Non-Euclidean Geometry Explained - Hyperbolica Devlog #1

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CodeParade

CodeParade

Күн бұрын

I present the easiest way to understand curved spaces, in both hyperbolic and spherical geometries. This is the first in a series about the development of Hyperbolica.
Chapters:
0:00 Intro
0:24 Spherical Geometry
2:33 Hyperbolic Introduction
3:53 Projections
5:37 Non-Euclidean Weirdness
8:31 Non-Euclidean Formulas
10:20 Outro
Hyperbolica
Trailer: • Hyperbolica: A Non-Euc...
Steam Page: store.steampowered.com/app/12...
Merch: crowdmade.com/collections/cod...
Henry Segerman
/ @henryseg
• Illuminating hyperboli...
HyperRogue
roguetemple.com/z/hyper/
If you like the things I do and want to support the channel:
/ codeparade
ko-fi.com/codeparade
Music:
"Glass Waves" By Phil K
www.phil-makes.com/noise

Пікірлер: 3 800
@outdateduser7036
@outdateduser7036 3 жыл бұрын
When you stop paying attention in calculus for 3 seconds
@illyias
@illyias 3 жыл бұрын
Too real
@RadeDobison
@RadeDobison 3 жыл бұрын
holy shit how did you do that lol
@axion986
@axion986 3 жыл бұрын
Sorry can someone explain this to me? I didn't take calculus and now I feel left out.
@Legendnewer
@Legendnewer 3 жыл бұрын
@@axion986 Basically you lost track of everything, you don't understand anything of what the professor is saying, it can be any topic but calculus is a prime example
@Nekiplex
@Nekiplex 3 жыл бұрын
We dont even need to know calculous in my country so i have no clue what it is. it is taught but you have to finish school. Its litterally not an option for any GCSE math tests. So you could just never know about it for your entire life
@Roter_Wolf
@Roter_Wolf 3 жыл бұрын
"Honey, can you knit me some non-euclidean planes?"
@Jellyjam14blas
@Jellyjam14blas 3 жыл бұрын
Lmao 😂
@xoddampro405
@xoddampro405 3 жыл бұрын
no :)
@warny1978
@warny1978 3 жыл бұрын
"Look at me eviscerating you, and you'll see some hyperbolic intestines" "Are you sure" "I was joking, here it is"
@omnificatorg4426
@omnificatorg4426 3 жыл бұрын
Search for Crocheting adventures in hyperbolic world
@columbus8myhw
@columbus8myhw 3 жыл бұрын
Daina Taimina did a nice Ted talk on hyperbolic crochet: kzfaq.info/get/bejne/rZeEdb2ZyZPXfmQ.html
@lordvincenteperez4196
@lordvincenteperez4196 2 жыл бұрын
can you just imagine beings of 4D using our 3D to explain 5D
@tyresefarrell
@tyresefarrell Жыл бұрын
Quite literally no🤣
@shouvik8267
@shouvik8267 Жыл бұрын
We perceive 3d with 2d images, so 4d beings would be able to percieve 4d with 3d images. It's like looking at all sides of a cube at the same time, but sadly I can't even begin to imagine it for I am confined within limits of 1d brain.
@NotRealChatGPT
@NotRealChatGPT Жыл бұрын
@@shouvik8267 i have a 0d brain
@reizinhodojogo3956
@reizinhodojogo3956 Жыл бұрын
@@shouvik8267 transparent cube: bro where i am i don't exist?
@NotRealChatGPT
@NotRealChatGPT Жыл бұрын
@@reizinhodojogo3956 no because i'm going on a walk and i and you are just being mad and not just being scared 😟 not being a pain to you help you with this and your life in your hand ✋ and a dream 🛌 and a new life you are a beautiful 🤩 woman 👩 you can do nothing but like 👍 you don't need a job that i you have no way more to get it into the center island 🏝️
@entitydotexe6138
@entitydotexe6138 2 жыл бұрын
CodeParade: "Stay Hyperbolic" Me: *proceeds to occupy the entire volume of the universe*
@lullabypoppera3914
@lullabypoppera3914 2 жыл бұрын
There's not enough room for the two of us!
@placeholdername3907
@placeholdername3907 Жыл бұрын
@@lullabypoppera3914 then we're just gonna have to share *cue just the two of us
@lavasqrl702
@lavasqrl702 Жыл бұрын
@@lullabypoppera3914 Correction: Three! That's right, I sort of understood it! *proceeds to occupy the entire volume of the multiverse*
@jackgreenearth452
@jackgreenearth452 Жыл бұрын
@@lullabypoppera3914 Just kidding! There's plenty of room here in hyperbolic space! (paraphrased from Hyperbolica because I can't be bothered to open up the game and talk to that guy in the badlands just for a youtube comment)
@Starnoxiar
@Starnoxiar 3 жыл бұрын
"But first we have to talk about parallel universes" nice.
@icicleditor
@icicleditor 3 жыл бұрын
I’ll be honest, that killed me.
@wacesferpit
@wacesferpit 3 жыл бұрын
specially love the Mario 64 extra reference with the music
@ber2996
@ber2996 3 жыл бұрын
To answer that, we need to talk about parallel universes
@OneShot_cest_mieux
@OneShot_cest_mieux 3 жыл бұрын
I think it's a reference to the youtube channel TerminalMontage
@yasd8493
@yasd8493 3 жыл бұрын
@@OneShot_cest_mieux *Pannenkoek2012 The meme started there
@TheVoidIsBees
@TheVoidIsBees 3 жыл бұрын
I feel like I just gained 100 braincells but lost 300 points psychic damage.
@Astlaus
@Astlaus 3 жыл бұрын
That's what math does to you. You gain insight, but you lose sanity.
@nintendofan222222222
@nintendofan222222222 3 жыл бұрын
I always knew math was black magic
@joda7697
@joda7697 3 жыл бұрын
@@Astlaus Thats a good description. I first had that when learning about cardinal numbers. Like, why the fuck are there just as many fractions as Integers, allthough the integers are a subset?! But then i learned why and booom, insight + psychic damage.
@CrescentUmbreon
@CrescentUmbreon 3 жыл бұрын
So it's Bloodborne. Oh god
@sameman6884
@sameman6884 3 жыл бұрын
+1 intelligence -10 HP
@rosearachnid879
@rosearachnid879 2 жыл бұрын
“Hyperbolic crochet” Come on in, sir. That’s the right password.
