Non-Euclidean Geometry Explained - Hyperbolica Devlog #1

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: 3 700

  • @outdateduser7036
    @outdateduser70363 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_Wolf3 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: kzread.info/dash/bejne/qWWIpLyhlJDZfpM.html

  • @entitydotexe6138
    @entitydotexe61382 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)

  • @lordvincenteperez4196
    @lordvincenteperez41962 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 🏝️

  • @ivojoosten
    @ivojoosten3 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
    @TheVoidIsBees3 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

  • @verylostdoommarauder
    @verylostdoommarauder2 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

  • @rosearachnid879
    @rosearachnid8792 жыл бұрын

    “Hyperbolic crochet” Come on in, sir. That’s the right password.

  • @MilesMetal
    @MilesMetal3 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

    2 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.

  • @etourdie
    @etourdie3 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

    kzread.info/dash/bejne/nKh2uJWAl7Syl5s.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

  • @karynjohnson
    @karynjohnson2 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

    8 ай бұрын

    yes @@The_Moth1

  • @wendysanchez3024

    @wendysanchez3024

    3 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 ?

  • @kirbee1113
    @kirbee11132 жыл бұрын

    Bro the "First I'll have to talk about parallel universes" had me DEAD LMAO. Shoutouts to pannenkoek2012!

  • @efeersoy8880
    @efeersoy88803 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

  • @PleasentDddd
    @PleasentDddd3 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

  • @99kylies15
    @99kylies152 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.

  • @ryanr27
    @ryanr273 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

    11 ай бұрын

    Wtf

  • @carykh
    @carykh3 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

  • @michaelzopff8862
    @michaelzopff88623 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

  • @darelfn
    @darelfn2 күн бұрын

    Meanwhile beings in a Hyperbolic Multiverse losing their minds over how strange the concept of a Euclidean universe seems to them

  • @josephcsible
    @josephcsible3 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
    @CasualCosta3 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*

  • @cynicap8584
    @cynicap85843 жыл бұрын

    "Courtesy of mrs. Parade" Awww, what a sweet, weird quality time

  • @alpkyu5201
    @alpkyu52016 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.

  • @kylehayden3113
    @kylehayden31132 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

  • @koda_pop
    @koda_pop3 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)

  • @rodeo_stomper
    @rodeo_stomper3 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...

  • @spoonkyscenvyscreeleton
    @spoonkyscenvyscreeleton3 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

  • @bigagabriel
    @bigagabriel2 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!

  • @woodant1981
    @woodant19813 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

  • @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

  • @joost5609
    @joost56092 жыл бұрын

    The Mario joke was hilarious and probably the only thing I truly understood. Very interesting and challenging subject!

  • @jeper3460
    @jeper34603 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.

  • @simonsixt2418
    @simonsixt24183 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

    3 ай бұрын

    ​@@marcinlechicki4019he changed his user to anonymous, hulk is retired now sadly

  • @Fulgur14
    @Fulgur143 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!

  • @thewarden4174
    @thewarden41748 ай бұрын

    I really like how you explain all this, it makes it much easier to understand than just the graphs

  • @fobo0053
    @fobo00532 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)

  • @BambinaSaldana
    @BambinaSaldana3 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

  • @enderstriker0718
    @enderstriker07183 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

  • @marcopivetta7796
    @marcopivetta77963 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!

  • @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!

  • @Addsomehappy
    @Addsomehappy3 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.

  • @miljanvideo
    @miljanvideo3 жыл бұрын

    2:23 Talking about spherical geometry me an intellectual: *beach balls*

  • @lobsterfork
    @lobsterfork2 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!

  • @jamesrosco4816
    @jamesrosco48162 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.

  • @centokiVA
    @centokiVA3 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

    8 ай бұрын

    ​@@pattyryopotybuttongamer3063bro what are you talking about

  • @thecheesybagel8589
    @thecheesybagel85893 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!!!

  • @cdawgswizzle7229
    @cdawgswizzle72293 жыл бұрын

    this is a perfect way to explain some of the complex concepts in Geometry Relativity and the 4th Dimension. Thanks a lot!

