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!
@@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: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-nQ2PeqGkQfk.html
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.
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 😑
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 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
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).
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.
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.
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
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.
(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.)
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
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.
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.
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!
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
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!
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~~"
Outstanding video. A little bit of nitpicking: In mathematics, a sphere *is* the surface, an object comprising the interior is called a ball (a closed ball if it also includes the surface, an open ball otherwise).
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.
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.
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.
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.
Overall pretty remedial communication allotted in this vid, good for laymen viewers. I really only had 1 gripe with this video. I'm surprised you didn't mention the fact schools teach that triangles only equal 180 degrees on Euclidean geometry and changes when that "surface" is not Euclidean/flat. About literally everyone who's taken 1 geometry course knows that. The whole "that's cheating, edges of those triangle aren't even strait lines" interpolate felt insulting to any academic, and paints academics as less knowledgeable about remedial subjects. Any academic would've instead said "well of course if you use a different geometric catalyst the structure would change.", or something along those lines. Outside of that your vid was pretty neat and I'm glad you sited some sources in the description. 👍 Hope your courses are doing well.
That's fair, thanks for the feedback! I don't know about you, but I wasn't learning about non-Euclidean geometry in my 8th grade math class at a California public school🙃
@@physicsforthebirds Sorry, I should mention by courses I meant a specified geometry course instead of a subject in a multi-subject course (grade school).
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
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?
Something I'm curious about that's largely unrelated to this video is HOW the universe cooled down during the big bang. I know this is an already solved question, because it's known that expanding a gas cools it down, but when trying to find actually good explanations on why, it all devolved into thermodynamics calculations that I couldn't understand as someone who has never studied it. The parts below outline how I went about trying to figure out an explanation and how I found my conclusion to be, most likely, false. Based on my prior knowledge, I have the assumptions that temperature is a measure of the average kinetic and potential energy of the molecules within an object, with a lot of the energy being from the molecules themselves moving around in some way relative to each other. As such, I am confused as to how this overall kinetic energy could ever decrease. Doing a bit of research, I think it's because of the force of attraction between two particles meaning that when one tries to get away from another, they pull themselves towards each other and using the frame of reference where the mean kinetic energy between the two particles is 0, both would get closer to 0. Except, there's a few problems with this. First, when doing these calculations many times for all the particles and then averaging out the value of 0, the 0 would be the average kinetic energy, not 0 degrees Kelvin. As such, the average kinetic energy, the temperature, would remain the same (slight oversimplification calling the average kinetic energy equivalent to temperature, but anyone who's read this far probably knows what I mean). The second issue is that of how the particles would actually pull themselves together. The force of attraction for neutrally charged particles only exists at incredibly small distances, so it'd have to be the attraction from charged particles, but there's also repulsion from those particles if they're of the same type. Since attraction would only play a significant role if there was a roughly equal mix of positive and negative charges, the overall changes would be basically completely nullified from the repulsion caused by the positive-positive and negative-negative interactions.
So you're telling me that since the curvature of the universe is not null across a small region, it could be much greater globally ? That makes perfect sense, now we just need to prove it.
Most of this I followed, but the jump to measuring angles of the CMB made no sense to me, at all. Could you provide some sources that explain that a little better? I think I could piece it together on my own if I even knew what I was looking for.
This very nicely made what's the point in titling the video "We live on a 4-dimensional Pringle"? The data you present in the video shows that we live in a nearly flat universe, with the small amount of curvature being positive (i.e. giving slightly elliptic geometry and not hyperbolic like a Pringle).
interesting. From what I saw, our universe is but a slice of either a sphere or a cylinder...I can't remember which one. Think of pages of a book. As they all come together, they make an illusion of a solid shape. Our universe is one of those pages, more near the middle. The shape of our universe is that of a halo, a disc, a circle or a flat doughnut. I believe the middle is nothing in which everything forms and as it goes out toward the outer edge of the halo, it becomes "more". I can't really explain that part as "more" meant it got bigger and while following a point on the disc, it expanded passed the universe it was contained in. Also, it seems that the Universe was just repeating itself like that of a mirror in quadrants. Due note this was all a dream, however I believe that our universe is a 3D flat plane in the shape of a halo or disc.
Because I reformed the paper with flour and water, it was pretty thick and fragile and it wouldn't take too many folds before ripping. So instead of folding like they did in the paper, I used a "straight edge" (a string stretched over the pseudosphere) along with a 90 degree angle to measure out equal lengths until I had a pentagon. I had to iteratively measure and correct a bit, but it came out close enough to look regular.
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.
I think it’s better to have no noise gate on your audio, the cutting in and out is distracting. Maybe adjust it if it’s a plug-in so it’s more subtle if you feel the need to use it
veritasium just did a very similar video to this, I don't think they stole the idea or anything but for the record the pringle idea was way more engaging and entertaining
I have a question I don't think I've ever really seen answered - how do we know our measurements were made on a large enough scale? Is it possible that, on the true scale of the universe (not just the observable universe), all we've done is the equivalent of putting a yardstick on the ground and declaring the world to be flat? Is there a way we could ever really even tell?
Man, i used to hate math, but then i smoked DMT while watching geometry videos and ive been fascinated by non euclidean geometry for the last few years now. Your video definetly cleared up alot of stuff So, if we are locally flat in the universe, but the universe is just an unfathomably large sphere, could you theoretically estimate how big it would have to be for the curvature to be as "negligible" as it is with our measurements of the anistotripes of the CMB? could you then like find out our current rate of expansion and find out if its enough to reach that minimum size?
Amusing as the flat earth historical myth is, just about anyone who lived on the coast at nearly any point in recorded history could tell you the earth was curved The curvature of the earth is such that the visual horizon for any person standing at sea level is only about three miles away. This number grows rapidly with height however, so the visual horizon of a person standing at a mere 100 feet above the ground is more than 12 miles Beyond this, the curvature of the earth is obvious in the way that objects cross the visual horizon. To an observer at sea, land always appears to emerge form the horizon from the top down. The peak of a seaside mountain will always be seen before its base, the tops of towers and the even the masts of other boats. Nothing ever emerges from a vanishing point, it always crosses the horizon Ptolemy's calculation of the Earth's circumference was impressive for it's accuracy, but that the earth even had a circumference surprised no one. The roundness of the earth is something so obvious and easily demonstrated that lumping our ancestors in with the smooth brained chimps known as flat earthers is a depressing failure of history education
Most of my drawings and diagrams I make in Procreate and I do the editing with Premiere. Both are intuitive enough to learn just by experimenting (but I'm still getting better...)
I think what he meant is that there are no straight parallel lines on a sphere. Latitude lines are parallel, but they aren't straight. To understand why, I suggest this video by Vsauce on "Which way is down?". He goes into straight lines on different surfaces at about 16:13 in the video. ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-Xc4xYacTu-E.html