@verylostdoommarauder
@verylostdoommarauder 2 жыл бұрын
Now I understand the lovecraftian horror of non-euclidean geometry better now. If it's this confusing to us, imagine what geometry would be like for an eldritch horror.
@lullabypoppera3914
@lullabypoppera3914 2 жыл бұрын
It's simple really
@efegokselkisioglu8218
@efegokselkisioglu8218 Жыл бұрын
@@lullabypoppera3914 how old are you?
@robyngwendolynshiloh5277
@robyngwendolynshiloh5277 Жыл бұрын
Now it makes me wonder how the final season of the Magnus Archives looked
@Two-BallTyrone
@Two-BallTyrone Жыл бұрын
@@efegokselkisioglu8218 counter-argument, how old are you if you can’t get a joke?
@wrongturnVfor
@wrongturnVfor Жыл бұрын
I think euclidean geometry is more horrific than hyperbolic. It confines your mind too much
@efeersoy8880
@efeersoy8880 3 жыл бұрын
"Hey honey, do you think you could knitt me a projection of a hyperbolic tiling in 3D?"
@Battletrolls
@Battletrolls 3 жыл бұрын
@SArpnt nice
@ej-jz5rc
@ej-jz5rc 3 жыл бұрын
@SArpnt but who asked
@ej-jz5rc
@ej-jz5rc 3 жыл бұрын
@SArpnt if nobody did, then why did you even bother to do it?
@ej-jz5rc
@ej-jz5rc 3 жыл бұрын
@SArpnt very obviously nobody and i pointed that out pretty clearly if you could read
@ej-jz5rc
@ej-jz5rc 3 жыл бұрын
@SArpnt thanks for criticizing your own response
@etourdie
@etourdie 3 жыл бұрын
Greenland looks like it's about the size of Africa, but in reality it's about the size of Greenland -Map Men
@BrightyLighty_
@BrightyLighty_ 3 жыл бұрын
kzfaq.info/get/bejne/oNpyiZZ4zLewl2w.html for the uninitiated
@coyraig8332
@coyraig8332 3 жыл бұрын
Map Men MAP Men MAP MAP men men
@d.l.7416
@d.l.7416 3 жыл бұрын
It’s actually MAP men MAP men MAP MAP MAP men men men
@gregli9821
@gregli9821 3 жыл бұрын
@@d.l.7416 MAP men MAP men MAP MAP MAP men men men
@Tomajdafrytrix
@Tomajdafrytrix 3 жыл бұрын
map men map men map map map men men
@kirbee1113
@kirbee1113 2 жыл бұрын
Bro the "First I'll have to talk about parallel universes" had me DEAD LMAO. Shoutouts to pannenkoek2012!
@99kylies15
@99kylies15 2 жыл бұрын
'isnt that neat?' while talking about non euclidean formulas almost made me tear up. This man's gentle, genuine enthusiasm really is so endearing and lovely. Thanks for this vid, can't wait to check out more.
@MilesMetal
@MilesMetal 3 жыл бұрын
"So I hope that's given all of you a little better understanding of curved spaces..." ...he says as the last remnants of my brain leak out of my ear.
@hyperbeast4340
@hyperbeast4340 3 жыл бұрын
Wait, if a black hole is spherical geometry, are white holes hyperbolic?
@proloycodes
@proloycodes 2 жыл бұрын
@@hyperbeast4340 maybe
@Armoire68
@Armoire68 2 жыл бұрын
The perfect crossover doesn't exi...
@karynjohnson
@karynjohnson 2 жыл бұрын
But I understood more and I am twelve years old. I am too nerdy for my own good
@MilesMetal
@MilesMetal 2 жыл бұрын
@@karynjohnson You will read your comment in 10 years and cringe.
@PleasentDddd
@PleasentDddd 3 жыл бұрын
“All the angles are 0 and the area is pi.” As someone who loves geometry, this statement really through me off.
@yuvs0
@yuvs0 3 жыл бұрын
PleasentDddd I guess you just gotta think it threw a little...
@PleasentDddd
@PleasentDddd 3 жыл бұрын
Yuvraj Sethia frick
@viktornicht260
@viktornicht260 3 жыл бұрын
As someone who also loves geometry, it really turned me on lol
@Waterwolf221
@Waterwolf221 3 жыл бұрын
threw*
@anrriveradxndsigamer1495
@anrriveradxndsigamer1495 3 жыл бұрын
I’m hungry now
@karynjohnson
@karynjohnson 2 жыл бұрын
Hey CodeParade! That knitting of the hyperbolic plane was really amazing. The first one with the squares is very unique and I haven’t been able to find it anywhere on the internet. So I’ve been making my own with a large piece of fabric cutting it into squares and drawing the black outline then stitching them together. I’m 12. Your video has really inspired me to look into hyperbolic geometry more. Thanks CodeParade. Hope this comment doesn’t get buried.
@CodeParade
@CodeParade 2 жыл бұрын
That's awesome! Yeah, I couldn't find anything like it online either. The closest thing I found is this skirt, it uses pentagons instead of squares, but it's the same idea: blog.andreahawksley.com/hyperbolic-airplane-skirt/
@Queer_Nerd_For_Human_Justice
@Queer_Nerd_For_Human_Justice Жыл бұрын
@@CodeParade Oh hey, she's friends with vi hart! Dang, small world. more people should do stuff like this ^^
@The_Moth1
@The_Moth1 Жыл бұрын
@@Queer_Nerd_For_Human_Justiceis she the flexagon person?
@disco-ifinite-easy
@disco-ifinite-easy 9 ай бұрын
yes @@The_Moth1
@wendysanchez3024
@wendysanchez3024 4 ай бұрын
I've been searching to find something like the one with the squares. I'm teaching a course on non-Euclidean geometries, and I'd love to have one of those. Did you say your wife made it? Would she be willing to sell one ?
@josephcsible
@josephcsible 3 жыл бұрын
If you want to use HyperRogue to explore the hyperbolic tiling used in this video (5 squares meeting at each vertex, first seen at 4:59), here's the sequence of menu options to do so: main menu -> special modes -> experiment with geometry -> basic tiling -> {5,4} (four pentagons) -> go back -> variations -> pure -> dual of current.
@CasualCosta
@CasualCosta 3 жыл бұрын
Instructions unclear, become a flat-earther.
