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

[@physicsforthebirds]

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]

I subbed

[@thetruthstrangerthanfictio954]

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]

@@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: kzbin.info/www/bejne/pIKVgZinfNCEnM0

[@joeyd12254]

you are a smart birb

[@stolasamon-seere5319]

What is the space around a massive object? (

[@jaytravis2487]

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

[@Fire_Axus]

Nope

[@jotarokujo1189]

@@Fire_Axus shut up

[@ICREAMTOHANDTIE]

real

[@ioium299]

Yes

[@SublimeWeasel]

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

[@lexinwonderland5741]

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

[@w花b]

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

[@Anonymous-ow6jz]

@@w花b says you!

[@joaomrtins]

I want to make them

[@trueKENTUCKY]

Being a creative has its perks

[@JohnDlugosz]

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

[@physicsforthebirds]

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]

@@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]

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

[@cheeseycheezy]

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

[@jettmthebluedragon]

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

[@viktorgrezu7874]

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.

[@scharpmeister]

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

[@daynhues]

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

[@physicsforthebirds]

I'm glad you liked it!

[@yumnuska]

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]

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

[@killermetalwolf2843]

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]

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

[@nice3294]

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

[@AndrewBrownK]

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]

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]

@@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]

@@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]

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]

@@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!

[@krow610]

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

[@ambrosebussey4672]

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]

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]

Calabi-Yau Manifolds: Allow us to introduce ourselves

[@wingedfeline5379]

@@rightwingsafetysquad9872Wouldn't our blood spill out of our bodies if that were true? It would mean our insides would be exposed

[@The_fusion_physics_guy]

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]

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

[@jabislawthegreat]

brooo... BROOOO.... 11:27 Imagine being that scientist, excited to make a HUGE discovery. The discovery being whether the number is bigger, equal, or smaller than zero. And The Universe is like "I'm like sliiiiightly above zero... or aproximetaly the same but below... ooooor three times that but above... or equal i just cant decide hihi~~"

[@TheNellNadie]

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

[@shipwreck9146]

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.

[@willi00willi]

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

[@nyuh]

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]

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

[@nyuh]

@@ZenoRogue omg ill try it then

[@danielson9007]

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

[@0-M72-0]

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.

[@iamtraditi4075]

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

[@Fire_Axus]

how?

[@iwatchedthevideo7115]

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.

[@Xetaas]

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

[@CognitiveOffense]

Truly excellent. Thank you for making this delight.

[@physicsforthebirds]

I'm really glad you enjoyed it!

[@donsanchodelapanza]

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

[@sirqueensby6052]

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

[@ninjxxitty]

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.

[@SpeedFranklin]

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!

[@syllabusgames2681]

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]

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

[@yumnuska]

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]

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

[@yumnuska]

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]

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

[@aki128_]

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

[@StainlessHelena]

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.

[@jayitsthenerdyninja9891]

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

[@willplaymusic1]

you are disgustingly underrated. i absolutely love your channel

[@dmc2925]

Dope vid! The algorithm really came through 🤟🏿

[@CookiePieMonster]

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

[@RafaelMunizYT]

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

[@frenstcht]

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.

[@xynonners]

damn production quality is insane

[@MartinDe123]

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

[@Costavka]

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

[@steadfastwolf2159]

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

[@ZenoRogue]

A pseudosphere is a nice embedding of a fragment of the hyperbolic plane (H2) in three-dimensional Euclidean space (E3). However, to get a similar nice embedding of a fragment of the hyperbolic three-dimensional space (H3), E4 is not enough, you would need E5 for this. So a 4D pringle is not enough! (Also -- hyperbolic crochets are cooler than pringles and pseudospheres -- they have constant curvature and also they do justice to the exponential growth, which is the coolest thing about hyperbolic geometry)

[@rhodykoop7672]

I love non-euclidian geometry and hope this gets more attention. Hopefully this comment will please the algorithm gods. Iirc, the largest any spherical triangle can be *cannot* be larger than 1 hemisphere. At most it must have angles that are sliiiiiiiightly below 180⁰. Otherwise it'd be just a great circle or a biangle shape lol

[@LoverOfMuch]

oh wow. i love the evolution from topic to topic

[@evaxu1325]

Wow, I am a math student studying non-Euclidean geometry but have never heard of the metaphor at the end of the video, that our “belief” that Euclidean geometry is the only “true” geometry is like people thinking the earth is flat. This video is so deep and simultaneously informing!

