A Trip to Infinity (2022) Movie Script
1
Four, five...
Well, the first time
that I thought about infinity,
I was looking up at the sky one night
when I was about ten years old.
I was really little,
it was before I had started school,
and I was sitting
under the dining room table
and counting.
And at a certain point,
I realize this goes on forever.
Lying on a beach late at night
and just wondering
the vastness of outer space.
Does it go on forever?
Mmm...
I want to start
with sort of the premise of the film,
which is that we're looking for infinity.
So where should we go looking?
Well, I don't think
everybody's looking for infinity.
So is infinity a number, a place,
an idea, a concept?
If you ask me, probably all of the above.
Numbers never end.
That's the basic idea of infinity.
If I imagine continuing to count
for as long as I can count,
infinity will definitely last
longer than my lifetime.
The funny thing is,
all these numbers that you can imagine,
they're like zero, nothing.
Any number, no matter how big,
is just absolutely insignificant
compared to infinity.
For me, infinity is not scary.
I find infinity beautiful,
and haunting, and thrilling.
I love Infinity.
You know, I guess if I start
thinking about, "I'll be dead forever..."
there's a side of me
that's worried about it.
But then again,
I don't plan to be thinking about it.
I think to be conscious
is to be wrangling with infinity.
I mean, not to be grandiose.
When our hearts are broken,
are we going to be in pain forever?
And if you really
fall in love with someone,
are you gonna be in love
with them forever?
Love is certainly infinite,
because when we are overwhelmed by love,
we have this constant sense
of breaking the limits and the boundaries.
All of these abstractions,
suddenly it seemed to me,
well, maybe they're just
the product of our minds.
Who invented infinity?
I think, uh, to some extent,
the concept goes back
earlier than anything that we know.
One, two, three...
In fact, counting
is the very earliest writing that we have.
...seven...
Whoever invented writing
already had the idea of counting,
and the idea
that you can always count one more
must surely go back at least that far.
...fifteen, sixteen...
We have all kinds of different
visions of things that are infinite,
and they're usually terrifying.
There's the vision of the bottomless pit.
There's the idea of time that never ends.
If you believe in hell,
and if you believe
about torture going on forever,
a nightmare that you could
never wake up from...
So I understand that a lot of people
find thinking about infinity terrifying,
or nauseating.
At least very upsetting.
But for some of us,
it's one of the deepest pleasures.
...2001...
We're so small...
...2003, 2004...
...and yet we can
touch something so...
...1000000, 10000002...
...explosively large.
...1000004...
That feeling of, "I'm bigger
because I know how small I am."
...399, 400, 401...
I've been chasing that feeling
my entire life.
But does infinity exist
outside of our minds?
So does infinity exist?
Um...
You know, in math, I think...
Can we wait
for this train to go by?
Oh yeah.
Okay.
All right. Sorry about that.
Oh, yeah. It's good to collect thoughts.
Um, okay, so I think
I was gonna make a comment
about what it means
to exist mathematically, right?
Um, so, in math, I think we have
an interesting relationship to stuff,
to things in existence, right?
If you can conceive of something,
if you can kind of
create rules for handling it,
then it exists.
So how does infinity fit into all that?
Well, okay, infinity
is super counterintuitive,
and it leads
to a lot of surprising paradoxes,
contradictions,
intellectual quagmires, quicksand.
Many of these are summed up in a parable
that goes by the name
of the Infinite Hotel.
Imagine a hotel
with infinitely many rooms.
It's a really popular hotel.
And in fact, it's always booked solid.
Every room is occupied.
Nevertheless, there's always room
at the Infinite Hotel.
So, one night, a new guest shows up.
Bang, bang, bang on the bell.
"I'd like a room."
And the manager says,
"Sure. Of course, we can accommodate you
here at the Infinite Hotel."
"Just hold on for one minute."
The manager tells everyone
over the loudspeaker...
Please gather your things.
Get ready to move
to the next room down the hall.
Person in room one
moves into room two.
Person in room two moves into room three.
You might think there's gonna be trouble
because all the rooms are occupied.
Nevertheless, as it's an Infinite Hotel,
I mean, this can happen, right?
The numbers never stop.
One can move to two,
two can move to three,
a million can move to a million and one.
So everybody moves down to the next room,
which means that now room one is open,
and the new guest can be accommodated.
You could keep everyone
in the same room
and just have the guest go to the end.
Yeah. So a tempting thought would be
just have the guest take the last room.
Why are we making
everybody else move for this one person?
Well, because there is no last room.
Infinity doesn't work like that.
You have to start at the beginning,
not at the end. There is no end.
Now, a bigger challenge for the manager
comes the next night
when, instead of just one guest
showing up,
suddenly a whole busload full of cranky,
sweaty, ill-tempered people
all pound on the bell at the same time,
saying, "We all want rooms."
There's infinitely many new guests.
They all want to be accommodated
at this hotel.
How can you do that?
Can you somehow find room
for infinitely many new people,
given that infinitely
many rooms are occupied?
It turns out the manager has seen
this problem before,
and so she calls out over the loudspeaker...
Everyone be prepared
in a few minutes
to move to the room
that is double your current room.
So, person in room one,
you're gonna be in room two.
Person in room two, you're now
going to be moving into room four.
Person in room three, you're going to six.
Now, it's a big inconvenience
for person in room one million.
They have to move to room two million,
which is a big schlep down the hall.
So all these people dutifully move
to their new rooms.
You'll notice thatwhat's happened is
all the odd-numbered rooms
have been vacated.
And so all those new guests
can just start filing in.
There's one other custom
at the Infinite Hotel,
which is that this manager
is very conscientious
and always checks in on the rooms,
infinitely many of them.
Fortunately, the manager is very speedy,
so she can get her whole job done
in a minute.
She spends half a minute
making sure everything's okay in room one,
and a quarter of a minute,
so 15 seconds, on room two,
and then half of that,
so 7.5 seconds, on room three,
and so on, going all the way down the hall
in the Infinite Hotel.
A half, plus a quarter,
plus an eighth, plus a sixteenth,
and if you add that up...
But if you just think about that,
when you go out to infinity,
that's gonna add up to one.
She's basically gonna be done
checking infinitely many rooms
in one minute.
How does she get back
from infinity?
She get... Oh, that's good. Well...
Yeah, let's see. So, um... Hmm.
That's an interesting puzzle.
Yeah. Where is she at the end? Uh...
Don't ask me.
I've been thinking about infinity
my whole career,
and even I don't really see
any way out for her.
She's out at the end
of this infinitely long hallway,
and I don't see
how she's gonna come back from there.
I told you it was a strange hotel.
Well, so I think that, you know,
the moral of this crazy parable
is that infinity doesn't behave
like anything we're used to.
We're used to thinking about
collections of finite numbers of things.
Fish, fish, fish.
That's three fish, you know.
So we're used to small numbers,
or even big numbers.
You hear nowadays
about trillions of dollars
needing to be spent
on the budget in the United States.
But, um, those are nothing like infinity.
Any finite number, no matter how big,
is nothing compared to infinity.
We just don't have good intuition
about how infinite things work.
Even very small children
can have a gut feeling about infinity.
It's the biggest possible thing.
It's bigger
than anything you can ever think of.
Well, what happens if you add one?
So if infinity
is the biggest thing there is,
then when you add one,
it should still be infinity. Maybe?
What happens if I subtract infinity
from both sides?
Then you get one equals zero.
And so immediately you've landed yourself
in some kind of an issue,
and that's just the start.
It turns out you can write things down
that don't have an answer.
I mean, that doesn't happen
in finite arithmetic.