@rehehehehehe4525
@rehehehehehe4525 3 жыл бұрын
I'm ok I don't want to be a flat earther
@mysterioushoodedguy2332
@mysterioushoodedguy2332 3 жыл бұрын
Lol the thing where the triangle on a sphere has 3 right angles has actually been used to disprove flat earthers since if you take a plane and fly it a certain distance, turn right 90 degrees, fly same distance, turn 90, fly same distance, you'll end up in same place where you started because of the earth's curvature
@Fulgur14
@Fulgur14 3 жыл бұрын
@@mysterioushoodedguy2332 Well, technically... but on Earth, that would be a trip of 30,000 km, so you could hardly do it without landing in-between. And that generally can't be done without turning, and how do you prove you continue in the same direction, etc. etc. Though it leads to an interesting question: what would be the easiest triple-90-degree triangle on Earth to travel? Or, for the matter, triple-72-degree, a part of an icosahedron?
@jfp0763
@jfp0763 3 жыл бұрын
Instructions unclear, Teleported to another plane in existence and start being trained by Sherk to fight against an Otaku army
@mgsgamer8340
@mgsgamer8340 3 жыл бұрын
Oh I became a non-Euclidean-earther. *i can hear melanie Martinez when a bird chirps now*
@woodant1981
@woodant1981 3 жыл бұрын
I actually just got non Euclidean tiling in my bathroom.
@thatboredinternetwanderer140
@thatboredinternetwanderer140 3 жыл бұрын
wait seriously
@ambrosxa
@ambrosxa 3 жыл бұрын
How was it?
@doppelrutsch9540
@doppelrutsch9540 3 жыл бұрын
You have a curved bathroom floor? Isn't that kind of impractical?
@CodeParade
@CodeParade 3 жыл бұрын
I too enjoy my showers in R'lyeh
@thatboredinternetwanderer140
@thatboredinternetwanderer140 3 жыл бұрын
@@doppelrutsch9540 yeah but i imagine it looks cool
@alpkyu5201
@alpkyu5201 7 ай бұрын
This game caught my attention because I was frantically looking for a non-euclidian game that I can play in VR. It really was one of a kind experience. The farm was most mind boggling and the best part in my opinion (which, now I see from the thumbnails for your other videos, was actually spherical space). Such concepts like non-euclidean spaces are hard to grasp because they are inherently abstract. Making a game around them is really a good way for people to "experience" it and make them less abstract. It was especially a treat in VR. Thanks for making this game.
@spoonkyscenvyscreeleton
@spoonkyscenvyscreeleton 3 жыл бұрын
scientists: a group of very serious people in glasses and lab coats who are investigating very complex serious things also scientists: S P A G G H E T T I F I C A T I O N
@onion2.
@onion2. 3 жыл бұрын
“Think about light bending around the curved space of a black hole.” Ah yes
@beanmcknee1610
@beanmcknee1610 3 жыл бұрын
It’s like a coin going down one of those donation things that make the coin spin around into the hole Except the coin is light and the hole is a black hole
@tristenarctician6910
@tristenarctician6910 3 жыл бұрын
@@beanmcknee1610 why would the color of the hole change? .
@beanmcknee1610
@beanmcknee1610 3 жыл бұрын
@@tristenarctician6910 no sorry what I meant was is that the coin represents light itself, not light in color I hope that helps
@michelekonakciu7052
@michelekonakciu7052 3 жыл бұрын
@@tristenarctician6910 particle get excited and emit radiation that we perceive as a colour change
@Tharmin.124
@Tharmin.124 3 жыл бұрын
Just think of a magnet and a ball bearing, just that they can't touch
@carykh
@carykh 3 жыл бұрын
whoa, that's crazy that you can figure out the areas of triangles just by knowing its angles. It feels like there's something missing in the formula but there's not!
@papskormsepic7670
@papskormsepic7670 3 жыл бұрын
whats a triangle
@jellevanderdrift1302
@jellevanderdrift1302 3 жыл бұрын
I think the channel 'think twice' has a video about the derivation.
@benlev3375
@benlev3375 3 жыл бұрын
It's a curved space so I think that the only radius/length is scaled by pi, so pi is defined maximum when projecting onto a 2D space.
@friedkeenan
@friedkeenan 3 жыл бұрын
Yeah that blew my mind. At first when he said there was no Euclidean equivalent, I thought "What? You can find the area of a triangle in Euclidean space, it's just 0.5bh" but then he said only using the angles and my whole concept of reality disintegrated. Btw, love your videos, cary
@vari1535
@vari1535 3 жыл бұрын
hi cary
@ryanr27
@ryanr27 3 жыл бұрын
Eventually, Mario will build so much negative speed, which he had built up for over 12 hours to leave this projection of 5D space
@friedayy
@friedayy Жыл бұрын
Wtf
@joost5609
@joost5609 2 жыл бұрын
The Mario joke was hilarious and probably the only thing I truly understood. Very interesting and challenging subject!
@michaelzopff8862
@michaelzopff8862 3 жыл бұрын
Oooh! Holonomy is the reason why, when rotating a 3D object with a mouse, the orientation quickly gets messed up, isn't it? That would explain why my trick of moving the mouse in small circles clockwise or counter-clockwise works, too.
@CodeParade
@CodeParade 3 жыл бұрын
Exactly!
@bencressman6110
@bencressman6110 3 жыл бұрын
@@CodeParade It's cool that when we hold a globe in our hands, we automatically rotate it as we, well, rotate it to compensate for this effect, so we always orient things the way we are used to seeing them in map projections (keeping north "up")
@thelegend8570
@thelegend8570 3 жыл бұрын
Oh hell, i knew i'd seen that somewhere before, i guess that explains it!
@rententee
@rententee 3 жыл бұрын
That's what came to mind for me as well!
@kosherkingofisrael6381
@kosherkingofisrael6381 3 жыл бұрын
It also reminds me of certain gears
@koda_pop
@koda_pop 3 жыл бұрын
The parallel universe bit caught me off guard lmao
@chakra6666
@chakra6666 3 жыл бұрын
surely the most ambitious crossover ever
@rehehehehehe4525
@rehehehehehe4525 3 жыл бұрын
those goddamn parallel universes just tell me where is Mario don't tell me he's 4 PU to the left, 29 PU down and performing a satanic ritual in the out of bounds area
@HokoraYinphine
@HokoraYinphine 3 жыл бұрын
PannenParade
@mynion24100
@mynion24100 3 жыл бұрын
an a press is an a press...
