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Downloaded from
YTS.MX

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Official YIFY movies site:
YTS.MX

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[crickets chirping]

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[eerie music playing]

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[dogs barking]

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[car alarm blaring]

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-[eerie music intensifies]
-[girl] Four, five…

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[man 1] Well, the first time
that I thought about infinity,

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I was looking up at the sky one night

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when I was about ten years old.

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[woman 1] I was really little,
it was before I had started school,

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and I was sitting
under the dining room table

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and counting.

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And at a certain point,

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I realize this goes on forever.

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[man 2] Lying on a beach late at night
and just wondering

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the vastness of outer space.

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Does it go on forever?

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[tense music plays]

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[music intensifies]

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[tense music ends]

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[jaunty jazz music plays]

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[cat] Mmm…

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[producer] I want to start
with sort of the premise of the film,

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which is that we're looking for infinity.

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-So where should we go looking?
-[chuckles]

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Well, I don't think
everybody's looking for infinity. [laughs]

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[upbeat music plays]

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[woman] So is infinity a number, a place,

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an idea, a concept?

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If you ask me, probably all of the above.

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[man 1] Numbers never end.
That's the basic idea of infinity.

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[man 2] If I imagine continuing to count
for as long as I can count,

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infinity will definitely last
longer than my lifetime.

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[man 3] The funny thing is,
all these numbers that you can imagine,

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they're like zero, nothing.

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Any number, no matter how big,

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is just absolutely insignificant
compared to infinity.

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For me, infinity is not scary.

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I find infinity beautiful,
and haunting, and thrilling.

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I love Infinity.

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You know, I guess if I start
thinking about, "I'll be dead forever…"

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there's a side of me
that's worried about it. [laughs]

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But then again,
I don't plan to be thinking about it.

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I think to be conscious
is to be wrangling with infinity.

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I mean, not to be grandiose.

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When our hearts are broken,
are we going to be in pain forever?

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And if you really
fall in love with someone,

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are you gonna be in love
with them forever?

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Love is certainly infinite,
because when we are overwhelmed by love,

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we have this constant sense
of breaking the limits and the boundaries.

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All of these abstractions,
suddenly it seemed to me,

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well, maybe they're just
the product of our minds.

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Who invented infinity?

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I think, uh, to some extent,

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the concept goes back
earlier than anything that we know.

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[woman] One, two, three…

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[Kenny] In fact, counting
is the very earliest writing that we have.

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[girl] …seven…

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[Kenny] Whoever invented writing
already had the idea of counting,

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and the idea
that you can always count one more

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must surely go back at least that far.

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[girl] …fifteen, sixteen…

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[Steven] We have all kinds of different
visions of things that are infinite,

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and they're usually terrifying.

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There's the vision of the bottomless pit.

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There's the idea of time that never ends.

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[clock ticking]

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If you believe in hell,

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and if you believe
about torture going on forever,

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a nightmare that you could
never wake up from…

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So I understand that a lot of people
find thinking about infinity terrifying,

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or nauseating.

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At least very upsetting.

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[Rebecca] But for some of us,
it's one of the deepest pleasures.

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[girl] …2001…

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[Rebecca] We're so small…

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[girl] …2003, 2004…

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[Rebecca] …and yet we can
touch something so…

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[girl] …1000000, 10000002…

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[Rebecca] …explosively large.

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[girl] …1000004…

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[Rebecca] That feeling of, "I'm bigger
because I know how small I am."

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[girl] …399, 400, 401…

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[Rebecca] I've been chasing that feeling

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my entire life.

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[girl continues counting]

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[Janna] But does infinity exist
outside of our minds?

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[Moon] So does infinity exist?

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Um…

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You know, in math, I think-- [smacks lips]

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[producer] Can we wait
for this train to go by?

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Oh yeah.

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[train rattling]

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[producer] Okay.

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All right. Sorry about that.

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Oh, yeah. It's good to collect thoughts.

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Um, okay, so I think
I was gonna make a comment

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about what it means
to exist mathematically, right?

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Um, so, in math, I think we have
an interesting relationship to stuff,

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to things in existence, right?

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If you can conceive of something,

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if you can kind of
create rules for handling it,

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then it exists.

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[train rattling]

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So how does infinity fit into all that?

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Well, okay, infinity
is super counterintuitive,

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and it leads
to a lot of surprising paradoxes,

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contradictions,
intellectual quagmires, quicksand.

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Many of these are summed up in a parable

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that goes by the name
of the Infinite Hotel.

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[jaunty jazz music plays]

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Imagine a hotel
with infinitely many rooms.

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It's a really popular hotel.

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And in fact, it's always booked solid.
Every room is occupied.

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Nevertheless, there's always room
at the Infinite Hotel.

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[Steven laughs]

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So, one night, a new guest shows up.

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-[bell dinging]
-Bang, bang, bang on the bell.

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"I'd like a room."

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And the manager says,

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"Sure. Of course, we can accommodate you
here at the Infinite Hotel."

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"Just hold on for one minute."

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The manager tells everyone
over the loudspeaker--

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[manager] Please gather your things.

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Get ready to move
to the next room down the hall.

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[Steven] Person in room one
moves into room two.

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Person in room two moves into room three.

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You might think there's gonna be trouble
because all the rooms are occupied.

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Nevertheless, as it's an Infinite Hotel,
I mean, this can happen, right?

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The numbers never stop.

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One can move to two,
two can move to three,

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a million can move to a million and one.

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So everybody moves down to the next room,

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which means that now room one is open,
and the new guest can be accommodated.

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[producer] You could keep everyone
in the same room

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and just have the guest go to the end.

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Yeah. So a tempting thought would be
just have the guest take the last room.

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[laughs] Why are we making
everybody else move for this one person?

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Well, because there is no last room.

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[jaunty jazz music plays]

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Infinity doesn't work like that.

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You have to start at the beginning,
not at the end. There is no end.

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Now, a bigger challenge for the manager
comes the next night

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when, instead of just one guest
showing up,

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suddenly a whole busload full of cranky,
sweaty, ill-tempered people

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all pound on the bell at the same time,
saying, "We all want rooms."

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There's infinitely many new guests.

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They all want to be accommodated
at this hotel.

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How can you do that?

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Can you somehow find room
for infinitely many new people,

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given that infinitely
many rooms are occupied?

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[panting]

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It turns out the manager has seen
this problem before,

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and so she calls out over the loudspeaker…

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[manager] Everyone be prepared
in a few minutes

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to move to the room
that is double your current room.

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[Steven] So, person in room one,
you're gonna be in room two.

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Person in room two, you're now
going to be moving into room four.

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Person in room three, you're going to six.

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Now, it's a big inconvenience
for person in room one million.

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They have to move to room two million,
which is a big schlep down the hall.

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[jaunty jazz music intensifies]

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So all these people dutifully move
to their new rooms.

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You'll notice that what's happened is
all the odd-numbered rooms

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have been vacated.

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And so all those new guests
can just start filing in.

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[jaunty jazz music ends]

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There's one other custom
at the Infinite Hotel,

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which is that this manager
is very conscientious

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and always checks in on the rooms,
infinitely many of them.

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Fortunately, the manager is very speedy,

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00:10:00,266 --> 00:10:02,935
so she can get her whole job done
in a minute.

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00:10:03,019 --> 00:10:04,979
-[jaunty jazz music plays]
-[grunts]

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00:10:05,062 --> 00:10:08,232
She spends half a minute
making sure everything's okay in room one,

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and a quarter of a minute,
so 15 seconds, on room two,

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and then half of that,
so 7.5 seconds, on room three,

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00:10:18,826 --> 00:10:22,038
and so on, going all the way down the hall
in the Infinite Hotel.

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A half, plus a quarter,
plus an eighth, plus a sixteenth,

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00:10:27,376 --> 00:10:28,419
and if you add that up…

181
00:10:30,129 --> 00:10:33,299
But if you just think about that,
when you go out to infinity,

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that's gonna add up to one.

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00:10:38,721 --> 00:10:40,598
She's basically gonna be done

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checking infinitely many rooms
in one minute.

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[producer] How does she get back
from infinity?

186
00:10:47,188 --> 00:10:50,775
She get-- Oh, that's good. Well… [laughs]

187
00:10:51,400 --> 00:10:54,445
Yeah, let's see. So, um… Hmm.

188
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That's an interesting puzzle.
Yeah. Where is she at the end? Uh…

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00:11:00,743 --> 00:11:01,577
Don't ask me.

190
00:11:02,828 --> 00:11:05,122
I've been thinking about infinity
my whole career,

191
00:11:05,206 --> 00:11:07,500
and even I don't really see
any way out for her.

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00:11:07,583 --> 00:11:09,585
[eerie music plays]

193
00:11:10,795 --> 00:11:13,673
She's out at the end
of this infinitely long hallway,

194
00:11:13,756 --> 00:11:16,592
and I don't see
how she's gonna come back from there.

195
00:11:19,762 --> 00:11:21,555
I told you it was a strange hotel.

196
00:11:23,974 --> 00:11:27,186
Well, so I think that, you know,
the moral of this crazy parable

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00:11:27,269 --> 00:11:30,398
is that infinity doesn't behave
like anything we're used to.

198
00:11:32,525 --> 00:11:36,112
We're used to thinking about
collections of finite numbers of things.

199
00:11:36,195 --> 00:11:38,948
Fish, fish, fish.
That's three fish, you know.

200
00:11:39,031 --> 00:11:41,617
So we're used to small numbers,
or even big numbers.

201
00:11:41,701 --> 00:11:43,953
You hear nowadays
about trillions of dollars

202
00:11:44,036 --> 00:11:46,956
needing to be spent
on the budget in the United States.

203
00:11:48,541 --> 00:11:52,128
But, um, those are nothing like infinity.

204
00:11:52,211 --> 00:11:55,881
Any finite number, no matter how big,
is nothing compared to infinity.

205
00:11:55,965 --> 00:11:58,426
[marching drum playing]

206
00:11:59,051 --> 00:12:02,221
We just don't have good intuition
about how infinite things work.

207
00:12:03,180 --> 00:12:05,182
[tense music plays]

208
00:12:09,520 --> 00:12:13,899
Even very small children
can have a gut feeling about infinity.

209
00:12:13,983 --> 00:12:15,276
It's the biggest possible thing.

210
00:12:15,359 --> 00:12:17,611
It's bigger
than anything you can ever think of.

211
00:12:21,157 --> 00:12:22,867
Well, what happens if you add one?

212
00:12:24,702 --> 00:12:26,704
So if infinity
is the biggest thing there is,

213
00:12:26,787 --> 00:12:30,750
then when you add one,
it should still be infinity. Maybe?

214
00:12:31,792 --> 00:12:35,087
What happens if I subtract infinity
from both sides?

215
00:12:35,671 --> 00:12:38,299
Then you get one equals zero.

216
00:12:38,382 --> 00:12:41,635
And so immediately you've landed yourself
in some kind of an issue,

217
00:12:41,719 --> 00:12:43,220
and that's just the start.

218
00:12:43,304 --> 00:12:46,265
It turns out you can write things down
that don't have an answer.

219
00:12:46,766 --> 00:12:49,018
I mean, that doesn't happen
in finite arithmetic.

220
00:12:49,101 --> 00:12:52,104
If I say one plus two,
the answer is three, and I'm done with it.

221
00:12:52,855 --> 00:12:55,566
But if I say one minus one,
plus one, minus one…

222
00:12:55,649 --> 00:12:56,817
[voice echoes]

223
00:12:56,901 --> 00:13:00,863
One minus one, plus one, minus one,
plus one, minus one, dot, dot, dot.

224
00:13:00,946 --> 00:13:02,490
Keep doing that forever.

225
00:13:05,284 --> 00:13:08,370
There is no answer to that.
It's not zero and it's not one.

