Daniel and Jorge Explain the UniverseDaniel and Jorge talk about how much dark chocolate can fit in Universes of various shapes and sizes.
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Hey or hey. If you were designing a universe, would you make it the shape of a snack food?
It's a very specific question, Daniel, Can I make it like a cheeto shaped or Dorito shaped?
Hey?
If you're making a universe, there are no rules.
Oh I can go nuts or bananas? Hey, can I make the universe banana shape? How about you?
I think instead of going for fruity inspiration, I might draw my inspiration from chocolate.
Hmm, what shape is chocolate?
Well, you know, I like my universe the way I like my chocolate, flat, dark, infinite.
You make it sound a little inappropriate. There isn't the universe expanding? Also? Is that due to dark chocolate energy?
That's also the reason that I'm expanding?
Are you going to be shaped like a banana? Soon?
I'm gonna be the size of the universe eventually.
We all have a dream.
Him Jorge Im, cartoonist and the creator of PhD Comics.
Hi, I'm Daniel. I'm a particle physicist and a professor a UC Irvine, and I really do feel like I have an infinite appetite for dark chocolate infinite.
Wow, that's a lot, you know if and it's no joke. That means you can eat it forever all the time.
Yeah, I feel like I've never reached the limit. You know, somebody puts a plate of chocolate there, I just keep snacking on it and eventually they got to take it away. So I've never reached the point where I'm like stop.
Sounds like you haven't tried hard enough, Daniel.
I need to do more experiments, that's what you're saying.
That's right. You need to explore the whole range of possibilities, the upper limits and the lower limits.
There's got to be a boundary, and I am devoted to finding it whatever.
The cost, even if it causes your belt line to go to be unbounded. But anyways, welcome to our podcast, Annuel and Jorge Explain the Universe, a production of iHeartRadio.
In which we snack our way to an understanding of the craziest questions of the universe. We try to take bite sized pieces out of some of the biggest questions in the universe. How big is it? What shape is it, where does it come from, where is it going to end, what is it made out of? And fundamentally, how does it all work. We talk about all of these questions and we try to explain all of them to you while you sample your favorite snack food.
Yes, it is it very tasty or, as Daniel says, crasty universe, crazy tasty universe for us to sample and enjoy and saber because it is out there. It's very dark and interesting and full of amazing things that we have yet to discover.
Speaking of snack foods, I know that people like to munch on something while they watch TV. Do you think people munch on something while they listen to podcasts?
Wait? I thought people fell asleep while listening to our podcasts. Are they eating and sleeping at the same time? Isn't it dangerous?
I don't know. Do they fall asleep with their hand in the Cheeto's bowl or something.
I'm sure there are people who snack while listening to us. I mean I watched dishes while listening to podcasts.
Well, I wondered if the crunching wind interfere with they're listening. Well, anyway, let us know if you have a favorite Daniel and Jorgey snack food, maybe we can get them to sponsor an episode.
Yeah, it's great. I mean, you're feeding your stomach and your mind at the same time. You're expanding in all directions everywhere.
Let's get episodes on dark energy funded by dark chocolate makers.
That's no joke, Daniel, we could do it.
Yeah, exactly. T happened to some of those Swiss chocolate funds.
Yeah, it happens a big chocolate money. But anyways, it is a pretty interesting universe out there that we can see from our little perch out here and then sitting on top of a round rock in the corner of the Milkway Galaxy, in a small corner of the gigantic universe that we are surrounded by.
And even though we are stuck on this rock so far, we can still ask some of the biggest, craziest questions about the whole universe, about what's going on super duper far away, because of course we can look out into the universe sort of like we're trapped in a tiny lighthouse and we're looking out at the horizon and wondering what's going on over there. We can't go visit it, but it's sending us messages that let us find answers to some of our biggest questions.
Yeah, it's pretty amazing that from our little point of view here in the little rock floating out in space, we've managed to know so much about the universe and what's out there. But you've got to kind of wonder what else is out there or what happens if you keep going out there in space. What are you going to encounter and what is the overall shape of the universe.
I think it's a great metaphor for our curiosity. You know, we think about what's going on on our planet, what's going on in our solar system, what's going on in the galaxy. No matter how far you explain, people will always wonder what's going on further than that. Right, there's no limit to our curiosity, just like there's no limit to my capacity to eat dark chocolate. No matter how far you explained, people will want to know what's past the edge of the universe.
One of those habits seems healthier than the other thing.
I think they're tied together. I think dark chocolate fuels my curiosity.
What does your doctor say about this type of curiosity?
This is why I stop going to doctors.
Really, you say you are a doctor, so really you don't need another doctor.
That's right. I tell myself to take off my pants because I no longer fit into them. But I think the two questions are connected. You know, could there be an infinite amount of dark chocolate in the universe for me to eat? Only if the universe is literally infinite?
Hmmm, I see you're saying we're sort of like humans are kind of like the eternal busy buddies, you know, we're always wondering what's going on out there beyond the horizon.
Yeah, exactly. We want to know what's just beyond our ability to understand. We'll never be satisfying and go, you know what, one hundred billion light years that's enough for me. There's always going to be somebody who wonders, but what's past that? What if you kept going? And I think the reason for that is that the universe and history of science is filled with crazy surprises. Every time we've looked further than we imagined, we found crazy stuff. Think all the way back to Edwin Hubble discovering that there are other galaxies out there. What a mind blowing realization to think it's not just our galaxy sitting in space, but that there are hundreds, thousands, trillions of other galaxies. That's the kind of realization we're going for.
Yeah, it's pretty mind blowing. And so far we can see pretty far out there into the universe. We can see up to about forty five forty six billion light years. That's as far as we can see, right, that's as far as humans are able and can see right, because of the limitations of the speed of light.
Yeah, it's a bit of a subtle question how far we can see in the universe. You might imagine it would be the age of the universe times the speed of light, that photons would be racing through space to us, and that we couldn't see anything past thirteen or fourteen billion light years away. But because the universe is expanding, some of the stuff that sent us photons a long time ago is now much much further away, and so we can see light from things that are now very very far away out to about forty five billion light years, and eventually we'll even see out to about sixty two billion light years.
Yeah, so that's kind of as far as we can see, Like, that's the range of our vision as human beings in this universe. But I guess, like you say, there are people who wonder what's beyond that. You know, if I keep going past sixty five billion light years, what am I going to find? Am I going to hit a wall? Is the universe going to go on forever? Or is it going to do something even crazier?
