terrified of living if our world was like this.
Euclidean space:
Apparent size is inversely proportional to distance
a ~ 1/d
Hyperbolic space:
Apparent size decreases _exponentially_ with distance
a ~ e^-d
Spherical space:
Apparent size is inversely proportional to _sine_ of distance
a ~ 1/sin d @ csc d
Huh, that's a good way to think about it. (I think it's more accurately 1/sinh(d) = csch(d) for hyperbolic space, but unless you're particularly close to the object then yeah it's basically the same thing.)
@@SSM24_ for significantly big d, the e^-d term in sinh d is negligible so e^d - e^-d ≈ e^d
however for small d it's more accurate to say a is inversely proportional to sinh d.
the earth isnt round, reality is
aCtUaLlY tHe eArTh iS fLaT
Close... It's Doughnut shaped ! - Homer Theory :)
@CrowGaming So close! Its actually a torus knot!
@@jumbledfox2098 Still not right. Its a dinosaur.
everybody knows the earth is an isododecahedron
1:40 "Are you ready to go one dimension higher?"
No,but do it anyway.
I can imagine a real funky platformer game like this
My friends dreams: I married my crush
My dreams: 1:49
Steam: "This game doesn't look like other things you've played in the past."
Me: 😂
👉 You’re fenced in!
👈 No you’re fenced in!
Life in a spherical world..
You're breathtaking!
We're perpetually fenced in!
props for the labrynth style music with the fretless bass, perfect :)
"Farther away objects can appear larger than closer ones."
Me: "ah, so *that's* how you make a TARDIS's interior."
I would love to see a much larger map in Sperical space...
Same, I feel it might be much harder to comprehend when it's this small.
Woah there's a giant beast out on the horizon!
Oh that's just my cat.
Why is your cat on the other side of the world?
There should be a shooting game like this. The creativity is endless
INCREDIBLE job with this!
Sphere geometry bullet hell games would be terrifying.
That bullet wasn't in front of you.
Alex Popov and yet it struck me in the knee.
@@Ratsos12 seems like you'll have to become a guard.
Huge props to Code Parade, he made a whole new code that could just have easily been its own game just to explain this concept.
It WILL be it's own game.store.steampowered.com/app/1256230/Hyperbolica/
boof
And who are you to tell me that this guy is joking when he could be simply not reading the description or watching the whole video?
Well I assume you're just a layperson on the internet then, so...yeah
I think the coolest part is that you can still tell that far away things are far away
the description of hyperbolic perspective makes me think it’d be excellent for horror games based around the more creepy type uncanny valley, while spheric geometry would be great for more “oh god that’s not x that’s DEFINITELY not x” uncanny valley
ok but isn't this like, almost EXACTLY how a black hole bends light around itself? either way, could be utilized in horror REALLY well lol
the corona formed by a black hole is just the light that reaches your eye. A large proportion of the light just falls thru the event horizon. Black holes don't really bend light around themselves, they just drag light towards them, and the rays that happen to be travelling tangentially to the event horizon go into orbit. It's a bit like saying the Sun bends the solar system and solar debris around itself, v strange wording.
The analogy is interesting though, because a black hole is an extreme "tightening" distortion of space, so from the outside "looking in" the geometry would appear spherical. Falling in, the very edge of the hole would represent a greater distortion, the dot of space opposite you magnified to infinity, while the infinity of space shrinks to a pinprick behind you. Cool!
It would be similar. Its what you would see if you could stand exactly at the event horizon and watch the light beams exactly circling around -- neither falling in nor escaping. Oh, and only for a non-rotating black hole with no charge.
Of course none of that is plausible in the real universe:
- You'd be spaghettified by tidal effects long before you got to the event horizon, never mind being able to stand on it/
- Quantum mechanics means the photons in those those light beams would eventually fall in or escape due to uncertainty (and new photons would join the party from wherever in space they originated.)
- Uncharged black holes are expected to be the norm (and we've so far never observed a charged one.) The universe as a whole has (essentially) zero net charge and there's little reason to believe a black hole would have a charge bias as it accumulates its mass. So that one wouldn't really be a problem. Phew!
- Non-rotation is much less likely though. I mean I guess on the absolutely grandest of scales, angular momentum should be zero (unless we want to assume that whatever caused the big bang had some pre-existing angular momentum that it fed into the early universe!) But angular momentum is a vector quantity (unlike charge which is a scalar) and the chances that the accumulated material all has angular momentum that exactly adds to zero is vanishingly small. AFAIK, we've never observed a non-rotating black hole in nature.
@@nicholasmitchell6025 Just a minor point: Rays that travel tangentially to the event horizon don't go into orbit, they go into the black hole. Photons can orbit around the photon sphere, 1.5 times farther out than the Schwarzschild radius/event horizon.
Also, I think it's pretty reasonable to say that 'black holes bend light around themselves'. It's very close to the technical explanation, that is, that black holes (and other massive objects, for that matter) warp spacetime so that null geodesics go around the object in space.
@Alexander M You're right! Tangential was a misnomer. But for your second point it's all a matter of perspective. This is more of a semantic concern, but I don't think it's accurate to say a black hole bends light around itself because it isn't an active pursuit. Black holes distort spacetime and a passive result of that is the "bending of light" (more of a straight line path in this curved space!).
