Non-Euclidean Geometry Explained - Hyperbolica Devlog #1
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- Опубліковано 14 тра 2024
- 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
When you stop paying attention in calculus for 3 seconds
Too real
holy shit how did you do that lol
Sorry can someone explain this to me? I didn't take calculus and now I feel left out.
@@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
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
"But first we have to talk about parallel universes" nice.
I’ll be honest, that killed me.
specially love the Mario 64 extra reference with the music
To answer that, we need to talk about parallel universes
I think it's a reference to the youtube channel TerminalMontage
@@OneShot_cest_mieux *Pannenkoek2012
The meme started there
can you just imagine beings of 4D using our 3D to explain 5D
Quite literally no🤣
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.
@@shouvik8267 i have a 0d brain
@@shouvik8267 transparent cube: bro where i am i don't exist?
@@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 🏝️
CodeParade: "Stay Hyperbolic"
Me: *proceeds to occupy the entire volume of the universe*
There's not enough room for the two of us!
@@lullabypoppera3914 then we're just gonna have to share
*cue just the two of us
@@lullabypoppera3914 Correction: Three! That's right, I sort of understood it! *proceeds to occupy the entire volume of the multiverse*
@@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)
I feel like I just gained 100 braincells but lost 300 points psychic damage.
That's what math does to you. You gain insight, but you lose sanity.
I always knew math was black magic
@@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.
So it's Bloodborne.
Oh god
+1 intelligence
-10 HP
"Honey, can you knit me some non-euclidean planes?"
Lmao 😂
no :)
"Look at me eviscerating you, and you'll see some hyperbolic intestines"
"Are you sure"
"I was joking, here it is"
Search for Crocheting adventures in hyperbolic world
Daina Taimina did a nice Ted talk on hyperbolic crochet: ua-cam.com/video/w1TBZhd-sN0/v-deo.html
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.
It's simple really
@@lullabypoppera3914 how old are you?
Now it makes me wonder how the final season of the Magnus Archives looked
@@efegokselkisioglu8218 counter-argument, how old are you if you can’t get a joke?
I think euclidean geometry is more horrific than hyperbolic. It confines your mind too much
“Hyperbolic crochet”
Come on in, sir. That’s the right password.
Greenland looks like it's about the size of Africa, but in reality it's about the size of Greenland
-Map Men
ua-cam.com/video/jtBV3GgQLg8/v-deo.html for the uninitiated
Map Men MAP Men MAP MAP men men
It’s actually MAP men MAP men MAP MAP MAP men men men
@@d.l.7416 MAP men MAP men MAP MAP MAP men men
men
map men map men map map map men men
"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.
Wait, if a black hole is spherical geometry, are white holes hyperbolic?
@@hyperbeast4340 maybe
The perfect crossover doesn't exi...
But I understood more and I am twelve years old. I am too nerdy for my own good
@@karynjohnson You will read your comment in 10 years and cringe.
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.
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/
@@CodeParade Oh hey, she's friends with vi hart! Dang, small world. more people should do stuff like this ^^
@@Queer_Nerd_For_Human_Justiceis she the flexagon person?
yes
@@The_Moth1
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 ?
Bro the "First I'll have to talk about parallel universes" had me DEAD LMAO. Shoutouts to pannenkoek2012!
“All the angles are 0 and the area is pi.”
As someone who loves geometry, this statement really through me off.
PleasentDddd I guess you just gotta think it threw a little...
Yuvraj Sethia frick
As someone who also loves geometry, it really turned me on lol
threw*
I’m hungry now
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!
whats a triangle
I think the channel 'think twice' has a video about the derivation.
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.
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
hi cary
'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.
Eventually, Mario will build so much negative speed, which he had built up for over 12 hours to leave this projection of 5D space
Wtf
"Hey honey, do you think you could knitt me a projection of a hyperbolic tiling in 3D?"
@SArpnt nice
@SArpnt but who asked
@SArpnt if nobody did, then why did you even bother to do it?
@SArpnt very obviously nobody and i pointed that out pretty clearly if you could read
@SArpnt thanks for criticizing your own response
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.
Exactly!
@@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")
Oh hell, i knew i'd seen that somewhere before, i guess that explains it!
That's what came to mind for me as well!
It also reminds me of certain gears
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.
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
The parallel universe bit caught me off guard lmao
surely the most ambitious crossover ever
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
PannenParade
an a press is an a press...
@@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)
I actually just got non Euclidean tiling in my bathroom.
wait seriously
How was it?
You have a curved bathroom floor? Isn't that kind of impractical?
I too enjoy my showers in R'lyeh
@@doppelrutsch9540 yeah but
i imagine it looks cool
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.
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!
“Think about light bending around the curved space of a black hole.” Ah yes
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
@@beanmcknee1610 why would the color of the hole change?
.