Yeah, well put me in that category. I'm not satisfied to only see sixty two billion light years away. I want to know all of it. I want to know what's beyond that. I want to know if it goes on forever, if it curves on back on itself, if there's some huge cosmic store of dark chocolate just past the edge of our vision.
That's your carrot, Daniel, like you know, the character that's driving you to do science. You just want to discover dark chocolate everywhere, even among the fundamental particles. When I know there's a dark choco latino.
Yeah, there could be a secret dark chocolate reservoir past the edge of the observable universe. You know what, in my next grant, I'm going to put funds for dark chocolate, and I'm going to argue that it's essential for doing.
Science, at least for Daniel. For Daniel to do science, you need a little motivation in the morning.
Well, you know, there is a clear correlation between chocolate consumption and Nobel Prize winning. I'm not saying it's causal, but there's a correlation. So you know, when I do apply to the Nessley Foundation for chocolate research, then I think I'm going to put that in there.
Is a causation. I think, you know, I think winning Nobel Prices makes you hungrier for chocolate, right, there's something about that, you know, Northern European, you know flare that makes you create with chocolate.
I don't know. I think it works either way. If you win the Nobel Prize, you celebrate by eating chocolate. If you don't win the Nobel Prize, you console yourself by eating chocolate.
I see. So the correlation doesn't make sense to your physics, at least the way you do it.
Not the way that I eat chocolate.
But it is an interesting question. What's out there beyond the universe, beyond the sixty five billion light years that we might be able to see someday or are you going to hit a wall? Is it going to come around? What is the size and shape of the universe?
And I love thinking about this question the shape of the universe, because it feels like something really deep and fundamental. It's something that must be like written into the real source code of the universe. It's not just like, oh, where is a planet or where are there aliens? Things that are affected by randomness. If something which is a deep truth about the universe it's something which reveals its nature.
Yeah, you're basically asking the biggest question you can ask, right, Like when you're asking about the size and shape of the universe, you're asking what is the sacchin shape of the entire universe? Like it has to encompass all of it, not just like a part of it, all of it.
Yeah, I guess you could ask what is the shape of the multiverse? That might be a bigger question.
Oh what, It just blew my mind? What is the shape of the multiverse? Shaped like a Marvel movie?
It's shaped like a dollar bill, I'm pretty.
Sure, shaped like the money they're raking in.
I hope they're spending some of that money on chocolate to celebrate.
But it is the biggest question we can ask, and it's a question we don't know the answer to, right. I mean, first of all, we can't see out to the edge of the universe, right at least we haven't an edge to it, And so it's kind of a weird question to ask what is the size and shape of the universe if we can't see all of it. It's like sitting in the middle of the United States and asking what is the shape of the United states. If you've never been to or can ever get to the coast.
That's right. But although it seems impossible, science always finds a way to like take the first nibble off of the question to think, well, well, what can we do if we can't answer the entire question directly? Then, you know, can we find some way to limit the possible answers? What can we do with our limited data and our limited view of the universe? And to me, it's incredible what we have learned, what we have been able to rule out about the universe just from looking around.
Wait, are you saying we can just ask the universe what its size and shape is?
You know, I emailed the universe and invited to be on the podcast, but it hasn't answered yet, and so I'm going to have to resort to the classic way, which is doing physics experiment, which is basically asking the universe question.
Interesting. Yeah, I guess if you ask anyone by email what their size and shape is, you probably won't get an answer.
I got to cease and desist from the universe legal department.
Yeah, stay away from me.
Blocked blocked by the universe. Wow, that's harsh, but.
It is an interesting question, and so today on the podcast, we'll be asking is the universe shaped like a donut? And does it taste like a donut too? Daniel, This seems like a very specific question.
It's a specific question, an idea motivated by some hints we've seen in some recent studies that suggested that maybe the universe is chocolate filled after all.
Wait, chocolate filled or shaped like a donut or like a donut with chocolate in it?
Exactly? The universe might be a chocolate filled donut in the end.
I don't think I've ever heard of a chocolate filled donut. Usually chocolate is on top.
You've never heard of a chocolate filled donut? Are you serious?
Well, if it has something in the inside, then it's not a donut, is it?
Oh man? What's a jelly filled donut? Then is it a jelly filled not donut?
It's a jelly filled cake. If you still have a hole in the middle, right to be a donut, doesn't it?
Oh Man? This is turned into a food argument podcast.
I hear those are more popular than science podcasts. Let's roll with it.
We've done the murder mystery podcast recently, and now we're doing the food argument podcast. Absolutely, I think there's lots of different shapes donuts can be. I think the classic shape you know is basically a torus with a hole in the middle. But you could still put chocolate inside that taurus.
Right, Oh, you mean a long like the ring of it. You can stuff it with chocolate.
Yeah, a ring of chocolate? Why not? Sounds delicious to me?
Sounds like a heart attack.
Well, we'll see if the universe agrees with me or with you by the end of the episode.
But anyways, apparently it's a possibility that the universe could be shaped like a donut, which sounds both blitchous and unfilling. And so that's the question we'll be trying to answer it today. And so, as usual, we were wondering how many people out there had thought about equating the universe with a treat like a donut.
So thanks to our ever rotating group of volunteers who answer these questions for us on the podcast, it's we's blend to hear your answers and it gives us a sense for what people are thinking. If you'd like to participate for a future episode, please don't be shy. I know you're out there. Waiting for an invitation. There's right to me two questions at Danielandjorge dot com.
And Daniel will send you a donut if you answer the question right. If you're a digital donut, a little Emogi donut. We'll think about it for a second. Do you think the universe is shaped like a donut? Here was what people had to say.
I think the universe could be shaped like a donut, and it could be that we just don't see all of the universe from our advantage point. But I doubt that it is, because I would think we would see some kind of evidence of it in the microwave background. So from that, it really appears that the universe does not have curvature to it.
I don't think the universe is shaped like a donut unless initial expansion was not uniform in every direction, I would guess it's more likely to be a hollow sphere.
Yeah, I mean, could it be as an interesting question? I uh, yeah, I mean I imagine it could be. I think I've heard about this before. I remember at some point, somebody, maybe in a documentary or something, saying that if you look straight forward, if you were able to like see into infinity, you would look at the back of your head, which I guess if you were on a donut you could probably do that if space was like sort of bent like that.