@Lance0
@Lance0 3 жыл бұрын
@@mynion24100 Were you gonna say, "it can't be only half? Well, Mynion"24" 100, hear me out. An A press has actually 3 parts to an A press, when A is pressed, when A is held, and when A is released. Now together, this forms 1 complete A press. Now usually, it's the pressing that's useful, because that's the only part that makes Mario jump. However sometimes, it's sufficient to just use the holding part, which allows Mario to do little kicks, to swim in water, to fall slowly while twirling, and to fall slowly with the wing cap. And as for the release, well there's currently no cases where that's useful or important, so don't worry about that. Now, if we map out the required A presses for Wing Mario Over the Rainbow, it would look like this. We merely need to hold A to reach the cannon platform, we need to press A to launch from the 1st cannon, and we need to press A again to launch from the 2nd platform. So how many A presses is that total? Well, it appears to be 3, and if we were doing this star in isolation, then yeah, it would be 3. But, in a full game A button challenge run, there are other A presses that occur earlier in the run, such as this A press needed to get into the course. So, if we take that A press into consideration as well, then how many A presses would it take? The naive answer would be 4, one to enter the course, and the 3 within the course that we established earlier. However, we can do better. We can actually do it in 3 by simply holding out the 1st A press to be used in the half A press because the half A press only requires A to be held, not actually pressed. So in this fashion, Wing Mario Over the Rainbow only adds on an additional 2 A presses, since the 1st A press just actually leeches off of a previous A press, so to capture this phenomenon, we call it 2.5 A presses. On a single-star basis, you round that up to 3, but in a full game run, you'd round it down to 2. So, in conclusion, since that 1st A press counts in some contexts, but adds no additional A presses in other contexts, we refer to it as a half A press. Edit: it's pannen time(all the words are now ripped out from pannen's video)
@bigagabriel
@bigagabriel 2 жыл бұрын
I have been reading the books of the fantasy novel The Wheel of Time. There is king of a parallel plane where one of the characters can move throw space and he describes as if things that looked really far came closer really fast. And that as he turned his head, the world would turn way faster. It might be the hyperbolic rendering you show and it might be awesome to connect that with the books fans!
@fobo0053
@fobo0053 2 жыл бұрын
you know.. i love you just by the fact that you're not "bad-repeating" something that you heard from a mathematician like the other youtubers and you are precise (it's a mathematician talking)
@cynicap8584
@cynicap8584 3 жыл бұрын
"Courtesy of mrs. Parade" Awww, what a sweet, weird quality time
@thecheesybagel8589
@thecheesybagel8589 3 жыл бұрын
No one: My brain at 1 am: let’s try to understand non Euclidean geometry when I already have a hard time with algebra
@theredneckdrummerco.6748
@theredneckdrummerco.6748 3 жыл бұрын
its one forty nine right now and I face the same dilemma
@goddamnit
@goddamnit 3 жыл бұрын
Same :'(
@sonetagu1337
@sonetagu1337 3 жыл бұрын
I dont even understand algebra wtf
@zinedsdrawkcab840
@zinedsdrawkcab840 3 жыл бұрын
same, but its 4:04 am for me
@erenjaeger1266
@erenjaeger1266 3 жыл бұрын
STOP IT PLEASE THIS IS SO FREAKING RELATABLE ITS 12:36 FREAKING AM I CSNT SLEEP!!!
@oglothenerd
@oglothenerd 8 күн бұрын
POV: The people in a hyperbolic universe making KZfaq videos about the weirdness that is Euclidean geometry.
@jeper3460
@jeper3460 3 жыл бұрын
Another interesting thing with curved space is travelling through something with a lot of reference points e.g. a forest with trees or space with stars. When you walk through a forest in euclidean space, the trees that are more directly in front of you seem to move towards you faster, while the trees more toward the sides seem to move slower. In hyperbolic space, all of the trees seem to move at the same speed towards you, no matter how far off the centre they are. In spherical space, the trees behind you appear in front of you, and the trees off to the side almost appear to be still.
@rodeo_stomper
@rodeo_stomper 3 жыл бұрын
Honestly, I have no clue what any of this means, but this dude's voice is really relaxing to me.
@astergh0st
@astergh0st 3 жыл бұрын
Jøhnny Rëtznøvishchä Yeah. Too bad my inability to understand what he’s saying gives me a headache.
@Mysideep
@Mysideep 3 жыл бұрын
I want to understand...
@enderstriker0718
@enderstriker0718 3 жыл бұрын
“We’re only looking down on it because we are higher dimensional beings living in a 3D universe.”
@daylenhigman8680
@daylenhigman8680 3 жыл бұрын
*The 4th dimensional being watching me take a dump
@satyampandey2222
@satyampandey2222 3 жыл бұрын
@UltimateGeek at the same time
@JotaC
@JotaC 3 жыл бұрын
We actually live in a 4D world as 3D beings That's why we can't see the full extent of time
@nykal1510
@nykal1510 3 жыл бұрын
@@JotaC Time is not a SPATIAL dimension, stating that we live in a four-dimensional world is irrelevant, we live in three-dimensional space
@ryanwolf1869
@ryanwolf1869 3 жыл бұрын
Nykal absolute brainlet
@lobsterfork
@lobsterfork 2 жыл бұрын
I saw your reddit post for this 1 or 2 years ago (I don't remember exactly when). Really cool that you are pushing this into mainstream. I bet what you are working on will have really cool applications in the near and distant future! BTW HOLY SHIT THAT KNITTING IS IMPRESSIVE!
@mustafamalik4211
@mustafamalik4211 Жыл бұрын
This is so fascianting. I can't believe I never thought about the geometrical visualizations of the hyperbolic and spherical equations I learned in Vector Calculus back in University. Thank you for this amazing video!
@simonsixt2418
@simonsixt2418 3 жыл бұрын
8:07 Imagine creating a black hole by throwing a baseball really hard in spherical geometry
@marcinlechicki4019
@marcinlechicki4019 3 жыл бұрын
Maby our universe is spherical, and that "realy hard" to get speed enough is force to give that baseball light speed.
@Anonymous-zd1ow
@Anonymous-zd1ow 3 жыл бұрын
@@marcinlechicki4019 If the ball was thrown that hard it would be ripped to shreds.