  • @MayBeSomething
    @MayBeSomething2 жыл бұрын

    "But first, I need to talk about parallel universes" You had me there!

  • @kurlyfryz
    @kurlyfryz3 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

  • @juancgonzalez6537
    @juancgonzalez65373 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

  • @Darthvanger
    @Darthvanger2 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!

  • @EternalPhoenix
    @EternalPhoenix2 жыл бұрын

    This has become my favorite topic to ramble about, ty

  • @Chrischi3TutorialLPs
    @Chrischi3TutorialLPs3 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 KZreadr 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

  • @grandstrategos1144
    @grandstrategos11443 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

    2 жыл бұрын

    I was wondering exactly that jaja! Thank you

  • @nicbajitogaming8947

    @nicbajitogaming8947

    Жыл бұрын

    Geodesics waving to the world 🤗 Hi, geodesic !!

  • @wa5657

    @wa5657

    9 ай бұрын

    oh thank you, i was just hung up on that :v

  • @DigitalDuelist
    @DigitalDuelist Жыл бұрын

    This makes so much more sense than any explanation I have ever seen. Thank you!

  • @centerofoperations9251
    @centerofoperations92516 ай бұрын

    This is the best explanation of the topic I've ever watched

  • @theosouris7063
    @theosouris70633 жыл бұрын

    5:47 I don’t know what I expected from this vid, but it certainly wasn’t a Pannenkoek2012 reference

  • @matsol2158
    @matsol21583 жыл бұрын

    7:30 This guy :"Now we've walked on a pentagon with five right angles" My math teacher :"Wait... that's illegal..."

  • @jarjbarj
    @jarjbarj3 жыл бұрын

    What is hyperbolic space Dragon Ball fans: Now this looks like a job for me

  • @Lobstro
    @Lobstro2 жыл бұрын

    Hey, I just finished playing through Hyperbolica! The thing that kept catching me off guard in the game was how much longer it would take to walk around the perimeter of each of the worlds instead of walking straight across their center. At first glance the world would seem small, but after reaching an edge and spending time walking around it would feel massive. I hope this encourages many more people to make hyperbolic games.

  • @Tubeytime
    @Tubeytime3 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

  • @MeteoritePlayz
    @MeteoritePlayz3 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

  • @sebastianmonten
    @sebastianmonten2 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

  • @unbekannter771
    @unbekannter7713 жыл бұрын

    Dude are you a university professor or something? This is literally the best visual representation of projection and space warping, along with the best and easiest to understand explanation Ive ever come across!

  • @SoftyWalterGames
    @SoftyWalterGames3 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.

  • @crackedemerald4930
    @crackedemerald49303 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

  • @havocmaverick
    @havocmaverick11 ай 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.

  • @greggreen5510
    @greggreen55106 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!

  • @BAVBAVBAV
    @BAVBAVBAV3 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

  • @crxstalline_
    @crxstalline_3 жыл бұрын

    TO ANSWER THAT, WE NEED TO TALK ABOUT *PARALLEL UNIVERSES*

  • @NickMirambeau
    @NickMirambeau2 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

  • @Grey-mo5py
    @Grey-mo5py2 жыл бұрын

    ive watched this video so many times and I love it every time

  • @MozartSrs
    @MozartSrs3 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

  • @JohnsontheFly
    @JohnsontheFly3 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

  • @blue-ou6uf
    @blue-ou6uf Жыл бұрын

    this is amazingly explained omg. so much content i expected to be overwhelming but isnt.

  • @adrienlawrence1024
    @adrienlawrence10242 жыл бұрын

    was reading about relativity and when the book started talking about the shape of the universe and stuff I was pretty lost, this video helped a lot, didn't even know this was going to be related to what I was trying to figure out

  • @leebee42069
    @leebee420693 жыл бұрын

    Me: I'm going to crochet a hat! The hat: 3:20 Me: why does this always happen?

