We (could) live on a 4D Pringle (Non-Euclidean Geometry and the shape of the Universe)

Рет қаралды 424,336

Күн бұрын

Everything we were taught in geometry falls apart if our universe is curved. This video is a friendly introduction to non-Euclidean geometry and how cosmologists used the Cosmic Microwave Background to calculate the curvature of our universe.
See Part Two of the shape of the universe duology here: • So, space isn't a 4D P...
This video is a submission to the second Summer of Math Exposition #some2. Hope you enjoy it!
Thank you to Caleb Birtwistle for captioning!
If you want to try out some of the code used in the video, check out this notebook on Geodesics on a Pringle: drive.google.com/file/d/1p2dv...
Become a Patreon member: / physicsforthebirds
0:00 Origami cranes, intro
3:04 Axioms of Euclidean geometry
5:24 Hyperbolic geometry
7:59 Curvature of our universe with the CMB
11:44 Conclusion
Alperin, Hayes, Lang, "Folding the Hyperbolic Crane": www.langorigami.com/wp-conten...
Euclid, Elements: archive.org/details/euclid_he...
Playfair's Axiom: archive.org/details/elementsg...
Bolyai, The Science Absolute of Space: jscholarship.library.jhu.edu/...
Liddle, An Introduction to Modern Cosmology: alpha.sinp.msu.ru/~panov/LibBo...
Olive, Peacock, "Big-Bang Cosmology": pdg.lbl.gov/2018/reviews/rpp2...
Planck 2018 results: arxiv.org/pdf/1807.06209.pdf
Image Credit NASA / WMAP Science Team.

Пікірлер: 635

@physicsforthebirds Жыл бұрын

Thanks for watching, everybody! To keep the video short and engaging for viewers with any background, there are many times that I make approximations, hand-wavy arguments, and even mistakes. Here are a few corrections: 8:27 makes it sound like there is a single wavelength of light emitted from hydrogen in the CMB. In reality, the neutral atoms that formed during recombination were less likely to interact with light, so the CMB is largely made up of the the thermal radiation that was able to propagate once atoms formed. It is (and was) a black-body with a spectrum of wavelengths. 10:59 Although this is the right motivation, cosmologists don't "measure" patches in the CMB to get the angular size. The circles that I drew might be misleading here. Instead, the sky map is decomposed into spherical harmonics and the components are then plotted. The peak angular features size is taken as what I called "theta" earlier. Please, have some discussion in the comments and always let me know if I miss anything!

@pyropulseIXXI Жыл бұрын

I subbed

@thetruthstrangerthanfictio954 Жыл бұрын

As an interesting fact, a trumpet/pringle shaped universe would have an infinite amount of 3D space on it's surface, but finite 4D volume inside.

@physicsforthebirds Жыл бұрын

@@thetruthstrangerthanfictio954 That's right! In fact, it would have the same volume as a hypersphere with the same radius. I show a way to figure that out without integrals in my video on the tractrix: kzfaq.info/get/bejne/pLdig8iirNG1lp8.html

@joeyd12254 Жыл бұрын

you are a smart birb

@stolasamon-seere5319 Жыл бұрын

What is the space around a massive object? (

@jaytravis2487 Жыл бұрын

All this guy needs is exposure. Already way better than some channels with 4million+ subs

@Fire_Axus Жыл бұрын

Nope

@jotarokujo1189 Жыл бұрын

@@Fire_Axus shut up

@ICREAMTOHANDTIE Жыл бұрын

real

@ioium299 Жыл бұрын

Yes

@SublimeWeasel Жыл бұрын

bro what the fuck i thought he had more subs until you said so he def. deserves more

@lexinwonderland5741 Жыл бұрын

I've been studying non-euclidean geometry for years, and I've never seen the examples of the cranes. Brilliant!!

@w花b Жыл бұрын

But the Pringles with ink in them are inedible now :(

@Anonymous-ow6jz Жыл бұрын

@@w花b says you!

@joaomrtins Жыл бұрын

I want to make them

@SnakeBush Жыл бұрын

Being a creative has its perks

@JohnDlugosz Жыл бұрын

Correction: the CMB is not a single spectral line of hydrogen. It is black-body radiation that covers a continuum of wavelengths.

@physicsforthebirds Жыл бұрын

Thanks for pointing that out! There were a lot of shortcuts I made for the sake of presentation, especially while describing the CMB, so this is helpful.