[@arinalikes5911]

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

[@cardboardturtle5470]

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

[@khaki.shorts]

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

[@ObiWanCannabi]

2:22 a line is a shortest line between 2 points, right, but in spacetime it is compressed. Flatten out spacetime for density of matter, and you will see that your straight line in 4D space, isnt even the shortest route. Its hard to imagine in spheres, but in cones in 3D: Showing gravitational potential and height from the core, it maps space in the dimension of time. The 4th dimension is time. Its curved spherical by mass. You live inside and on it. On a 3D map, the lowest point of potential is x,y,z=0 that is the core of the planet, if you are there then there is no more down, you do not witness a 3D world, its 4D. down becomes up and up becomes down at a certain point. but the math all works the same. Take the radius of your mass as the height of the cone and circumference as the diameter of the circle on top, you made a time cone out of the planet, you can map any perfectly circular orbit as a flat line on the horizon, inside or outside the earth or massive object, extending the outer lines of causality to infinity and you can plot any smaller masses orbit, until it is influenced by another mass his is how reality looks in 3D, same as Einstein and Minkowski did to the Universe. If I was to flatten out this cone map for density inside the earth it becomes cylindrical or trapezoid like.. it would show that its not the shortest route through spacetime, for anything but ghost particles perhaps, and im pretty sure they are as massless as light. The shortest flattest route on a planet is the horizon, it is the flattest straightest geometry in curved spacetime, up and down being the other, the dimension of time curves everything spherical, we exist in the 4D, people think its where hyperspheres exist, but nope thats where we sit right now. 5D is hyperspherical, to imagine that i map the universe in the dimension of density. My cone map or even cylinder gets funky, the distance between atoms becomes the constant. This is the 5D reality, it would melt your brain trying to work out your straight line geodesics, especially if you are mapping routes for light speed in straight lines.. we don't work so well like that, being bound by special relativity, but what if you was a ghost particle? would it experience more time inside a planet than out, if it had memory or could be a witness to its travel through space, what would it see? is it phased by density or even the fundamental forces? does it experience time slower through mass than it does in empty space, mapping the universe in the dimension of density might be useful if we want to understand it, or how things like it are bound to the universe. If I map a bridge thats flat in time, on the horizon, its flat with the ocean and parallel with its curve, it should allow a glass rod to be made and extended onto V shaped spinning rollers that support the rod, say every 30cm, it should be able to extend to 99% around the earth if it was uninterrupted and flat in time, spinning and extending, and it shouldnt break, but say we tunnel from LA to Dubai like you did with the orange at 2:36, its not a straight line in time, it doesnt go thru the core of the planet, a glass factory pumping a rod onto rollers wouldnt work here, each end is a drop into a pit, which flattens and then ends in a climb, straight for light and straight for mass arent the same things in 4D space. You should be able to spin the glass rod at a pretty fast RPM on the bridge and it should roll like nothing changes, every point still agrees on its altitude, and relative position to the next atom. We use molten tin to float glass to cool it flat, at what point is it not flat? that pool curves with the curve of space and time and the planet, but its the flattest we can do.. Flat geometries in curved spacetime are wird and counter intuitive in 4D if you cant un bend your mind. Try docking 2 craft in KSP in orbit that are 3KM away from eachother on the same orbit by locking them to targets and hitting the gas, it doesnt work. You quickly realise that straight lines for you arent the same for light, everything with mass is bound by orbital mechanics, except light, its weird we use it as any kind of yard stick idk why but if we had a bar extending around the planet, people imagine its deformed, and that atoms need to dislocate for it to roll, but if im right spacetime does the dislocating, so flat in time, truly is flat in spacetime, if you have mass and are working at relativistic speeds. On a 3D cone map all orbits are the same speed across their relative horizons, your line just has further to travel if you have more speed. its intuitive, at the core all momentum is orbital velocity, up 4000 miles from the core you need to cancel out quite a bit of distance before you start to find the correct point in space and time for your relative speed in it. Once your orbital position and speed match up, you will always feel weightless. Everything travels in space at the same speed, you just orbit different, depending on your momentum. It maps so nice in cones of potential in 3D or spheres in 4D, but its all straight continuity geodesics, time can bend so things with mass seem bent from an outside perspective, just how any time line on a non-Euclidean map looks curved to another observer. Its all the same thing, perspective. Thought experiment: Say you was in a box that could ignore collision, a 2 mtr cube of spacetime with no windows. Inside you have a tape measure, a laser and a set of scales. Could you tell your resting point in the universe using the 3 tools you have. At the core of the planet you would be weightless, the tape measure and box all fill spacetime as spacetime allows, inside it seems pretty normal right? But you wouldnt be able to tell if you was in orbit would you.. so you cant be sure.. Would the box still look like a cube to an outside observer? If you was around a black hole, you again might not be able to tell, if you are at orbital velocity then you cancel out the gravity of the singularity, so you are weightless, but is a 2mtr cube of spacetime still looking the same.. Common belief if you are turned into ramen noodles.. but are you? or does your local box of spacetime exist as if nothing happened.. Everything inside the box that you can see tells you that straight lines are still all pretty straight.. at what point do you need to be away from you feet, to see the difference.. Could you measure it if your tape measure and scales and even light all seem to work the same.. This is the confusion about Earth having curvature. Does it curve.. that is the fundamental question, important to the Planet and observer in a box.. It sure looks curved in space, but its not curved in time is it. When you see the earth you see a 4D object, in 3D space, mapped in the dimension of time its conical. I can use the cones to track clocks ticks around different stars, useful for GPS satellites, or for quick gravity estimates of a planets surface. Put into python given enough time and information and I could map the galaxy or the universe. I bet it shows that no matter how far you go back, your cone always stays with the same scaling.