@marcinlechicki4019
@marcinlechicki4019 3 жыл бұрын
@@Anonymous-zd1ow You are talking from experience Hulk?
@ynntari2775
@ynntari2775 3 жыл бұрын
People in general have too many misconceptions about big strength. Like lifting cars and sofas, which actually just folds the whole thing and rips off the small part you're holding. And "lifting a building" would be just passing your hands through the floor and making holes
@reizinhodojogo3956
@reizinhodojogo3956 4 ай бұрын
​@@marcinlechicki4019he changed his user to anonymous, hulk is retired now sadly
@miljanvideo
@miljanvideo 3 жыл бұрын
2:23 Talking about spherical geometry me an intellectual: *beach balls*
@marcopivetta7796
@marcopivetta7796 3 жыл бұрын
bro i've been watching a lot of conferences and lectures on this topic and NONE have explained it better than your videos. YOU ROCK! I'm considering taking up a math degree after getting my master in architecture next year, in part thanks to these videos. Love!
@thewarden4174
@thewarden4174 9 ай бұрын
I really like how you explain all this, it makes it much easier to understand than just the graphs
@Fulgur14
@Fulgur14 3 жыл бұрын
One thing that might need mentioning is that non-Euclidean geometries, unlike the Euclidean one, possess preferred lengths. (The video only mentions "assigning unit curvature" without actually explaining what it means.) Simply said, in Euclidean plane, we may set our length unit to be anything. Pythagorean theorem, circumference of circle, everything will work the same no matter what units we measure in. In spherical geometry, we have a natural unit that is equal to the radius of the sphere. Even if the space is not actually embedded in anything and doesn't have an actual "radius", we still know what it should be because that is the only length unit in which r can be measured so the formula "2 pi sin(r)" works. This has colossal consequences! It means, for example, that the "similar shapes" in Euclidean geometry, where you can increase a size of, say, a triangle or a square and still keep all its angles intact. No such luck here: a triangle with sides twice as long as an original will have completely different angles. This would make things like making plans, schemes or maps harder. In hyperbolic geometry, a natural length unit is not that easy to see as in spherical geometry, but it nevertheless exists. There's only one possible length unit which makes the 2 pi sinh(r) formula work! Finally, note that spherical geometry has some additional problems the other two geometries don't have. Main one is that if you draw two straight lines on a sphere, not only will they always intersect, but they will always intersect in two antipodal points. This spoils the geometry somewhat (straight lines should only intersect in one point). The solution is so-called "elliptic" geometry, in which every pair of antipodal points on the sphere is considered just a single point. That one has its weird moments as well (for example, if you wander in a straight line, you will eventually arrive back to your starting point, but as a mirror opposite).
@Stetofire
@Stetofire 3 жыл бұрын
Marek Čtrnáct You are indeed... A Super Nerd! *Guitar Riff*
@csicee
@csicee 3 жыл бұрын
tl;dr?
@Fulgur14
@Fulgur14 3 жыл бұрын
@@csicee TLDR: In non-Euclidean geometries, you are forced to measure lengths in a very specific units in order to get simplest possible formulas.
@Fulgur14
@Fulgur14 3 жыл бұрын
​@@Stetofire Well, I have been involved with HyperRogue for quite some time -- for example, you can see some of my tessellation results here: zenorogue.github.io/tes-catalog/
@AlxM96
@AlxM96 3 жыл бұрын
@@Fulgur14 phenomenal insight and work, thanks! keep it up!
@BambinaSaldana
@BambinaSaldana 3 жыл бұрын
"But first we have to talk about parallel universe-I mean parallel lines." *We were on the verge of greatness,we were this close.*
@GlyphicEnigma
@GlyphicEnigma 3 жыл бұрын
We just needed enough speed to get to the next PU!!!
@YashBeanz
@YashBeanz 2 жыл бұрын
@@GlyphicEnigma just blj for 11 hours and you should have enough!
@TheaPeanut_69old
@TheaPeanut_69old 2 жыл бұрын
the music tho its from another video about weird stuff a bit similar to this
@YashBeanz
@YashBeanz 2 жыл бұрын
@@TheaPeanut_69old it's the file select music from Mario 64
@Qsie
@Qsie 2 жыл бұрын
Man, makes me miss watching Pannen
@Memerath
@Memerath 3 жыл бұрын
was NOT expecting a simpleflips reference, but i love it even more because of that
@ej-jz5rc
@ej-jz5rc 3 жыл бұрын
pannenkoek2012*
@Memerath
@Memerath 3 жыл бұрын
@@ej-jz5rc simpleflips*
@jamesrosco4816
@jamesrosco4816 2 жыл бұрын
I watched this a year ago and now finally have started playing Hyperbolica. It is quite the experience. Now I am back w a tching this again trying to wrap my head around it. Big thanks for making the game and these videos.
@juancgonzalez6537
@juancgonzalez6537 3 жыл бұрын
"But first we have to talk about parallel universes." I'm having a panic attack.
@rhaeven
@rhaeven 3 жыл бұрын
*quick creepy distorted version of the Mario 64 File Select music starts*
@ej-jz5rc
@ej-jz5rc 3 жыл бұрын
pannen attack*
@spikey288
@spikey288 3 жыл бұрын
No you aren't
@thatoneguy9582
@thatoneguy9582 2 жыл бұрын
@@spikey288 youre not their dad
@spikey288
@spikey288 2 жыл бұрын
@@thatoneguy9582 not you again
@Addsomehappy
@Addsomehappy 3 жыл бұрын
"Stay Hyperbolic!" oh so you wish me to tear myself apart every time i walk anywhere gee thanks
@Anonymous-zd1ow
@Anonymous-zd1ow 3 жыл бұрын
That only happens when you apply a significant amount of force to yourself.
@diophantine1598
@diophantine1598 3 жыл бұрын
The Incredible Hulk Correction, velocity. Depending on the hyperbolic space (depending on r) even walking or breathing could tear you apart.
@olli3b3ar27
@olli3b3ar27 3 жыл бұрын
this is what happens when you try and and be parallel, but you'll learn.
@justinaccurate347
@justinaccurate347 3 жыл бұрын
I think OP was joking by being hyperbolic in his reaction?
@Anonymous-zd1ow
@Anonymous-zd1ow 3 жыл бұрын
@@diophantine1598 Oh thank you for correcting me! Oh Jesus this is 7 months late XD.
