We (could) live on a 4D Pringle (Non-Euclidean Geometry and the shape of the Universe)
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- Опубликовано: 25 июл 2024
- 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.
![Cordae - Saturday Mornings (feat. Lil Wayne) [Official Music Video]](http://i.ytimg.com/vi/z2GYJua09F0/mqdefault.jpg)
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!
I subbed
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.
@@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: ruclips.net/video/nQ2PeqGkQfk/видео.html
you are a smart birb
What is the space around a massive object? (
All this guy needs is exposure. Already way better than some channels with 4million+ subs
Nope
@@Fire_Axus shut up
real
Yes
bro what the fuck i thought he had more subs until you said so
he def. deserves more
I've been studying non-euclidean geometry for years, and I've never seen the examples of the cranes. Brilliant!!
But the Pringles with ink in them are inedible now :(
@@w花b says you!
I want to make them
Being a creative has its perks
Correction: the CMB is not a single spectral line of hydrogen. It is black-body radiation that covers a continuum of wavelengths.
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.
@@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 😑
@@jettmthebluedragon i dont mean to make fun of what u said the quantity of 😑 in this comment is hillarious 😑
but* would correct it but cant edit for some reason 😑
@@cheeseycheezy well THIS means 😑like bruh seriously? This means or this means I’m serious 😐😑
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.
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.
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!
@@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!
@@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!
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
@@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!
This was super cool!! Really nicely done and I really like your bigger picture message at the end!
I'm glad you liked it!
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.
I'm glad you enjoyed it! It always helps to know what people like and what they don't.
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
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
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
I loved the origami crane intro! It really added to the mystery of how you managed to break the interior angle sum
this guy explains stuff so well i actually feel smart after watching this video he deserves at least like 2 mil subs
LOVED the origami. really a great way to explane this topic. Thanks for the great vid. more attention needed.
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.
Found your youtube channel recently and it's quickly become one of my favorites, thank you
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.
I LOVE THIS GUY!!!! This is the first video I have watched on his channel I really hope you reach millions soon!
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.
Great job! Really cool way of explaining these concepts. I was hooked in since the beginning.
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!
Have you tried HyperRogue though? :) It does more non-Euclidean things than Hyperbolica and it has a free version.
@@ZenoRogue omg ill try it then
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!
Great video! You bring out a lot of real life equivalents that really makes the subject easy to digest
i'm so glad youtube recommended me this channel, you're doing such a great job
I am so happy I found your channel it is soo exciting and beautiful and inspiring! waiting for more 🎉🎉🎉
Truly excellent. Thank you for making this delight.
I'm really glad you enjoyed it!
Damn. Love all of it. Love your reading, love your explanation, love your animation.
beautifully explained! Great work, keep it up
I LOVE your intro. I usually hate intros no matter the content but oh my goodness, you made it an art!
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.
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
This video was incredible. Great job my dude
Dude, this is really really good! Loved every second of it
how?
Great video and a very nice explanation of non-Euclidian geometry
Magnificent work. Bless.
oh wow. i love the evolution from topic to topic
Amazing video! Really expanded my perspective about curved geometry:)
incredible content, so glad i found this channel
I know the concepts presented here but this is my favorite some2 video. And a nice little lesson at the end.
This one might be my favourite SoME2 entry, good job.
Magnificent video, well done.
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
This was fantastic! Subscribed!
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
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
We need more intellectually interesting RUclipsrs like you bro, hope you keep growing.
Absolutely excellent video!
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.
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).
Calabi-Yau Manifolds: Allow us to introduce ourselves
Hey,,,, great video and a soothing voice.
Earned a s sub man, ill binge watch all your content now
This video was awesome, hope you get even more popular, you deserve it :)
very important knowledge, hope you get the light. well deserved
UNDERRATED YOU DESERVE MORE RECOGNITION
This is such a good explanation of non Euclidean geometry. Thx bird
Amazing video, keep up the good work :)
Perfect video! Origami, maths, physics, astronomy? Dream combo!
Just discovered your channel. What a good video!
:)
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.
Thanks for the feedback! I learned a ton about editing while working on the video and I definitely have improvements to make
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.
@@physicsforthebirds see my reply to the parent for this. Great work!
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.
@@physicsforthebirds I like the cuts to black. It reminds me of History of the Universe's videos on RUclips, and that's one of my favorite channels! Wonderful video
Dope vid! The algorithm really came through 🤟🏿
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.
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.
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.
you are disgustingly underrated. i absolutely love your channel
love your video! more please!
Incredible. So glad you're getting picked up by the algorithm this early
I love this video so much
HOLY MOTHER OF UNDERRATEDDDD!!
Brilliant video dude. New subscriber ✌🏻
Excellent, thank you
Love the video!
Wonderful video, thankyou.
This video was beautiful
Commenting just to say I was here at 6.6k subs! This channel will go far.
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
damn, this is cool, make more of this, you should be a HUGE content creator in future
Thank you for making geometry fun
I am often excited about things, but man I forgot how awesome math can be
Cool video this is a topic i love to learn more about
Great video, thank you.
Dis the quality content we deserve❤
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.
damn production quality is insane
Great video!
this is the best named video I’ve seen in months 😂
i love this!
I feel that I just watched an essay, that was actually top-teir
4 minutes in this is already so great
too fire
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.
Glad to see u growing
bro/bud/g
love this
Thanks for sharing
this video is fire
Brilliant, brilliant, brilliant stuff. Incredibly paced, excellent examples, concise writing. Subscribing and anxiously awaiting more high effort, high value videos
Great video 😘
Great video👍
I actually believe that time is a compact dimension and that we live on a closed surface, which is why conservation. That the manifold represents energy density on the z axis as well as time, since gravity says everything gets more dense over time.
Surface(cos(u/2)cos(v/2),cos(u/2)sin(v/2),sin(u)/2),u,0,2pi,v,0,4pi
A single sided closed surface. The lost Klein?
Notice that 4pi, 2 full rotations, are needed to complete the surface. Electron half spin?
what a cool video
This was great
Nice animations
Wait a sec, so that phrase "drow me 3 lines, and each perpendicular to each other" from video Profesional is in fact possible?..
this helped me fall asleep 😃
I love Pringles. I’m going to watch this video more than once.
nice video, subbed!