  • @Epicvibes999
    @Epicvibes9993 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”*

  • @DenethorDurrandir
    @DenethorDurrandir2 жыл бұрын

    Before watching this, non-euclidean geometry ment "It's not supposed to make sense", after watching this, it makes perfect sense. As a fan of SCP wiki I hear/read about non-euclidean spaces quite a lot, now I can perfectly imagine just how a non-euclidean space described in the article (usually hyperbolic geometry but it sounds cooler) would look like

  • @Franceoceano
    @Franceoceano7 ай бұрын

    It's very interesting how hyperbolic movement resembles the formation of fractals. My experiences with ayhuaska are geometric and are very similar to the dynamics of hyperbolic space.

  • @hytalefanboi7471
    @hytalefanboi74713 жыл бұрын

    "do u like maths or programming?" code parade: "yes"

  • @randairp

    @randairp

    3 жыл бұрын

    Fun fact: by the Curry-Howard Correspondence, maths and programming are literally identical (two perspectives of the same thing).

  • @jedizombiekiller9065

    @jedizombiekiller9065

    3 жыл бұрын

    @@randairp Fun Fact: semicolon

  • @LionsInBoots
    @LionsInBoots3 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

  • @mixadengitti
    @mixadengitti2 жыл бұрын

    This is extremely fascinating.

  • @mordechailevinson8646
    @mordechailevinson86462 жыл бұрын

    ....Thank you so much for posting this video & the "heads-up" on Henry Segerman.....

  • @bubblehead9548
    @bubblehead95483 жыл бұрын

    Ok I was completely lost until my drowning brain just screamed YOU CAN FIT MORE SPACE IN SPACE and I understood this for approximately a quarter of a second before my dumb mortal brain decided that was too much. You have obviously entered into some terrible contract with Yog-sothoth to have such a deep understanding of hyperbolic space, and for that I fear and respect you, and legit can’t wait to play hyperbolica

  • @Brindlebrother
    @Brindlebrother3 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 😉

  • @renormalization
    @renormalization11 ай бұрын

    This is a great video to motivate the anti-de Sitter spacetime (hyperbolic spacetime) for holography. Nicely done!

  • @mellymoore8390
    @mellymoore8390 Жыл бұрын

    Having never known any of this even existed before and suddenly being thrown at Lobachevski’s Theory of Parallels and asked to write a paper on it, THIS helps. Thank you!

  • @tentimestay9181
    @tentimestay91813 жыл бұрын

    "But first, we have to talk about parallel univers-- I mean parallel lines" so unexpected, genuinely cackled

  • @hitzcritz
    @hitzcritz3 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

  • @MiScusi69
    @MiScusi692 жыл бұрын

    Incredible! I've always thought that non-euclidean spaces were something impossible to think about and that only the most skilled mathematicians could have a grasp about the math behind it; you've been really helpful! I've just got a question: why aren't these geometries explained in lyceums?

  • @IllyTVuk
    @IllyTVuk4 ай бұрын

    ‘Stay hyperbolic’ I don’t think I’d want to because every time I would try to move I would experience extreme pain

  • @albingrahn5576
    @albingrahn55763 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

  • @Lugmillord
    @Lugmillord3 жыл бұрын

    When the Mario 64 music kicks in, I knew what was coming and I wasn't disappointed.

  • @dieguillo93
    @dieguillo93 Жыл бұрын

    Absolutely interesting! THank you so much! To me, the parabolical movement feels so smooth and in a sense quite natural. I see as well as the 3 methods could simbolize the unity between the macrocosmos and the microcosmos, being the sherical as a reflection of the macro, euclidian as the eye of the observer and parabolic as the ladder to the microsystems. For example you can see how parabolical estructures relate more to organic growings and spherical more to celestial objects.

  • @Memerath
    @Memerath3 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*

  • @alpha3836
    @alpha38363 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

    2 ай бұрын

    I see what you did.

  • @JotaC
    @JotaC3 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.

  • @andredominguez3199
    @andredominguez31992 жыл бұрын

    I don't know why KZread recommended me this, but I love it.

  • @lifeofalonelywhale
    @lifeofalonelywhale4 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.