226
00:13:08,454 --> 00:13:10,915
It's neither. It's both. What is it?

227
00:13:10,998 --> 00:13:14,335
You can try adding infinity to infinity.
Multiply it.

228
00:13:14,418 --> 00:13:15,961
You get these weird paradoxes.

229
00:13:16,045 --> 00:13:18,172
Well, what's infinity plus infinity?

230
00:13:18,255 --> 00:13:20,966
That should also be infinity
because it's the biggest thing.

231
00:13:21,050 --> 00:13:23,677
Then you subtract infinity from both sides

232
00:13:23,761 --> 00:13:25,638
and you get infinity equals zero.

233
00:13:25,721 --> 00:13:27,973
That's even worse. So this is terrible.

234
00:13:28,057 --> 00:13:30,559
[tense music continues]

235
00:13:30,643 --> 00:13:33,979
But it's wonderful,
because what is going on?

236
00:13:34,063 --> 00:13:36,065
[waves crashing]

237
00:13:38,567 --> 00:13:41,737
Is infinity beautiful?
Of course, it's beautiful.

238
00:13:41,821 --> 00:13:43,322
I mean, yeah, it's--

239
00:13:43,405 --> 00:13:46,659
Like I say, it's beautiful because it is…

240
00:13:47,243 --> 00:13:48,202
Uh…

241
00:13:49,078 --> 00:13:50,162
Maybe…

242
00:13:51,539 --> 00:13:53,833
a good way to think about it
is with our circle.

243
00:13:53,916 --> 00:13:55,334
Shall we talk about the circle?

244
00:13:55,417 --> 00:13:57,419
[eerie music plays]

245
00:14:02,383 --> 00:14:04,009
[Steven] There's a very beautiful shape

246
00:14:04,093 --> 00:14:07,221
that often people think of
as the most perfect shape, a circle.

247
00:14:09,765 --> 00:14:12,351
Perfectly round, never-ending.

248
00:14:13,644 --> 00:14:15,187
We see circles everywhere.

249
00:14:16,105 --> 00:14:18,732
I look in your eyes,
I see the circle of your iris.

250
00:14:18,816 --> 00:14:20,401
I see the circle of your pupil.

251
00:14:21,610 --> 00:14:23,863
I see the circle of the sun and the moon.

252
00:14:24,363 --> 00:14:26,782
I've got my wedding ring
in the shape of a circle.

253
00:14:27,867 --> 00:14:28,993
[Eugenia] I love circles.

254
00:14:29,618 --> 00:14:32,162
But if you sit down and think about
what they are for a second,

255
00:14:32,246 --> 00:14:36,250
how many sides do they have, for example?
How many corners do they have?

256
00:14:36,333 --> 00:14:39,420
[Steven] That immediately brings us
into face-to-face confrontation

257
00:14:39,503 --> 00:14:40,754
with the infinite,

258
00:14:41,297 --> 00:14:44,425
because you can't think about a circle
in terms of straight lines.

259
00:14:45,676 --> 00:14:48,470
[Eugenia] If we think about pointy shapes,
say a triangle,

260
00:14:49,096 --> 00:14:50,848
if we tried to use it as a wheel,

261
00:14:50,931 --> 00:14:53,726
it would be kind of painful
going up the street.

262
00:14:55,311 --> 00:14:59,690
If we had ten corners,
then that wouldn't be so bad as a wheel.

263
00:15:00,441 --> 00:15:03,027
And then, if you keep going,
you can go, "Oh, wait,

264
00:15:03,110 --> 00:15:06,113
if we then had infinity sides,

265
00:15:06,196 --> 00:15:09,116
then we would be completely like a circle,

266
00:15:09,199 --> 00:15:13,579
and we would have infinity corners,
which is like having no corners."

267
00:15:13,662 --> 00:15:17,958
And so, somehow, infinity has come round
to being just like zero.

268
00:15:18,042 --> 00:15:18,876
[bell rings]

269
00:15:24,006 --> 00:15:26,592
One of the amazing things about infinity

270
00:15:26,675 --> 00:15:30,721
is that, if you scale it,
it's still infinity.

271
00:15:30,804 --> 00:15:33,557
Whereas if you take any finite number,
if you scale it,

272
00:15:33,641 --> 00:15:36,268
which is like multiplying it,
it gets bigger.

273
00:15:36,352 --> 00:15:38,812
But infinity doesn't do that somehow,

274
00:15:38,896 --> 00:15:42,149
and that's a very odd thing
for us to get our heads around.

275
00:15:44,109 --> 00:15:45,861
So let's try and picture this, right?

276
00:15:46,487 --> 00:15:51,033
When it comes to a circle
as a set of points…

277
00:15:51,116 --> 00:15:53,994
'Cause that's what it is.
It's an infinite collection of points.

278
00:15:54,495 --> 00:15:56,705
I would like to try to convince you

279
00:15:56,789 --> 00:16:00,042
that a small circle,
like a circle of radius one,

280
00:16:00,751 --> 00:16:04,380
um, has the same number of points
as a huge circle,

281
00:16:04,463 --> 00:16:05,798
a circle of radius billion.

282
00:16:06,382 --> 00:16:07,508
Right? Okay.

283
00:16:07,591 --> 00:16:09,093
So, to do that,

284
00:16:09,176 --> 00:16:12,429
I need to get you to agree
on what it means to be the same size.

285
00:16:12,513 --> 00:16:15,432
Like, anytime you're making
a high-stakes bet with a friend,

286
00:16:15,516 --> 00:16:17,726
you wanna settle…
This is good advice, by the way.

287
00:16:17,810 --> 00:16:21,063
You want to settle in advance
what qualifies as winning.

288
00:16:23,482 --> 00:16:27,444
I propose that two sets
will be said to have the same size

289
00:16:27,528 --> 00:16:30,781
if I can put their elements
in a perfect one-to-one correspondence.

290
00:16:32,533 --> 00:16:36,912
Now, all I need to give you is a rule
that puts the points of a small circle

291
00:16:36,996 --> 00:16:39,498
in correspondence
with the points of a larger circle.

292
00:16:39,581 --> 00:16:42,042
You can't count the points on the circle,

293
00:16:42,126 --> 00:16:45,713
but you can match them up
with the points on a bigger circle.

294
00:16:45,796 --> 00:16:47,131
I take my small circle

295
00:16:47,631 --> 00:16:50,426
and I just center it somewhere at a point,

296
00:16:50,509 --> 00:16:53,470
and then I take the huge circle
and I center it at the same point.

297
00:16:53,971 --> 00:16:58,892
I'm gonna-- From that center point,
I'm gonna draw all the radii. Right?

298
00:16:58,976 --> 00:17:01,437
I'll draw these kind of line segments

299
00:17:01,520 --> 00:17:04,023
stretching out from the center
to the outer circle.

300
00:17:04,732 --> 00:17:08,152
Well, each of those line segments
hits the outer circle on one point

301
00:17:08,736 --> 00:17:12,072
and hits the inner circle on one point,
and that's the correspondence.

302
00:17:12,156 --> 00:17:16,452
I'm gonna say the point, um,
on a particular radius in the small circle

303
00:17:16,535 --> 00:17:20,164
is matched to its corresponding point
from the large circle.

304
00:17:20,706 --> 00:17:23,292
Well, by sweeping those radii
all the way around,

305
00:17:23,375 --> 00:17:26,879
I clearly hit
all the points on each circle.

306
00:17:26,962 --> 00:17:28,380
And so I'm done.

307
00:17:29,631 --> 00:17:32,092
I've got a perfect
one-to-one correspondence.

308
00:17:32,176 --> 00:17:33,677
You now have to agree

309
00:17:33,761 --> 00:17:36,221
that the two infinite sets
have the same size.

310
00:17:36,305 --> 00:17:38,724
[upbeat music plays]

311
00:17:38,807 --> 00:17:43,604
So mathematicians don't literally
sit there counting to infinity.

312
00:17:43,687 --> 00:17:46,440
We just match things up in pairs.

313
00:17:46,523 --> 00:17:48,942
And if you can find a way
to match things up in pairs,

314
00:17:49,026 --> 00:17:51,070
you can go, "Oh, that's the same then."

315
00:17:51,153 --> 00:17:55,157
So, for example, we can match up
all the numbers, the whole numbers,

316
00:17:55,240 --> 00:17:59,244
with the even numbers
by just multiplying each one by two.

317
00:17:59,328 --> 00:18:02,539
You sit there and go, "Wait,
the even numbers is only half of them."

318
00:18:02,623 --> 00:18:04,958
And then you go,
"But wait, I can match them up,

319
00:18:05,042 --> 00:18:07,753
because if I pair up one with two,

320
00:18:07,836 --> 00:18:09,379
and two with four,

321
00:18:09,463 --> 00:18:10,756
and three with six,

322
00:18:10,839 --> 00:18:12,800
then they pair up exactly."

323
00:18:12,883 --> 00:18:15,594
So then you go,
"Wait, there's the same number,

324
00:18:15,677 --> 00:18:17,262
even though it's half of them."

325
00:18:17,346 --> 00:18:20,933
And that's the amazing thing
about infinity.

326
00:18:21,892 --> 00:18:24,436
Once you've figured out
this way of matching things up

327
00:18:24,520 --> 00:18:26,855
to see how big an infinite set is,

328
00:18:26,939 --> 00:18:30,609
it turns out that there might be some
that you can never match up,

329
00:18:30,692 --> 00:18:34,238
which means that there is
some kind of bigger possible infinity.

330
00:18:34,321 --> 00:18:36,323
[tense music plays]

331
00:18:38,909 --> 00:18:40,536
[Moon] How can there be larger infinities?

332
00:18:40,619 --> 00:18:43,997
Infinity is already
as big as we can imagine, right?

333
00:18:44,081 --> 00:18:45,624
No. No.

334
00:18:46,500 --> 00:18:48,836
[hesitates] There's something beyond that.

335
00:18:50,379 --> 00:18:52,422
-Let me see if this works for you.
-[producer] Okay.

336
00:18:52,506 --> 00:18:55,134
Um, so, provably the smallest infinity

337
00:18:55,217 --> 00:18:58,011
is the one that goes
one, two, three, dot, dot, dot.

338
00:18:58,512 --> 00:19:01,390
If I was to take the numbers zero and one

339
00:19:01,473 --> 00:19:04,143
and ask you
how many numbers are there between that,

340
00:19:04,226 --> 00:19:06,478
well, you could keep
dividing and dividing.

341
00:19:06,562 --> 00:19:08,355
No matter how many times you divide,

342
00:19:09,273 --> 00:19:10,691
there's always a number

343
00:19:10,774 --> 00:19:14,736
that you could add another zero
behind the last decimal you had put.

344
00:19:15,863 --> 00:19:18,657
[Eugenia] And I can make
a one-to-one little map,

345
00:19:18,740 --> 00:19:22,202
like a little dictionary between
those numbers and the whole numbers.

346
00:19:22,286 --> 00:19:24,079
One, two, three, four, five.

347
00:19:26,832 --> 00:19:31,295
And so what we say is that
those two infinite sets are the same size.

348
00:19:34,464 --> 00:19:36,425
But then there's also other numbers.

349
00:19:36,508 --> 00:19:38,719
Things like the square root of two,

350
00:19:38,802 --> 00:19:41,054
and pi, and E.

351
00:19:41,138 --> 00:19:43,807
And those are just a few
that we know about and use.

352
00:19:44,892 --> 00:19:47,477
These are numbers
that aren't ordinary fractions,

353
00:19:47,561 --> 00:19:49,646
and if we try
and write them down as decimals,

354
00:19:49,730 --> 00:19:53,734
they'll somehow go on forever
without ever repeating themselves.

355
00:19:55,402 --> 00:19:57,696
So how can we ever say what they are?