I don't think the universe is shaped like a donut.
I think if it was, we would have noticed by now, because there'd be a lot less photons and activity coming from the center of the donut.
I think, so long as information is consistently available across the entire universe, it really doesn't matter what the shape is. And as long as time and space are concentric, I think the universe can be any shape, and there are problem universes of all shapes and sizes out there.
Frankly, I think that the universe could be shaped like anything, and it wouldn't surprise me. There's this idea that you know, you start in one place and you go in one direction, and then eventually you're just back at that place, and yeah, that fits donut shaped to me.
It's me all right. A pretty wide range of answers. Some people seem skeptical, some people were like, sure, why not, the universe is weird and surprising it could be shaped like anything.
Exactly, and some people even commenting that donuts have jam inside of them, and so they're arguing. I think they agree with you. You know that the shape we're talking about is more like a bagel than a donut. Mmm.
Interesting, whoa should we rename the episode?
Then?
Could the universe be shaped like a bagel?
Well, the question then is can you put chocolate inside of a bagel?
Obviously? Yes, Daniel, you can put chocolate inside of anything.
All right, then I'm fine with it, what I call it, whatever, as long as you put chocolate inside of it.
Oh wow, man, you're really agree here to day, Daniel, Have you had your daily dose of chocolate yet?
I'll reward myself after the podcast.
I mean, this podcast is not infinite, I guess.
So.
Yeah.
So let's get into this idea of the shape of the universe because it's kind of weird to think about the universe having a shape, right, because it could the universe could be infinite. And even if it's not infinite, are you saying like the walls of the universe or shape like a donut? What exactly do you mean by the shape of space?
So the shape of space refers to basically how the universe is connected on a really really big scale, you know, we are used to thinking about space is like something we are floating in, and we're also used to thinking about spaces like maybe being curved. General relativity tells us that mass and energy and all this kind of stuff can curve space. That's sort of a local curvature. But you know, if you have curvature in space, if space bends in some way, then you can imagine putting it together into some big shape. Like if space doesn't curve, if it's flat, you can make an infinite sheet. That would be the shape of space. Space does curve, you can imagine it being like a sphere or a donut or some other we shape. So the curvature of space is connected to this other question of the shape of space. Curvature are sort of local. The shape of space is sort of global. It's asking like, how is all of space put together? Think in two dimensions for a moment, because it's easier. Imagine you have a bunch of rings and you have to connect them together into a two D surface. You could loop them together into a flat sheet, or you could make it into a sphere or something else. These are different shapes because they have fundamentally different properties and mathematically speaking, two shapes are fundamentally the same if you can smoothly morph one into another. So two different shaped spheres, or even a sphere and an ellipsoid are basically the same shape. But a sphere and an infinite flat sheet are not the same. One is infinite, the other is finite. There are other shapes, like ones with a hole in it, like a doughnut, that are not the same as a sphere or a flat sheet. That's the meaning of shape in a global sense, which is related to but different from curvature in a local sense.
I see, and I guess just to be clear, you actually mean space time, right, because when you're talking about gravity kind of bending or giving space curvature, you're actually talking about the curvature of space time.
Right.
You kind of have to take time into consideration as well. Well.
We do think about how the shape of space evolves with time, and the shape also contributes to how the universe expands or contracts or doesn't. So, yes, this is a dynamical thing. The shape of the universe, the curvature of the universe can change, although its fundamental shape cannot. Yes, it is interesting to think about it as a function of time.
Right, And it's kind of interesting that you related to this idea because I know we've talked a lot in this podcast about how gravity and energy kind of bends space time in the sense that you know, we're not going around the Sun because it's pulling on us. We're going around the Sun because the space time around it is sort of shaped like a bowl, and so we're kind of stuck in this loop around it. Is that sort of what you're saying, like, on a global or universal scale, does the universe have some sort of like curvature to it?
It's a really fascinating idea that you know, space is curved, like gravity is not like a force the way we think about other forces, but instead it's a fictitious force. It's a force that appears to act because we can't see that space is curved. Like if I look at a piece of space, I can't tell you is it curved, But I could shine a light through it, and if I see where that light goes, then I can tell you whether space is curved. So we can see the effect of curved space even though we can't see the curvature directly. So now imagine you're building a universe, and I'm giving you pieces of it, and each piece has curvature. So if I only give you curved pieces, what kind of big universe shape can you build? Well, you can't build like an infinitely flat space, like a huge sheet, but you could build like a sphere or a circle, or a donut or something else that has a curved surface. So the building blocks of the local curvature I'm giving you do constrain the kind of overall shape that you can build for the universe.
I think what you're saying is is kind of like, you know, if I measure the land around me, and I see that the land curves around me downwards or towards the center of the Earth, then it kind of tells you that the whole Earth is round exactly.
If you can measure the curvature on the surface of the Earth, then you know that the Earth can't go on forever or can't be flat, because you see that it's curved. Right. If you imagine that the rest of the Earth is curved the way the piece you're standing on is curved, then that suggests that probably it's a big sphere, although you know it could also.
Be a donut or I guess it could also be kind of like a dome, right, A dome goes on forever. Like if you're standing on a parabola. At the bottom of a parabol you think it's curved, but it could keep going forever.
Right, Mathematically, a parabola has the opposite curvature of a sphere. But yeah, parabola is an open construction, so you can have curvature and still have an infinite shape, so that curvature is negative instead of positive. But that's a detail, right.
So you're saying that, you know, somehow we can't see the entire universe, but maybe by measuring the curvature around us, we could, maybe you know, get a sense or an idea of what the overall shape to the universe is exactly.
And what we want is the curvature on the biggest scale. We don't really care about how much the Sun is bending the shape of space in our neighborhood. That doesn't affect the overall shape of the universe. We want to know, like, how much is all the stuff in the universe bending the shape of space? What shape of space is that consistent with? Just in the same way as like, if you want to measure the surface of the Earth. You could be standing locally on something flat or something pointd or you know, in a bowl or something. Doesn't change the overall structure. So when we measure the curvature of the universe, we want to make measurements on as big a scale as possible to avoid like the local fluctuations and deviations.
Are you saying that the universe might have a curvature to it, or that space might have a curvature to it without stuff in it, you know, like, or are you saying space has a curvature to it because there's stuff in it?