@jettmthebluedragon Жыл бұрын

@@physicsforthebirds even so the Big Bang does NOT mean big bang it’s just microwave background 😑the same energy we use to cook our food 😑and even so you could make a satellite that only measures infered light meaning the CIB 😑so energy alone does NOT mean big bang it goes WAY deeper 😑

@cheeseycheezy Жыл бұрын

@@jettmthebluedragon i dont mean to make fun of what u said the quantity of 😑 in this comment is hillarious 😑

@cheeseycheezy Жыл бұрын

but* would correct it but cant edit for some reason 😑

@jettmthebluedragon Жыл бұрын

@@cheeseycheezy well THIS means 😑like bruh seriously? This means or this means I’m serious 😐😑

@viktorgrezu7874 Жыл бұрын

This video is a goddamn experience. From the beginning I felt there was something special in the way you convey ideas. This is the only channel from the SoME2 i've subscribed to and I really hope you can make more.

@daynhues Жыл бұрын

This was super cool!! Really nicely done and I really like your bigger picture message at the end!

@physicsforthebirds Жыл бұрын

I'm glad you liked it!

@scharpmeister Жыл бұрын

You know you’re a great educator when the video is interesting enough to divert my attention from watching shorts to a video on geometry

@AndrewBrownK Жыл бұрын

I absolutely love this. I think humans will be able to intuitively grasp 4 dimensions and MAYBE more if/once we have the right tools to explore them, especially with VR. We'll never grasp it like a hypothetical native 4D being, but I'm sure we can get a pretty solid grip with enough exposure. And after we have a generation of people who've played with this enough, we'll have a generation of scientists reading totally new insights from Einstein's work.

@physicsforthebirds Жыл бұрын

That's a good insight. In the last decades, LEGOs and computer graphics have made the average human much more comfortable with thinking in 3D and you can see it rubbing off on today's scientists and engineers. If we come up with a clever way to visualize it, then the same thing could happen with higher dimensions!

@flyingjudgement Жыл бұрын

@@physicsforthebirds Hi me and my team making a racing / fightig game, half of the maps will be in 4D. My aim is to give an intuiteve feel for 4D space and how to exist and achive goals in it. So far i can only understand the 4D tourus idea and its variants if you can point me in the right direction how to digest this difficult topology topick we could probably gexpand and make the idea stronger. By the way Love this video its wery well explained how non euclidien geometry throws everything in chaos, yet its all around us in from a swerly broccoly to rock formations. Thanks for your video again Before I havent considered a gentle 4D curve in our maps but now.. I cant even imagine what visual distortions starts to appear if we build everything this way, cant wait to simulte it and see the results!

@physicsforthebirds Жыл бұрын

@@flyingjudgement It feels like a crime to not mention topology in a video about the shape of the universe, so I was close to covering it. But I think the most useful way to understand alternate 3D topologies is to first understand 2D surfaces as square planes with their boundaries glued together. Here's a silly but helpful page on that: pi.math.cornell.edu/~mec/Winter2009/Victor/part1.htm From there it's a little more straightforward to image 3D hypersurfaces as cubes with their boundaries pastes together in different ways. I think that would make a sweet game!

@pyropulseIXXI Жыл бұрын

It is impossible to ever visualize 4D. VR won't change that. All you can do is project 4D into lower dimensions and look at projections

@flyingjudgement Жыл бұрын

@@pyropulseIXXI There is a lot more one can do! Think about a slim papper how many ways you can warp its shape! Like in this video this didnt occour to me before its an added complexity. You can wrap it aroun a 3D space spin it in 3D space, rotate its axis to another axis x to y till its upside down glue it however you like and still bend it. Like planets bend space towards them forming gravity. Physics for the Birds Thanks for the resource ! I make sure who ever plays our game gets a good feel of hyperspaces!

@killermetalwolf2843 Жыл бұрын

i actually encountered this concept while writing a paper last month, cool to see it explained in detail here! I would love to see a video on the expansion of the universe, the hubble constant, and the hubble tension, which is what i was researching when i came across this concept

@physicsforthebirds Жыл бұрын

Thanks for the suggestion! I was actually going to include some of that in the video I'm working on now, but I decided to hold it for the future. Maybe I'll make it sooner than later

@yumnuska Жыл бұрын

This was a great video, I hope you make more. The journey for me was wonderful! Origami: I’m interested, and I learned something about appendages to shape that I didn’t know! And I loved the background props reinforcing the point. Geometry: I’ve casually studied different geometries, so nothing new here for me but you presented it wonderfully. Cosmology: I like to pay attention, but don’t study it, so there were some details I hadn’t thought about before. And then the punch line. Wait what‽ We’re confident that the universe is flat‽ I mean, I can see the connections, but I really wish you’d spent more time there. I hope you’ll make a follow up with more detail. I really loved this video. Great work.