356
00:19:58,405 --> 00:20:02,826
It took mathematicians hundreds of years
to figure out how to do it rigorously,

357
00:20:02,910 --> 00:20:06,330
and when they did,
they realized that they're so complicated,

358
00:20:06,413 --> 00:20:10,125
it's actually impossible
to put them in a list.

359
00:20:10,209 --> 00:20:12,294
No matter how we try to list them,

360
00:20:12,377 --> 00:20:15,964
we're doomed to miss some out
along the way.

361
00:20:16,673 --> 00:20:19,301
We can't make a one-to-one correspondence

362
00:20:19,384 --> 00:20:22,221
between those numbers
and the counting numbers.

363
00:20:26,683 --> 00:20:28,685
Now that we have two infinities,

364
00:20:28,769 --> 00:20:30,604
would we really stop there?

365
00:20:31,897 --> 00:20:33,857
[Moon] There are bigger and bigger
and bigger ones.

366
00:20:34,358 --> 00:20:37,778
This is a trail that just keeps on going.

367
00:20:37,861 --> 00:20:39,863
[eerie music plays]

368
00:20:42,115 --> 00:20:45,994
[Eugenia]
An infinite hierarchy of infinities.

369
00:20:48,956 --> 00:20:50,415
This is the kind of thing

370
00:20:50,499 --> 00:20:53,460
that, hopefully, turns some people
into mathematicians.

371
00:20:53,961 --> 00:20:57,547
And no doubt sends other people running
in the other direction. [laughs]

372
00:21:00,050 --> 00:21:02,761
[Steven] My wife gets nauseous
when I bring up infinity.

373
00:21:04,513 --> 00:21:06,765
And my kids don't want
to hear about it either.

374
00:21:09,184 --> 00:21:11,436
[Eugenia] Some people love
peering over cliff edges.

375
00:21:11,520 --> 00:21:13,605
There are now those glass bridges

376
00:21:13,689 --> 00:21:16,149
where you can step out
over the Grand Canyon.

377
00:21:16,233 --> 00:21:18,485
There's no way I would do that.

378
00:21:18,568 --> 00:21:22,823
But when it's a mathematical cliff edge,
I love it.

379
00:21:24,241 --> 00:21:27,494
I think this gets back
to this concept of the sublime.

380
00:21:30,038 --> 00:21:32,249
When you're out by a waterfall…

381
00:21:32,332 --> 00:21:34,876
[water running]

382
00:21:37,254 --> 00:21:40,507
…you have this feeling of this thing
that is so much larger than yourself.

383
00:21:40,590 --> 00:21:44,761
But then you climb onto the mountain peak
and you look out at the next valley,

384
00:21:44,845 --> 00:21:47,306
and you see another waterfall
that's even larger,

385
00:21:47,389 --> 00:21:49,308
but it's in the distance,
so it looks tiny.

386
00:21:49,391 --> 00:21:51,393
[birds singing]

387
00:21:55,397 --> 00:21:58,984
Infinity is some kind of monster
that has to be tamed.

388
00:21:59,067 --> 00:22:01,361
[violin music plays]

389
00:22:03,322 --> 00:22:07,534
"INFINITY"

390
00:22:13,915 --> 00:22:15,667
[loud thump]

391
00:22:17,377 --> 00:22:19,129
[roars]

392
00:22:20,797 --> 00:22:24,509
[roars, grunts]

393
00:22:27,846 --> 00:22:30,057
[alarm blaring]

394
00:22:31,683 --> 00:22:35,187
[in Japanese]
It's infinity! It's attacking the city!

395
00:22:35,979 --> 00:22:39,566
[Moon in English] Mathematicians needed
to invent ways to deal with infinity.

396
00:22:39,649 --> 00:22:42,652
Taking something totally weird
and unintuitive

397
00:22:42,736 --> 00:22:45,072
and taming it to the point where you can

398
00:22:45,155 --> 00:22:47,282
walk around and study it from all sides.

399
00:22:47,366 --> 00:22:49,951
[roars]

400
00:22:54,831 --> 00:22:56,124
[grunts]

401
00:23:01,171 --> 00:23:06,259
And the ways that they came up with
led to the field of rigorous calculus.

402
00:23:06,343 --> 00:23:08,428
There's one idea at the heart of calculus,

403
00:23:08,512 --> 00:23:11,515
and it's an idea
I like to call the infinity principle.

404
00:23:11,598 --> 00:23:14,434
[upbeat music plays]

405
00:23:15,018 --> 00:23:20,732
[Steven] You can make sense
of any complicated motion or phenomenon,

406
00:23:20,816 --> 00:23:23,777
or anything that's changing,
or any curved shape,

407
00:23:24,528 --> 00:23:28,573
by thinking of it
as being made of an infinite number

408
00:23:28,657 --> 00:23:33,370
of infinitesimally small simpler motions
or shapes.

409
00:23:35,497 --> 00:23:37,666
This is one of the greatest ideas
in history.

410
00:23:38,375 --> 00:23:40,502
[monster roars]

411
00:23:40,585 --> 00:23:43,880
Everything to do with movement,

412
00:23:43,964 --> 00:23:47,259
and everything to do with things
that are continuously changing,

413
00:23:47,342 --> 00:23:50,137
can only be studied rigorously
using calculus.

414
00:23:50,220 --> 00:23:51,513
[roars]

415
00:23:51,596 --> 00:23:53,348
[woman] Hmm…

416
00:23:53,432 --> 00:23:58,437
[in Japanese] Maybe it's trying
to communicate with us!

417
00:23:58,520 --> 00:24:02,441
We can use calculus to study its roar!

418
00:24:02,524 --> 00:24:04,359
[Steven in English]
So the infinity principle is

419
00:24:04,443 --> 00:24:06,153
you can make sense of complicated things

420
00:24:06,236 --> 00:24:09,990
by breaking them up
into infinitely many simpler things.

421
00:24:11,783 --> 00:24:13,076
[graphic beeps]

422
00:24:13,160 --> 00:24:15,454
Solve the problem for the simpler things

423
00:24:17,038 --> 00:24:20,834
and then add the results back together
to get the original whole.

424
00:24:20,917 --> 00:24:22,919
[upbeat music continues]

425
00:24:33,638 --> 00:24:36,975
[in Japanese]
A picture encoded in the roar!

426
00:24:37,058 --> 00:24:39,436
Stop fighting infinity!

427
00:24:39,519 --> 00:24:42,105
It's peaceful. Look!

428
00:24:43,273 --> 00:24:44,691
[electrical sparking]

429
00:24:45,650 --> 00:24:48,195
[Eugenia in English]
The understanding of electricity

430
00:24:48,278 --> 00:24:49,988
was made possible by calculus.

431
00:24:50,071 --> 00:24:50,906
[loud thump]

432
00:24:52,657 --> 00:24:54,784
[roars]

433
00:24:54,868 --> 00:24:58,205
And electricity has enabled
the entire modern world.

434
00:24:59,080 --> 00:25:00,081
[phone dials]

435
00:25:00,165 --> 00:25:02,042
Moshi moshi!

436
00:25:02,125 --> 00:25:05,295
[talks indistinctly]

437
00:25:05,378 --> 00:25:07,130
So does infinity exist?

438
00:25:07,214 --> 00:25:10,258
Well, in one of the senses of math,

439
00:25:10,342 --> 00:25:14,346
absolutely no question about it,
because we have a symbol for it,

440
00:25:14,429 --> 00:25:16,264
we know how to manipulate that symbol,

441
00:25:16,348 --> 00:25:19,643
we can agree on the conclusions
that we reach when doing so.

442
00:25:20,268 --> 00:25:23,855
And by doing so,
we can solve practical questions.

443
00:25:24,523 --> 00:25:28,401
Right? So, from a pure math point of view,

444
00:25:28,485 --> 00:25:30,904
that's your certificate of existence
right there.

445
00:25:35,158 --> 00:25:38,119
So then, does infinity exist out there?

446
00:25:39,871 --> 00:25:41,540
[upbeat music ends]

447
00:25:41,623 --> 00:25:44,042
That's above my pay grade. [laughs]

448
00:25:45,377 --> 00:25:46,711
[loud thump]

449
00:25:47,587 --> 00:25:50,048
If you mean does it physically exist,

450
00:25:51,383 --> 00:25:52,217
who knows?

451
00:25:52,300 --> 00:25:54,761
That's a question
for the physicists to answer.

452
00:25:56,638 --> 00:26:00,350
And so now they've got to go
do their expensive things, right?

453
00:26:00,433 --> 00:26:06,565
And figure out whether space-time
is infinite or not. It's a real question.

454
00:26:06,648 --> 00:26:08,650
[mysterious music plays]

455
00:26:12,237 --> 00:26:16,324
Oh, this is a great question.
So where can one look for real infinities?

456
00:26:17,951 --> 00:26:20,120
[Brian] We've been struggling
with the question

457
00:26:20,203 --> 00:26:25,709
of whether the infinite infinity
is a real thing

458
00:26:25,792 --> 00:26:30,463
or something that is a human invention
for a very long time.

459
00:26:31,339 --> 00:26:33,425
[Stephon]
Maybe we could approach the infinite.

460
00:26:33,925 --> 00:26:36,428
As a physicist,
that's the business I'm in.

461
00:26:37,512 --> 00:26:41,308
[Anthony] How thrilling would that be,
to do something in the physical world

462
00:26:41,391 --> 00:26:44,227
that would tell us
that something is physically infinite?

463
00:26:47,230 --> 00:26:49,316
[Carlo]
I think all of us have this experience

464
00:26:49,399 --> 00:26:55,155
of, you know, going out in the night
in the starry sky.

465
00:26:55,238 --> 00:26:57,907
[Stephon] Lying on a beach
late at night in Trinidad.

466
00:26:57,991 --> 00:27:00,035
I mean, I probably was, like,
eight years old

467
00:27:00,535 --> 00:27:04,039
and just wondering
the vastness of outer space.

468
00:27:07,834 --> 00:27:09,169
Does it go on forever?

469
00:27:13,423 --> 00:27:17,385
I question the notion of infinity

470
00:27:18,136 --> 00:27:23,099
when I am using a particular yardstick

471
00:27:23,183 --> 00:27:25,518
which is, can we measure it?

472
00:27:29,773 --> 00:27:33,401
Can we access it? [voice echoes]

473
00:27:33,485 --> 00:27:36,196
Can we, in any point

474
00:27:36,279 --> 00:27:39,991
wrap our arms around it
and say, "Here it is."

475
00:27:40,575 --> 00:27:41,951
"There's the infinite."

476
00:27:43,620 --> 00:27:47,666
And using that particular yardstick,
the answer is no.

477
00:27:47,749 --> 00:27:52,712
There's simply no way
that we can measure the infinite.

478
00:27:52,796 --> 00:27:58,259
[Janna] Nobody will ever give you back pi
to all of its infinite digits

479
00:27:58,343 --> 00:28:00,720
as the result of a measurement.

480
00:28:02,889 --> 00:28:06,559
All I'll ever measure, um,
in a laboratory,

481
00:28:06,643 --> 00:28:09,062
or my friends
will measure in laboratories,

482
00:28:09,145 --> 00:28:13,108
are approximations of infinite numbers.

483
00:28:15,819 --> 00:28:19,989
But then you start to wonder,
"Maybe these numbers don't really exist."

484
00:28:20,073 --> 00:28:23,201
"And nature doesn't actually
make use of them."

485
00:28:24,035 --> 00:28:25,120
And, um…

486
00:28:26,329 --> 00:28:28,456
And I don't know
the answer to that question.

487
00:28:28,540 --> 00:28:31,418
That's why sometimes you think,
"Oh, when the universe was created,

488
00:28:31,501 --> 00:28:35,964
maybe the speed
at which it came out expanding

489
00:28:36,047 --> 00:28:38,299
is an irrational number,

490
00:28:38,383 --> 00:28:43,513
like 0.500187923… [voice echoes]

491
00:28:43,596 --> 00:28:47,475
…and the universe is going to compute
that infinite list of digits

492
00:28:47,559 --> 00:28:49,227
over the course of time."