This is a really important point and subtle. One. Universe has some curvature and some shape, right, Either the curvature is positive like a sphere, or it's flat like an infinite surface, or it's negative like a parabola as you described, and that just is part of the nature of the universe. And you can put stuff in the universe and that can change the amount of curvature. You can make the universe more or less curved by putting stuff into it, but you can't change the fundamental nature of the curvature or topology of the universe. You can't like make a sphere universe into a flat universe by putting stuff into it or the other way around.
I see because I think, you know, there's sort of two things, right, there's stuff and energy and then there's space. Those are two kind of separate things, and so you can imagine an empty universe where it's just space, or like if you took out all the stuff and energy in our universe, we would just be left with the space we have. And so you're saying, like, without any stuff in it, what is the shape of that space? Does that space have curvature or is it totally like flat and even.
Yeah, although we're into in our universe which does have stuff in it, and the stuff affects the amount of curvature. You know. For example, one of the things in our universe is dark energy, which we don't understand at all, but it's expanding the universe that tends to decrease the curvature of the universe. It like stretches everything out. Imagine you're like the little prints. You're standing on a tiny little planet, and then that planet expands to be huge. The curvature you experience decreases, the amount the planet curves away under you. Decreases. So the stuff that's in the universe can't affect the amount of curvature, but it can't affect the shape, right, Like you can't take a curved universe and put stuff into it and make it flat. You can contract it. Like you put a bunch of mass into a universe that's a sphere, it's going to make that collapse into a point.
Interesting, So you're saying that if I take out of all the stuff and energy in the universe, I would be left with space, and that space could be in the shape of a sphere or a donut or something, and the stuff in it wouldn't be able to change that.
Wouldn't be able to change that. And it's connected to this other idea that you know, the shape of space, it's topology. It's global curvature plus the amount of stuff, the amount of the density, and the dark energy. All those together determine like whether the universe is expanding or contracting. This is one element of that. We're talking about the shape of space, which is not something that can be changed by dark energy or dark matter or the arrangement of stuff. It's just like it's something that's deep and true about the universe itself. It's just baked in.
I mean, it's it's safe, right, like you know nothing, But the universe can change.
It's safe, yeah, in shape in a very specific way, right. You know, we're not talking about size. You can have a universe that's a sphere and it can grow or it can collapse. So in that sense, the universe can change, but it can't change from like a sphere to an infinitely flat universe or to a parabolic universe. That kind of thing can't change.
Right, And you know that sort of mathematically or how do you know that it can't change?
Well, I guess we know that mathematically, but you can also just think about it intuitively, like how could you take a finite universe which is a sphere and suddenly transform it into an infinite flat plane. And you can imagine a sphere even growing, you know, arbitrarily large, and how do you suddenly transform that smoothly into a flat universe. The universe can change, it can't evolve, but it has to happen in a smooth way. You can't have like a sudden jump with the universes all of a sudden completely different. This is like a basic element of the nature of the universe. It doesn't seem like you could change it from one moment to the next.
All right, well, let's get into what are the possible shapes and curvatures of the universe and what it all means. But first let's take a quick break.
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Right, Dan, we're talking about the size and shape of the universe, which seems a little rude to be asking these questions about the universe. Maybe the universe is very bashful about these things.
Physics asking rude questions since fifteen eighty.
Four, being nosy about people's size and shape.
Exactly, upsetting the apple carts since forever. That's our goal. You know, we don't care if the truth is offensive. We just want to.
Know discarding with social conventions since the beginning of a ton of time.
As if we understood social conventions. Right, that's one reason we went into physics, because we just don't know how to do the other stuff.
Oh man, your meetings must be pretty interesting or not, man or not. You know, a world without subtlety might be a little boring.
No, that's a fun stereotype. But you know, physicists are social creatures. I work in a collaboration of thousands of people, and we have lots of meeting and politics and have to deal with each other. And you know, people work together and don't work together, and it's all sorts of stuff exactly the same way you find in every other field of human endeavors.
Right right, it is a human endeavor. And we were talking about the size and shape to the universe, and you were telling me that, you know, the universe can have a shape even if I take like if I take out all this stuff and energy in it, put it somewhere. I don't know where, but you put it somewhere the universe. That's left over would have a shape to it. What exactly does that mean? A shape like doesn't mean it has walls and a boundary like edges to it.
It tells you how space is connected. I think about space not as just like where stuff happens. I think of it's sort of like a fabric and it's woven together. And if I move to the left, then I'm moving into a new bit of space. And then you can ask, like, well, what happens if you keep going you just encounter new space, or potentially space could be connected in such a way that if you keep going, you come back to where you started right, sort of like a Packman universe. And so that's entirely possible, and that tells you something about the shape of space. So when we say, like, what if space was a sphere, what do we mean by that? We don't mean that space is literally a three D sphere. We're talking about the surface of the sphere, the two D surface of the sphere, as an analogy to our three dimensional space, because it's hard to think about three D surfaces of four D spheres. But if you're on the surface of a sphere, that surface is finite. It doesn't go on forever, but it also doesn't have an edge. That's an example of how space could be connected. So really we're talking about like how to weave bits of space together into a larger fabric, and then what is the shape of that fabric?
Right? But I think it sounds to me like you're making an assumption about the universe, which is that it doesn't have an edge or a wall to it, right, Like, it doesn't seem like you're considering that possibility that if I just hop on a space ship and I keep going for you know, ninety billion light years, eventually I'm maybe going to hit a wall. Like that's not a possibility that physicists seem to consider because maybe it doesn't make sense to you.
That's a possibility I'm totally open to considering. You're right that it doesn't make sense to me. It would break a lot of things and be very very odd. That would make it super fun and interesting to discover. I wouldn't think it's something that's likely as a description of our universe because it would mean that one part of the universe is very different from another part of the universe. The edge would have to have a different nature than the rest of the universe, and so far, what we've seen is that every part of the universe sort of seems to be the same as every other part. But you know, maybe it's like we're in the very sense of a huge lake and we just can't see the edges, but they are there. It's possible that the universe has edges, that there's another kind of space and edgy kind of space that's different. That's a possibility. We can't rule it out that it would be weird, right.
Right, So then when we're talking about the shape of space, I mean, if it does have walls in a boundary, it could be shaped like anything, right, could be shaped like a cube or a banana, or you know, like like being trapped inside of a banana, Because that could be one way to talk about the shape of the universe. But I think for our discussion today, what you actually mean by the shape of the universe is like, let's assume that that's not possible, Like, let's assume that the universe can't have walls or boundaries. Then what are the possibilities left?