[@swancrunch]

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

[@JPMESrocks]

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

[@coopergates9680]

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.

[@silvesterreen2902]

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

[@Sugar3Glider]

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.

[@prof_as]

beautifully explained! Great work, keep it up

[@themightyripples6582]

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

[@OneGamerCat]

personally, i believe that the universe is hyperbolic, mainly because the sphere that we live on would seem flat, but we know it is spherical, let 1 represent curvature, if you add positive 1 (positive curvature) and negative 1 (negative curvature), you would get zero, no curvature, or euclidean space, in which we know that we live on a sphere, and it looks flat, which would mean that the hyperbolic geometry of the universe would cancel out the earth's curvature.

[@Vinzmannn]

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

[@abbe1255]

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

[@disnecessaurorex4908]

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

[@jessywang1672]

UNDERRATED YOU DESERVE MORE RECOGNITION

[@maxtretikov]

3:43 i've always heard #5 as "two parallel lines will never intersect". I've also heard #1 as "a straight line is the shortest distance between two points" but I think that's provable so it doesn't have to be axiomatic

[@nweoodropz]

The frozen ball is the most iconic part of the video

[@MPHshoots]

This video was incredible. Great job my dude

[@siddharthjadhav9233]

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

[@Shay-i4n]

Dis the quality content we deserve❤

[@Troloze]

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

[@mxandrew]

I’ve been scared of math for a long time but I do like birds and the rational part of my brain really appreciates the lizard part being tricked into enjoying it by little bird cartoons.