493
00:28:50,145 --> 00:28:54,399
So the universe itself
is performing a computation,

494
00:28:54,482 --> 00:28:57,527
and it's computing
infinite numbers possibly.

495
00:28:57,610 --> 00:29:02,073
[voices echoing]
Five, zero, one, seven, eight…

496
00:29:04,617 --> 00:29:07,036
[voices echoing indistinctly]

497
00:29:11,166 --> 00:29:12,792
[voices stop]

498
00:29:14,669 --> 00:29:16,212
I feel like I'm freaking you out,

499
00:29:16,296 --> 00:29:18,923
but, you know, Steven Strogatz had
to be pretty out there.

500
00:29:19,007 --> 00:29:20,216
-[producer] Oh.
-[laughs]

501
00:29:20,300 --> 00:29:21,509
-Oh yeah.
-[laughs]

502
00:29:21,593 --> 00:29:23,011
You think of a piece of Jell-O.

503
00:29:25,680 --> 00:29:27,640
You know, a blob, a block of Jell-O

504
00:29:27,724 --> 00:29:29,893
jiggling on the table or on a plate.

505
00:29:32,937 --> 00:29:34,689
You don't picture it as made of atoms.

506
00:29:34,773 --> 00:29:38,067
You think it's a continuum of Jell-O stuff

507
00:29:38,151 --> 00:29:40,612
that is infinitely subdivisible
and has no gaps.

508
00:29:40,695 --> 00:29:42,155
It hangs together perfectly.

509
00:29:42,238 --> 00:29:44,866
It's what most of us think
stuff really is like.

510
00:29:44,949 --> 00:29:46,868
[eerie music plays]

511
00:29:51,998 --> 00:29:54,793
The mathematicians are great
in talking about the continuum.

512
00:29:56,753 --> 00:30:01,716
And continuity is the idea
that if I take a line, just a short line,

513
00:30:02,258 --> 00:30:04,093
I can cut it in half,

514
00:30:05,178 --> 00:30:08,306
and then in half again,
and then in half again, and in half again.

515
00:30:10,391 --> 00:30:13,394
And I always have a line,
and I never stop.

516
00:30:13,478 --> 00:30:14,479
I can go forever.

517
00:30:16,940 --> 00:30:18,942
But a completely different question

518
00:30:19,025 --> 00:30:21,694
is whether things
are actually continuous in reality.

519
00:30:24,280 --> 00:30:26,157
Take a rope, cut it in half,

520
00:30:27,408 --> 00:30:29,869
and then again in half,
and then again in half.

521
00:30:31,371 --> 00:30:32,455
Can we go forever?

522
00:30:34,499 --> 00:30:38,545
And this is a question
that was debated since antiquity.

523
00:30:39,170 --> 00:30:41,381
[food processor whirring]

524
00:30:41,464 --> 00:30:48,346
Now, we have understood quite clearly
that a piece of rope is not continuous.

525
00:30:48,429 --> 00:30:51,140
That no piece of matter is continuous.

526
00:30:51,891 --> 00:30:57,313
It's made by little individual pieces
that we call molecules, atoms, particles.

527
00:31:04,070 --> 00:31:04,904
My job,

528
00:31:05,989 --> 00:31:07,031
as a physicist,

529
00:31:07,866 --> 00:31:12,996
is to study another kind of continuity,
which is a continuity--

530
00:31:13,079 --> 00:31:17,584
It's not of matter. String,
or a piece of wood, or a piece of metal.

531
00:31:17,667 --> 00:31:20,003
But the continuity of space itself.

532
00:31:21,004 --> 00:31:23,423
So just consider
the space between my hands

533
00:31:23,506 --> 00:31:26,092
and imagine to have it divide in half,

534
00:31:26,175 --> 00:31:28,136
and half, and half, and half.

535
00:31:29,679 --> 00:31:30,763
Can we go forever?

536
00:31:33,975 --> 00:31:36,144
[Brian] Is space truly continuous?

537
00:31:37,228 --> 00:31:39,480
Could it be infinitely divided?

538
00:31:41,941 --> 00:31:43,735
My gut feeling is that it can't.

539
00:31:44,277 --> 00:31:47,989
[Carlo] I think if we take
what we best know about the world,

540
00:31:48,072 --> 00:31:51,451
which is Einstein's General Relativity
Theory and quantum mechanics,

541
00:31:51,534 --> 00:31:53,077
and we bring them together,

542
00:31:53,703 --> 00:31:56,581
the clear consequence of that

543
00:31:57,165 --> 00:32:01,878
is that there's a minimal amount of space.
It's very small. Incredibly small.

544
00:32:02,670 --> 00:32:06,257
[Brian] Ten to the minus 33 centimeters,
the so-called Planck length.

545
00:32:06,925 --> 00:32:09,093
So incredibly tiny

546
00:32:09,177 --> 00:32:12,513
that it certainly stretches
the human imagination to…

547
00:32:14,474 --> 00:32:15,308
think about.

548
00:32:18,061 --> 00:32:18,978
So if you were to…

549
00:32:20,188 --> 00:32:21,397
take an individual atom

550
00:32:22,523 --> 00:32:27,195
and magnify it, expand it
to be as large as the observable universe,

551
00:32:27,278 --> 00:32:29,447
that's a huge scale of magnification.

552
00:32:29,530 --> 00:32:31,908
The Planck length under that magnification

553
00:32:31,991 --> 00:32:35,620
would grow to roughly be the size
of an average tree.

554
00:32:36,329 --> 00:32:41,793
So a tree is to the observable universe
as the Planck length is to an atom.

555
00:32:41,876 --> 00:32:43,795
So even on atomic scales,

556
00:32:44,587 --> 00:32:46,631
the distances that we're talking about

557
00:32:46,714 --> 00:32:50,426
where the notion of continuity
may break down,

558
00:32:50,510 --> 00:32:54,180
where discreteness may emerge,
they are fantastically small.

559
00:32:54,263 --> 00:32:56,265
[ethereal music plays]

560
00:32:58,601 --> 00:33:01,521
So I have a sort of, uh,

561
00:33:02,438 --> 00:33:07,068
pixelated vision of reality
at this small scale.

562
00:33:07,151 --> 00:33:11,406
It's like, uh,
if God didn't draw the universe

563
00:33:11,489 --> 00:33:14,784
with continuous lines
but just little pixels.

564
00:33:17,370 --> 00:33:21,290
It's many, many, many, many little things,
but it's not continuity.

565
00:33:21,374 --> 00:33:22,500
It's discreteness.

566
00:33:23,710 --> 00:33:24,752
It's finite.

567
00:33:25,837 --> 00:33:28,047
There is nothing infinitely small.

568
00:33:28,131 --> 00:33:29,465
[tense music plays]

569
00:33:35,388 --> 00:33:38,558
My favorite example
where we can find real infinities

570
00:33:38,641 --> 00:33:41,477
is when thinking about black holes.

571
00:33:41,561 --> 00:33:43,563
[tense music continues]

572
00:34:04,292 --> 00:34:06,794
Black holes are these massive objects

573
00:34:06,878 --> 00:34:09,797
where all the matter
is condensed so tightly

574
00:34:09,881 --> 00:34:12,925
that we get this region around it
called the event horizon,

575
00:34:13,009 --> 00:34:14,677
from which we get no information.

576
00:34:27,648 --> 00:34:30,735
[Janna] Now, there's nothing infinite
about the event horizon.

577
00:34:30,818 --> 00:34:33,821
It's actually empty.
A neutral region of space.

578
00:34:37,909 --> 00:34:40,286
You wouldn't even notice
when you cross the event horizon.

579
00:34:40,787 --> 00:34:43,539
You wouldn't feel anything weird happen
to your body.

580
00:34:43,623 --> 00:34:47,168
[Janna] What happens that's problematic
is on the inside of the black hole.

581
00:34:49,712 --> 00:34:51,714
[somber music plays]

582
00:35:01,808 --> 00:35:04,018
[Delilah] In the very literal sense,
we know nothing about

583
00:35:04,102 --> 00:35:06,312
what goes on inside of the black hole.

584
00:35:07,355 --> 00:35:09,357
But Einstein's theory
of general relativity

585
00:35:09,440 --> 00:35:12,401
says that, once you make it
past the event horizon,

586
00:35:13,528 --> 00:35:15,947
eventually if you keep just falling in…

587
00:35:18,407 --> 00:35:20,409
you'll reach a point called
the singularity.

588
00:35:21,786 --> 00:35:25,456
[Janna] A region which is
an infinite curvature in space-time.

589
00:35:26,040 --> 00:35:29,418
[Delilah] Where all the mass
of the black hole is concentrated.

590
00:35:29,502 --> 00:35:34,006
[Janna] Infinite densities,
and completely catastrophic.

591
00:35:34,841 --> 00:35:40,138
What happens that's really, um,
considered such a horror show

592
00:35:40,221 --> 00:35:42,640
is that, in a finite time,

593
00:35:43,766 --> 00:35:45,768
in microseconds, in fact,

594
00:35:45,852 --> 00:35:50,398
you would hit this region
of infinite curvature and infinite density

595
00:35:50,481 --> 00:35:52,817
and simply fall out of existence.

596
00:35:57,196 --> 00:35:58,698
[somber music ends]

597
00:35:58,781 --> 00:36:02,076
As though you weren't part of
the natural world anymore,

598
00:36:02,160 --> 00:36:03,828
so you weren't-- Physics stopped.

599
00:36:07,582 --> 00:36:09,250
It's really a violation

600
00:36:09,333 --> 00:36:11,836
of the whole continuity of the program

601
00:36:12,795 --> 00:36:14,380
of understanding nature.

602
00:36:14,463 --> 00:36:16,966
It starts to say
nature's fundamentally unknowable

603
00:36:17,049 --> 00:36:19,552
in this one secret place
inside this black hole.

604
00:36:19,635 --> 00:36:21,262
And that just doesn't feel right.

605
00:36:23,389 --> 00:36:25,474
[Stephon] What do you do
when you have a theory

606
00:36:25,558 --> 00:36:26,684
that works really well

607
00:36:27,810 --> 00:36:29,937
except for when you have this infinity?

608
00:36:30,563 --> 00:36:32,899
Do you throw the baby out
with the bathwater,

609
00:36:32,982 --> 00:36:35,234
or is the infinity trying
to tell you something?

610
00:36:36,027 --> 00:36:38,446
The singularity,
this region of infinite curvature,

611
00:36:38,529 --> 00:36:41,449
infinite density,
I bet that doesn't really happen.

612
00:36:42,450 --> 00:36:46,162
[Stephon] The infinity
the equations predict is a hint.

613
00:36:46,871 --> 00:36:50,583
It hints at us,
"Hey, there's something new there."

614
00:36:52,710 --> 00:36:54,629
[Janna] Sometimes,
when I think about the infinity

615
00:36:54,712 --> 00:36:56,297
at the center of a black hole, like,

616
00:36:56,380 --> 00:36:58,716
I think about it as like a dying man

617
00:36:58,799 --> 00:37:02,428
scratching a clue in the dirt, telling us…

618
00:37:04,805 --> 00:37:07,141
"General relativity doesn't work here."

619
00:37:17,318 --> 00:37:18,569
I'm of the opinion

620
00:37:19,153 --> 00:37:23,950
that there is a new physics, actually,
in a black hole.

621
00:37:24,033 --> 00:37:26,035
[tense music plays]

622
00:37:28,329 --> 00:37:31,040
I think that one thing
that could be happening there

623
00:37:31,123 --> 00:37:33,709
is that there's some sort of portal…

624
00:37:35,336 --> 00:37:36,379
into a new realm.