@Darthvanger
@Darthvanger 2 жыл бұрын
Awesome! The best explanation of the curved spaces I've seen actually. And at the same time it's gonna be a game, to really experience it!
@kylehayden3113
@kylehayden3113 2 жыл бұрын
"So I hope that's given all of you a little better understanding about curved spaces..." Well, it sure hasn't, but I appreciate the effort
@theosouris7063
@theosouris7063 3 жыл бұрын
5:47 I don’t know what I expected from this vid, but it certainly wasn’t a Pannenkoek2012 reference
@kurlyfryz
@kurlyfryz 3 жыл бұрын
that feeling when non-euclidean geometry makes more sense than euclidean geometry
@Shrek_es_mi_pastor
@Shrek_es_mi_pastor 3 жыл бұрын
Completamente difiero.
@maxnewdf
@maxnewdf 3 жыл бұрын
@@Shrek_es_mi_pastor why your pastor is shrek?
@TaiFerret
@TaiFerret 3 жыл бұрын
Euclidean geometry is just what happens when you zoom in on a surface infinitely.
@realnub235
@realnub235 3 жыл бұрын
oof lol
@luizg8034
@luizg8034 3 жыл бұрын
@@TaiFerret sounds strange to me, but i dont know enough topology to disprove it
@cdawgswizzle7229
@cdawgswizzle7229 3 жыл бұрын
this is a perfect way to explain some of the complex concepts in Geometry Relativity and the 4th Dimension. Thanks a lot!
@centerofoperations9251
@centerofoperations9251 7 ай бұрын
This is the best explanation of the topic I've ever watched
@matsol2158
@matsol2158 3 жыл бұрын
7:30 This guy :"Now we've walked on a pentagon with five right angles" My math teacher :"Wait... that's illegal..."
@MeteoritePlayz
@MeteoritePlayz 3 жыл бұрын
CodeParade: oh god, PLEASE STOP USING THIS! Pringles: no u Edit: how do I have about 200 more likes a month later ty
@pwnmeisterage
@pwnmeisterage 3 жыл бұрын
Anticlastic diagrams are confusing because they force the viewer to visualize a non-intuitive concept in an even more non-intuitive way. They just overcomplicate stuff too much. Everyone immediately understands Pringles. Pringles are tasty.
@EliteOcto
@EliteOcto 3 жыл бұрын
PRINGLES IN 4D
@Kromiball
@Kromiball 3 жыл бұрын
@@EliteOcto lol
@unblorbosyourshows9635
@unblorbosyourshows9635 3 жыл бұрын
@@EliteOcto N O N E U C L I D E A N P R I N G L E S
@jamiecasimir5040
@jamiecasimir5040 3 жыл бұрын
ElPseudocrítico E A T
@MayBeSomething
@MayBeSomething 2 жыл бұрын
"But first, I need to talk about parallel universes" You had me there!
@DigitalDuelist
@DigitalDuelist Жыл бұрын
This makes so much more sense than any explanation I have ever seen. Thank you!
@Chrischi3TutorialLPs
@Chrischi3TutorialLPs 3 жыл бұрын
"But first we have to talk about parallel universes" *SM64 music plays* Ah, i see you are a man of culture aswell.
@joseg.matamoros2847
@joseg.matamoros2847 3 жыл бұрын
Bismuth be like
@haimric8603
@haimric8603 3 жыл бұрын
Explain
@Chrischi3TutorialLPs
@Chrischi3TutorialLPs 3 жыл бұрын
@@haimric8603 Its a meme about Super Mario 64. Basically due to a programming oversight theres parallel universes in the game which speedrunners use in Tool-Assisted Speedruns (Basically speedruns where you have bots make perfect inputs rather than playing yourself) to get around. And well, theres this KZfaqr called Pannenkoek2012 who made a video explaining some things about speedruns, and well, that line "But first we need to talk about parallel universes" became a thing.
@knockrotter9372
@knockrotter9372 3 жыл бұрын
@@Chrischi3TutorialLPs YOU CAN'T JUST PRESS THE A BUTTON A HALF OF A TIME IT'S STILL AN A PRESS
@centokiVA
@centokiVA 3 жыл бұрын
this genuinely has taught me more about non-euclidean geometry than my classes have
@pattyryopotybuttongamer3063
@pattyryopotybuttongamer3063 2 жыл бұрын
and after that you have to plug the red wire into the socket to make sure the engine boots at launch. Wrap the green wire around it's coil that sits directly beside the A button. After you put the back shell on, place the battery in the slot. Screw the Vr26 Jeeper back up and press the reset button. If everything worked according to plan you're device should show a thumbs up sprite. Plug the HDMI port into a monitor and wait three seconds. If it boots up on TV your in the good side. If it doesn't boot in less then 5 seconds quickly unplug. This can severely damage your TV and possibly start a fire
@diamante8864
@diamante8864 2 жыл бұрын
this genuinely has taught me more about *euclidean* geometry than my classes have
@Crazyclay78YT
@Crazyclay78YT Жыл бұрын
bruh why tf would you be taking non euclidean geometry in school
@ThomasTheThermonuclearBomb
@ThomasTheThermonuclearBomb 9 ай бұрын
​@@pattyryopotybuttongamer3063bro what are you talking about
@Acoolaccountmans
@Acoolaccountmans 2 жыл бұрын
8:29 wow amazing ripping sound
@EternalPhoenix
@EternalPhoenix 2 жыл бұрын
This has become my favorite topic to ramble about, ty
@grandstrategos1144
@grandstrategos1144 3 жыл бұрын
Clarification for everyone in the comments. When he talks about lines in spherical geometry, he is mentioning the spherical geometry definition of a line. In spherical geometry, the definition of a line is one of the great circles of the sphere. So you can’t use different latitudes or longitudes.
@PotatoPatatoVonSpudsworth
@PotatoPatatoVonSpudsworth 3 жыл бұрын
This clarifies things quite a but for me. Thank you!
@nancyburgos1231
@nancyburgos1231 3 жыл бұрын
I was wondering exactly that jaja! Thank you
@nicbajitogaming8947
@nicbajitogaming8947 2 жыл бұрын
Geodesics waving to the world 🤗 Hi, geodesic !!
