Could the Universe be shaped like a donut?

Daniel and Jorge talk about how much dark chocolate can fit in Universes of various shapes and sizes. 

See omnystudio.com/listener for privacy information.

Episode Transcript

Speaker 1 (00:08):
Or Hey, if you were designing a universe, would you
make it the shape of a snack food? M M.
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

(00:30):
for fruity inspiration, I might draw my inspiration from chocolate.
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

(00:52):
to be shaped like a banana? Soon? I'm going to
be the size of the universe Eventually. We all have
a dreamy. Hi am or Hammon, cartoonists and the creator

(01:13):
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 that's a lot. You know, if and it's
no joke. The music 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

(01:34):
snacking on it and eventually I gotta take it away.
So I've never reached the port where I'm like stop.
It 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 possibility, the
upper limits and the lower limits. There's got to be
a boundary, and I am devoted to finding it wherever

(01:54):
the cost, even if it causes your belt line to
go to be on bounded But anyways, welcome to our
podcast Daniel and Jorge Explain the Universe, a production of
I Heart Radio 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,

(02:16):
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 talked 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 a very tasty or, as Daniel says, crazy universe,
crazy tasty universe for us to sample and enjoy and

(02:36):
savor 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

(02:57):
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 this year Is while listening to podcasts. Well,
I wondered if the crunching with interviewer they're listening. Well, anyway,
let us know if you have a favorite Daniel and
Jorhey 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

(03:20):
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 happened to some of those
Swiss chocolate funds. Yeah, it happens a big chocolate moundy.
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

(03:41):
the corner of the Milk Way gaxy 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 could look out into
the universe sort of like we're trapped in a tiny

(04:03):
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 to be
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

(04:23):
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

(04:44):
what's going on further than that. Right, there's a 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 want to know what's past the edge
of the universe. One of those habits seems healthier than
the other, then I think they're tied together. I think
dark chocolate fuels my curiosity. What did your doctor say

(05:06):
about this type of curiosity? This is why I stop
going to doctors. Really, sorry, 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? I see you're saying we're

(05:28):
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. Will never
be satisfiment go you know what, a 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

(05:50):
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

(06:13):
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

(06:35):
be the age of the universe times the speed of
light that photons would be racing through space to us,
and then 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

(06:56):
very far away, out to about forty five billion light years,
and it actually we'll even see after 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 said, there are people who wonder what's beyond that.
You know, if I keep going past sixty five billion

(07:17):
light years, what am I going to find a Am
I gonna hit a wall? Is this the universe gonna
go on forever? Or is it going to do something
even crazier? Yeah, we'll 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

(07:38):
past the edge of our vision. That's your carrot, Daniel, like,
you know, the 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 chocko 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 gonna put funds for dark chocolate, and

(08:00):
I'm gonna 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 Nestly Foundation
for Chocolate Research, then I think I'm gonna put that in.

(08:21):
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 flair
that makes you create the chocolate. I don't know. I
think it works either way. If you win the Nobel Prize,
you celebrate byating 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

(08:43):
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 some day or you're
gonna 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

(09:04):
something that must be like written into the real source
code of the universe. It's not just like, oh, where
is the planet or where are there aliens? Things that
are affected by randomness. Is 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

(09:24):
the universe, you're asking what is the cion 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,
you just blew my mind? What is the shape of
the multiverse? Shape like a Marble movie? It's shaped like

(09:45):
a dollar bill, I'm pretty sure, shaped like the money
they're they're breaking 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 seen 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

(10:06):
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

(10:29):
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 where
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

(10:50):
I'm gonna 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 that you probably
won't get an answer. I got a cease and desist
from the universe legal department. Yeah, stay away from me,
blocked blocked by the universe. Wow, that's harsh. But it

(11:12):
is an interesting question. And so today on the podcast
we'll be asking is the universe shaped like a doughnut?
And does it taste like a donut? To Daniel, this
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

(11:36):
filled after all, chocolate filled or shaped like a donut
or like a donut wood chocolate in it exactly, the
universe might be a chocolate field donut in the end.
I don't think I've ever heard of a chocolate field 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. Man?
What's a jelly filled donut? Then? Is it a jelly

(11:58):
filled not donut? It's a jelly filled cake and p
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 the
science podcast. 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.