625
00:37:36,462 --> 00:37:38,547
Maybe a new universe, for example.

626
00:37:41,550 --> 00:37:43,636
There's something I'm working on now

627
00:37:43,719 --> 00:37:47,098
that seems to show that that could happen
if the math works out.

628
00:37:50,726 --> 00:37:52,561
You could have certain portals

629
00:37:52,645 --> 00:37:54,855
where you can actually go through
the black hole.

630
00:37:58,442 --> 00:38:00,278
We call these things wormholes.

631
00:38:05,825 --> 00:38:07,576
[tense music intensifies]

632
00:38:11,914 --> 00:38:13,833
[Anthony] A wormhole is something where,

633
00:38:14,667 --> 00:38:18,045
at some point, I say, "Here's a sphere."

634
00:38:18,129 --> 00:38:22,174
"And I have a sphere inside this one
that's got a bigger area."

635
00:38:23,384 --> 00:38:24,260
Okay?

636
00:38:28,431 --> 00:38:32,351
And then inside that one is another sphere
with a bigger area than that.

637
00:38:38,107 --> 00:38:41,861
So the-- At some level,
you know, we are confined by

638
00:38:41,944 --> 00:38:45,489
our normal understanding
of space and time, right?

639
00:38:45,573 --> 00:38:47,742
Something inside another thing is smaller.

640
00:38:50,578 --> 00:38:53,998
But that bigger thing is… in here.

641
00:38:54,081 --> 00:38:57,251
If I went in there,
I would be in that bigger thing.

642
00:38:57,960 --> 00:39:01,005
And yet I'm just seeing
the sort of outside of it.

643
00:39:03,007 --> 00:39:04,258
[producer] Do you understand it?

644
00:39:04,884 --> 00:39:07,345
Uh, it's totally clear mathematically,

645
00:39:07,428 --> 00:39:09,680
and when I look at this,
I have no idea how that could be.

646
00:39:09,764 --> 00:39:10,848
[chuckles]

647
00:39:11,849 --> 00:39:13,851
[tense music continues]

648
00:39:25,571 --> 00:39:26,447
Okay.

649
00:39:27,365 --> 00:39:29,909
[producer]
So I want you to think about this

650
00:39:29,992 --> 00:39:33,245
and tell me what it makes you
think about with infinity.

651
00:39:34,663 --> 00:39:35,664
Well, um,

652
00:39:36,749 --> 00:39:37,958
I would say that

653
00:39:38,959 --> 00:39:44,548
if I were some microscopic being
living at the surface of this… ball,

654
00:39:45,883 --> 00:39:48,010
I may conclude
that this surface is infinite,

655
00:39:48,677 --> 00:39:51,013
'cause it would take
an infinite amount of time, for example,

656
00:39:51,097 --> 00:39:53,265
in my imagination of infinity,

657
00:39:53,349 --> 00:39:55,935
to go from one side of the ball
to the other side.

658
00:39:56,435 --> 00:40:00,898
But, you know, it's not infinite, right?
For me, it's not infinite.

659
00:40:02,817 --> 00:40:05,528
[producer] So you're not holding infinity
in your hand?

660
00:40:06,904 --> 00:40:08,697
[laughs]

661
00:40:08,781 --> 00:40:11,158
Well, poetically, I am.

662
00:40:12,076 --> 00:40:13,994
I'm holding infinity in my hand.

663
00:40:14,954 --> 00:40:17,706
I see everything in this room
reflected in this sphere.

664
00:40:18,374 --> 00:40:19,875
If we didn't have walls in this room,

665
00:40:19,959 --> 00:40:23,003
I'd be able to see
the entire universe in this sphere.

666
00:40:23,087 --> 00:40:25,923
Well, the entire universe
that's behind me,

667
00:40:26,006 --> 00:40:31,512
because there's a path from everything
to this sphere and then to my eye.

668
00:40:33,472 --> 00:40:36,308
The one thing we cannot do in space-time

669
00:40:36,392 --> 00:40:38,936
is look down on the universe like this.

670
00:40:39,019 --> 00:40:42,481
And this is one of the,
in some terms, mistakes we make,

671
00:40:42,565 --> 00:40:45,151
uh, when we try to imagine
a finite universe.

672
00:40:45,234 --> 00:40:50,156
We imagine being in a space higher up,

673
00:40:50,239 --> 00:40:53,451
an extra dimension out,
and looking down on it.

674
00:40:53,534 --> 00:40:56,704
But, of course,
that would be part of the universe.

675
00:40:56,787 --> 00:40:59,790
If light could get to me,
that's part of the universe.

676
00:40:59,874 --> 00:41:01,792
So there is never such a thing.

677
00:41:01,876 --> 00:41:05,796
You can't jump out of the universe
and look down on it. Ever.

678
00:41:06,547 --> 00:41:08,632
[producer]
You're holding infinity. It's real.

679
00:41:09,967 --> 00:41:10,843
It's not.

680
00:41:11,510 --> 00:41:12,845
[Steven chuckles]

681
00:41:12,928 --> 00:41:16,307
Do you know the old story from Plato,
the prisoners in the cave?

682
00:41:16,390 --> 00:41:18,309
Right. So it's an old bit of philosophy,

683
00:41:18,392 --> 00:41:20,644
that the prisoners
are trapped in the cave,

684
00:41:20,728 --> 00:41:23,105
their backs are to the opening
of the cave,

685
00:41:24,023 --> 00:41:25,649
light is streaming into the cave,

686
00:41:25,733 --> 00:41:29,778
but all the prisoners can see
is shadows on the wall of the cave

687
00:41:29,862 --> 00:41:31,780
of things happening
out there in the world.

688
00:41:32,698 --> 00:41:35,451
To me, this is the shadow.

689
00:41:36,035 --> 00:41:39,497
This is not the real sphere.
This is not the perfect sphere.

690
00:41:39,580 --> 00:41:44,293
The perfect sphere would have infinitely
many points on its surface and inside.

691
00:41:44,877 --> 00:41:46,545
This thing is made of atoms.

692
00:41:47,296 --> 00:41:50,007
There's a lot of 'em,
but not infinitely many.

693
00:41:50,674 --> 00:41:52,218
It's a shadow of infinity.

694
00:41:54,553 --> 00:41:57,598
I love this shadow… [laughs]

695
00:41:57,681 --> 00:42:00,184
…because it gives me
a glimpse of infinity.

696
00:42:05,314 --> 00:42:07,316
[somber music plays]

697
00:42:11,278 --> 00:42:13,531
[Anthony] It… feels almost inconceivable.

698
00:42:16,742 --> 00:42:19,078
We're finite creatures,
we have access to finite things.

699
00:42:19,161 --> 00:42:21,372
We can only do so much in a lifetime.

700
00:42:22,498 --> 00:42:23,874
[static]

701
00:42:23,958 --> 00:42:26,627
Could we somehow nonetheless

702
00:42:26,710 --> 00:42:29,338
get a glimpse
into something that is truly infinite?

703
00:42:30,881 --> 00:42:32,967
And I think this is not impossible.

704
00:42:35,386 --> 00:42:38,430
An example that I've spent
quite a lot of time thinking about is,

705
00:42:38,514 --> 00:42:40,641
" What would happen to a physical system

706
00:42:40,724 --> 00:42:43,018
if you just wait
an infinite amount of time?"

707
00:42:48,649 --> 00:42:53,529
So let's imagine we take a box.
It's an excellent box.

708
00:42:54,029 --> 00:42:56,156
Nothing can come in. Nothing can go out.

709
00:42:57,408 --> 00:43:00,035
So we put an apple in the box,
close the box.

710
00:43:08,168 --> 00:43:09,503
We might come back in a month

711
00:43:09,587 --> 00:43:12,881
and the apple is looking
kind of mealy and decayed.

712
00:43:33,986 --> 00:43:36,280
Come back in a year,
the apple is a real mess.

713
00:43:36,905 --> 00:43:40,075
The apple is rotted.
Bacteria have done their thing.

714
00:43:51,045 --> 00:43:54,131
Come back in, you know, a hundred years…

715
00:43:57,384 --> 00:44:00,012
the apple is probably a kind of dust.

716
00:44:02,640 --> 00:44:04,266
The apple contains chemical energy,

717
00:44:04,350 --> 00:44:08,103
the same kind of energy you'd get
if you ate the apple or burned an apple.

718
00:44:08,187 --> 00:44:10,189
That energy will eventually come out,

719
00:44:10,898 --> 00:44:13,817
and so the apple inside the box
will get very hot,

720
00:44:13,901 --> 00:44:15,611
uh, probably thousands of degrees.

721
00:44:17,321 --> 00:44:20,157
Those particles can start
to nuclear-fuse together.

722
00:44:20,240 --> 00:44:21,825
[quiet thumps]

723
00:44:21,909 --> 00:44:23,285
This will take a really long time,

724
00:44:23,369 --> 00:44:26,789
because nuclear reactions happen
incredibly slowly at thousands of degrees,

725
00:44:26,872 --> 00:44:28,749
but eventually it will happen.

726
00:44:32,252 --> 00:44:37,341
Your apple has turned into millions
of degree plasma of fundamental particles

727
00:44:37,424 --> 00:44:39,885
and, you know,
burning into higher and higher things.

728
00:44:39,968 --> 00:44:43,514
Eventually, you'll end up
with probably some iron nuclei

729
00:44:43,597 --> 00:44:45,557
and lots of photons.

730
00:44:55,359 --> 00:44:57,361
[static]

731
00:45:01,156 --> 00:45:03,242
Billions and billions of years later…

732
00:45:07,830 --> 00:45:12,668
neutrons will decay into protons
and other fundamental particles,

733
00:45:13,627 --> 00:45:16,755
and then it'll sit there
for a very, very long time.

734
00:45:24,304 --> 00:45:27,307
Let's think about what the particles,
the protons and neutrons, and stuff.

735
00:45:27,391 --> 00:45:29,351
What do they--
How do they experience this?

736
00:45:30,686 --> 00:45:33,522
They are just cranking along,
obeying the laws of physics.

737
00:45:33,605 --> 00:45:37,151
The state of the box is changing
from one to the other, to the other.

738
00:45:37,651 --> 00:45:41,613
So, if there's 10 to the 24 particles
in an apple,

739
00:45:41,697 --> 00:45:46,660
there's something like
10 to the 10 to the 24 different states

740
00:45:46,744 --> 00:45:48,871
that those particles can be in.

741
00:45:50,873 --> 00:45:52,332
That's a gigantic number.

742
00:45:55,335 --> 00:45:56,587
But it isn't infinite.

743
00:45:57,296 --> 00:45:58,756
And what that means is that,

744
00:45:58,839 --> 00:46:01,675
if you let the box sit there
for an infinite amount of time,

745
00:46:01,759 --> 00:46:02,926
it will use them all up.

746
00:46:04,094 --> 00:46:06,722
It will go through
every possible state that it can,

747
00:46:06,805 --> 00:46:10,350
all 10 to the 10 to the 24
or whatever of them.

748
00:46:12,478 --> 00:46:14,897
And eventually,
it will start having to reuse

749
00:46:14,980 --> 00:46:16,690
states that it's been in before

750
00:46:16,774 --> 00:46:19,151
because there just aren't any more
that it can evolve into.

751
00:46:21,904 --> 00:46:25,032
And so, eventually,
if you wait a long time,

752
00:46:25,866 --> 00:46:27,117
something will happen.

753
00:46:27,618 --> 00:46:32,206
And this is the power
that infinity has over the finite.

754
00:46:34,708 --> 00:46:35,667
At some point,

755
00:46:36,668 --> 00:46:38,003
you could open the box

756
00:46:39,963 --> 00:46:41,673
and there's your apple again.