@physicsforthebirds Жыл бұрын

I'm glad you enjoyed it! It always helps to know what people like and what they don't.

@krow610 Жыл бұрын

this guy explains stuff so well i actually feel smart after watching this video he deserves at least like 2 mil subs

@nice3294 Жыл бұрын

I loved the origami crane intro! It really added to the mystery of how you managed to break the interior angle sum

@The_fusion_physics_guy Жыл бұрын

You make truly fantastic videos. As a physicist I don’t know if I’ve ever watched this entertaining/engaging but also knowledgeable content, I was really surprised I hadn’t seen your videos sooner and that you had a relatively small audience. Good luck, I really hope your engagement increases, you’re making great content! Your voicing and editing are also very good for this genre, beyond just the content itself.

@lolzboiii8371 Жыл бұрын

I LOVE THIS GUY!!!! This is the first video I have watched on his channel I really hope you reach millions soon!

@nyuh Жыл бұрын

omg i love the art and the animations are so neat. and the information was explained very clearly. also, the ending was quite nice and satisfying. so, really nice video over all!! btw i highly recommend everyone to play the game hyperbolica. it takes place in a world with hyperbolic geometry. its super trippy!

@ZenoRogue Жыл бұрын

Have you tried HyperRogue though? :) It does more non-Euclidean things than Hyperbolica and it has a free version.

@nyuh Жыл бұрын

@@ZenoRogue omg ill try it then

@danielson9007 Жыл бұрын

LOVED the origami. really a great way to explane this topic. Thanks for the great vid. more attention needed.

@shipwreck9146 Жыл бұрын

Awesome explanation of curved spaces. I took a differential geometry course in college, and this type of stuff is where math starts to get really cool to me.

@sirqueensby6052 Жыл бұрын

Found your youtube channel recently and it's quickly become one of my favorites, thank you

@ambrosebussey4672 Жыл бұрын

Why was I actually so relieved by the ending, it's weirdly comforting that this universe has the number of dimensions that I think it does.

@rightwingsafetysquad9872 Жыл бұрын

The universe could still have several more dimensions, it's just flat in those dimensions. Think of a cylinder. It's round on the X-Y plane, but flat on the Z axis. Still very much a 3D object. Or think of a piece of paper suspended in air. It's a 2D object (sort of) in a 3D world (probably).

@wisconsinwintergreen6296 2 ай бұрын

Calabi-Yau Manifolds: Allow us to introduce ourselves

@DanaTheLateBloomingFruitLoop Жыл бұрын

Really interesting and thought provoking! The bit at the end juxtaposing humanity's understanding of the earth's and the universe's curvature, or lack thereof, was very neat.

@TheNellNadie Жыл бұрын

I LOVE your intro. I usually hate intros no matter the content but oh my goodness, you made it an art!

@aki128_ Жыл бұрын

i'm so glad youtube recommended me this channel, you're doing such a great job

@SpeedFranklin Жыл бұрын

Such a great video! Thanks for sharing and I didn't mind the mistakes (especially when you found them and mentioned them below). Perfection is not even possible, so let's not even entertain the idea that we will get there. Animations, music , and pace are all on point!

@CognitiveOffense Жыл бұрын

Truly excellent. Thank you for making this delight.

@physicsforthebirds Жыл бұрын

I'm really glad you enjoyed it!

@iwatchedthevideo7115 Жыл бұрын

So rare and refreshing these days for the YT algo to recommend new and great science channels. This is A+ level science communication in an interesting and fun way.

@abbe1255 Жыл бұрын

Great video! You bring out a lot of real life equivalents that really makes the subject easy to digest

@JPMESrocks Жыл бұрын

Great job! Really cool way of explaining these concepts. I was hooked in since the beginning.

@NoahAlbrecht Жыл бұрын

I’m currently a part of a research stream at my university focused on the “geometry of space”, so this video was a super cool breakdown of non-euclidean geometry

@iamtraditi4075 Жыл бұрын

Dude, this is really really good! Loved every second of it

@Fire_Axus Жыл бұрын

how?

@MPHshoots Жыл бұрын

This video was incredible. Great job my dude

@Vinzmannn Жыл бұрын

Damn. Love all of it. Love your reading, love your explanation, love your animation.

@nadaelnokaly4950 Жыл бұрын

I am so happy I found your channel it is soo exciting and beautiful and inspiring! waiting for more 🎉🎉🎉

@pairadeau Жыл бұрын

Magnificent work. Bless.

@Troloze Жыл бұрын

This one might be my favourite SoME2 entry, good job.