@wa5657
@wa5657 10 ай бұрын
oh thank you, i was just hung up on that :v
@Tubeytime
@Tubeytime 3 жыл бұрын
Holonomy is something I've known about for years due to playing around in various programs/simulations/games but I never knew there was a word for it until now!
@pluspiping
@pluspiping 3 жыл бұрын
Same! I build 3D models for my job and I guess it's why you need "reset view" buttons when you're zooming around the model in "3D space". You get real lost real fast. Now I know there's a word for it! Cool!
@eugenegarcia6155
@eugenegarcia6155 2 жыл бұрын
Tell me about it
@cheesepop7175
@cheesepop7175 Жыл бұрын
holonomy happens in gmod
@Crazyclay78YT
@Crazyclay78YT Жыл бұрын
@@cheesepop7175 bro it happens fucking everywhere
@Crazyclay78YT
@Crazyclay78YT Жыл бұрын
yeah 3d modeling really showed me that. if you just click and drag in circles, moving the camera around the object, it rotates. at first i was like "wtf why does it do that" and i thought it was a glitch or something in the software. now that i know that it has a word, i will definitely try to squeeze that into my vernacular
@drenz1523
@drenz1523 3 жыл бұрын
Code Parade: So glad i grew up with this 0:07 But damn this is much better 0:05
@sebastianmonten
@sebastianmonten 2 жыл бұрын
Dude, super interesting video! Glad that I found this! I have become more and more interested in computer science, glad that I found your channel
@Epicvibes999
@Epicvibes999 3 жыл бұрын
“It only looks 3D because we are higher dimensional beings, looking down on the flatlanders.” Hip Hop Artists: *”haha , fisheye go wobble wobble”*
@SoftyWalterGames
@SoftyWalterGames 3 жыл бұрын
As soon as you said "there wouldn't even be a horizon" my mind exploded trying to visualise earth without horizons
@elietheprof5678
@elietheprof5678 3 жыл бұрын
If you live in America, the sky is Australia.
@greggreen5510
@greggreen5510 7 ай бұрын
@CodeParade I recently have been learning about the hyperbolic trigonometric functions. I am having a hard time finding information on how a hyperbolic triangle relates to the hyperbolic functions. Where did you find out so much information about spherical and hyperbolic geometry? This video is astoundingly amazing!
@lifeofalonelywhale
@lifeofalonelywhale 5 ай бұрын
The Mario 64 music at the mention of parallel universes... 50 bucks you've seen the Mario 64 conspiracy iceberg XD Spot on, spot on.
@JohnsontheFly
@JohnsontheFly 3 жыл бұрын
That awkward moment when hitting a baseball in spherical space creates a naked singularity and by extension accidentally creates 0-dimentional space
@sebastianrojasgutierrez.2063
@sebastianrojasgutierrez.2063 3 жыл бұрын
So relatable
@leebee42069
@leebee42069 3 жыл бұрын
Me: I'm going to crochet a hat! The hat: 3:20 Me: why does this always happen?
@andredominguez3199
@andredominguez3199 2 жыл бұрын
I don't know why KZfaq recommended me this, but I love it.
@e-pops
@e-pops 7 ай бұрын
To simplify: Dimension is just a space where locations have unique coordinates. Like 1D (x), 2D (x, y), 3D (x, y, z), etc. Geometry is a concept that describes rules of how things work in that space. For example in euclidean 2D space there is only one unique line between two points, but in a spherical 2D space there are infinite amount of lines between two points. This is because of the geometry (rules/postulates) describing how things work in that space.
@LionsInBoots
@LionsInBoots 3 жыл бұрын
5:44 „I was already 5 PUs ahead of you...“
@ej-jz5rc
@ej-jz5rc 3 жыл бұрын
4* because then he'd be QPU misaligned
@MozartSrs
@MozartSrs 3 жыл бұрын
No one: My blanket when I’m trying to find the short end at 3am: 3:00
@MoltenSamurai
@MoltenSamurai 3 жыл бұрын
Underrated
@QuartzOfficial
@QuartzOfficial 3 жыл бұрын
its even 3:00
@neilpetrarca7395
@neilpetrarca7395 3 жыл бұрын
Lol
@ashtonsmith1730
@ashtonsmith1730 3 жыл бұрын
what blanket did you buy?
@Querens
@Querens 3 жыл бұрын
why "no one:" is needed everywhere. How is it helping the joke
@blue-ou6uf
@blue-ou6uf Жыл бұрын
this is amazingly explained omg. so much content i expected to be overwhelming but isnt.
@Grey-mo5py
@Grey-mo5py 2 жыл бұрын
ive watched this video so many times and I love it every time
@BAVBAVBAV
@BAVBAVBAV 3 жыл бұрын
An A press is just an A press. You can’t just call it a half.
@cmdrkradenguard6808
@cmdrkradenguard6808 3 жыл бұрын
Bro, how many QPUs are you on?
@dougneon9550
@dougneon9550 3 жыл бұрын
@@cmdrkradenguard6808 like maybe 5 or 6 my dude
@EpicBlackflame07
@EpicBlackflame07 3 жыл бұрын
This a reference to that half A press Mario run?
@quincyyeager6249
@quincyyeager6249 3 жыл бұрын
you half Alive or half dead?
@wynfarthing
@wynfarthing 3 жыл бұрын
Ok TJ 'Henry' Yoshi
@tentimestay9181
@tentimestay9181 3 жыл бұрын
"But first, we have to talk about parallel univers-- I mean parallel lines" so unexpected, genuinely cackled
@Queer_Nerd_For_Human_Justice
@Queer_Nerd_For_Human_Justice Жыл бұрын
I've played hyperrouge! I do reccomend it, ti's great. What it felt like is traveling on the bark of a tree.. you can go from the trunk to a branch to a subbranch to a leaf, but to go to a neighboring subbranch you'd best backtrack first, because traveling across hundreds of leaves to get to the neighboring leaves is impractical. In another sense, it felt like opening folders full of folders with more folders inside... in order to move "sideways", it's best to move "up" first, unless you wanted to explore "deep" into a specific pathway.
@exintrovert1337
@exintrovert1337 2 жыл бұрын
Very nice explanation! Thank you.
@crackedemerald4930
@crackedemerald4930 3 жыл бұрын
Hyperbolic space: when you have more space every space you space
@Kaiveran
@Kaiveran 3 жыл бұрын
Xzibit would like to know your location
@Lugmillord
@Lugmillord 3 жыл бұрын
When the Mario 64 music kicks in, I knew what was coming and I wasn't disappointed.