757
00:46:45,052 --> 00:46:49,973
How did that happen?
How did this hot gas turn into an apple?

758
00:46:50,057 --> 00:46:52,017
But eventually, it has to.

759
00:46:54,311 --> 00:46:59,441
In fact, every possible thing
that could exist in the box will exist.

760
00:46:59,525 --> 00:47:02,319
[fast motion sound]

761
00:47:02,402 --> 00:47:05,864
And they will each exist
an infinite number of times.

762
00:47:10,869 --> 00:47:13,038
[slow motion sound]

763
00:47:13,121 --> 00:47:14,498
Why do we care?

764
00:47:17,543 --> 00:47:20,462
Well, we might be in the box.

765
00:47:20,546 --> 00:47:22,548
[tense music plays]

766
00:47:24,299 --> 00:47:26,426
[Brian] In any finite region of space,

767
00:47:26,510 --> 00:47:29,471
like the observable universe
that we now inhabit,

768
00:47:29,555 --> 00:47:31,557
there's a finite amount of energy,

769
00:47:32,057 --> 00:47:34,852
which is carried
by a finite number of particles.

770
00:47:35,352 --> 00:47:37,020
And those finite number of particles

771
00:47:37,104 --> 00:47:41,483
can only be arranged
in finitely many distinct patterns.

772
00:47:41,567 --> 00:47:42,901
[tense music plays]

773
00:47:44,987 --> 00:47:47,406
Because there are only
finitely many distinct ways

774
00:47:47,489 --> 00:47:49,491
that the particles can be arranged,

775
00:47:49,575 --> 00:47:52,077
if space does go on infinitely far,

776
00:47:53,036 --> 00:47:55,664
the particle pattern
has to ultimately repeat.

777
00:47:55,747 --> 00:47:57,749
[tense music continues]

778
00:48:00,127 --> 00:48:03,422
And that would mean
there'd be copies of us out there.

779
00:48:05,340 --> 00:48:06,758
There'd be copies of us.

780
00:48:06,842 --> 00:48:09,177
-An infinite number of copies.
-Out there.

781
00:48:09,261 --> 00:48:11,179
-An infinite number of copies.
-Of us.

782
00:48:11,263 --> 00:48:13,974
Infinitely many of us
at very far parts of the universe

783
00:48:14,057 --> 00:48:16,685
doing exactly the same thing
that this copy of us is doing.

784
00:48:16,768 --> 00:48:20,397
Copies of me that continue,
and copies of me that die at any moment.

785
00:48:20,480 --> 00:48:23,775
Anything that can happen will happen
an infinite number of times.

786
00:48:23,859 --> 00:48:25,277
Suddenly, we're in a wild…

787
00:48:25,360 --> 00:48:27,988
-So somewhere there's an Earth…
-…inhuman…

788
00:48:28,071 --> 00:48:30,991
-…where I'm having this conversation…
-…place.

789
00:48:31,074 --> 00:48:34,119
Where instead of being very hot right now,
it would be air-conditioned.

790
00:48:34,202 --> 00:48:36,204
An infinite number of copies where…

791
00:48:36,288 --> 00:48:39,082
An elephant suddenly appears
in front of me.

792
00:48:39,166 --> 00:48:40,792
-[laughs]
-There could be

793
00:48:40,876 --> 00:48:43,086
our exact universe,
but with a different history.

794
00:48:43,170 --> 00:48:45,881
Hillary Clinton won the election.
Germany won the war.

795
00:48:45,964 --> 00:48:49,051
And on that Earth,
the dinosaurs might still rule.

796
00:48:49,760 --> 00:48:53,221
[Anthony] I think when a lot of people
hear some of these ideas,

797
00:48:53,305 --> 00:48:57,768
they're like, "God, they were just up late
drinking and having a good time

798
00:48:57,851 --> 00:48:59,311
and came up with this crazy idea

799
00:48:59,394 --> 00:49:01,688
'cause they wanted to think it
in science fiction."

800
00:49:01,772 --> 00:49:02,648
[roars]

801
00:49:03,774 --> 00:49:07,069
But this is reality-based. [laughs]

802
00:49:07,152 --> 00:49:09,696
[Brian] If the universe is infinite
in extent,

803
00:49:09,780 --> 00:49:13,283
there would be an infinite number
of Einsteins in our universe.

804
00:49:13,784 --> 00:49:15,619
And some of them would be talking to you

805
00:49:15,702 --> 00:49:18,413
and probably be giving much better answers
that I'm giving.

806
00:49:18,914 --> 00:49:21,833
[Einstein echoing] According to
the general theory of relativity,

807
00:49:22,501 --> 00:49:27,047
it is probable
that the universe is not infinite

808
00:49:27,839 --> 00:49:30,384
but closed in upon itself.

809
00:49:30,968 --> 00:49:34,721
Something like the surface of a sphere.

810
00:49:35,305 --> 00:49:38,433
One thing I have learned in a long life…

811
00:49:38,517 --> 00:49:40,227
[Brian] But those other Einsteins,

812
00:49:41,520 --> 00:49:43,021
they're very far away.

813
00:49:43,105 --> 00:49:45,148
[Einstein talks indistinctly]

814
00:49:45,232 --> 00:49:47,901
[Brian] We may never be
in contact with them,

815
00:49:47,985 --> 00:49:51,113
because, according
to his theory of relativity,

816
00:49:51,822 --> 00:49:57,369
nothing can go faster
than 186,000 miles per second,

817
00:49:57,452 --> 00:49:59,121
which is the speed of light.

818
00:50:01,623 --> 00:50:03,625
[mellow music plays]

819
00:50:06,336 --> 00:50:10,757
We have this view of reality that--

820
00:50:10,841 --> 00:50:13,301
We look at it in front of us, right?

821
00:50:13,385 --> 00:50:15,512
I mean, I see you,

822
00:50:15,595 --> 00:50:17,764
I see that white screen,

823
00:50:17,848 --> 00:50:21,768
I see the camera, as they are now, right?

824
00:50:21,852 --> 00:50:26,314
Which means if I see them
as all you are now,

825
00:50:26,398 --> 00:50:27,899
I see immediately.

826
00:50:27,983 --> 00:50:31,570
So the light
that comes from all these objects to me

827
00:50:31,653 --> 00:50:34,781
arrives instantaneously at infinite speed.

828
00:50:35,449 --> 00:50:41,163
Once upon a time, we did think that
perhaps things happened instantaneously

829
00:50:41,246 --> 00:50:45,250
and that information
between one point and another

830
00:50:45,333 --> 00:50:48,920
could be conveyed in the blink of an eye,
in a single instance.

831
00:50:49,004 --> 00:50:52,716
Well, no, of course.
It doesn't come at infinite speed.

832
00:50:52,799 --> 00:50:54,801
It takes some time to come.

833
00:50:54,885 --> 00:50:58,305
So I don't see the now.
I see the past in reality.

834
00:50:58,388 --> 00:51:00,724
Why? Because there's no infinite speed.

835
00:51:05,771 --> 00:51:07,898
[jaunty jazz music plays]

836
00:51:15,906 --> 00:51:18,408
[announcer]
Ladies and gentlemen, there he is.

837
00:51:18,492 --> 00:51:24,498
The whizzingest wave,
the peppiest particle. Philo T. Photon!

838
00:51:26,083 --> 00:51:27,542
Move over, Magellan.

839
00:51:27,626 --> 00:51:31,922
Philo is primed to perform
his most fabulous feat of derring-do yet.

840
00:51:32,005 --> 00:51:36,802
Circumnavigating the globe
eight times in a single second.

841
00:51:36,885 --> 00:51:37,928
[crowd cheers]

842
00:51:38,011 --> 00:51:39,888
On your mark, Philo.

843
00:51:39,971 --> 00:51:41,973
[old Western music plays]

844
00:51:52,984 --> 00:51:54,569
[crowd cheering]

845
00:51:55,487 --> 00:51:58,824
He did it, ladies and gentlemen.
The son of a gun did it!

846
00:51:58,907 --> 00:52:00,283
Oh…

847
00:52:00,367 --> 00:52:01,660
[crowd cheers and applauds]

848
00:52:02,994 --> 00:52:05,038
Let's see that again in real-time.

849
00:52:08,750 --> 00:52:10,168
Do it again! Encore!

850
00:52:10,252 --> 00:52:12,838
And now I'm sure Philo is pooped.

851
00:52:13,463 --> 00:52:14,297
What's this?

852
00:52:15,048 --> 00:52:18,468
He's going to fly
to the next galaxy and back?

853
00:52:19,219 --> 00:52:22,514
No one has ever attempted
a stunt like this before.

854
00:52:22,597 --> 00:52:25,100
Ladies and gentlemen, I can't watch!

855
00:52:25,183 --> 00:52:27,894
[jaunty jazz music plays]

856
00:52:48,498 --> 00:52:51,084
[Delilah] The speed of light is
the maximum speed

857
00:52:51,168 --> 00:52:53,795
at which anything can travel in the
universe.

858
00:52:53,879 --> 00:52:55,881
[somber music plays]

859
00:53:00,927 --> 00:53:02,179
[clock ticks]

860
00:53:02,262 --> 00:53:04,222
[Carlo] The speed of light, it's…

861
00:53:05,098 --> 00:53:06,892
it's incredibly fast.

862
00:53:09,519 --> 00:53:13,273
And the speed of light
is horrendously slow.

863
00:53:16,318 --> 00:53:21,114
If we wanna travel in the galaxy,
it's hard enough, uh,

864
00:53:21,740 --> 00:53:25,243
but if you want to travel in the universe
from galaxy to galaxy,

865
00:53:26,870 --> 00:53:29,623
we just cannot, because we cannot--
We're too slow.

866
00:53:30,207 --> 00:53:33,001
And light is too slow. Incredibly slow.

867
00:53:33,877 --> 00:53:35,879
[somber music continues]

868
00:53:40,050 --> 00:53:42,761
[Delilah] So is the universe infinite?

869
00:53:48,600 --> 00:53:51,144
[Carlo] It's hard to think
what is the universe.

870
00:53:54,564 --> 00:53:59,736
We know that we see the universe
as many billion light years,

871
00:54:00,403 --> 00:54:03,615
uh, and we know
the universe is larger than what we see.

872
00:54:03,698 --> 00:54:05,909
We have indications of that.

873
00:54:05,992 --> 00:54:10,413
But it could be maybe ten times larger.
Maybe a hundred times larger.

874
00:54:13,750 --> 00:54:16,378
There are parts of the universe
most probably

875
00:54:16,461 --> 00:54:20,257
in which, even if we send a signal now,
it will never get there.

876
00:54:23,343 --> 00:54:27,055
So the universe is very,
very, very, very, very big.

877
00:54:27,138 --> 00:54:30,016
And it makes our heads spin.

878
00:54:39,109 --> 00:54:41,111
[somber music continues]

879
00:54:56,626 --> 00:54:58,461
[somber music ends]

880
00:54:58,545 --> 00:55:00,547
[piano music plays]

881
00:55:04,426 --> 00:55:06,761
[Alan]
I was looking up at the sky one night

882
00:55:07,929 --> 00:55:09,764
when I was about ten years old.

883
00:55:12,392 --> 00:55:13,226
And…

884
00:55:17,314 --> 00:55:20,817
I felt like my life didn't matter.

885
00:55:29,242 --> 00:55:33,997
And I guess it was converting
large space to large time.

886
00:55:37,584 --> 00:55:40,337
One star after another star
after another star…

887
00:55:40,420 --> 00:55:42,088
[water dripping]

888
00:55:43,214 --> 00:55:45,759
…and wondering whether
that would keep going…

889
00:55:47,635 --> 00:55:49,637
[wind chimes tinkling]

890
00:55:49,721 --> 00:55:50,555
…forever.