[@NoferTrunions]

5:35 reminds me of a humorous comment Hetenyi made in his book, Finite Beams on Elastic Foundations (I think), where he is deriving a family of solutions for finite length, perhaps variable cross-section or whatever and he says in his bood something to the effect, "I will not show these derivations since that would spoil a rather large number of perfectly good pages."

[@andrebenites9919]

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

[@notagoat281]

9:14 Hold on, if nothing can move faster than light, then that means the edge of the universe couldn't have expanded more than 370,000 lightyears from the center, doesn't it? So that would make 370,000 lightyears the maximum distance for the radius of the universe at that time, which still matches with what you're saying, the universe is still bigger than 370,000 lightyears, but the image seems to indicate that 370,000 lightyears is much smaller than even the radius. Is that some sort of oversight, or am I missing something?

[@marselo1316]

What exactly constitutes as the edge of the universe? Wouldn’t the edge be defined as the furthermost particles from the center, and if so, wouldn’t the edge at 9:14 be the photons 370k light yrs from the center? Is the edge of the universe space time itself, cuz if so then that opens another can of worms

[@pairadeau]

Magnificent work. Bless.

[@SteveAcomb]

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

[@nadaelnokaly4950]

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

[@jacobscrackers98]

Just because you want to be surprised about the shape of the universe because the shape of the earth was surprising, doesn't mean it actually is surprising.

[@Arxareon]

(Unrelated but hope it helps: The letter S in Hungarian names & words are pronounced as "sh" like in shore and not "s" like in sore. Therefore, Farkas would be "Farkash" for example. Also, "LY" next to each other is a traditional spelling of just a "Y" like in Yellow, and "i" never turns into a "Y or J" like in.. "like" where "i" is "aj" or "ay" depending on your preference. So, Boya-i Janosh would be the best estimate - I flipped the family and given names for the Hungarian way of saying names but you get the idea.)

[@kayburcky7146]

Seeing how this is a recurring thing on lots of words with different spellings with this sound I'm pretty sure he can't help it. Admittedly it is a bit distracting tho

[@Thejosiphas]

4 minutes in this is already so great

[@Thejosiphas]

too fire

[@syednaqvi7489]

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

[@AnimatedPlayer]

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

[@Anonymous95202]

incredible content, so glad i found this channel

[@pillowslasher831]

The real question, what flavor is the pringle?

[@mharkianescaro3920]

This was a great video! :D can I ask what title of the music at 11:47?

[@v.j.271]

A small correction/clarification at the intersection of history and mathematics. I forget where I learnt this, but spherical geometry is not a counterexample to the parallel postulate problem. Indeed, as you point out, it would be surprising if the mathematicians of the past hadn't considered spherical geometry. It was a well known field of study, as it was critical to navigation, and it also went back to the Greek mathematicians. The trouble with spherical geometry is that it doesn't just violate the parallel postulate, it also violates another of Euclid's other axioms. The parallel postulate problem was not just to find a geometry that violates the parallel postulate, but to find a geometry that both violates it, and holds for all the other axioms. Spherical geometry violates the axiom that you can construct a unique line through any two points (consider antipodal points). I think appreciating this fact is helpful, so as not to cheapen the achievement of Bolyai and Lobachevsky. They had to imagine geometries truly unthought of in order to solve this problem.

[@blacklight683]

But how is it flat? Cuz from the second the big bang started light gone in the 6directions(forward,backwards,upwards,downwards,left,right) which should make a sphere or an egg-loke shape like earth

[@reppich1]

I am glad to see my pringle methaphor spreading, it has only been 27 years.

[@ObserveRecordRepeat]

Wait a sec, so that phrase "drow me 3 lines, and each perpendicular to each other" from video Profesional is in fact possible?..

[@kubaskrzypkowski6445]

Thank you for making geometry fun

[@Jerotero]

I really love imagining geometry in 3 dimensions even if it does hurt my brain sometimes. If our world is flat how would a creature outside our world look in? Would they see a 2D projection of our world would it look something like a multi-layered sculpture?