@prof_as 8 ай бұрын

beautifully explained! Great work, keep it up

@CookiePieMonster Жыл бұрын

We need more intellectually interesting KZfaqrs like you bro, hope you keep growing.

@LoverOfMuch Жыл бұрын

oh wow. i love the evolution from topic to topic

@MartinDe123 Жыл бұрын

Great video and a very nice explanation of non-Euclidian geometry

@willi00willi Жыл бұрын

oh neat, this channel features two of my favorite things: birds and physics! immediately subscribed! also, the storytelling in this video is amazing, and the concept of making an origami crane out of a sheet with non-zero curvature will now haunt me forever

@disnecessaurorex4908 Жыл бұрын

I know the concepts presented here but this is my favorite some2 video. And a nice little lesson at the end.

@themightyripples6582 Жыл бұрын

This video was awesome, hope you get even more popular, you deserve it :)

@Anonymous95202 Жыл бұрын

incredible content, so glad i found this channel

@emrezkc Жыл бұрын

Magnificent video, well done.

@jessywang1672 Жыл бұрын

UNDERRATED YOU DESERVE MORE RECOGNITION

@dmc2925 Жыл бұрын

Dope vid! The algorithm really came through 🤟🏿

@willplaymusic1 Жыл бұрын

you are disgustingly underrated. i absolutely love your channel

@xynonners Жыл бұрын

damn production quality is insane

@cardboardturtle5470 Жыл бұрын

Incredible. So glad you're getting picked up by the algorithm this early

@syednaqvi7489 Жыл бұрын

Amazing video! Really expanded my perspective about curved geometry:)

@ace1234LIVE Жыл бұрын

This was fantastic! Subscribed!

@donchaput8278 Жыл бұрын

Absolutely excellent video!

@andrebenites9919 Жыл бұрын

Those are great! I just heard about your channel in the Jazz video. I hope you keep doing your great work, it is fantastic and very interesting

@siddharthjadhav9233 Жыл бұрын

very important knowledge, hope you get the light. well deserved

@donlasagnotelamangia Жыл бұрын

Perfect video! Origami, maths, physics, astronomy? Dream combo!

@syllabusgames2681 Жыл бұрын

Well that was an absolute journey. While you bring in quite a few separate ideas, everything flows together very well. I’ve been trying to give SoME2 creators feedback, but the only real suggestion I have for your video is to remove the cuts to black between sections. They’re a little jarring. Regardless, this was great, and this is the only channel I’ve subscribed to from this years SoME event.

@physicsforthebirds Жыл бұрын

Thanks for the feedback! I learned a ton about editing while working on the video and I definitely have improvements to make

@yumnuska Жыл бұрын

I quite liked the black cuts, they gave me a chance to digest what was said before. But I do understand feeling that they’re jarring; to each their own.

@yumnuska Жыл бұрын

@@physicsforthebirds see my reply to the parent for this. Great work!

@yumnuska Жыл бұрын

However, on my second time through (I rarely watch something twice on purpose, BTW, so take this with that in mind) there’s a section about 3 minutes in with several cuts to black that I did find excessive and pointless. But there are others, after you make a point, or before changing direction, that I did appreciate. Those cuts gave me a chance to think and breathe.

@OpenSourceAnarchist Жыл бұрын

@@physicsforthebirds I like the cuts to black. It reminds me of History of the Universe's videos on KZfaq, and that's one of my favorite channels! Wonderful video

@arinalikes5911 Жыл бұрын

This is such a good explanation of non Euclidean geometry. Thx bird

@user-oe3kz8ww7d 11 ай бұрын

This just randomly appears in my recomended for no reason and suddenly this guy goes ahead and explains to me what the CMB is, which is something I had been wanting to know for a while as I knew it was evidence for the Big Bang theory. Tbh, I'm sticking around.

@khaki.shorts Жыл бұрын

Commenting just to say I was here at 6.6k subs! This channel will go far.

@fusion325 Жыл бұрын

HOLY MOTHER OF UNDERRATEDDDD!!

@Garrida Жыл бұрын

This video was beautiful

@Asterism_Desmos Жыл бұрын

I love this video so much

@Sugar3Glider Жыл бұрын

Funny Birb, you remind me of the time I was given "The Impossible Problem," wherein you draw an X inside of a Square inside of a Diamond. With instructions to draw this without lifting the pen and without tracing the same line more than once. I started with a post-it note pack, and 6 hours later finally had the realization that it can be solved; it requires you to fold the four corners into a single point, and then draw across the newly created plane.