891
00:55:56,394 --> 00:56:01,232
I had this sense that the universe,
it existed a long time before I was born…

892
00:56:03,693 --> 00:56:06,613
and it would exist
a long time after I was dead.

893
00:56:10,658 --> 00:56:14,829
And I was just a speck…
that didn't matter.

894
00:56:24,339 --> 00:56:27,092
I don't matter. My parents don't matter.

895
00:56:28,885 --> 00:56:30,261
Nothing matters.

896
00:56:34,307 --> 00:56:36,351
We're all just specks.

897
00:56:36,434 --> 00:56:38,895
We're just living in this brief moment.

898
00:56:41,689 --> 00:56:45,443
None of us were here a million years ago.

899
00:56:47,612 --> 00:56:50,323
None of us will be here
a million years from now.

900
00:56:53,910 --> 00:56:55,703
And the universe doesn't care.

901
00:56:58,790 --> 00:57:00,750
It just goes on and on and on.

902
00:57:05,380 --> 00:57:06,214
So…

903
00:57:07,340 --> 00:57:09,384
why are we wasting time,

904
00:57:09,467 --> 00:57:12,679
you know, going to school,
having dentist appointments?

905
00:57:14,180 --> 00:57:15,014
All of that.

906
00:57:15,765 --> 00:57:18,810
Why are we wasting our time?
Because none of it matters.

907
00:57:25,775 --> 00:57:26,693
And then…

908
00:57:31,364 --> 00:57:33,241
[birds singing]

909
00:57:33,324 --> 00:57:34,367
…I fell in love.

910
00:57:38,079 --> 00:57:39,747
And that changed everything.

911
00:57:44,419 --> 00:57:47,005
That mattered. [laughs]

912
00:57:47,088 --> 00:57:50,967
Even though we might both
be specks in the cosmos.

913
00:57:55,180 --> 00:57:57,182
[mellow music plays]

914
00:58:04,147 --> 00:58:10,403
[Carlo] One of the oldest questions
that thinkers puzzled on

915
00:58:10,487 --> 00:58:15,241
is what happens in the universe
if I could fly forever?

916
00:58:15,325 --> 00:58:16,826
What would happen?

917
00:58:20,205 --> 00:58:23,124
In the past, it seemed
that there were two alternatives.

918
00:58:23,208 --> 00:58:25,543
Both too strange.

919
00:58:27,462 --> 00:58:30,965
One is that the universe is infinite
and I could go forever.

920
00:58:34,761 --> 00:58:37,597
And the other is that it's finite
and there is a wall.

921
00:58:39,474 --> 00:58:41,059
But if there is a wall,

922
00:58:41,768 --> 00:58:44,854
then I could go through the wall,

923
00:58:45,730 --> 00:58:47,106
and so what's next?

924
00:58:50,193 --> 00:58:52,904
And Einstein published
this spectacular paper.

925
00:58:52,987 --> 00:58:57,200
He said, "No, no, no.
The universe can be finite,

926
00:58:58,535 --> 00:59:01,746
but without walls,
because if I go in one direction,

927
00:59:01,829 --> 00:59:04,624
I keep going, and I come back
from the other direction."

928
00:59:06,251 --> 00:59:07,627
Like it happens on the Earth.

929
00:59:07,710 --> 00:59:10,421
If I walk on the Earth towards east,

930
00:59:10,505 --> 00:59:13,216
I walk, walk, walk, walk.
Do I find a wall? No.

931
00:59:13,716 --> 00:59:17,679
Is Earth infinite? No. What happened?
I just come back from the other side.

932
00:59:17,762 --> 00:59:19,764
[somber music plays]

933
00:59:30,191 --> 00:59:32,277
And it's very possible today

934
00:59:33,403 --> 00:59:35,822
that the universe in fact has this shape.

935
00:59:38,199 --> 00:59:42,537
Namely, has no boundary, there's no wall
at the end of the universe,

936
00:59:42,620 --> 00:59:43,830
but it's finite.

937
00:59:46,291 --> 00:59:47,834
Huge, but finite.

938
00:59:51,004 --> 00:59:55,341
[Rebecca] There's actually way more ways
to make the universe finite,

939
00:59:56,092 --> 01:00:00,346
just geometrically, abstractly playing
around with whatever you want,

940
01:00:00,430 --> 01:00:02,307
than there are to make it infinite.

941
01:00:04,767 --> 01:00:10,148
In fact, there's an infinite number
of ways to make the universe finite,

942
01:00:10,231 --> 01:00:13,026
and there's really only a couple of ways
to make it infinite.

943
01:00:13,109 --> 01:00:15,111
[upbeat music plays]

944
01:00:18,323 --> 01:00:21,784
[Delilah] We do know
that the universe could be infinite,

945
01:00:22,452 --> 01:00:28,124
but we don't actually have a mechanism
to measure an infinite amount of length.

946
01:00:30,918 --> 01:00:34,922
And because light travels
at a finite speed

947
01:00:35,006 --> 01:00:37,050
and the age of the universe is finite,

948
01:00:37,133 --> 01:00:41,471
there will only ever be
a finite subset of the universe

949
01:00:41,554 --> 01:00:43,431
that we'll ever be able to observe.

950
01:00:44,474 --> 01:00:46,851
Whether beyond that
it's finite or infinite,

951
01:00:46,934 --> 01:00:49,062
we just will never
be able to experimentally know.

952
01:00:49,812 --> 01:00:51,189
[upbeat music ends]

953
01:00:55,777 --> 01:00:57,403
When we talk about infinity,

954
01:00:57,487 --> 01:01:03,326
we can certainly talk about infinity
in the extent of the spatial domain.

955
01:01:03,910 --> 01:01:07,330
We can also talk about infinity
in the temporal domain.

956
01:01:07,413 --> 01:01:09,832
The duration of the universe.

957
01:01:09,916 --> 01:01:13,086
It's possible that the universe
will continue on expanding

958
01:01:13,586 --> 01:01:16,881
into an infinite time in the future.

959
01:01:16,964 --> 01:01:19,676
That's what
the equations predict, actually.

960
01:01:27,058 --> 01:01:28,309
[Brian] In 1998,

961
01:01:29,644 --> 01:01:35,400
we discovered that the universe
is not only expanding,

962
01:01:35,483 --> 01:01:39,195
but the rate of expansion is accelerating.

963
01:01:41,614 --> 01:01:44,534
[tense music plays]

964
01:01:44,617 --> 01:01:48,538
The galaxies are moving away
from each other with increasing speed.

965
01:01:54,001 --> 01:01:57,046
And what this means

966
01:01:57,130 --> 01:02:01,759
is that, eventually, we will be cut off

967
01:02:02,969 --> 01:02:04,721
from other galaxies.

968
01:02:13,813 --> 01:02:19,694
And so, as the stars in our galaxy
eventually burn out…

969
01:02:22,321 --> 01:02:23,531
as they will,

970
01:02:24,490 --> 01:02:27,785
'cause all of them
have a limited amount of nuclear fuel…

971
01:02:31,330 --> 01:02:37,003
there eventually will not be
any new energy sources in our galaxy.

972
01:02:46,262 --> 01:02:48,264
[ethereal music plays]

973
01:03:11,370 --> 01:03:16,417
And since we will be cut off
from all other galaxies eventually,

974
01:03:16,501 --> 01:03:19,212
maybe about 100 billion years from now…

975
01:03:22,256 --> 01:03:25,426
there will not be
any energy sources at all

976
01:03:27,094 --> 01:03:31,015
and life will completely…

977
01:03:33,100 --> 01:03:34,101
end.

978
01:03:39,148 --> 01:03:43,236
And so, roughly 100 billion years
from now…

979
01:03:45,655 --> 01:03:47,365
that will be the end of life.

980
01:03:52,703 --> 01:03:56,666
And if we keep on going along
the cosmological timeline,

981
01:03:57,834 --> 01:03:59,961
galaxies, planets, black holes,

982
01:04:00,044 --> 01:04:03,381
everything that we know about,
it will all disintegrate.

983
01:04:10,888 --> 01:04:14,433
So all that would be left at that point

984
01:04:14,517 --> 01:04:19,105
are particles wafting
through the darkness.

985
01:04:19,188 --> 01:04:21,190
[wind howling]

986
01:04:30,366 --> 01:04:32,368
[tense music plays]

987
01:04:35,288 --> 01:04:39,417
Now, if the universe exists
in an infinite amount of time,

988
01:04:39,500 --> 01:04:41,377
as we now think that it will,

989
01:04:43,129 --> 01:04:48,217
the era of life is just a sliver of time

990
01:04:48,301 --> 01:04:52,805
when you look at the full unfolding
of the universe and time.

991
01:04:59,562 --> 01:05:02,982
Even though 100 billion years
seems like a long time,

992
01:05:05,693 --> 01:05:07,778
it's nothing compared to infinity.

993
01:05:22,084 --> 01:05:26,213
[Janna] Even if human beings make it
past this particular… [laughs]

994
01:05:26,297 --> 01:05:30,760
…immediate crisis,
or other sentient life emerges,

995
01:05:32,303 --> 01:05:34,722
there will be a last sentient being.

996
01:05:34,805 --> 01:05:37,016
There will be a last living creature.

997
01:05:40,269 --> 01:05:42,313
Even if the universe is infinite,

998
01:05:43,648 --> 01:05:46,275
there will be a last thought.

999
01:06:12,051 --> 01:06:17,723
[Delilah] A lot of people have kind of
this visceral anxiety about not existing.

1000
01:06:20,351 --> 01:06:22,019
But, personally,
I don't have this feeling.

1001
01:06:22,103 --> 01:06:25,439
I'm like, you know,
once I didn't exist, before I was born.

1002
01:06:25,523 --> 01:06:29,694
There will be a point in time
when I don't exist because I'll die.

1003
01:06:33,698 --> 01:06:35,992
And the same is true for our species.

1004
01:06:40,121 --> 01:06:41,414
And all life.

1005
01:06:59,849 --> 01:07:03,936
[drum music plays]

1006
01:07:04,020 --> 01:07:04,895
Um,

1007
01:07:05,438 --> 01:07:10,359
It's, it's-- You know,
even physicists have feelings. [laughs]

1008
01:07:10,443 --> 01:07:12,987
And so we can ask,
"How does that make you feel?"

1009
01:07:13,070 --> 01:07:16,741
"Are you--
As a physicist, is it daunting?"

1010
01:07:16,824 --> 01:07:19,994
"Is it, you know, an existential crisis?"

1011
01:07:20,077 --> 01:07:22,329
I… I have never--

1012
01:07:22,413 --> 01:07:24,165
I've always had the opposite reaction,

1013
01:07:24,248 --> 01:07:28,044
even to some of
the most apocalyptic predictions

1014
01:07:28,127 --> 01:07:29,587
for the future of the universe.

1015
01:07:29,670 --> 01:07:35,092
It gives me a great sense
of meaning and connectedness

1016
01:07:35,176 --> 01:07:39,221
to appreciate that you're part
of this grand picture.

1017
01:07:39,305 --> 01:07:42,725
Nothing is permanent in that sense.

1018
01:07:42,808 --> 01:07:46,353
And to… to my mind, that's freeing.

1019
01:07:47,021 --> 01:07:49,899
It frees us
from this focus on the permanent

1020
01:07:49,982 --> 01:07:52,568
as the place
where value ultimately resides,

1021
01:07:53,277 --> 01:07:58,282
to a focus
on the brief moment that we have,

1022
01:07:58,365 --> 01:08:02,453
in which we can understand things,
and create beauty,

1023
01:08:02,995 --> 01:08:08,584
and experience wonder, regardless
of how fleeting that experience may be.

1024
01:08:08,667 --> 01:08:12,379
That the universe itself
gets to have its window of life,

1025
01:08:12,463 --> 01:08:15,883
its window of consciousness
and beauty and love,

1026
01:08:15,966 --> 01:08:17,843
and then, poof.