[@emrezkc]

Magnificent video, well done.

[@Nick-bh5uk]

It is worth noting that the CMB only gives the spatial curvature of the universe, which on large scales is flat. If you include time you get the full Minkowski space which is indeed the 4-dimensional pringle the title mentions so it's not clickbait.

[@vimaxus]

What would a curvature (omega k) of 0.002 (strongest still inline with measurement) mean exactly? how many ly or maybe "visible universes" would one need to go through to come back where they started? Thank for the video!

[@omargoodman2999]

That's a more difficult question than it first seems. Since we know that the space-time, itself, of the universe is expanding based on current observations (though, the exact rate is in question) the "size of the hyperball" would be tough to evaluate. No matter how fast you go, even at the speed of light, the medium through which you're traveling (space-time) is acting like a treadmill; you're not only not making any forward progress, you're actually *losing ground* to the cosmic expansion. _If_ the universe were a huge hypersphere and you started out right now even at 2-3 times _c,_ the distance left to travel even after an infinite amount of time would be *greater than* what it was when you started. And we have no clue how to even figure out what multiple of _c_ you'd even have to go to actually *start* making forward progress.

[@1papaya2papaya]

Awesome video! I just have one question. In the middle of the video, you say that hyperbolic geometry takes place on surfaces with negative curvature and positive geometry takes place on surfaces with positive geometry. Later in the video you say that the curvature of the universe was measured at positive 0.007. Wouldn't that mean that we live on a 4-dimensional sphere, and not a 4-dimensional pringle?

[@physicsforthebirds]

You might have noticed that the error is bigger than 0.0007. That doesn't mean that the experiment was bad, it means that 0.0007 is insignificantly small, so we are confident that the universe is flat (not a pringle...) I think that this was the most confusing part of the video, so my next video is going to clarify it!

[@januszkobayashi1361]

@@physicsforthebirds is there a possibility that the universe is so big that it only appears to be flat, just like earth is is much bigger than us that it only looks flat but is curved?

[@fusion325]

HOLY MOTHER OF UNDERRATEDDDD!!

[@pumpkinman1041]

It's exciting to consider a four-dimensional world with a pringles-like form. Honestly, I've been impressed by whoever developed this idea and have their admiration (I'm assuming it was "Physics for the Birds"). They think that in addition to being three-dimensional, our world has a fourth dimension that is curvy, and this idea is supported by general relativity and space-time theories. From what I have learned as a student, space-time is a single entity that combines both space and time; and because matter and energy are present, it is curved, which has an impact on how objects move through it. The Earth is thought to be a four-dimensional object with a three-dimensional surface that is bent into a fourth dimension, similar to a Pringles chip, according to the said pringle theory. Some of the mysteries of the cosmos, including dark matter, dark energy, and the universe's accelerating expansion, are explained by this theory, according to its proponents. I've personally heard some claims that the curvature of space-time is brought on by the presence of matter and that energy is the only explanation for these events. The universe is expanding faster than ever because of this curvature, which causes items there to move differently. I'll sum up by saying that I find the concept of a four-dimensional pringle to be fascinating and absolutely thought-provoking. Although its veracity is still debatable, it offers a fresh viewpoint on the cosmos and our planet. It's always interesting to investigate theories and notions and to take into account other worldviews. The concept of a four-dimensional Pringle merits discussion, regardless of its veracity and/or credibility.

[@afreakingbird]

finally a physics channel for me

[@JonMurray]

Brilliant video dude. New subscriber ✌🏻

[@domenkastelic2611]

Hey, great video! I just jave one question: we measured the universe to be flat, but wouldn't that only be true for the observable universe? If I'm not mistaken, it would be entirely possible for the whole universe to be curved, but the observable universe to be just too small to notice. The same way you can't notice that the earth is curved from the ground.

[@Foervraengd]

Those were the most brutal first 18 seconds of my adult life