Yeah, And so if you assume that every point in space is the same as every other point, right, you have like one kind of lego piece and you have to build a whole universe with just that one lego piece, then what are your options? So, for example, if I only give you those flat pieces of lego, then what can you do? You could just make a big flat sheet, right, just like quilt together space, so that every piece is just next to other pieces adjacent to it, and nothing is more complicated. Space just goes on forever, totally flat. Right, That's one simple idea for what space might be.
Right, because I think, you know, maybe a lot of people might be confused with this because you know, if you tell me that the universe can have boundaries or like walls or edges to it, then to me, I would think that it has to go on sort of forever. Then, you know, to me, it would seems like the only possibilities for the universe to be infinite and have no shape. But I think, you know, physicists think about it differently, like it could still be sort of infinite and continuous without bandaries and still have a shape.
No, I think you're right. If it's flat and it's infinite, that is, it doesn't repeat and there's no special edges to it, then it has to be infinite. I can't think of another way to arrange space. It is possible, though, for space to be flat and not infinite, right. Imagine the pac Man universe or the asteroids universe, where at some point space just repeats. You know, you get to some point in space and it just is now connected to a spot you've already been without any curvature.
Right.
It's just like the way space is. It's sort of the same way we talked about for wormholes. Space can have non trivial connections, like you can connect this bit of space to that bit of space and just say, these two bits are now next to each other, meaning you can step from one to the other, even though in the larger fabric of space they seem to be far apart. In that same sense, you could have like a whole seam where you connect like a whole line of space to another whole line of space, effectively making like infinitely sized wormhole.
I think what's interesting is that the idea that space can have no it could have no boundaries, no walls, but still have a shape. And I think what you're telling me is that the one way it can do that is if space sort of wraps around itself, sort of like if I keep going in one direction, I eventually come back from the other direction. Like somehow space is curved or connected to itself in a strange way so that I can keep going forever, but I sort of keep going around circles. And in that case, the universe sort of has the shape, but it has no edges to it.
And there's two possibilities there. One is space is actually curved, sort of like a sphere, right, and so it's natural to put it together in that way that space is curved and finite, and if you keep going in one direction, you come back to where you are. There's another possibility, which is that space is flat, it doesn't have curvature, and yet it doesn't have edges and it's finite. And that's like the asteroids or the pac Man universe, where without space being curved, it's just connected in that way. That's why local curvature is a little bit different from this question of like global topology the connectedness or shape of space.
Right, right, But maybe let's take a step back and break it down, so it's possible for the universe to for it to be sort of continuous all the way through, no boundaries, no edges, but still be finane. And you're telling me, I think that there are different ways in which that can happen. So one of those ways has to do with curvature and the other one doesn't. So let's maybe break it down a little bit more about what this idea of curvature is like, is what does curvature mean for you? Like for me, curvature means that the ground is uneven or has a slope to it. But what does it mean in terms of space?
In terms of space locally, it means what is the path of a photon? If you shine a laser beam through a chunk of space, where does it go? And if space is curved, then you can't see that curvature, but it affects the flight of the photon, and so the photon will bend. It's taking what's actually the shortest distance through that space, right, because photons always take the shortest path. But the shortest path is now something that looks bent to you because you can't see the relationships between those bits of space. Remember, the curvature of space is intrinsic, meaning it just changes the relative distances between bits of space. So that's what I mean by the curvature of space. I mean like the path of a photon through that piece of space.
And again I think you mean space time, right, or I guess do you lump it all together?
Yeah, Well, relativity definitely mixes space and time together. There's a lot of connected effects there. But you know, space and time are also different. You know, space has these properties that time doesn't have. And here we're talking specifically about the spatial part of space time. But yeah, you can't really think about space without thinking about the four D structure that it sits in. Wage is space time?
Well, And another thing that I think I've read is that, you know, this idea of curvature is not just about whether one foot like if you shoot one photon and it sort of leans to the right or to the left. It's more about, like, if you shoot two photons, do they curve away from each other or towards each other. That's really more about the curvature of space, right.
You know, one way to measure the curvature of space is to look at the path of two photons. Another way, which is equivalent, is to like draw a triangle and ask, like, what are the angles of that triangle. If you draw a triangle on a flat surface, then its angles at up to one hundred and eighty. If you draw a triangle on the surface of a sphere, its angles are bigger than one eighty. And that's the same notion. Right, If you shoot two photons and they have to move along the surface of a sphere, then they can appear to curve towards each other, for example, And if you are on a parabola, then they appear to curve away from each other. And it's equivalent to saying that a triangle on that surface has angles less than one hundred and eighty degrees.
Well, it's kind of strange to think of a spheres and convery between two D and four D and three D. But I think what you're saying is like if the universe, like if the curvature of the universe is flat, or at least around us, things are flat, it means that if I shoot two photons, they're not going to curve, or at least they're going to curve together maybe, but they're not going to sort of move away from each other or move towards each other, right, They're just going to keep going in the same direction, side by side forever. That's what it means for a space to be flat.
Right, that's a way to test it. In flat space, two photons moving in parallel will not approach each other, whereas in curved space, two photons initially moving what appears to be parallel to you will either approach each other or divert from each other. Same way as if you're on the equator of the Earth, which is a curved surface, and you and your friend both walk north, do north, which feels like you know we're moving parallel, You'll notice that you get closer and closer to each other because eventually you're going to hit the same point. So motion constrained along a curved surface or motion through curved space can make things that initially were parallel move towards each other.
So the Earth is not flat, Slash, It's not flat, right. I mean, if the Earth was flat and you and I started walking in one direction, we would keep walking at the same distance from each other all the time. But that doesn't happen on Earth, right. That's one way we know the Earth is not flat.
Exactly, although I don't know what north would mean on an infinite flat Earth, though I'm sure the flat earths have figured that out somehow, all.
Right, So that's flat universe and you're seeing a curved universe. Means that the two photons would eventually either collide or move away from each other forever.
M hm, depending on the sign of the curvature. So if you're on a sphere, for example, then those photons eventually will hit each other, they'll come closer to each other. If you're on a parabola or in three D it's called a hyperbolic paraboloid, then they will eventually move away from each other.