@Thejosiphas Жыл бұрын

4 minutes in this is already so great

@Thejosiphas Жыл бұрын

too fire

@appidydafoo 7 ай бұрын

Excellent, thank you

@AnimatedPlayer Ай бұрын

Hey,,,, great video and a soothing voice. Earned a s sub man, ill binge watch all your content now

@jayitsthenerdyninja9891 Жыл бұрын

I am often excited about things, but man I forgot how awesome math can be

@user-tw4no3db8v Жыл бұрын

Dis the quality content we deserve❤

@RafaelMunizYT Жыл бұрын

funny how I always hated math (and still do) but I love astronomy so the deeper I get into this subject the more I see about maths. I only like the theoretical part so I tend to stay away from all the calculations but sometimes I happen to come across them and over time I'm starting to watch more and more math videos related to physics. I don't know if I'll ever like or be good at math but I wish I did because that would remove the barrier that keeps me from pursuing an astrophysics career

@asdf56790 Жыл бұрын

Amazing video, keep up the good work :)

@silvesterreen2902 Жыл бұрын

I thought that sub count said 8 mil, not 8k, the quality of the video is so high! Thank you for the fun explanation of a complex topic, subbed

@realthepingvin Жыл бұрын

damn, this is cool, make more of this, you should be a HUGE content creator in future

@megacarls9894 Жыл бұрын

Just discovered your channel. What a good video! :)

@stevenyang4370 Жыл бұрын

love your video! more please!

@kubaskrzypkowski6445 Жыл бұрын

Thank you for making geometry fun

@SteveAcomb Жыл бұрын

this is the best named video I’ve seen in months 😂

@Costavka Жыл бұрын

"Today were going to prove that the universe is a pringle using some paper and a brain"

@markzambelli Жыл бұрын

Wonderful video, thankyou.

@JonMurray Жыл бұрын

Brilliant video dude. New subscriber ✌🏻

@steadfastwolf2159 Жыл бұрын

I feel that I just watched an essay, that was actually top-teir

@theylhompst Жыл бұрын

Great video, thank you.

@mihailmilev9909 Жыл бұрын

Glad to see u growing

@mihailmilev9909 Жыл бұрын

bro/bud/g

@austinarcher90 Жыл бұрын

i love this!

@tanzimulemam5820 Жыл бұрын

Love the video!

@dustinm3116 Жыл бұрын

Cool video this is a topic i love to learn more about

@swancrunch Жыл бұрын

Ngl, non-euclidean origami is the one thing i haven't expected to see today.

@GimbertLane Жыл бұрын

Great video!

@minekrafines Жыл бұрын

what a cool video

@frenstcht Жыл бұрын

Talk about non-Euclidean geometry and urban planning. A lot of theory revolves around using Euclidean-geometry distance measurements, when really they should be using taxi-cab geometry. Something like 36% of the urban landscape is excluded from planning because planners don't know enough geometry.

@coopergates9680 Жыл бұрын

My favorite physical model is when I made the hyperbolic equivalent of a snub dodecahedron (in other words, vertex figure {7, 3, 3, 3, 3}). It's mild enough that I could tape over 40 polygons before it got too puckered and was harder to manage, and more than 3 polygons to a vertex prevented the polygons themselves from getting bent. Beyond something like that, I turned to programming and flying a virtual camera around higher dimensional hyperbolic space. As you've pointed out, the education system significantly fails to cover it properly, usually just briefly mentioning the triangular angle sum below pi radians, negative Gaussian curvature, and a quick and dirty saddle shape drawing. It doesn't usually discuss a Poincare disk model, half space model, Klein model, or hyperboloid model, let alone horocycles, horospheres, or hypercycles.

@lno_onel4404 Жыл бұрын

this video is fire

@nweoodropz Жыл бұрын

The frozen ball is the most iconic part of the video

@theidealengineer Жыл бұрын

Great video 😘

@NoahSpurrier Жыл бұрын

I love Pringles. I’m going to watch this video more than once.

@happdoggo1336 Жыл бұрын

this helped me fall asleep 😃

@01k Жыл бұрын

Thanks for sharing

@happytoaster1 5 ай бұрын

Nice animations

@IWasAlwaysNeverAnywhere Жыл бұрын

the counter arguement i would like to make about the expectation of theta is the consideration of how much time passes for us within a gravitationally bound timeline compared to the time which light experiences in empty space. while light moves its regular speed it has to pass by all sorts of stars and galaxies in order to arrive at our eyes which means light coming from the cmb is forced to travel a longer distance as it is curved by the gravity of massive objects and is slowed by the altered passage of time as it passes by causing it to take longer for it reach us than is recorded by the light itself.