If I say one plus two,
the answer is three, and I'm done with it.
But if I say one minus one,
plus one, minus one...
One minus one, plus one, minus one,
plus one, minus one, dot, dot, dot.
Keep doing that forever.
There is no answer to that.
It's not zero and it's not one.
It's neither. It's both. What is it?
You can try adding infinity to infinity.
Multiply it.
You get these weird paradoxes.
Well, what's infinity plus infinity?
That should also be infinity
because it's the biggest thing.
Then you subtract infinity from both sides
and you get infinity equals zero.
That's even worse. So this is terrible.
But it's wonderful,
because what is going on?
Is infinity beautiful?
Of course, it's beautiful.
I mean, yeah, it's...
Like I say, it's beautiful because it is...
Uh...
Maybe...
a good way to think about it
is with our circle.
Shall we talk about the circle?
There's a very beautiful shape
that often people think of
as the most perfect shape, a circle.
Perfectly round, never-ending.
We see circles everywhere.
I look in your eyes,
I see the circle of your iris.
I see the circle of your pupil.
I see the circle of the sun and the moon.
I've got my wedding ring
in the shape of a circle.
I love circles.
But if you sit down and think about
what they are for a second,
how many sides do they have, for example?
How many corners do they have?
That immediately brings us
into face-to-face confrontation
with the infinite,
because you can't think about a circle
in terms of straight lines.
If we think about pointy shapes,
say a triangle,
if we tried to use it as a wheel,
it would be kind of painful
going up the street.
If we had ten corners,
then that wouldn't be so bad as a wheel.
And then, if you keep going,
you can go, "Oh, wait,
if we then had infinity sides,
then we would be completely like a circle,
and we would have infinity corners,
which is like having no corners."
And so, somehow, infinity has come round
to being just like zero.
One of the amazing things about infinity
is that, if you scale it,
it's still infinity.
Whereas if you take any finite number,
if you scale it,
which is like multiplying it,
it gets bigger.
But infinity doesn't do that somehow,
and that's a very odd thing
for us to get our heads around.
So let's try and picture this, right?
When it comes to a circle
as a set of points...
'Cause that's what it is.
It's an infinite collection of points.
I would like to try to convince you
that a small circle,
like a circle of radius one,
um, has the same number of points
as a huge circle,
a circle of radius billion.
Right? Okay.
So, to do that,
I need to get you to agree
on what it means to be the same size.
Like, anytime you're making
a high-stakes bet with a friend,
you wanna settle...
This is good advice, by the way.
You want to settle in advance
what qualifies as winning.
I propose that two sets
will be said to have the same size
if I can put their elements
in a perfect one-to-one correspondence.
Now, all I need to give you is a rule
that puts the points of a small circle
in correspondence
with the points of a larger circle.
You can't count the points on the circle,
but you can match them up
with the points on a bigger circle.
I take my small circle
and I just center it somewhere at a point,
and then I take the huge circle
and I center it at the same point.
I'm gonna... From that center point,
I'm gonna draw all the radii. Right?
I'll draw these kind of line segments
stretching out from the center
to the outer circle.
Well, each of those line segments
hits the outer circle on one point
and hits the inner circle on one point,
and that's the correspondence.
I'm gonna say the point, um,
on a particular radius in the small circle
is matched to its corresponding point
from the large circle.
Well, by sweeping those radii
all the way around,
I clearly hit
all the points on each circle.
And so I'm done.
I've got a perfect
one-to-one correspondence.
You now have to agree
that the two infinite sets
have the same size.
So mathematicians don't literally
sit there counting to infinity.
We just match things up in pairs.
And if you can find a way
to match things up in pairs,
you can go, "Oh, that's the same then."
So, for example, we can match up
all the numbers, the whole numbers,
with the even numbers
by just multiplying each one by two.
You sit there and go, "Wait,
the even numbers is only half of them."
And then you go,
"But wait, I can match them up,
because if I pair up one with two,
and two with four,
and three with six,
then they pair up exactly."
So then you go,
"Wait, there's the same number,
even though it's half of them."
And that's the amazing thing
about infinity.
Once you've figured out
this way of matching things up
to see how big an infinite set is,
it turns out that there might be some
that you can never match up,
which means that there is
some kind of bigger possible infinity.
How can there be larger infinities?
Infinity is already
as big as we can imagine, right?
No. No.
There's something beyond that.
- Let me see if this works for you.
- Okay.
Um, so, provably the smallest infinity
is the one that goes
one, two, three, dot, dot, dot.
If I was to take the numbers zero and one
and ask you
how many numbers are there between that,
well, you could keep
dividing and dividing.
No matter how many times you divide,
there's always a number
that you could add another zero
behind the last decimal you had put.
And I can make
a one-to-one little map,
like a little dictionary between
those numbers and the whole numbers.
One, two, three, four, five.
And so what we say is that
those two infinite sets are the same size.
But then there's also other numbers.
Things like the square root of two,
and pi, and E.
And those are just a few
that we know about and use.
These are numbers
that aren't ordinary fractions,
and if we try
and write them down as decimals,
they'll somehow go on forever
without ever repeating themselves.
So how can we ever say what they are?
It took mathematicians hundreds of years
to figure out how to do it rigorously,
and when they did,
they realized that they're so complicated,
it's actually impossible
to put them in a list.
No matter how we try to list them,
we're doomed to miss some out
along the way.
We can't make a one-to-one correspondence
between those numbers
and the counting numbers.
Now that we have two infinities,
would we really stop there?
There are bigger and bigger
and bigger ones.
This is a trail that just keeps on going.
An infinite hierarchy of infinities.
This is the kind of thing
that, hopefully, turns some people
into mathematicians.
And no doubt sends other people running
in the other direction.
My wife gets nauseous
when I bring up infinity.
And my kids don't want
to hear about it either.
Some people love
peering over cliff edges.
There are now those glass bridges
where you can step out
over the Grand Canyon.
There's no way I would do that.
But when it's a mathematical cliff edge,
I love it.
I think this gets back
to this concept of the sublime.
When you're out by a waterfall...
...you have this feeling of this thing
that is so much larger than yourself.
But then you climb onto the mountain peak
and you look out at the next valley,
and you see another waterfall
that's even larger,
but it's in the distance,
so it looks tiny.
Infinity is some kind of monster
that has to be tamed.
"INFINITY"
It's infinity! It's attacking the city!
Mathematicians needed
to invent ways to deal with infinity.
Taking something totally weird
and unintuitive
and taming it to the point where you can
walk around and study it from all sides.
And the ways that they came up with
led to the field of rigorous calculus.
There's one idea at the heart of calculus,
and it's an idea
I like to call the infinity principle.
You can make sense
of any complicated motion or phenomenon,
or anything that's changing,
or any curved shape,
by thinking of it
as being made of an infinite number
of infinitesimally small simpler motions
or shapes.
This is one of the greatest ideas
in history.
Everything to do with movement,
and everything to do with things
that are continuously changing,
can only be studied rigorously
using calculus.
Hmm...
Maybe it's trying
to communicate with us!
We can use calculus to study its roar!
So the infinity principle is
you can make sense of complicated things
by breaking them up
into infinitely many simpler things.
Solve the problem for the simpler things
and then add the results back together
to get the original whole.
A picture encoded in the roar!
Stop fighting infinity!
It's peaceful. Look!
The understanding of electricity
was made possible by calculus.
And electricity has enabled
the entire modern world.
Moshi moshi!
So does infinity exist?
Well, in one of the senses of math,
absolutely no question about it,
because we have a symbol for it,
we know how to manipulate that symbol,
we can agree on the conclusions
that we reach when doing so.