@@tristenarctician6910 no sorry what I meant was is that the coin represents light itself, not light in color
I hope that helps
@@tristenarctician6910 particle get excited and emit radiation that we perceive as a colour change
Just think of a magnet and a ball bearing, just that they can't touch
“We’re only looking down on it because we are higher dimensional beings living in a 3D universe.”
*The 4th dimensional being watching me take a dump
@UltimateGeek at the same time
We actually live in a 4D world as 3D beings
That's why we can't see the full extent of time
@@JotaC Time is not a SPATIAL dimension, stating that we live in a four-dimensional world is irrelevant, we live in three-dimensional space
Nykal absolute brainlet
The Mario joke was hilarious and probably the only thing I truly understood. Very interesting and challenging subject!
"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
"Courtesy of mrs. Parade"
Awww, what a sweet, weird quality time
No one:
My brain at 1 am: let’s try to understand non Euclidean geometry when I already have a hard time with algebra
its one forty nine right now and I face the same dilemma
Same :'(
I dont even understand algebra wtf
same, but its 4:04 am for me
STOP IT PLEASE THIS IS SO FREAKING RELATABLE ITS 12:36 FREAKING AM I CSNT SLEEP!!!
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!
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.
Honestly, I have no clue what any of this means, but this dude's voice is really relaxing to me.
Jøhnny Rëtznøvishchä Yeah. Too bad my inability to understand what he’s saying gives me a headache.
I want to understand...
"But first we have to talk about parallel universe-I mean parallel lines."
*We were on the verge of greatness,we were this close.*
We just needed enough speed to get to the next PU!!!
@@GlyphicEnigma just blj for 11 hours and you should have enough!
the music tho
its from another video about weird stuff a bit similar to this
@@TheaPeanut_69old it's the file select music from Mario 64
Man, makes me miss watching Pannen
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!
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!
8:07 Imagine creating a black hole by throwing a baseball really hard in spherical geometry
Maby our universe is spherical, and that "realy hard" to get speed enough is force to give that baseball light speed.
@@marcinlechicki4019 If the ball was thrown that hard it would be ripped to shreds.
@@Anonymous-zd1ow You are talking from experience Hulk?
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
@@marcinlechicki4019he changed his user to anonymous, hulk is retired now sadly
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).
Marek Čtrnáct You are indeed... A Super Nerd!
*Guitar Riff*
tl;dr?
@@csicee TLDR: In non-Euclidean geometries, you are forced to measure lengths in a very specific units in order to get simplest possible formulas.
@@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/
@@Fulgur14 phenomenal insight and work, thanks! keep it up!
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.
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)
that feeling when non-euclidean geometry makes more sense than euclidean geometry
Completamente difiero.
@@Shrek_es_mi_pastor why your pastor is shrek?
Euclidean geometry is just what happens when you zoom in on a surface infinitely.
oof lol
@@TaiFerret sounds strange to me, but i dont know enough topology to disprove it
"But first we have to talk about parallel universes." I'm having a panic attack.
*quick creepy distorted version of the Mario 64 File Select music starts*
pannen attack*
No you aren't
@@spikey288
youre not their dad
@@thatoneguy9582 not you again
I really like how you explain all this, it makes it much easier to understand than just the graphs
This has become my favorite topic to ramble about, ty
Instructions unclear, become a flat-earther.
I'm ok I don't want to be a flat earther
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
@@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?
Instructions unclear, Teleported to another plane in existence and start being trained by Sherk to fight against an Otaku army
Oh I became a non-Euclidean-earther.
*i can hear melanie Martinez when a bird chirps now*
"Stay Hyperbolic!"
oh so you wish me to tear myself apart every time i walk anywhere gee thanks
That only happens when you apply a significant amount of force to yourself.
The Incredible Hulk Correction, velocity. Depending on the hyperbolic space (depending on r) even walking or breathing could tear you apart.
this is what happens when you try and and be parallel, but you'll learn.
I think OP was joking by being hyperbolic in his reaction?
@@diophantine1598 Oh thank you for correcting me! Oh Jesus this is 7 months late XD.
this is a perfect way to explain some of the complex concepts in Geometry Relativity and the 4th Dimension. Thanks a lot!
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!
5:47 I don’t know what I expected from this vid, but it certainly wasn’t a Pannenkoek2012 reference
2:23 Talking about spherical geometry
me an intellectual:
*beach balls*
This is the best explanation of the topic I've ever watched
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
CodeParade: oh god, PLEASE STOP USING THIS!
Pringles: no u
Edit: how do I have about 200 more likes a month later ty
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.
PRINGLES IN 4D
@@EliteOcto lol
@@EliteOcto N O N E U C L I D E A N P R I N G L E S
ElPseudocrítico E A T
"But first we have to talk about parallel universes"
*SM64 music plays*
Ah, i see you are a man of culture aswell.
Bismuth be like
Explain
@@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 UA-camr 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.