(12:20):
I think the classic shape, you know, it was basically
a tourist with a hole in the middle. But you
could still put chocolate inside that taurus right, Oh, you
mean along like the ring of it you can stuff
with with chocolate. Ring of chocolate? Why not? Sounds delicious
to me? It 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

(12:41):
a possibility that the universe could be shaped like a doughnut,
which sounds both bulgeous and filling. And so that's the
question we'll be trying to answer 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
the questions for us on the podcast. It's always fun

(13:02):
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 Daniel and Jorge dot com and
Dennie will send your donut if you answer the question right.
You're a digital donut, a little emoji donut. Well, think
about it for a second. Do you think the universe

(13:24):
is shaped like a donut? Here's what people have 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.

(13:46):
So from that, it really appears that the universe, uh
does not have curvature to it. I don't think the
universe has 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

(14:08):
about this before. I remember at some point somebody, maybe
in a documentary or something, saying that if you look straightforward,
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 bat like that.

(14:29):
I don't think the universe has shaped like a donut.
I think if it was, we would have noticed by now,
because there'll be a lot less potions 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

(14:51):
as time and space are concentric, I think the universe
can be any shape, and there are probably universes of
all ships 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

(15:13):
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
is weird and surprising. It could be shaped like anything exactly,
and some people even commenting that donuts have jam inside

(15:34):
of them, and so they're arguing, I think they agree
with you. You know that the shape we're talking about,
it's more like a bagel than a donut. 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

(15:54):
long as you with chocolate inside of it. Man, you
really hungry 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.

(16:16):
Are you saying, like the walls of the universe are
shaped 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 space is like maybe
being curved. General relativity tells us that mass and energy

(16:39):
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,
and 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.
Where space does curve, you can imagine it being like
a sphere or a donut or some other weird shape.

(17:02):
So the curvature of space is connected to this other
question of the shape of space. Curvature 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

(17:24):
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

(17:44):
a sphere and 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 donut,
that are not the same as a sphere or a
flat sheet. That's the meaning of shape in a global sense,

(18:05):
which is related to, but different from curvature in a
local sense. Mm hmm, 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

(18:26):
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 it's 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

(18:49):
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 on 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

(19:09):
you know, space is curved, that gravity is not like
a force the way we think about other forces, but
instead it's a fictitious force, the 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

(19:30):
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? But you can't build like an infinitely flat space,
like a huge sheet, But you can build like a

(19:50):
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.
M I think what you're saying is it's kind of like,
you know, if I measure the land around me, and
I see that the land occurs around me downwards or
towards the end of the Earth, then it kind of

(20:13):
tells you that me 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 its curved, then that suggests that probably it's a
big sphere, although you know, it could also be a donut,

(20:34):
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 parable at the bottom of parable,
you think it's it's curved, but it could keep going forever. Right. Mathematically,
a problem 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

(20:55):
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

(21:16):
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 spaces that
consistent with just in the same way, like if you
want to measure the surface of the Earth, you could
be standing locally on something flat or something point de
or you know, in a bowl or something, doesn't change

(21:37):
the overall structure. So when we measure the curvature 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 um or
are you saying space as a curvature to it because

(21:59):
there's stuff in it? This is a really important point
and a 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.

(22:21):
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.
M I see, because I think you know, there's sort
of two things, right, there's stuff and energy and then

(22:41):
there's space. Those are two kind of separate things, and
so you can imagine that 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? Then even yeah, although we're interested in

(23:02):
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
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,

(23:24):
the amount that planet curves away under you decreases. So
the stuff that's in the universe can 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

(23:44):
the stuff and energy in the universe, I would be
left foot space and that space could be in the
shape of a sphere or a donut or something and
the stuff and 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 apology. It's global curvature plus the amount of stuff,
the mount of the density, and the dark energy all
those together determine like whether the universe is expanding or contracting.

(24:08):
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 it's it's sape right, like you know nothing,
but the universe can change its safe yeah, and shape
in a very specific way, right. You know, we're not

(24:29):
talking about size. You can have a universe that's a
sphere and it can grow or it can collapse. 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 change? Well, I guess we
know that mathematically, but you can also just think about

(24:49):
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
grow going you know, arbitrarily large, But then how do
you suddenly transform that smoothly into a flat universe. You know,
the universe can change, it can't evolve, but it has

(25:09):
to happen in a smooth way. You can't have like
a sudden jump where the universe is 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. Right then, we're talking about

(25:42):
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 four, being nosy about people's
size and shape exactly upsetting the apple carts. Since for ever,
that's our goal. You know, we don't care if the
truth is offensive. We just want to know. Discarding with

(26:07):
social conventions since the beginning of the ton of time,
as if we understood social conventions, right, that's the reason
we went into physics, because we just don't know how
to do the other stuff. Oh man, your meetings would
must be pretty interesting or not or not. You know,
a world without subtlety might be a little boring. You know,
that's a fun stereotype. But you know, physicists are social creatures.