And by doing so,
we can solve practical questions.
Right? So, from a pure math point of view,
that's your certificate of existence
right there.
So then, does infinity exist out there?
That's above my pay grade.
If you mean does it physically exist,
who knows?
That's a question
for the physicists to answer.
And so now they've got to go
do their expensive things, right?
And figure out whether space-time
is infinite or not. It's a real question.
Oh, this is a great question.
So where can one look for real infinities?
We've been struggling
with the question
of whether the infinite infinity
is a real thing
or something that is a human invention
for a very long time.
Maybe we could approach the infinite.
As a physicist,
that's the business I'm in.
How thrilling would that be,
to do something in the physical world
that would tell us
that something is physically infinite?
I think all of us have this experience
of, you know, going out in the night
in the starry sky.
Lying on a beach
late at night in Trinidad.
I mean, I probably was, like,
eight years old
and just wondering
the vastness of outer space.
Does it go on forever?
I question the notion of infinity
when I am using a particular yardstick
which is, can we measure it?
Can we access it?
Can we, in any point
wrap our arms around it
and say, "Here it is."
"There's the infinite."
And using that particular yardstick,
the answer is no.
There's simply no way
that we can measure the infinite.
Nobody will ever give you back pi
to all of its infinite digits
as the result of a measurement.
All I'll ever measure, um,
in a laboratory,
or my friends
will measure in laboratories,
are approximations of infinite numbers.
But then you start to wonder,
"Maybe these numbers don't really exist."
"And nature doesn't actually
make use of them."
And, um...
And I don't know
the answer to that question.
That's why sometimes you think,
"Oh, when the universe was created,
maybe the speed
at which it came out expanding
is an irrational number,
like 0.500187923...
...and the universe is going to compute
that infinite list of digits
over the course of time."
So the universe itself
is performing a computation,
and it's computing
infinite numbers possibly.
Five, zero, one, seven, eight...
I feel like I'm freaking you out,
but, you know, Steven Strogatz had
to be pretty out there.
Oh.
Oh yeah.
You think of a piece of Jell-O.
You know, a blob, a block of Jell-O
jiggling on the table or on a plate.
You don't picture it as made of atoms.
You think it's a continuum of Jell-O stuff
that is infinitely subdivisible
and has no gaps.
It hangs together perfectly.
It's what most of us think
stuff really is like.
The mathematicians are great
in talking about the continuum.
And continuity is the idea
that if I take a line, just a short line,
I can cut it in half,
and then in half again,
and then in half again, and in half again.
And I always have a line,
and I never stop.
I can go forever.
But a completely different question
is whether things
are actually continuous in reality.
Take a rope, cut it in half,
and then again in half,
and then again in half.
Can we go forever?
And this is a question
that was debated since antiquity.
Now, we have understood quite clearly
that a piece of rope is not continuous.
That no piece of matter is continuous.
It's made by little individual pieces
that we call molecules, atoms, particles.
My job,
as a physicist,
is to study another kind of continuity,
which is a continuity...
It's not of matter. String,
or a piece of wood, or a piece of metal.
But the continuity of space itself.
So just consider
the space between my hands
and imagine to have it divide in half,
and half, and half, and half.
Can we go forever?
Is space truly continuous?
Could it be infinitely divided?
My gut feeling is that it can't.
I think if we take
what we best know about the world,
which is Einstein's General Relativity
Theory and quantum mechanics,
and we bring them together,
the clear consequence of that
is that there's a minimal amount of space.
It's very small. Incredibly small.
Ten to the minus 33 centimeters,
the so-called Planck length.
So incredibly tiny
that it certainly stretches
the human imagination to...
think about.
So if you were to...
take an individual atom
and magnify it, expand it
to be as large as the observable universe,
that's a huge scale of magnification.
The Planck length under that magnification
would grow to roughly be the size
of an average tree.
So a tree is to the observable universe
as the Planck length is to an atom.
So even on atomic scales,
the distances that we're talking about
where the notion of continuity
may break down,
where discreteness may emerge,
they are fantastically small.
So I have a sort of, uh,
pixelated vision of reality
at this small scale.
It's like, uh,
if God didn't draw the universe
with continuous lines
but just little pixels.
It's many, many, many, many little things,
but it's not continuity.
It's discreteness.
It's finite.
There is nothing infinitely small.
My favorite example
where we can find real infinities
is when thinking about black holes.
Black holes are these massive objects
where all the matter
is condensed so tightly
that we get this region around it
called the event horizon,
from which we get no information.
Now, there's nothing infinite
about the event horizon.
It's actually empty.
A neutral region of space.
You wouldn't even notice
when you cross the event horizon.
You wouldn't feel anything weird happen
to your body.
What happens that's problematic
is on the inside of the black hole.
In the very literal sense,
we know nothing about
what goes on inside of the black hole.
But Einstein's theory
of general relativity
says that, once you make it
past the event horizon,
eventually if you keep just falling in...
you'll reach a point called
the singularity.
A region which is
an infinite curvature in space-time.
Where all the mass
of the black hole is concentrated.
Infinite densities,
and completely catastrophic.
What happens that's really, um,
considered such a horror show
is that, in a finite time,
in microseconds, in fact,
you would hit this region
of infinite curvature and infinite density
and simply fall out of existence.
As though you weren't part of
the natural world anymore,
so you weren't... Physics stopped.
It's really a violation
of the whole continuity of the program
of understanding nature.
It starts to say
nature's fundamentally unknowable
in this one secret place
inside this black hole.
And that just doesn't feel right.
What do you do
when you have a theory
that works really well
except for when you have this infinity?
Do youthrow the baby out
with the bathwater,
or is the infinity trying
to tell you something?
The singularity,
this region of infinite curvature,
infinite density,
I bet that doesn't really happen.
The infinity
the equations predict is a hint.
It hints at us,
"Hey, there's something new there."
Sometimes,
when I think about the infinity
at the center of a black hole, like,
I think about it as like a dying man
scratching a clue in the dirt, telling us...
"General relativity doesn't work here."
I'm of the opinion
that there is a new physics, actually,
in a black hole.
I think that one thing
that could be happening there
is that there's some sort of portal...
into a new realm.
Maybe a new universe, for example.
There's something I'm working on now
that seems to show that that could happen
if the math works out.
You could have certain portals
where you can actually go through
the black hole.
We call these things wormholes.
A wormhole is something where,
at some point, I say, "Here's a sphere."
"And I have a sphere inside this one
that's got a bigger area."
Okay?
And then inside that one is another sphere
with a bigger area than that.
So the... At some level,
you know, we are confined by
our normal understanding
of space and time, right?
Something inside another thing is smaller.
But that bigger thing is... in here.
If I went in there,
I would be in that bigger thing.
And yet I'm just seeing
the sort of outside of it.
Do you understand it?
Uh, it's totally clear mathematically,
and when I look at this,
I have no idea how that could be.
Okay.
So I want you to think about this
and tell me what it makes you
think about with infinity.
Well, um,
I would say that
if I were some microscopic being
living at the surface of this... ball,
I may conclude
that this surface is infinite,
'cause it would take
an infinite amount of time, for example,
in my imagination of infinity,
to go from one side of the ball
to the other side.
But, you know, it's not infinite, right?
For me, it's not infinite.
So you're not holding infinity
in your hand?
Well, poetically, I am.
I'm holding infinity in my hand.
I see everything in this room
reflected in this sphere.
If we didn't have walls in this room,
I'd be able to see
the entire universe in this sphere.
Well, the entire universe
that's behind me,
because there's a path from everything
to this sphere and then to my eye.
The one thing we cannot do in space-time
is look down on the universe like this.