Saying that light is pulled towards them was completely wrong, though, it's not appropriate to use Newtonian physics in a discussion about black holes (lol). Probably should have looked that one over, it was late at night though. Thanks for pointing that out
i feel like im being made fun of because I have no idea what yall are saying
lost you guys a bit after photons and it just took off from there
3:26 "Are you fenced in or fenced out?"
...
Yes.
i always come back to this video because it's just so magical. it reminds me of the final scene in the movie interstellar, when the main character looks out the window in the future and sees this surreal world where hills wrap around the sky and gravity is warped. i'd love to be able to simulate spherical realities too.
You're a great tutor. We appreciate you helping visual cortexes and concept cells. Thank you
Jesus this is so trippy, I love it.
I'm so excited to play it! :D
Fofo
ô rapaz
sim policial, é ele sim. quero uma multa de 40 mil agora nesse rapaz
Ué
O que vc faz aqui
"are you fenced in or fenced out" - like a box defined as excluding the universe. Your description immediately seemed casually familiar at the outset though, perhaps partly from playing a lot with incomplete convex mirror spheres. Fascinating stuff! But for some reason I'm imagining this sort of visualisation being used in dentistry... 🤔☺️😲
Damn the visualization is neat, but the eerie and calming music adds so much to the video, great choice!
This felt very comforting to me, like something out of my dreams. Maybe now I have an explanation for why they always feel like I'm both inside and outside - they take place in spherical space!
My dream my fifth dimension was nightmarish ‼️
. But it’s interesting to know others have had dreams of the fifth dimension spherical universe as well
Feel the same. Cozy little worlds.
I said "holy sh*t" out loud when watching this because it was so close to something I dreamed. Even the realization that I was inside and outside a house at the same time.
This makes me sick and dizzy. Imagine seeing it now in VR.
I would panic. When the first person perspective started I got chills already.
and seizures 👍👍👍🤦♀️🤦♀️🤦♀️
Imagine playing it in vr stoned.
3:27 "Are you fenced in, or are you fenced out?"
Yes.
This was so cool bro! Thanks for uploading! 👍👍
House: *flips inside out*
Me: _Brain.exe stopped working._
(ITS A JOKE STOP ARGUING ABOUT IT)
Actually it flips outside in
thank you for clarifying
@@RandomNameLastName811 CONDUsed ScrEAMiNG
@@RandomNameLastName811 It appears inside out though. What you are seeing is the outside of the house, but it appears to be around you
notice that the roof remains the roof is still right side up, relative to you, while the walls are upside down. And that you get out of being surrounded by approaching any given wall.
Can't wait for flat earthers to misinterpret this as proof of a flat earth
**GRABS SNIPER RIFLE; IM READY TO TURN PEOPLE INTO GIBBLETS*
it is tho!
@@SpaceMissile no it's not. you live on a spherical *object* resting in a *euclidian* space. this video is a demonstration of what would happen if *space itself* was spherical
@@benthomason3307 (feedest ye not the trolls! lol)
@@benthomason3307 If light was more strongly affected by gravity such that it was bound to the surface of the earth, would that simulate spherical space in that case?
I love to seeing more games and videos exploring or explaining non-euclidean spaces like this. It is absolutely mind blowing!
This would be so cool as a trippy puzzle game. You’d need to walk away from signs with small print to read them. You’d also be able to peek above objects by walking away. Finally, some objects will obscure your view as they grow from distance, and you’d need to figure out which position to be to observe something from afar.
I have a question. Isn’t there a ray that travels parallel to the ecuator, goes all the way around the sphere and interesects the back of your Head, allowing you to see yourself?
Yes! Even in higher-dimensional spheres such as the 3-sphere, every direction is described not by an extending coordinate, but by a periodic angle. In particular, there is a geodesic ("straight line") that starts and ends in your head. However, since the 3-sphere has finite volume, your enjoyment of seeing your back would not last long since any reliable source of light steadily fills the world with energy, and everything would melt or burn after some time
It looks like he didn't use a model for his first-person avatar, so there wasn't a 'yourself' to see in his example. I'm not entirely sure what it would have looked like if he had.
Earth block this ray in this particular set up. If you are floating in empty spherical space, then yes, you would see the specially inversed image of the back of your head.
@@AdenSerenity The light ray coming from his eyes would hit the ground before getting to the back of his head, because on the sphere, the ground is a great circle but the light ray is also a great circle, and you can't make two different great circles that doesn't touch on a sphere.
The same apply on a hypersphere.
not really. if your head was actually at the equator then yes but otherwise the strait path would dip "up" and "down" a bit. in his example since his head was "above" the equator and everything below the equator was ground your line of sight must always hit the ground.
more interesting landscapes will be more interesting tho. you can have a see the back of your head situation but it requires slightly different landscape.
This "close things appear quite normal" effect is a defining property of manifolds. All n-dimensional Riemannian manifolds resemble R^n around every point in a small neighborhood. This video portrays that fact really nicely. Fantastic work.
Thank you, poop catapult
This absolutely trips me out. I watched it when it came out and just got reminded of it and it still blows my mind
"Is that it? Is that how you turn a house inside out?"
now for the version that discusses incest >:)
I remember seeing another video on what a galaxy in a spherical world would look like and honestly that house was such a better explanation/example of how things on the other end look inside out
Link?
Me for the entire length of the demo:
“whoa”
“dude”
“whoooa”
“no way”
“whoa”
i was thinking about how much i'd love to play a game like this and then you said it was gonna be a game! this is a really cool effect!
This video really made me want Hyperbolica. Nice job!