(26:29):
I work in a collaboration of thousands of people, and
we have lots of meetings 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 the universe can have a shape even if I

(26:51):
take like if I take out all this stuff and
energy in it, put it somewhere out of nowhere, But
you put it somewhere, the universe that's left over would
have a shape to it. What exactly does mean a shape?
Does it mean it has walls and a boundary like
edges to it? It tells you how space is connected.
I think about space not it's just like where stuff happens.
But I think if it's sort of like a fabric

(27:13):
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 a 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,

(27:34):
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

(27:55):
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 do we've 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

(28:18):
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 spaceship and I keep going
for you know, a ninety billion light years, eventually I'm
maybe you're gonna hit a wall. Like that's not a
possibility that physicists seemed to consider because it 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

(28:38):
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

(28:59):
of the of our sort of seems to be the
same as every other part. But you know, maybe it's
like we're in the very center 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, an 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 base, I mean if it does

(29:20):
have walls and a boundary could be shaped by anything, right,
could be shaped like a cube or a banana or
you know, like um, 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 do 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.

(29:42):
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 pieast then what are
your options? So, for example, if I only give you
those flat pieces of lego, then what can you do?
You can just make a big flat sheet, right, just

(30:03):
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

(30:24):
think that it has to go on forever. Then, you know,
to me, it seems like the only possibilities for the
universe to be infinite and have no shape. But I think,
you know, I physicists think about it differently, like it
could still be sort of infinite and continuous without boundaries
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

(30:47):
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 repeat. 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 sort of the same way we

(31:09):
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 the
same sense, you could have like a whole seam where
you connect like a whole line of space to another

(31:30):
whole line of space, effectively making like an 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 it's 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

(31:53):
space is curved or connected to itself in a strange
way so that I can't 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

(32:14):
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

(32:34):
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 finite. 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

(32:55):
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, what does what does curvature mean for you?
Like for me, curvature means that the ground is uneven
or it has a slope to it. But what does
it mean in terms of space? In terms of space?
It locally, it means what is the path of a photon?
If you shine a laser beam through a chunk of space,

(33:16):
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,

(33:39):
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 it means space time, right, or
I guess that the lump it all together. Yeah, Well,
relativity definitely mixes space and time together. There's a connected

(34:00):
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
images 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 ft like if you

(34:21):
shoot one photon and it 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, Yeah,
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,

(34:41):
what are the angles of that triangle. If you draw
a triangle on a flat surface, then it's angles add
up two, And if you draw triangle on the surface
of a sphere, it's angles are bigger than one a
d um 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're on a parabola,
then they appear to curve away from each other. And

(35:03):
it's equivalent to saying that a triangle on that surface
as angles less than degrees. Well, it's kind of strange
to think of a sears and converted between two the
and four D 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,

(35:24):
they're not going to curve, or at least they're gonna
curve together maybe, but they're not gonna sort of move
away from each other or move towards each other. Right,
They're just gonna keep going in the same direction, side
by side forever. That's what it means for space to
be flat, Right, that's the 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

(35:44):
what appears to be parallel to you will either approach
each other or divert from each other the 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 due 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 gonna hit the same point.
It's a motion constrained along a curved surface, or motion

(36:05):
through curved space can make things that initially were parallel
moved towards each other. So the Earth is not flat.
Need slash, it's not slash, 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 but that doesn't
happen on Earth, right. That's one way we know the

(36:25):
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 Earth 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, depending on
the sign of the curvature. So if you're on a sphere,

(36:46):
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 curvature. If the universe has positive culture, then two
photons would eventually hit each other, even if you shoot
in parallel to each other. And if it has negative curvature,

(37:07):
deligious diverge and never hit each other exactly. But that's curvature.
What does that tells 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 parabloh, you can't make an infinite
flat universe. Right, you can make a sphere. You could

(37:30):
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

(37:51):
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 not here there's the mid of

(38:11):
a subtle point of geometry, the picture you have in
your mind. If 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

(38:31):
is actually like a flat plane connected on itself, like
the pac Man universe we were talking about. So there's
the donut you eat, which has curvature, and then there's
a mathematical donut which is actually flat on the surface,
and we could also consider 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,