And this is one of the,
in some terms, mistakes we make,
uh, when we try to imagine
a finite universe.
We imagine being in a space higher up,
an extra dimension out,
and looking down on it.
But, of course,
that would be part of the universe.
If light could get to me,
that's part of the universe.
So there is never such a thing.
You can't jump out of the universe
and look down on it. Ever.
You're holding infinity. It's real.
It's not.
Do you know the old story from Plato,
the prisoners in the cave?
Right. So it's an old bit of philosophy,
that the prisoners
are trapped in the cave,
their backs are to the opening
of the cave,
light is streaming into the cave,
but all the prisoners can see
is shadows on the wall of the cave
of things happening
out there in the world.
To me, this is the shadow.
This is not the real sphere.
This is not the perfect sphere.
The perfect sphere would have infinitely
many points on its surface and inside.
This thing is made of atoms.
There's a lot of 'em,
but not infinitely many.
It's a shadow of infinity.
I love this shadow...
...because it gives me
a glimpse of infinity.
It... feels almost inconceivable.
We're finite creatures,
we have access to finite things.
We can only do so much in a lifetime.
Could we somehow nonetheless
get a glimpse
into something that is truly infinite?
And I think this is not impossible.
An example that I've spent
quite a lot of time thinking about is,
"What would happen to a physical system
if you just wait
an infinite amount of time?"
So let's imagine we take a box.
It's an excellent box.
Nothing can come in. Nothing can go out.
So we put an apple in the box,
close the box.
We might come back in a month
and the apple is looking
kind of mealy and decayed.
Come back in a year,
the apple is a real mess.
The apple is rotted.
Bacteria have done their thing.
Come back in, you know, a hundred years...
the apple is probably a kind of dust.
The apple contains chemical energy,
the same kind of energy you'd get
if you ate the apple or burned an apple.
That energy will eventually come out,
and so the apple inside the box
will get very hot,
uh, probably thousands of degrees.
Those particles can start
to nuclear-fuse together.
This will take a really long time,
because nuclear reactions happen
incredibly slowly at thousands of degrees,
but eventually it will happen.
Your apple has turned into millions
of degree plasma of fundamental particles
and, you know,
burning into higher and higher things.
Eventually, you'll end up
with probably some iron nuclei
and lots of photons.
Billions and billions of years later...
neutrons will decay into protons
and other fundamental particles,
and then it'll sit there
for a very, very long time.
Let's think about what the particles,
the protons and neutrons,and stuff.
What do they...
How do they experience this?
They are just cranking along,
obeying the laws of physics.
The state of the box is changing
from one to the other, to the other.
So, if there's 10 to the 24 particles
in an apple,
there's something like
10 to the 10 to the 24 different states
that those particles can be in.
That's a gigantic number.
But it isn't infinite.
And what that means is that,
if you let the box sit there
for an infinite amount of time,
it will use them all up.
It will go through
every possible state that it can,
all 10 to the 10 to the 24
or whatever of them.
And eventually,
it will start having toreuse
states that it's been in before
because there just aren't any more
that it can evolve into.
And so, eventually,
if you wait a long time,
something will happen.
And this is the power
that infinity has over the finite.
At some point,
you could open the box
and there's your apple again.
How did that happen?
How did this hot gas turn into an apple?
But eventually, it has to.
In fact, every possible thing
that could exist in the box will exist.
And they will each exist
an infinite number of times.
Why do we care?
Well, we might be in the box.
In any finite region of space,
like the observable universe
that we now inhabit,
there's a finite amount of energy,
which is carried
by a finite number of particles.
And those finite number of particles
can only be arranged
in finitely many distinct patterns.
Because there are only
finitely many distinct ways
that the particles can be arranged,
if space does go on infinitely far,
the particle pattern
has to ultimately repeat.
And that would mean
there'd be copies of us out there.
There'd be copies of us.
- An infinite number of copies.
- Out there.
- An infinite number of copies.
- Of us.
Infinitely many of us
at very far parts of the universe
doing exactly the same thing
that this copy of us is doing.
Copies of me that continue,
and copies of me that die at any moment.
Anything that can happen will happen
an infinite number of times.
Suddenly, we're in a wild...
- So somewhere there's an Earth...
- ...inhuman...
- ...where I'm having this conversation...
- ...place.
Where instead of being very hot right now,
it would be air-conditioned.
An infinite number of copies where...
An elephant suddenly appears
in front of me.
There could be
our exact universe,
but with a different history.
Hillary Clintonwon the election.
Germany won the war.
And on that Earth,
the dinosaurs might still rule.
I think when a lot of people
hear some of these ideas,
they're like, "God, they were just up late
drinking and having a good time
and came up with this crazy idea
'cause they wanted to think it
in science fiction."
But this is reality-based.
If the universe is infinite
in extent,
there would be an infinite number
of Einsteins in our universe.
And some of them would be talking to you
and probably be giving much better answers
that I'm giving.
According to
the general theory of relativity,
it is probable
that the universe is not infinite
but closed in upon itself.
Something like the surface of a sphere.
One thing I have learned in a long life...
But those other Einsteins,
they're very far away.
We may never be
in contact with them,
because, according
to his theory of relativity,
nothing can go faster
than 186,000 miles per second,
which is the speed of light.
We have this view of reality that...
We look at it in front of us, right?
I mean, I see you,
I see that white screen,
I see the camera, as they are now, right?
Which means if I see them
as all you are now,
I see immediately.
So the light
that comes from all these objects to me
arrives instantaneously at infinite speed.
Once upon a time, we did think that
perhaps things happened instantaneously
and that information
between one point and another
could be conveyed in the blink of an eye,
in a single instance.
Well, no, of course.
It doesn't come at infinite speed.
It takes some time to come.
So I don't see the now.
I see the past in reality.
Why? Because there's no infinite speed.
Ladies and gentlemen, there he is.
The whizzingest wave,
the peppiest particle. Philo T. Photon!
Move over, Magellan.
Philo is primed to perform
his most fabulous feat of derring-do yet.
Circumnavigating the globe
eight times in a single second.
On your mark, Philo.
He did it, ladies and gentlemen.
The son of a gun did it!
Oh...
Let's see that again in real-time.
Do it again! Encore!
And now I'm sure Philo is pooped.
What's this?
He's going to fly
to the next galaxy and back?
No one has ever attempted
a stunt like this before.
Ladies and gentlemen, I can't watch!
The speed of light is
the maximum speed
at which anything can travel in the
universe.
The speed of light, it's...
it's incredibly fast.
And the speed of light
is horrendously slow.
If we wanna travel in the galaxy,
it's hard enough, uh,
but if you want to travel in the universe
from galaxy to galaxy,
we just cannot, because we cannot...
We're too slow.
And light is too slow. Incredibly slow.
So is the universe infinite?
It's hard to think
what is the universe.
We know that we see the universe
as many billion light years,
uh, and we know
the universe is larger than what we see.
We have indications of that.
But it could be maybe ten times larger.
Maybe a hundred times larger.
There are parts of the universe
most probably
in which, even if we send a signal now,
it will never get there.
So the universe is very,
very, very, very, very big.
And it makes our heads spin.
I was looking up at the sky one night
when I was about ten years old.
And...
I felt like my life didn't matter.
And I guess it was converting
large space to large time.
One star after another star
after another star...
...and wondering whether
that would keep going...
...forever.
I had this sense that the universe,
it existed a long time before I was born...
and it would exist
a long time after I was dead.
And I was just a speck...
that didn't matter.
I don't matter. My parents don't matter.
Nothing matters.
We're all just specks.
We're just living in this brief moment.