Right, And that's what you mean by like positive curvature and negative curlature, Like if the universe has positive curlature, then two photons would eventually hit each other, even if you shoot in parallel to each other, And if it has negative curvature, they'll just diverge and never hit each other.
Mm hm exactly.
But that's curvature. What does that tell us about the shape of the universe.
Because the curvature of space determines what shapes are possible. Like if the curvature is positive, like on the surface of a sphere, then you are building up your universe. You can't make a parabolo. You can't make an infinite flat universe. Right, you can make a sphere, you could make a donut. You can make a donut with more holes in it. Right, you have to build a universe where every piece of space has that curvature and sort of like have it all fit together without any edges. There are only a few shapes that are possible. The curvature of the universe on the large scales determines the shapes that are possible. So if you measure the curvature doesn't tell you the shape, it tells you what shapes are allowed.
M I see. So you're saying, like, if it's positively curved everywhere, then there's only one sort of shape ish that the universe can be, which is a sphere or closed right like something that wraps around itself.
Although it could be other shapes than just a sphere like a donut. But note here there's a bit of a subtle point of geometry. The picture you have in your mind of a donut has lots of spots on it with positive curvature. They sort of bend away from you, but not everywhere on the donut has positive curvature. There are spots there with negative curvature. And if you talk to professional geometrs like mathematicians, they think of a donut as actually like a fly plane connected on itself, like the pac Man universe we were talking about. So there's the donate you eat, which has curvature, and then there's a mathematical doughnut which is actually flat on the surface. And we could also consider it more exotic shapes, like a donut with two holes in it. I don't even know what you call that, like a double bagel. But yes, it couldn't be totally flat if space is curved positively, I see.
But if we measure its space to be flat, then there's no shape it can be. It has to be infinite kind of.
That's right. If space is flat, then it can't be a sphere. It could still be that weird pac Man universe, or as you say, it could have a weird edge to it right beyond what we're measuring, but it can't be a sphere, or it can't be a paraboloid or a hypobloid or anything like that. So measuring the curvature of space does rule out some possibilities for the shape of space.
Okay, so depending on the curvature that we measure around as in all space, they'll determine whether the universe is shaped like an infinite sort of space sheet, or whether it's shaped maybe closed like a ball, like a sphere, or whether it has more interesting shape like a donut. And so let's talk about what we've measured out there, whether the universe is flat or curved. But first let's take another quick break.
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Ok I know, we are talking about the size and shape of the universe, and now we're doing something even ruder, which is actually measuring the size and shape of the universe. Like, wouldn't that be rude to somebody came out to me and be like, hey, I wonder how big you are? Let me measure it.
Well, you know, I think if you're a tailor, for example, you ask somebody to waste size and then you measure it because you want to deliver a suit that fits, not an aspirational suit that they hoped to one day fit in.
Oh I see our physicists, the tailors of the universe. What kind of suit are we making for the universe?
I don't know, But if we ask the universe it's size and it gave us an answer, I'd still want to go out and measures just to make sure it wasn't being modest.
Oh man, you think the universe is lying to you?
Maybe you always got a double check and then double check your double checks.
I guess the universe could have been eating more dark chocolate than it thought. And you know its measurements are outdated.
That's right. Maybe in between the time it sent in its measurements, it had a bunch more snacks, and so hey, we just want to make sure to make a suit that fits.
We were talking about how knowing that the curvature of space tells you at least not maybe the total or exact shape of the universe tell you kind of what kinds of shape the universe can be, whether it's sort of closed like a sphere, or open like an infinite sheet, or maybe has some weird shape like a doughnut or a hyperbola. And so I guess the big question is how do we measure the curvature of space, Like, how do we measure if it's curving one way or another?
Yeah, the best way to do it would be to have a huge triangle, right, to like draw out a huge triangle in space and to measure its angles. You know, shoot photons in straight lines between three points and then measure the opening angles between those photons, and that would tell you just like if you did that on the surface of the Earth, you could literally measure the curvature of the Earth because you would measure that a triangle actually has more than one hundred and eighty degrees in it you laid it out on the surface of the Earth. So that would be the best way to do it. You know, huge lasers really really far apart deep in space.
Oh, I see. You mean, like you send out three satellites, put an arrangement a triangle, and you shoot lasers at each other.
Mm hmmm. Yeah. You make sure they're in a triangle by shooting lasers at each other. This is totally fantastical, right you never actually do it. Imagine one satellite in this galaxy and one an Andromeda and one in another galaxy, and they shoot lasers at each other so you know they're lined up, and then you just measure the angles between those lasers.
So like if I'm shooting an Andromeda from here and I'm shooting at Alpha's in another galaxy from here, I would literally just use take like a protractor and measure the angle between the lasers. That would tell me whether the universe is curved.
Mm hmm yeah. And the same way you could on the surface of the Earth. Right, you got two friends, you guys stand in a triangle and you spool out string between yourselves. You could just measure the angle between those strings and that would tell you the curvature of the Earth. Same way you could do it with photons deep in space. What you want is a really really big triangle because the curvature, if it exists, is going to be pretty small. Just like on the surface of the Earth. You'd want a really big triangle because it's pretty hard to measure the curvature of the Earth in just your bedroom.
I see, Well, technically you could do it in your bedroom. You just need like a super precise protractor, right.
Yeah, but then you're also measuring the curvature of your bedroom instead of the Earth. But if your bedroom follows the perfect curvature of the Earth, then yes, and so that's what you'd like to do ideally. Obviously we can't do that. So what we have to do is sort of look for existing triangles in space, Like, you know, is there a place where two photons were sent to us from really distant locations and we can sort of reconstruct like an existing cosmic triangle.
Mmmm. So meaning like looking at galaxies or looking at sort of like the background of the universe.
Yeah, So the oldest light in the universe is a really helpful resource for this. So we're talking about light from the cosmic microwave background back when the universe was really hot. And really dense and only a few hundred thousand years old. There was a moment when those particles came together and became transparent, and we still see light from that plasma glowing. That light is really really helpful because it's so old, so it's traversed a lot of the universe and we can kind of put it together in a sort of cosmic triangle to get a sense for whether the universe is curved in one way or another or whether it's flat.
Right. And this light is kind of interesting because it's like the earliest light in the universe, so it's very kind of like primal right, Like it's sort of like the og light, like the original light of the universe, like when it was born, they did it have a curvature to it, And you can tell from the you said, the wiggles of this light.