(38:54):
I see. But if we measured space to be flat,
then there's no shape. It can't beat has to be
in it kind of. That's right. A space is flat,
and it can't be a sphere. It could still be
that weird Pacman 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 hyperboloid or anything like that. So
measuring the curvature of space does rule out some possibilities

(39:18):
for the shape of space. Okay, So depending on the
curvature that we measure around is in all space, they'll
determine whether the universe is shaped like an infinite sort
of space sheet, or whether it's shape maybe closed like
a ball, like a sphere, or whether it has a
more interesting shape like I don't. And so let's talk
about what we've measured out there whether the universe is

(39:38):
flat or curved. But first let's take another quick break. Okay.
I know we are talking about the size and shape
of the universe, and now we're doing something even router,
which is actually measuring the size in shape of the universe. Like,

(40:01):
wouldn't that be rude? Or something came up to and
be like, hey, I wonder how big you are? Let
me measure? 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 into. 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

(40:22):
asked the universe it's size and it gives us an answer,
I'd still want to go out and measure 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's sent in

(40:42):
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 the curvature
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 a infinite sheet,
or maybe has some weird shaped like a doughnut or

(41:03):
a hyperbola. And so I guess the big question now
is how do we measure the curvature of space? Like,
how do we measure if its 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

(41:24):
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 eight degrees in it if 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

(41:44):
I see. I mean, like you send out three satellites,
put arrangement a triangle, and you shoot lasers at each other. 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
and Andromeda one and another galaxy, and they shoot lasers
at each other so you know they're lined up, and

(42:05):
then you just measure the angles between those lasers. So
like if I'm shooting an Andromeda from here and I'm
shooting at Alphas, another gassy from here, I would literally
just us take like a protractor and measure the angle
between the lasers. That would tell me whether the universe
is curved. Yeah, in the same way you could on
the surface of the Earth. Right, You've got two friends,
you guys stand in the triangle and you spool out

(42:26):
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, it's 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

(42:48):
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 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,

(43:09):
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. Mmmmm.
It's so meaning like looking at galaxies, are 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

(43:30):
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

(43:51):
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 it's sort
of like the o G light, like the original light
of the universe, like when it was born, they didn't
have a curvature to it. And you can tell from

(44:12):
the you said, the wiggles of the 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, like one part in tens of thousands.

(44:35):
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 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

(44:55):
universe is curved in one way positively, say, for example,
and maybe the universe is sort of like a sphere,
then the universe could acts like a magnifying glass. Right,
So you should see these um 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

(45:16):
for like how matter and dark matter and the photons
were all slashing 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

(45:39):
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 spaces flat than 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 we know those photons and tell whether they've been

(46:01):
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
glass if you're near sighted or something magnifying glass, you know,
like a piece of glass, it has the opposite kind
of curve, like the curse inwards in the middle, then
things sord have looked smaller through it. Right, so the

(46:24):
spots to look smaller, and we can do these simulations.
We say, here's where 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 and 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

(46:45):
what we see? You know, is the universe look like
it's flat or does it look like it's curved one
way or the other. So this is a very powerful
way to measure the curved to the universe over a
very very large scale, because even though those photons started
out not that far apart from each other, they traversed
a huge amount of the universe because of that expansion. Right, yeah,

(47:07):
so is the universe amplifying or 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. We measure is zero point

(47:29):
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've flipped a coin a
thousand times and it's a fair coin, you'd expect on
average to get of those to be heads, but you know,
sometimes you get a fluctuation up or down. So that's

(47:50):
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

(48:12):
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 way the whole universe,
Like add up all the mass of all the stuff

(48:33):
that's in the universe, the matter, the dark matter, the
dark energy, and that will 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, has to have positive curvature.
And so that's another completely separate, totally independent way to
measure the curvature of the universe, and that also comes
up consistent with flat. Well, wait, you teld me earlier

(48:55):
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

(49:17):
amount of stuff in the universe helps us measure the curvature,
which determines what shapes it can be. Mm hmmm, I see.
So okay, so we 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 is infinite and boring

(49:42):
in that sense and goes on forever and 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 less

(50:06):
much just because it's lunchtime maybe, or you need to
sugar fix But wait, it's like I said, bag, you said,
so we measured the universe 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 doesn't
have a shape. Well, I mean that is a shape, right,
you know, mathematically speaking, that the shape If the universe