None of us were here a million years ago.
None of us will be here
a million years from now.
And the universe doesn't care.
It just goes on and on and on.
So...
why are we wasting time,
you know, going to school,
having dentist appointments?
All of that.
Why are we wasting our time?
Because none of it matters.
And then...
...I fell in love.
And that changed everything.
That mattered.
Even though we might both
be specks in the cosmos.
One of the oldest questions
that thinkers puzzled on
is what happens in the universe
if I could fly forever?
What would happen?
In the past, it seemed
that there were two alternatives.
Both too strange.
One is that the universe is infinite
and I could go forever.
And the other is that it's finite
and there is a wall.
But if there is a wall,
then I could go through the wall,
and so what's next?
And Einstein published
this spectacular paper.
He said, "No, no, no.
The universe can be finite,
but without walls,
because if I go in one direction,
I keep going, and I come back
from the other direction."
Like it happens on the Earth.
If I walk on the Earth towards east,
I walk, walk, walk, walk.
Do I find a wall? No.
Is Earth infinite? No. What happened?
I just come back from the other side.
And it's very possible today
that the universe in fact has this shape.
Namely, has no boundary, there's no wall
at the end of the universe,
but it's finite.
Huge, but finite.
There's actually way more ways
to make the universe finite,
just geometrically, abstractly playing
around with whatever you want,
than there are to make it infinite.
In fact, there's an infinite number
of ways to make the universe finite,
and there's really only a couple of ways
to make it infinite.
We do know
that the universe could be infinite,
but we don't actually have a mechanism
to measure an infinite amount of length.
And because light travels
at a finite speed
and the age of the universe is finite,
there will only ever be
a finite subset of the universe
that we'll ever be able to observe.
Whether beyond that
it's finite or infinite,
we just will never
be able to experimentally know.
When we talk about infinity,
we can certainly talk about infinity
in the extent of the spatial domain.
We can also talk about infinity
in the temporal domain.
The duration of the universe.
It's possible that the universe
will continue on expanding
into an infinite time in the future.
That's what
the equations predict, actually.
In 1998,
we discovered that the universe
is not only expanding,
but the rate of expansion is accelerating.
The galaxies are moving away
from each other with increasing speed.
And what this means
is that, eventually, we will be cut off
from other galaxies.
And so, as the stars in our galaxy
eventually burn out...
as they will,
'cause all of them
have a limited amount of nuclear fuel...
there eventually will not be
any new energy sources in our galaxy.
And since we will be cut off
from all other galaxies eventually,
maybe about 100 billion years from now...
there will not be
any energy sources at all
and life will completely...
end.
And so, roughly 100 billion years
from now...
that will be the end of life.
And if we keep on going along
the cosmological timeline,
galaxies, planets, black holes,
everything that we know about,
it will all disintegrate.
So all that would be left at that point
are particles wafting
through the darkness.
Now, if the universe exists
in an infinite amount of time,
as we now think that it will,
the era of life is just a sliver of time
when you look at the full unfolding
of the universe and time.
Even though 100 billion years
seems like a long time,
it's nothing compared to infinity.
Even if human beings make it
past this particular...
...immediate crisis,
or other sentient life emerges,
there will be a last sentient being.
There will be a last living creature.
Even if the universe is infinite,
there will be a last thought.
A lot of people have kind of
this visceral anxiety about not existing.
But, personally,
I don't have this feeling.
I'm like, you know,
once I didn't exist, before I was born.
There will be a point in time
when I don't exist because I'll die.
And the same is true for our species.
And all life.
Um,
It's, it's... You know,
even physicists have feelings.
And so we can ask,
"How does that make you feel?"
"Are you...
As a physicist, is it daunting?"
"Is it, you know, an existential crisis?"
I... I have never...
I've always had the opposite reaction,
even to some of
the most apocalyptic predictions
for the future of the universe.
It gives me a great sense
of meaning and connectedness
to appreciate that you're part
of this grand picture.
Nothing is permanent in that sense.
And to... to my mind, that's freeing.
It frees us
from this focus on the permanent
as the place
where value ultimately resides,
to a focus
on the brief moment that we have,
in which we can understand things,
and create beauty,
and experience wonder, regardless
of how fleeting that experience may be.
That the universe itself
gets to have its window of life,
its window of consciousness
and beauty and love,
and then, poof.
It's sort of like the universe as a whole
is living the way we do.
We're only here for a short time
compared to infinity,
and, to me, that's a holy thought.
I mean, that's...
as close as I can get to being religious.
The gift that you have of consciousness
for the short time that you're here.
Wait, what was I trying to say?
Something popped into my head.
There are interesting concepts
in abstract math
where you can take something
that appears to have one characteristic,
but you can put it inside something else
or put it around something else
and it will look different
from that point of view.
And, in a way, I think that the universe
is infinite in some sense,
compared with our own lives,
because we just won't be there.
We won't be there to see it.
Whether it's really infinite or not,
I don't know,
and I think that's wonderful.
Not knowing doesn't make me sad.
As a scientist,
for me, not knowing is exciting.
There are things that I believe
that our minds can't know,
but they are real and they exist.
If we want to call that the infinite,
if we want to call that spirit,
if we want to call that God,
whatever you want to call that thing,
I believe thatthing is for real,
but not knowable.
Infinity's very large.
It's too big, infinity.
To me, infinity isan emotion that we get
in front of the immensity of nature.
We are little teeny things.
We do science. It's great.
I love to do science.
Try to figure out
the quantum properties of gravity,
trying to figure out
what is the shape of the cosmos.
But the reality is
we are, you know, like a little cat
trying to understand quantum mechanics.
The cat isn't going
to understand quantummechanics
because he has the brain it has.
A poor human like me won't understand
everything about the universe
because of the poor brain I have.
The number of neurons in our brain
is comparable to the number of stars
in the galaxies.
It is immense.
Which means that the space
of thinkable thoughts
is a fantastically big number.
It's a one followed by billions of digits.
It's an incredibly large number.
Larger than anything we have encountered.
But, look, our brain,
it's a kilogram of meat
which can be in one configuration
or the other, and that's it.
Uh, you can list all of them in principle.
Once again, there's no Infinity here,
and we have to confront
the fundamental finiteness,
not of nature, but of ourselves.
One, two, three, four, five...
Do you think
that human creativity is infinite?
- ...eight, nine, ten...
- Uh...
...eleven, twelve, thirteen...
I sort of recoil at that suggestion.
I don't know. Oh, good gracious. I...
I don't know.
I don't know that we are infinite.
Twenty-one, twenty-two,
twenty-three. Seven, eight, nine,
ten, eleven, twelve.
Ninety-one, ninety-two, ninety-three,
ninety-four, ninety-five, ninety-six...
For some reason, thinking about
anything about human beings being infinite
doesn't seem right to me.
We feel very bounded, to me.
Bounded in our rationality,
bounded in our creativity.
Yeah, I don't even really know
how to visualize infinity.
One, two, three...
Can I even picture a thousand?
...nine, five, two...
Even that number
is too big for me to properly imagine.
I find that...
it's hard for me to really imagine
numbers bigger than ten.
Is it real or fantasy?
Is it just a game we play
To pass the time while slips away
In front of me
Possibilities to find
As we walk the line
Faster and slower
And over and over
We tumble and we intertwine
Solving the riddle
And little by little we find
It goes on and on
Forever and ever and ever and ever
Forever and ever and ever and ever
Forever and ever and ever and ever
Forever and ever and ever and ever
Love it's all that matters in the end
At the end of forever
Space is staring back at me
It's not easy to explain
Where all just links in the daisy chain
Will you recognize just what you see?