What we do is we look in this light for lumps. We don't really just measure the angles between things. What we look for is the size of lumps that are evidenced in the cosmic microwave background light. So if you look in one direction, if you look in another direction, you see this light. But it turns out this light has slightly different temperatures. If you look in different directions, it's really really minute. It's like one part in tens of thousands. Mostly it's just the same. But there are these little wiggles, and if you look for the size of those wiggles, like how big is a hot spot or how big is a cold spot? You can use the apparent size of those wiggles to tell you whether the universe is curved and how how it's curved.
Yeah, this is pretty cool because I was thinking about this. It's almost like the universe is acting like a lens, right, Like if the universe is curved in one way positively, say, for example, and maybe the universe is sort of like a sphere, then the universe could of acts like a magnifying glass. Right, So you should see these spots in the background radiation kind of bigger than they actually are.
Exactly, And we have an idea for how big we expect those spots to be, right, that's key. We have some idea for like how madder and dark matter and the photons we're all sloshing back and forth together against each other, how big should those lumps be. We can predict how big they should be. And then we can go and measure how big they are. And as you say, if the universe is curved, then photons, for example, from really far apart, will curve towards each other, and so those lumps will appear to be slightly bigger than they actually are because you look in one direction, you look in another direction, you'll be seeing like two sides of the same lump. But really those edges were closer than what you're seeing. Space is flat, then the photons are just flying straight, and so that's sort of like a cosmic triangle because you have these like two different sources of light all coming at you, and you can look at the angle basically between those photons and tell whether they've been bent together or bent apart or flown.
True right, And like if the universe has negative curvature, then it sort of acts like what's the opposite of a magnifying glass a glass if you're iner sided or.
Something demagnifying glass, you.
Know, like a piece of glass that has the opposite kind of curve, like the curse inwards in the middle. Then things sort of looked smaller through it, right, So the spots to look.
Smaller, and we can do these simulations, we say, here's what the hot spots and cold spots should look like if the universe was flat, And then we can dial up the curvature of the universe. And in our simulations we can say, oh, look the spots get bigger, and then we can dial down the curvature to negative we say, oh, look the spots get smaller. And then we go out and we look in the actual universe and we say which of these best describes what we see? You know, is the universe look like it's flat or it does look like it's curved one way or the other. So this is a very powerful way to measure the curve to the universe over a very very large scale, because even though those photons started out not that far apart from each other, they've traversed a huge amount of the universe because of that expansion.
Right, yeah, So is the universe amplifying or are shrinking the cosmic microwave background?
And so what we found when we measure this is that the universe seems to be very very close to flat within zero point four percent. It's flat, like this is a number we measure. So it's not an exact thing. You can never get like zero point zero zero zero zero zero with infinite zeros. What we measure is zero point zero zero four curvature.
Meaning that as far as we think, the universe is not curved, it's flat.
That's right. It's consistent with zero that we measure something a little bit above zero. It's like if you flipped a coin a thousand times and it's a fair coin, you'd expect on average to get fifty percent of those to be heads, but you know, sometimes you got a flat suctuation up or down. So that's what we see here. Space is either perfectly flat or it's slightly positively curved, but it's consistent with flat.
But I guess you know, one question I would have as a skeptic is that you just told me that this is based on our measurement of the universe compared to what we expect, But isn't what we expect also sort of warped by our view of the universe, Like what if what we expect is somehow distorted to.
Absolutely this could be wrong. Right, It's one measurement, and there are always assumptions built into any measurement. We have other ways to measure the curvature of the universe, and those other ways agree with this measurement. Another way to measure the curvature of the universe is to go back to something we were talking about earlier, like what stuff is there in the universe? You sort of like weigh the whole universe, Like add up all the mass of all the stuff that's in the universe, the matter, the dark matter, the dark energy, and that'll tell you like, is there enough stuff in the universe to be consistent with flat or is there too much stuff in the universe that the universe has to be closed, it has to have positive curvature. And so that's another completely separate, totally dependent way to measure the curvature of the universe, and that also comes up consistent with flat.
Well, wait, you told me earlier that the curvature of the universe doesn't depend on the stuff in it.
Well, the overall shape, the way it's connected, whether it's infinite or looped or finite, that cannot be changed by the stuff in the universe. But the stuff in the universe can change the amount of curvature. Collapsing a large sphere into a smaller one, for example, if it has more than the critical density and knowing the amount of stuff in the universe helps us measure the curvature, which determines what shapes it can be.
Mmmmm, I see so okay, so we've measured out the cosmic microwave background and we it fits our predictions for a flat universe, which means that probably the universe is flat. What does that mean for the shape of the universe.
Probably the universe is flat, which means probably it's infinite and boring in that sense and goes on forever in that sort of naive sense. But you know, people look at these measurements and they see some weird stuff in there, Like, first of all, it's flat, but you know, there's a little bit of positive curvature there, so maybe it's something different. And when they look in more detail at these wiggles, they see something a little bit unexpected, something a little surprising, which makes them think about donuts.
Are you sure that's much? Just because it's lunchtime maybe or you need to sugar fix the wait. It's likeke a set back. You said, so we've measured the unit speed, probably flat, mostly flat, and what does that mean for the shape of the universe? Like if it is flat, what does that mean. It means it doesn't have a shape, right. It means that it can only be infinite and go on forever, meaning it doesn't have a shape.
Well, I mean that is a shape, right, you know, mathematically speaking, that's a shape. If the universe is flat and has no boundaries and goes on forever, that's a shape.
Yeah, I see. And if it was closed, if it had positive curvature, it would be a sphere. But we are not measuring that.
Yeah, although remember, positive curvature can also be consistent with a donut. Donut is positively curved on its surface. That's for a physical donut. A mathematically donut is technical flat. So remember that little subtlety.
Okay, so we're measuring the universe to be a little positive curvature. Is that what you're saying? It has a little bit of a positive curvature.