(50:28):
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. A donut
is positively curved on its surface. That's for a physical donut.
A mathematically donut is technically flat. So remember that little subtlety. Okay,

(50:51):
so we're measuring the university a little positive curvature. Is
that what you're saying? It has a little bit of
a positive curvature, a little bit of a positive curvature.
And also some details the cosmic microwave background radiation are
really interesting and tantalizing, and I've led some people to
suspect that maybe a doughnut is the best description of
our universe. As the universe expands, we get these lumps

(51:12):
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

(51:35):
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, Like you 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 unms be

(51:56):
a little bit positive curvature, which means that it can
still be a spear. Couldn't it connects to still be
a sphere? Could be a sphere? I see, but there's
something about the doughnut that makes it makes you think
that it could be a donut. What's special about a
donut that would fit what you're saying, 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

(52:17):
about a very small effect here, and above sixty degrees
in the sky we should see fluctuations about a hundred microclevins,
but what we see is fluctuations like twenty microclevin's. 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

(52:39):
radius than a sphere for the same curvature. A donut
has sort of like shorter length scales, right, then a
sphere does. Well. I guess maybe we need to talk
about the differences between donuts and meatball standing because a
donut is interesting, right because it's it's a close shape, um,
but it has a hole in it, and it's kind
of interesting because like if you go in one direction,

(52:59):
like a around the wide rim of the doughnut, 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

(53:20):
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, so really really huge, right,
really un enormous scales, just just so nobody is confused.
We're not like the little prints here standing on a
tiny donuts, the ginormous donut. Yeah. But they did a
bunch of simulations and they discovered that a donut is
better at causing the sort of lack of ripples that

(53:42):
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 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,

(54:03):
So it's the difference between these lengths the scales that
it is giving you the clues like you're seeing some
weird kind of like oblong shaped and 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

(54:24):
a radius of curvature that's not consistent with what we
have measured. A doughnut 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 theorists getting too excited and eating too
much chocolate and thinking about donuts. But it's sort of

(54:46):
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 it's deer or is it even a donut is
still unanswered. It's still something we don't know the actual
answer to. Oh, but it seems like we have a
sort of a big clue, which is that the university
is flat around us. Could it be that we're just

(55:07):
measuring local curvature, like are we just a dimple or
like a flat spot in a you know, teacup 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,

(55:28):
our vantage point is limited, right, And so it could
be that we're a flat spot on a very large doughnut,
or that we could be a slightly curved spot on
otherwise flat universe. Um, you know, we can't really confidently
extrapolate path what we can see. The Remember that the
CMB measurements do cover a lot of space. It's not
that local. Interesting or so you're saying kind of stay tuned,

(55:52):
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. It's the simplest, it's harmonious. It's
what most physicists believe. If you ask them if the
is the universe slat, 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

(56:13):
with a donut shape than a sphere or a flat universe.
So yeah, stay tuned. We still got big realizations ahead
of us. So if you're the gamping type, maybe invest
in donuts, that's what you're saying. And if you win,
eat a donut, and if you lose, eat a doughnut.
Either way you win said. If you don't win, you don't.
You win, you don't, but you don't don't donut. If

(56:34):
you win. If the is still dark chocolate, how would
that change the curvature, Daniel M. I think would make
it more closed exactly. Dark chocolate is pretty dense stuff
and so we tend to compact on itself. And how
would mean the universe is not infinitely 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,

(56:56):
So eventually you might eat physicists might eat at all.
That's right, I better go ahead and get started on
my snack. You might 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, he
talked about not making assumptions, right, you know, we're exploring
the university in mind. What shape is Daniel or Daniel's
pants he doesn't have pants. Maybe it's a good question.

(57:19):
There actually is a pants diagram for black hole mergers.
We're going to talk about 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 and they wear shorts over their socks and sand
neither mom jeans or that cargo pants. All right. Well,

(57:42):
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 universe is when
it's so far away, you know, nineties, sixty billion light
years away. We're still we can still have conversations about it,
and we we might be right, which is the crazy thing. Yeah,
and thank you very much duper users, Leo, Stein and
Evans gonna be echo for consulting with us on this

(58:03):
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 were

(58:26):
the craziest 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. Thanks for listening,
and remember that Daniel and Jorge explained. The universe is
a production of I Heart Radio. For more podcast from

(58:49):
my Heart Radio, visit the I Heart Radio app, Apple Podcasts,
or wherever you listen to your favorite shows. No