Search and you won't miss the signs
The ones the universe left behind
From the beginning
We're spinning and spinning
And spiraling out of control
It's never-ending
We never know where we will go
It's goes on and on
Forever and ever and ever and ever
Forever and ever and ever and ever
Forever and ever and ever and ever
Forever and ever and ever and ever
Faster and slower
And over and over
We tumble and we intertwine
It's never-ending
We never know what we'll find
It goes on and on
Forever and ever and ever and ever
Forever and ever and ever and ever
Forever and ever and ever and ever
Forever and ever and ever and ever
Love isall that matters in the end
At the end of forever
Forever
Four, five...
Well, the first time
that I thought about infinity,
I was looking up at the sky one night
when I was about ten years old.
I was really little,
it was before I had started school,
and I was sitting
under the dining room table
and counting.
And at a certain point,
I realize this goes on forever.
Lying on a beach late at night
and just wondering
the vastness of outer space.
Does it go on forever?
Mmm...
I want to start
with sort of the premise of the film,
which is that we're looking for infinity.
So where should we go looking?
Well, I don't think
everybody's looking for infinity.
So is infinity a number, a place,
an idea, a concept?
If you ask me, probably all of the above.
Numbers never end.
That's the basic idea of infinity.
If I imagine continuing to count
for as long as I can count,
infinity will definitely last
longer than my lifetime.
The funny thing is,
all these numbers that you can imagine,
they're like zero, nothing.
Any number, no matter how big,
is just absolutely insignificant
compared to infinity.
For me, infinity is not scary.
I find infinity beautiful,
and haunting, and thrilling.
I love Infinity.
You know, I guess if I start
thinking about, "I'll be dead forever..."
there's a side of me
that's worried about it.
But then again,
I don't plan to be thinking about it.
I think to be conscious
is to be wrangling with infinity.
I mean, not to be grandiose.
When our hearts are broken,
are we going to be in pain forever?
And if you really
fall in love with someone,
are you gonna be in love
with them forever?
Love is certainly infinite,
because when we are overwhelmed by love,
we have this constant sense
of breaking the limits and the boundaries.
All of these abstractions,
suddenly it seemed to me,
well, maybe they're just
the product of our minds.
Who invented infinity?
I think, uh, to some extent,
the concept goes back
earlier than anything that we know.
One, two, three...
In fact, counting
is the very earliest writing that we have.
...seven...
Whoever invented writing
already had the idea of counting,
and the idea
that you can always count one more
must surely go back at least that far.
...fifteen, sixteen...
We have all kinds of different
visions of things that are infinite,
and they're usually terrifying.
There's the vision of the bottomless pit.
There's the idea of time that never ends.
If you believe in hell,
and if you believe
about torture going on forever,
a nightmare that you could
never wake up from...
So I understand that a lot of people
find thinking about infinity terrifying,
or nauseating.
At least very upsetting.
But for some of us,
it's one of the deepest pleasures.
...2001...
We're so small...
...2003, 2004...
...and yet we can
touch something so...
...1000000, 10000002...
...explosively large.
...1000004...
That feeling of, "I'm bigger
because I know how small I am."
...399, 400, 401...
I've been chasing that feeling
my entire life.
But does infinity exist
outside of our minds?
So does infinity exist?
Um...
You know, in math, I think...
Can we wait
for this train to go by?
Oh yeah.
Okay.
All right. Sorry about that.
Oh, yeah. It's good to collect thoughts.
Um, okay, so I think
I was gonna make a comment
about what it means
to exist mathematically, right?
Um, so, in math, I think we have
an interesting relationship to stuff,
to things in existence, right?
If you can conceive of something,
if you can kind of
create rules for handling it,
then it exists.
So how does infinity fit into all that?
Well, okay, infinity
is super counterintuitive,
and it leads
to a lot of surprising paradoxes,
contradictions,
intellectual quagmires, quicksand.
Many of these are summed up in a parable
that goes by the name
of the Infinite Hotel.
Imagine a hotel
with infinitely many rooms.
It's a really popular hotel.
And in fact, it's always booked solid.
Every room is occupied.
Nevertheless, there's always room
at the Infinite Hotel.
So, one night, a new guest shows up.
Bang, bang, bang on the bell.
"I'd like a room."
And the manager says,
"Sure. Of course, we can accommodate you
here at the Infinite Hotel."
"Just hold on for one minute."
The manager tells everyone
over the loudspeaker...
Please gather your things.
Get ready to move
to the next room down the hall.
Person in room one
moves into room two.
Person in room two moves into room three.
You might think there's gonna be trouble
because all the rooms are occupied.
Nevertheless, as it's an Infinite Hotel,
I mean, this can happen, right?
The numbers never stop.
One can move to two,
two can move to three,
a million can move to a million and one.
So everybody moves down to the next room,
which means that now room one is open,
and the new guest can be accommodated.
You could keep everyone
in the same room
and just have the guest go to the end.
Yeah. So a tempting thought would be
just have the guest take the last room.
Why are we making
everybody else move for this one person?
Well, because there is no last room.
Infinity doesn't work like that.
You have to start at the beginning,
not at the end. There is no end.
Now, a bigger challenge for the manager
comes the next night
when, instead of just one guest
showing up,
suddenly a whole busload full of cranky,
sweaty, ill-tempered people
all pound on the bell at the same time,
saying, "We all want rooms."
There's infinitely many new guests.
They all want to be accommodated
at this hotel.
How can you do that?
Can you somehow find room
for infinitely many new people,
given that infinitely
many rooms are occupied?
It turns out the manager has seen
this problem before,
and so she calls out over the loudspeaker...
Everyone be prepared
in a few minutes
to move to the room
that is double your current room.
So, person in room one,
you're gonna be in room two.
Person in room two, you're now
going to be moving into room four.
Person in room three, you're going to six.
Now, it's a big inconvenience
for person in room one million.
They have to move to room two million,
which is a big schlep down the hall.
So all these people dutifully move
to their new rooms.
You'll notice thatwhat's happened is
all the odd-numbered rooms
have been vacated.
And so all those new guests
can just start filing in.
There's one other custom
at the Infinite Hotel,
which is that this manager
is very conscientious
and always checks in on the rooms,
infinitely many of them.
Fortunately, the manager is very speedy,
so she can get her whole job done
in a minute.
She spends half a minute
making sure everything's okay in room one,
and a quarter of a minute,
so 15 seconds, on room two,
and then half of that,
so 7.5 seconds, on room three,
and so on, going all the way down the hall
in the Infinite Hotel.
A half, plus a quarter,
plus an eighth, plus a sixteenth,
and if you add that up...
But if you just think about that,
when you go out to infinity,
that's gonna add up to one.
She's basically gonna be done
checking infinitely many rooms
in one minute.
How does she get back
from infinity?
She get... Oh, that's good. Well...
Yeah, let's see. So, um... Hmm.
That's an interesting puzzle.
Yeah. Where is she at the end? Uh...
Don't ask me.
I've been thinking about infinity
my whole career,
and even I don't really see
any way out for her.
She's out at the end
of this infinitely long hallway,
and I don't see
how she's gonna come back from there.
I told you it was a strange hotel.
Well, so I think that, you know,
the moral of this crazy parable
is that infinity doesn't behave
like anything we're used to.
We're used to thinking about
collections of finite numbers of things.
Fish, fish, fish.
That's three fish, you know.
So we're used to small numbers,
or even big numbers.
You hear nowadays
about trillions of dollars
needing to be spent
on the budget in the United States.
But, um, those are nothing like infinity.
Any finite number, no matter how big,
is nothing compared to infinity.