@havocmaverick
@havocmaverick Жыл бұрын
Twenty five years ago when I was sick I had a fever dream about playing a hyperbolic game. I had to place a tower or skyscraper then when my opponent would place one it would make mine shorter. It was kind of like a three dimensional version of GO. Very neat.
@NickMirambeau
@NickMirambeau 2 жыл бұрын
i had to figure out how to calculate hyperbolic sin, cos, etc. for a calcator app i'm developing. and the whole time I was learning about it, I was like "what even is hyperbolic trig anyway? who even uses this??" i can now answer that question. it's you. you use it
@hitzcritz
@hitzcritz 3 жыл бұрын
5:44 "But first, we have to talk about parallel ̶u̶n̶i̶v̶e̶r̶s̶e̶s̶ lines!" *_my disappointment is immeasurable and my day is ruined_*
@1sub2videos60
@1sub2videos60 3 жыл бұрын
mario
@TheaPeanut_69old
@TheaPeanut_69old 2 жыл бұрын
the lines are still universes
@L1M.L4M
@L1M.L4M 2 жыл бұрын
@@TheaPeanut_69old one dimensional, yes
@albingrahn5576
@albingrahn5576 3 жыл бұрын
can’t wait to see the 0.5 A-press run for hyperbolica!
@Lance0
@Lance0 3 жыл бұрын
well, we need 4 things: HSPW, forcing scuttlebugs to have a jamboree, pannen, and TJ """"Henry"""" Yoshi.
@ej-jz5rc
@ej-jz5rc 3 жыл бұрын
@@Lance0 don't forget groundpounding the misalignment
@renormalization
@renormalization Жыл бұрын
This is a great video to motivate the anti-de Sitter spacetime (hyperbolic spacetime) for holography. Nicely done!
@jamalford961
@jamalford961 2 жыл бұрын
Thanks for this, your channel helps my mind.
@aethershard463
@aethershard463 3 жыл бұрын
CodeParade: Wanna guess what the hyperbolic opposite is? Me: cosine(r)? I mean that’s the “opposite” of sine. CodeParade: No you fool it’s hyPErBoLiC sine!!!
@XDinky
@XDinky 3 жыл бұрын
Isn't the opposite of sine just minus sine? I guess you need to define "opposite"
@zacozacoify
@zacozacoify 3 жыл бұрын
I would say the opposite of sin is either -sin, or inverse sin (arcsin). Cos is more like the complement to sin, it’s what you get when you shift sin by -90 degrees.
@anonymousperson6228
@anonymousperson6228 3 жыл бұрын
Or it could be cosecant. It’s the reciprocal of sine.
@Fulgur14
@Fulgur14 3 жыл бұрын
@@zacozacoify sinh is, in a way, sin rotated 90 degrees: sinh(x) = -i sin (ix)
@Fulgur14
@Fulgur14 3 жыл бұрын
@Multorum Unum It can be if sin(ix) is pure imaginary.
@alpha3836
@alpha3836 3 жыл бұрын
0:49 *_We're only looking at it in 3D, because we are higher dimentional beings looking down at the flat-earthers_*
@felixplays4229
@felixplays4229 3 ай бұрын
I see what you did.
@SSM24_
@SSM24_ 3 жыл бұрын
My favorite example of how much "bigger" hyperbolic space is compared to Euclidean space is that *_you can tile the plane with apeirogons._* For those who don't know what that means, let me elaborate. An apeirogon is a polygon with an _infinite number of sides._ They don't really exist properly in Euclidean space - the best you can do is a degenerate form composed of a line (or rather an infinite number of line segments that form a line) and a half-plane. However, in hyperbolic space, you can have _genuine_ apeirogons - every angle is less than 180 degrees, and yet it never quite meets back up with itself, because of how the space curves. And not only that, but you can have an _infinite number of them tiling the plane,_ the same way you can create a grid of triangles or squares in Euclidean space. You don't run into any problems with them intersecting each other - hyperbolic space is legitimately big enough to fit an infinite number of infinite polygons, each of which has infinite area. If you don't believe me, just look up "apeirogon tiling".
@Anonymous-df8it
@Anonymous-df8it 2 жыл бұрын
Also, every vertex can have infinitely many apeirogons around it!
@GamerX-2000
@GamerX-2000 2 жыл бұрын
7:10 is this what is going on when I rotate a 3D model in a cad software?
@Marci124
@Marci124 3 жыл бұрын
I didn't think there were too many interesting tidbits in this topic that I wasn't aware of, but this video proved me wrong!
@sreyam7
@sreyam7 3 жыл бұрын
Same! I realised I have very little intuition about these things beyond the standard "hyperbolic spaces as saddle-shaped with all lines eventually diverging" basic picture.
@JotaC
@JotaC 3 жыл бұрын
"I hope this made you understand hyperbolic spaces better" Me, with questions I didn't even know I would ask someday: Sure, thanks.
@mixadengitti
@mixadengitti 2 жыл бұрын
This is extremely fascinating.
@mordechailevinson8646
@mordechailevinson8646 2 жыл бұрын
....Thank you so much for posting this video & the "heads-up" on Henry Segerman.....
@Brindlebrother
@Brindlebrother 3 жыл бұрын
Mrs. Parade: "I'm about to crochet in a whole other dimension"
@czaplorandomclips5003
@czaplorandomclips5003 3 жыл бұрын
POV: Her grandchildren are Watching This.
@jellyfish0311
@jellyfish0311 3 жыл бұрын
This is clearer than any other way visualize it
@czaplorandomclips5003
@czaplorandomclips5003 3 жыл бұрын
Ok jelly 😉
@edit3891
@edit3891 3 жыл бұрын
Really cool to see him mention HyperRogue, been playing that for quite some time now, it really shows off how crazy long the circumference of something can get while still having a reasonable radius. It's interesting to think of how a hyperbolic space and plain has more space while still letting you get to areas in a straight line just as fast, but oh boy you're screwed if you didn't go in an exact straight line to where you are going.
@Sgrunterundt
@Sgrunterundt 3 жыл бұрын
0:40 Interesting how the way you actually accomplish morphing the plane into a sphere is to use a hyperbolic horosphere.
@cruepprich
@cruepprich 2 жыл бұрын
Very well done. Thanks!
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