@@Chrischi3TutorialLPs YOU CAN'T JUST PRESS THE A BUTTON A HALF OF A TIME IT'S STILL AN A PRESS
This makes so much more sense than any explanation I have ever seen. Thank you!
this is amazingly explained omg. so much content i expected to be overwhelming but isnt.
this genuinely has taught me more about non-euclidean geometry than my classes have
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
this genuinely has taught me more about *euclidean* geometry than my classes have
bruh why tf would you be taking non euclidean geometry in school
@@pattyryopotybuttongamer3063bro what are you talking about
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.
This clarifies things quite a but for me. Thank you!
I was wondering exactly that jaja! Thank you
Geodesics waving to the world 🤗 Hi, geodesic !!
oh thank you, i was just hung up on that :v
....Thank you so much for posting this video & the "heads-up" on Henry Segerman.....
ive watched this video so many times and I love it every time
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!
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!
Tell me about it
holonomy happens in gmod
@@cheesepop7175 bro it happens fucking everywhere
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
No one:
My blanket when I’m trying to find the short end at 3am: 3:00
Underrated
its even 3:00
Lol
what blanket did you buy?
why "no one:" is needed everywhere. How is it helping the joke
@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!
This is a great video to motivate the anti-de Sitter spacetime (hyperbolic spacetime) for holography. Nicely done!
7:30 This guy :"Now we've walked on a pentagon with five right angles"
My math teacher :"Wait... that's illegal..."
As soon as you said "there wouldn't even be a horizon" my mind exploded trying to visualise earth without horizons
If you live in America, the sky is Australia.
Thanks for this, your channel helps my mind.
I love that reference at 5:46, made me laugh. thanks for that
That awkward moment when hitting a baseball in spherical space creates a naked singularity and by extension accidentally creates 0-dimentional space
So relatable
“It only looks 3D because we are higher dimensional beings, looking down on the flatlanders.”
Hip Hop Artists: *”haha , fisheye go wobble wobble”*
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!
I love this concept so much.
And Hyperbolica is an amazing game.
Me: I'm going to crochet a hat!
The hat: 3:20
Me: why does this always happen?
5:44 "But first, we have to talk about parallel ̶u̶n̶i̶v̶e̶r̶s̶e̶s̶ lines!"
*_my disappointment is immeasurable and my day is ruined_*
mario
the lines are still universes
@@TheaPeanut_69old one dimensional, yes
This is extremely fascinating.
"But first, I need to talk about parallel universes"
You had me there!
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!!!
Isn't the opposite of sine just minus sine?
I guess you need to define "opposite"
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.
Or it could be cosecant. It’s the reciprocal of sine.
@@zacozacoify sinh is, in a way, sin rotated 90 degrees: sinh(x) = -i sin (ix)
@Multorum Unum It can be if sin(ix) is pure imaginary.
An A press is just an A press. You can’t just call it a half.
Bro, how many QPUs are you on?
@@cmdrkradenguard6808 like maybe 5 or 6 my dude
This a reference to that half A press Mario run?
you half Alive or half dead?
Ok TJ 'Henry' Yoshi
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.
Very nice explanation! Thank you.
Hyperbolic space: when you have more space every space you space
Xzibit would like to know your location
"But first, we have to talk about parallel univers-- I mean parallel lines" so unexpected, genuinely cackled
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.
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
When the Mario 64 music kicks in, I knew what was coming and I wasn't disappointed.
5:44 „I was already 5 PUs ahead of you...“
4* because then he'd be QPU misaligned
it hurts the brain to watch your videos. I love it
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.
can’t wait to see the 0.5 A-press run for hyperbolica!
well, we need 4 things:
HSPW, forcing scuttlebugs to have a jamboree, pannen, and TJ """"Henry"""" Yoshi.
@@Lance0 don't forget groundpounding the misalignment
"do u like maths or programming?"
code parade: "yes"
Fun fact: by the Curry-Howard Correspondence, maths and programming are literally identical (two perspectives of the same thing).
@@randairp Fun Fact: semicolon
I've been following for ages and finally I can play it. My brain liked your game. My stomach did not. 10/10.
this is giving me very good insight for special relativity. Thank you!
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
Mrs. Parade: "I'm about to crochet in a whole other dimension"
POV: Her grandchildren are Watching This.
This is clearer than any other way visualize it
Ok jelly 😉
ive been always thinking of wormholes and space bent in 4D but ive never seen this simple explanation, daaamn! nice video!
also, if we count the time axis too, like adding one more axis on spheric 2D world it would be confusing as hell but it would look really cool lol.
This is gorgeous! (And very hard to comprehend)
"I hope this made you understand hyperbolic spaces better"
Me, with questions I didn't even know I would ask someday: Sure, thanks.
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!
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.
I bought a VR headset for the first time and was super excited when I saw Hyperbolica on Steam as a VR compatible title. I'm really looking forward to trying it out!
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!