We just don't have good intuition
about how infinite things work.
Even very small children
can have a gut feeling about infinity.
It's the biggest possible thing.
It's bigger
than anything you can ever think of.
Well, what happens if you add one?
So if infinity
is the biggest thing there is,
then when you add one,
it should still be infinity. Maybe?
What happens if I subtract infinity
from both sides?
Then you get one equals zero.
And so immediately you've landed yourself
in some kind of an issue,
and that's just the start.
It turns out you can write things down
that don't have an answer.
I mean, that doesn't happen
in finite arithmetic.
If I say one plus two,
the answer is three, and I'm done with it.
But if I say one minus one,
plus one, minus one...
One minus one, plus one, minus one,
plus one, minus one, dot, dot, dot.
Keep doing that forever.
There is no answer to that.
It's not zero and it's not one.
It's neither. It's both. What is it?
You can try adding infinity to infinity.
Multiply it.
You get these weird paradoxes.
Well, what's infinity plus infinity?
That should also be infinity
because it's the biggest thing.
Then you subtract infinity from both sides
and you get infinity equals zero.
That's even worse. So this is terrible.
But it's wonderful,
because what is going on?
Is infinity beautiful?
Of course, it's beautiful.
I mean, yeah, it's...
Like I say, it's beautiful because it is...
Uh...
Maybe...
a good way to think about it
is with our circle.
Shall we talk about the circle?
There's a very beautiful shape
that often people think of
as the most perfect shape, a circle.
Perfectly round, never-ending.
We see circles everywhere.
I look in your eyes,
I see the circle of your iris.
I see the circle of your pupil.
I see the circle of the sun and the moon.
I've got my wedding ring
in the shape of a circle.
I love circles.
But if you sit down and think about
what they are for a second,
how many sides do they have, for example?
How many corners do they have?
That immediately brings us
into face-to-face confrontation
with the infinite,
because you can't think about a circle
in terms of straight lines.
If we think about pointy shapes,
say a triangle,
if we tried to use it as a wheel,
it would be kind of painful
going up the street.
If we had ten corners,
then that wouldn't be so bad as a wheel.
And then, if you keep going,
you can go, "Oh, wait,
if we then had infinity sides,
then we would be completely like a circle,
and we would have infinity corners,
which is like having no corners."
And so, somehow, infinity has come round
to being just like zero.
One of the amazing things about infinity
is that, if you scale it,
it's still infinity.
Whereas if you take any finite number,
if you scale it,
which is like multiplying it,
it gets bigger.
But infinity doesn't do that somehow,
and that's a very odd thing
for us to get our heads around.
So let's try and picture this, right?
When it comes to a circle
as a set of points...
'Cause that's what it is.
It's an infinite collection of points.
I would like to try to convince you
that a small circle,
like a circle of radius one,
um, has the same number of points
as a huge circle,
a circle of radius billion.
Right? Okay.
So, to do that,
I need to get you to agree
on what it means to be the same size.
Like, anytime you're making
a high-stakes bet with a friend,
you wanna settle...
This is good advice, by the way.
You want to settle in advance
what qualifies as winning.
I propose that two sets
will be said to have the same size
if I can put their elements
in a perfect one-to-one correspondence.
Now, all I need to give you is a rule
that puts the points of a small circle
in correspondence
with the points of a larger circle.
You can't count the points on the circle,
but you can match them up
with the points on a bigger circle.
I take my small circle
and I just center it somewhere at a point,
and then I take the huge circle
and I center it at the same point.
I'm gonna... From that center point,
I'm gonna draw all the radii. Right?
I'll draw these kind of line segments
stretching out from the center
to the outer circle.
Well, each of those line segments
hits the outer circle on one point
and hits the inner circle on one point,
and that's the correspondence.
I'm gonna say the point, um,
on a particular radius in the small circle
is matched to its corresponding point
from the large circle.
Well, by sweeping those radii
all the way around,
I clearly hit
all the points on each circle.
And so I'm done.
I've got a perfect
one-to-one correspondence.
You now have to agree
that the two infinite sets
have the same size.
So mathematicians don't literally
sit there counting to infinity.
We just match things up in pairs.
And if you can find a way
to match things up in pairs,
you can go, "Oh, that's the same then."
So, for example, we can match up
all the numbers, the whole numbers,
with the even numbers
by just multiplying each one by two.
You sit there and go, "Wait,
the even numbers is only half of them."
And then you go,
"But wait, I can match them up,
because if I pair up one with two,
and two with four,
and three with six,
then they pair up exactly."
So then you go,
"Wait, there's the same number,
even though it's half of them."
And that's the amazing thing
about infinity.
Once you've figured out
this way of matching things up
to see how big an infinite set is,
it turns out that there might be some
that you can never match up,
which means that there is
some kind of bigger possible infinity.
How can there be larger infinities?
Infinity is already
as big as we can imagine, right?
No. No.
There's something beyond that.
- Let me see if this works for you.
- Okay.
Um, so, provably the smallest infinity
is the one that goes
one, two, three, dot, dot, dot.
If I was to take the numbers zero and one
and ask you
how many numbers are there between that,
well, you could keep
dividing and dividing.
No matter how many times you divide,
there's always a number
that you could add another zero
behind the last decimal you had put.
And I can make
a one-to-one little map,
like a little dictionary between
those numbers and the whole numbers.
One, two, three, four, five.
And so what we say is that
those two infinite sets are the same size.
But then there's also other numbers.
Things like the square root of two,
and pi, and E.
And those are just a few
that we know about and use.
These are numbers
that aren't ordinary fractions,
and if we try
and write them down as decimals,
they'll somehow go on forever
without ever repeating themselves.
So how can we ever say what they are?
It took mathematicians hundreds of years
to figure out how to do it rigorously,
and when they did,
they realized that they're so complicated,
it's actually impossible
to put them in a list.
No matter how we try to list them,
we're doomed to miss some out
along the way.
We can't make a one-to-one correspondence
between those numbers
and the counting numbers.
Now that we have two infinities,
would we really stop there?
There are bigger and bigger
and bigger ones.
This is a trail that just keeps on going.
An infinite hierarchy of infinities.
This is the kind of thing
that, hopefully, turns some people
into mathematicians.
And no doubt sends other people running
in the other direction.
My wife gets nauseous
when I bring up infinity.
And my kids don't want
to hear about it either.
Some people love
peering over cliff edges.
There are now those glass bridges
where you can step out
over the Grand Canyon.
There's no way I would do that.
But when it's a mathematical cliff edge,
I love it.
I think this gets back
to this concept of the sublime.
When you're out by a waterfall...
...you have this feeling of this thing
that is so much larger than yourself.
But then you climb onto the mountain peak
and you look out at the next valley,
and you see another waterfall
that's even larger,
but it's in the distance,
so it looks tiny.
Infinity is some kind of monster
that has to be tamed.
"INFINITY"
It's infinity! It's attacking the city!
Mathematicians needed
to invent ways to deal with infinity.
Taking something totally weird
and unintuitive
and taming it to the point where you can
walk around and study it from all sides.
And the ways that they came up with
led to the field of rigorous calculus.
There's one idea at the heart of calculus,
and it's an idea
I like to call the infinity principle.
You can make sense
of any complicated motion or phenomenon,
or anything that's changing,
or any curved shape,
by thinking of it
as being made of an infinite number
of infinitesimally small simpler motions
or shapes.
This is one of the greatest ideas
in history.
Everything to do with movement,
and everything to do with things
that are continuously changing,
can only be studied rigorously
using calculus.
Hmm...
Maybe it's trying
to communicate with us!
We can use calculus to study its roar!