1027
01:08:19,303 --> 01:08:22,431
It's sort of like the universe as a whole
is living the way we do.

1028
01:08:23,891 --> 01:08:27,061
We're only here for a short time
compared to infinity,

1029
01:08:27,978 --> 01:08:30,106
and, to me, that's a holy thought.

1030
01:08:30,189 --> 01:08:33,859
I mean, that's…
as close as I can get to being religious.

1031
01:08:33,943 --> 01:08:38,114
The gift that you have of consciousness
for the short time that you're here.

1032
01:08:38,197 --> 01:08:40,199
[majestic music plays]

1033
01:08:44,161 --> 01:08:46,163
[majestic music ends]

1034
01:08:59,009 --> 01:09:01,554
Wait, what was I trying to say?
Something popped into my head.

1035
01:09:08,936 --> 01:09:10,938
[eerie music plays]

1036
01:09:16,485 --> 01:09:19,321
[Eugenia] There are interesting concepts
in abstract math

1037
01:09:19,405 --> 01:09:24,243
where you can take something
that appears to have one characteristic,

1038
01:09:24,326 --> 01:09:27,788
but you can put it inside something else
or put it around something else

1039
01:09:27,872 --> 01:09:30,749
and it will look different
from that point of view.

1040
01:09:30,833 --> 01:09:34,920
And, in a way, I think that the universe

1041
01:09:35,796 --> 01:09:40,885
is infinite in some sense,
compared with our own lives,

1042
01:09:40,968 --> 01:09:42,636
because we just won't be there.

1043
01:09:42,720 --> 01:09:44,388
We won't be there to see it.

1044
01:09:45,723 --> 01:09:48,017
Whether it's really infinite or not,

1045
01:09:48,559 --> 01:09:50,603
I don't know,
and I think that's wonderful.

1046
01:09:53,564 --> 01:09:55,691
[Delilah] Not knowing doesn't make me sad.

1047
01:09:57,526 --> 01:10:00,779
As a scientist,
for me, not knowing is exciting.

1048
01:10:01,989 --> 01:10:05,659
[Stephon] There are things that I believe
that our minds can't know,

1049
01:10:05,743 --> 01:10:07,953
but they are real and they exist.

1050
01:10:09,914 --> 01:10:13,125
If we want to call that the infinite,
if we want to call that spirit,

1051
01:10:13,209 --> 01:10:16,503
if we want to call that God,
whatever you want to call that thing,

1052
01:10:16,587 --> 01:10:19,423
I believe that thing is for real,

1053
01:10:20,758 --> 01:10:21,759
but not knowable.

1054
01:10:21,842 --> 01:10:24,220
[crickets chirping]

1055
01:10:24,303 --> 01:10:26,388
Infinity's very large.
It's too big, infinity.

1056
01:10:28,849 --> 01:10:34,355
To me, infinity is an emotion that we get
in front of the immensity of nature.

1057
01:10:36,649 --> 01:10:38,484
We are little teeny things.

1058
01:10:39,485 --> 01:10:42,696
We do science. It's great.
I love to do science.

1059
01:10:42,780 --> 01:10:45,366
Try to figure out
the quantum properties of gravity,

1060
01:10:45,449 --> 01:10:47,826
trying to figure out
what is the shape of the cosmos.

1061
01:10:48,327 --> 01:10:49,787
But the reality is

1062
01:10:51,372 --> 01:10:53,749
we are, you know, like a little cat

1063
01:10:53,832 --> 01:10:55,793
trying to understand quantum mechanics.

1064
01:10:56,835 --> 01:10:58,963
The cat isn't going
to understand quantum mechanics

1065
01:10:59,046 --> 01:11:01,173
because he has the brain it has.

1066
01:11:01,257 --> 01:11:04,426
A poor human like me won't understand
everything about the universe

1067
01:11:04,510 --> 01:11:06,720
because of the poor brain I have.

1068
01:11:14,728 --> 01:11:16,397
The number of neurons in our brain

1069
01:11:16,480 --> 01:11:18,899
is comparable to the number of stars
in the galaxies.

1070
01:11:18,983 --> 01:11:20,067
It is immense.

1071
01:11:23,237 --> 01:11:27,700
Which means that the space
of thinkable thoughts

1072
01:11:27,783 --> 01:11:30,786
is a fantastically big number.

1073
01:11:30,869 --> 01:11:33,831
It's a one followed by billions of digits.

1074
01:11:34,581 --> 01:11:36,667
It's an incredibly large number.

1075
01:11:37,584 --> 01:11:40,045
Larger than anything we have encountered.

1076
01:11:42,089 --> 01:11:44,717
But, look, our brain,

1077
01:11:44,800 --> 01:11:47,052
it's a kilogram of meat

1078
01:11:47,678 --> 01:11:51,598
which can be in one configuration
or the other, and that's it.

1079
01:11:51,682 --> 01:11:54,268
Uh, you can list all of them in principle.

1080
01:11:55,477 --> 01:11:58,105
Once again, there's no Infinity here,

1081
01:11:59,148 --> 01:12:03,277
and we have to confront
the fundamental finiteness,

1082
01:12:03,360 --> 01:12:05,529
not of nature, but of ourselves.

1083
01:12:05,612 --> 01:12:11,160
[girl] One, two, three, four, five…

1084
01:12:11,243 --> 01:12:14,121
[producer] Do you think
that human creativity is infinite?

1085
01:12:14,788 --> 01:12:18,334
-[girl] …eight, nine, ten…
-[laughs] Uh…

1086
01:12:18,417 --> 01:12:21,503
[girl] …eleven, twelve, thirteen…

1087
01:12:21,587 --> 01:12:24,048
I sort of recoil at that suggestion.

1088
01:12:24,131 --> 01:12:26,884
I don't know. Oh, good gracious. I…

1089
01:12:28,010 --> 01:12:31,430
I don't know.
I don't know that we are infinite.

1090
01:12:31,513 --> 01:12:36,977
[girl] Twenty-one, twenty-two,
twenty-three. Seven, eight, nine,

1091
01:12:37,644 --> 01:12:41,315
ten, eleven, twelve.

1092
01:12:41,398 --> 01:12:48,322
Ninety-one, ninety-two, ninety-three,
ninety-four, ninety-five, ninety-six…

1093
01:12:48,405 --> 01:12:50,407
[girl continues to count indistinctly]

1094
01:12:55,704 --> 01:12:59,124
[Steven] For some reason, thinking about
anything about human beings being infinite

1095
01:12:59,208 --> 01:13:00,709
doesn't seem right to me.

1096
01:13:01,794 --> 01:13:03,962
We feel very bounded, to me.

1097
01:13:04,046 --> 01:13:07,674
Bounded in our rationality,
bounded in our creativity.

1098
01:13:07,758 --> 01:13:12,679
[girl continues to count indistinctly]

1099
01:13:15,182 --> 01:13:18,727
[Delilah] Yeah, I don't even really know
how to visualize infinity.

1100
01:13:18,811 --> 01:13:21,271
[girl] One, two, three…

1101
01:13:21,355 --> 01:13:23,148
[Kenny] Can I even picture a thousand?

1102
01:13:23,232 --> 01:13:25,150
[girl] …nine, five, two…

1103
01:13:25,234 --> 01:13:28,695
[Kenny] Even that number
is too big for me to properly imagine.

1104
01:13:28,779 --> 01:13:31,698
[girl continues to count indistinctly]

1105
01:13:33,325 --> 01:13:34,993
I find that…

1106
01:13:35,077 --> 01:13:38,205
it's hard for me to really imagine
numbers bigger than ten.

1107
01:13:38,288 --> 01:13:40,290
[upbeat music plays]

1108
01:13:44,670 --> 01:13:47,881
♪ Is it real or fantasy ? ♪

1109
01:13:49,800 --> 01:13:51,969
♪ Is it just a game we play ♪

1110
01:13:52,052 --> 01:13:58,183
♪ To pass the time while slips away
In front of me ♪

1111
01:13:59,935 --> 01:14:05,065
♪ Possibilities to find
As we walk the line ♪

1112
01:14:05,149 --> 01:14:09,903
♪ Faster and slower
And over and over ♪

1113
01:14:09,987 --> 01:14:13,907
♪ We tumble and we intertwine ♪

1114
01:14:15,284 --> 01:14:21,832
♪ Solving the riddle
And little by little we find ♪

1115
01:14:21,915 --> 01:14:25,461
♪ It goes on and on ♪

1116
01:14:25,544 --> 01:14:30,799
♪ Forever and ever and ever and ever ♪

1117
01:14:30,883 --> 01:14:35,888
♪ Forever and ever and ever and ever ♪

1118
01:14:35,971 --> 01:14:40,851
♪ Forever and ever and ever and ever ♪

1119
01:14:40,934 --> 01:14:46,231
♪ Forever and ever and ever and ever ♪

1120
01:14:46,315 --> 01:14:49,776
♪ Love it's all that matters in the end ♪

1121
01:14:49,860 --> 01:14:53,989
♪ At the end of forever ♪

1122
01:14:56,450 --> 01:14:59,411
♪ Space is staring back at me ♪

1123
01:15:01,747 --> 01:15:06,668
♪ It's not easy to explain
Where all just links in the daisy chain ♪

1124
01:15:06,752 --> 01:15:10,380
♪ Will you recognize just what you see? ♪

1125
01:15:12,007 --> 01:15:14,259
♪ Search and you won't miss the signs ♪

1126
01:15:14,343 --> 01:15:17,095
♪ The ones the universe left behind ♪

1127
01:15:17,179 --> 01:15:21,850
♪ From the beginning
We're spinning and spinning ♪

1128
01:15:21,934 --> 01:15:26,396
♪ And spiraling out of control ♪

1129
01:15:27,397 --> 01:15:29,399
♪ It's never-ending ♪

1130
01:15:29,483 --> 01:15:33,946
♪ We never know where we will go ♪

1131
01:15:34,029 --> 01:15:37,449
♪ It's goes on and on ♪

1132
01:15:37,533 --> 01:15:42,663
♪ Forever and ever and ever and ever ♪

1133
01:15:42,746 --> 01:15:47,626
♪ Forever and ever and ever and ever ♪

1134
01:15:47,709 --> 01:15:52,965
♪ Forever and ever and ever and ever ♪

1135
01:15:53,048 --> 01:15:58,220
♪ Forever and ever and ever and ever ♪

1136
01:15:58,303 --> 01:16:03,392
♪ Faster and slower
And over and over ♪

1137
01:16:03,475 --> 01:16:07,271
♪ We tumble and we intertwine ♪

1138
01:16:08,605 --> 01:16:10,941
♪ It's never-ending ♪

1139
01:16:11,024 --> 01:16:14,987
♪ We never know what we'll find ♪

1140
01:16:15,070 --> 01:16:18,615
♪ It goes on and on ♪

1141
01:16:18,699 --> 01:16:23,787
♪ Forever and ever and ever and ever ♪

1142
01:16:23,870 --> 01:16:29,001
♪ Forever and ever and ever and ever ♪

1143
01:16:29,084 --> 01:16:33,797
♪ Forever and ever and ever and ever ♪

1144
01:16:33,880 --> 01:16:39,136
♪ Forever and ever and ever and ever ♪

1145
01:16:39,219 --> 01:16:42,889
♪ Love isall that matters in the end ♪

1146
01:16:44,057 --> 01:16:47,019
♪ At the end of forever ♪

1147
01:16:47,102 --> 01:16:50,314
[echoing] ♪ Forever ♪

1148
01:16:52,941 --> 01:16:54,651
[upbeat music ends]

1149
01:17:07,247 --> 01:17:09,249
[somber music plays]

1150
01:18:19,069 --> 01:18:21,071
[somber music ends]