Got a little bit of a positive curvature. And also some details in the cosmic microwave background radiation are really interesting and tantalizing and have led some people to suspect that maybe a donut is the best description of our universe. As the universe expands, we get these lumps in the cosmic microwave background. Right, These lumps come from quantum fluctuations in the very early universe during inflation. But as the universe is inflating, you're getting fluctuations all the time. So you should see lumps at all different sizes. It's like the biggest lump. And that's when we're using to measure the curvature. You should see big lumps, you should see small lumps, you should see very very small lumps. And so when we look at these fluctuations the amounts of lumpiness in the universe, we should see big lumps and small lumps, and smaller lumps and even smaller lumps. And so when people go out and measure this stuff, they see that mostly, but they see that sort of like the biggest scales, some of those lumps seem to be missing. Don't see necessarily correlations between things that are as far apart as you expect.
Wait, let's maybe take a step back. We measure the US to be a little bit positive a curvature, which means that it can still be a sphere. Could it can still be a sphere?
Could be a sphere?
I see, But there's something about the donut that makes it makes you think that it could be a donut. What's special about a donut that would fit what you're seeing.
Well, what we're seeing is that at very very large angles, there aren't as many correlations as we expect. You know, we're talking about a very small effect here, and above sixty degrees in the sky we should see fluctuations about one hundred microclevins, but what we see is fluctuations like twenty microkelevins. So it's a small effect. But a donut topology turns out to suppress these large scale fluctuations because it makes the universe finite. And donuts have a sort of a smaller radius than a sphere for the same curvature. A donut has sort of like shorter length scales, right than a sphere does.
Well, I guess maybe we need to talk about the differences between donut and meatball standing all like, because a donut is interesting, right because it's it's a close shape, but it has a hole in it, and it's kind of interesting because like if you go in one direction, like around the wide rim of the donut, you go in a circle. And also if you go towards the center of the doughnut. You also go in a circle, so it sort of loops around in all directions, sort of like a sphere, but it's not a sphere. It's more like a like a closed cylinder.
Yeah, And it's got two different length scales, as you say, it's got like the one way around and the other way around, whereas a sphere only has one length scale, it's just the radius. And you know, even if the universe is curved and it's a sphere or a donut, we're talking about something very slightly curved. It's really really huge, right, really on enormous scales. Just just so nobody is confused. We're not like the little prints here standing on a tiny donut.
It's a ginormous donut.
Yeah. But they did a bunch of simulations and they discover that a donut is better at causing the sort of lack of ripples that they see in CMB. You know, in the cosmic microwave background radiation, we don't see some of the bigger ripples that we expect, and a donut is better at suppressing those because it has these two length scales, the long way around and the short way around. And so you just sort of like, don't get as big lumps on a donut as you do on a sphere, and so that makes people wonder maybe the universe is shaped like a donut.
Right, So it's the difference between these lengths scales that it is giving you the clues like you're seeing some weird kind of like oblong shape than the cosmic microwave background.
Yes, the fact that you don't see as big lumps as you expect from a flat universe or even from a spherical universe. It's not impossible to suppress these long distance effects on a sphere. It's just that you would need a radius of curvature that's not consistent with what we have measured. A donut gives you another length scale to play with, so it's easier to suppress the long distance correlations. Now, this is not a smoking gun. This is like a weird little hint that could just be random noise, right. It could be theorious getting too excited and eating too much chocolate and thinking about donuts. But it's sort of like a fun hint. And we'll get more data and we'll see if this holds up. But it's fascinating to me that this question is the universe flat or is it a spear or is it even a donut? Is still unanswered. It's still something we don't know the actual answer to.
WHOA. But it seems like we have a sort of a big clue, which is that the universe's flat around us. Could it be that we're just measuring local curvature, like are we just a dimple or like a flat spot in a you know, t cup shape universe?
Absolutely, you know, what we're doing is we're assuming that the curvature we measure here is the same as the curvature we're measuring somewhere else. And we're hoping that that's true because we're measuring in lots of different ways and we're trying to measure in different directions. But in the end, our vantage point is limited, right, And so it could be that we're a flat spot on a very large donut, or that we could be a slightly curved spot on an otherwise flat universe. You know, we can't really confidently extrapolate paths what we can see. They'll remember that the CMB measurements do cover a lot of space.
It's not that interesting, or so you're saying, kind of stay tuned, like we actually don't know what the shape of the universe is.
That's right. If you're betting, I think flat is the best bet, right, It's the simplest, it's harmonious. It's what most physicists believe. If you ask them if the is the universe flat, they would say yes. But you know, the data say it's either flat or slightly positively curved. And there are these interesting wiggles that are more consistent with a donut shape than a spear or a flat universe. So yeah, stay tuned. We still got big realizations ahead of us.
So if you're the gampling type, maybe invest in donuts. It's what you're saying.
And if you win, eat a donut, and if you lose, eat a donut. Either way you.
Win, you said. If you don't win, you donut, you win, you don't, or you donut, don't donut.
If you win.
If the universe is still with dark chocolate, how would that change the Currichard danul M.
I think we would make it more closed exactly. Dark chocolate's pretty dense stuff and so we tend to compact on itself. And how would mean the universe is not in definitely filled with chocolate, and eventually my snacking days must end.
Right, But if it's closed, then there's a finite amount of dark chocolate, so eventually you might eat physicists might eat it. All.
That's right, I better go ahead and get started on my snack.
I might want to buy some new belts or pants, assuming you wear pants. I mean, we talked about social conventions and physicists. Who knows, right, we.
Talked about not making assumptions, right, you know, we're exploring the university.
Keep pype in what shape is Daniels or Daniel's pants? He doesn't have pants? Maybe it's a mood question.
There actually is a pants diagram for black hole mergers. We're going to talk about it a few weeks, all right?
Is that rude to ask what black Hole's pants are?
We'll find out.
Are they bill bottoms or tapered low rising?
They wear shorts over their socks.
And sandw may their mom jeans or that cargo pants? All right? Well, it's interesting to think that, you know, from our little spot in the universe, we can, you know, have these conversations about what the shape of the the universe is when it's so far away, you know, ninety sixty billion light years away, We're still we can still have conversations about it, and we might be right, which is the crazy thing.
Yeah, and thank you very much to professors Leo Stein and Evans kennab Echo for consulting with us on this tricky topic. Any remaining inaccuracies and ambiguities are our responsibility, not there, And no matter how big and how crazy the question is, we can eventually always think about some way to try to answer it, some clever wrinkle in the nature of the universe that forces it to answer our questions. But even the biggest, hardest, craziest questions with the crastiest answers.
That's right, even the tasty and crazy answers about the universe. Well, we hope you enjoyed that. Thanks for joining us, See you next time.
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