So the infinity principle is
you can make sense of complicated things
by breaking them up
into infinitely many simpler things.
Solve the problem for the simpler things
and then add the results back together
to get the original whole.
A picture encoded in the roar!
Stop fighting infinity!
It's peaceful. Look!
The understanding of electricity
was made possible by calculus.
And electricity has enabled
the entire modern world.
Moshi moshi!
So does infinity exist?
Well, in one of the senses of math,
absolutely no question about it,
because we have a symbol for it,
we know how to manipulate that symbol,
we can agree on the conclusions
that we reach when doing so.
And by doing so,
we can solve practical questions.
Right? So, from a pure math point of view,
that's your certificate of existence
right there.
So then, does infinity exist out there?
That's above my pay grade.
If you mean does it physically exist,
who knows?
That's a question
for the physicists to answer.
And so now they've got to go
do their expensive things, right?
And figure out whether space-time
is infinite or not. It's a real question.
Oh, this is a great question.
So where can one look for real infinities?
We've been struggling
with the question
of whether the infinite infinity
is a real thing
or something that is a human invention
for a very long time.
Maybe we could approach the infinite.
As a physicist,
that's the business I'm in.
How thrilling would that be,
to do something in the physical world
that would tell us
that something is physically infinite?
I think all of us have this experience
of, you know, going out in the night
in the starry sky.
Lying on a beach
late at night in Trinidad.
I mean, I probably was, like,
eight years old
and just wondering
the vastness of outer space.
Does it go on forever?
I question the notion of infinity
when I am using a particular yardstick
which is, can we measure it?
Can we access it?
Can we, in any point
wrap our arms around it
and say, "Here it is."
"There's the infinite."
And using that particular yardstick,
the answer is no.
There's simply no way
that we can measure the infinite.
Nobody will ever give you back pi
to all of its infinite digits
as the result of a measurement.
All I'll ever measure, um,
in a laboratory,
or my friends
will measure in laboratories,
are approximations of infinite numbers.
But then you start to wonder,
"Maybe these numbers don't really exist."
"And nature doesn't actually
make use of them."
And, um...
And I don't know
the answer to that question.
That's why sometimes you think,
"Oh, when the universe was created,
maybe the speed
at which it came out expanding
is an irrational number,
like 0.500187923...
...and the universe is going to compute
that infinite list of digits
over the course of time."
So the universe itself
is performing a computation,
and it's computing
infinite numbers possibly.
Five, zero, one, seven, eight...
I feel like I'm freaking you out,
but, you know, Steven Strogatz had
to be pretty out there.
Oh.
Oh yeah.
You think of a piece of Jell-O.
You know, a blob, a block of Jell-O
jiggling on the table or on a plate.
You don't picture it as made of atoms.
You think it's a continuum of Jell-O stuff
that is infinitely subdivisible
and has no gaps.
It hangs together perfectly.
It's what most of us think
stuff really is like.
The mathematicians are great
in talking about the continuum.
And continuity is the idea
that if I take a line, just a short line,
I can cut it in half,
and then in half again,
and then in half again, and in half again.
And I always have a line,
and I never stop.
I can go forever.
But a completely different question
is whether things
are actually continuous in reality.
Take a rope, cut it in half,
and then again in half,
and then again in half.
Can we go forever?
And this is a question
that was debated since antiquity.
Now, we have understood quite clearly
that a piece of rope is not continuous.
That no piece of matter is continuous.
It's made by little individual pieces
that we call molecules, atoms, particles.
My job,
as a physicist,
is to study another kind of continuity,
which is a continuity...
It's not of matter. String,
or a piece of wood, or a piece of metal.
But the continuity of space itself.
So just consider
the space between my hands
and imagine to have it divide in half,
and half, and half, and half.
Can we go forever?
Is space truly continuous?
Could it be infinitely divided?
My gut feeling is that it can't.
I think if we take
what we best know about the world,
which is Einstein's General Relativity
Theory and quantum mechanics,
and we bring them together,
the clear consequence of that
is that there's a minimal amount of space.
It's very small. Incredibly small.
Ten to the minus 33 centimeters,
the so-called Planck length.
So incredibly tiny
that it certainly stretches
the human imagination to...
think about.
So if you were to...
take an individual atom
and magnify it, expand it
to be as large as the observable universe,
that's a huge scale of magnification.
The Planck length under that magnification
would grow to roughly be the size
of an average tree.
So a tree is to the observable universe
as the Planck length is to an atom.
So even on atomic scales,
the distances that we're talking about
where the notion of continuity
may break down,
where discreteness may emerge,
they are fantastically small.
So I have a sort of, uh,
pixelated vision of reality
at this small scale.
It's like, uh,
if God didn't draw the universe
with continuous lines
but just little pixels.
It's many, many, many, many little things,
but it's not continuity.
It's discreteness.
It's finite.
There is nothing infinitely small.
My favorite example
where we can find real infinities
is when thinking about black holes.
Black holes are these massive objects
where all the matter
is condensed so tightly
that we get this region around it
called the event horizon,
from which we get no information.
Now, there's nothing infinite
about the event horizon.
It's actually empty.
A neutral region of space.
You wouldn't even notice
when you cross the event horizon.
You wouldn't feel anything weird happen
to your body.
What happens that's problematic
is on the inside of the black hole.
In the very literal sense,
we know nothing about
what goes on inside of the black hole.
But Einstein's theory
of general relativity
says that, once you make it
past the event horizon,
eventually if you keep just falling in...
you'll reach a point called
the singularity.
A region which is
an infinite curvature in space-time.
Where all the mass
of the black hole is concentrated.
Infinite densities,
and completely catastrophic.
What happens that's really, um,
considered such a horror show
is that, in a finite time,
in microseconds, in fact,
you would hit this region
of infinite curvature and infinite density
and simply fall out of existence.
As though you weren't part of
the natural world anymore,
so you weren't... Physics stopped.
It's really a violation
of the whole continuity of the program
of understanding nature.
It starts to say
nature's fundamentally unknowable
in this one secret place
inside this black hole.
And that just doesn't feel right.
What do you do
when you have a theory
that works really well
except for when you have this infinity?
Do youthrow the baby out
with the bathwater,
or is the infinity trying
to tell you something?
The singularity,
this region of infinite curvature,
infinite density,
I bet that doesn't really happen.
The infinity
the equations predict is a hint.
It hints at us,
"Hey, there's something new there."
Sometimes,
when I think about the infinity
at the center of a black hole, like,
I think about it as like a dying man
scratching a clue in the dirt, telling us...
"General relativity doesn't work here."
I'm of the opinion
that there is a new physics, actually,
in a black hole.
I think that one thing
that could be happening there
is that there's some sort of portal...
into a new realm.
Maybe a new universe, for example.
There's something I'm working on now
that seems to show that that could happen
if the math works out.
You could have certain portals
where you can actually go through
the black hole.
We call these things wormholes.
A wormhole is something where,
at some point, I say, "Here's a sphere."
"And I have a sphere inside this one
that's got a bigger area."
Okay?
And then inside that one is another sphere
with a bigger area than that.
So the... At some level,
you know, we are confined by
our normal understanding
of space and time, right?
Something inside another thing is smaller.
But that bigger thing is... in here.
If I went in there,
I would be in that bigger thing.
And yet I'm just seeing
the sort of outside of it.
Do you understand it?
Uh, it's totally clear mathematically,
and when I look at this,
I have no idea how that could be.
Okay.
So I want you to think about this
and tell me what it makes you
think about with infinity.
Well, um,
I would say that
if I were some microscopic being
living at the surface of this... ball,
I may conclude
that this surface is infinite,
'cause it would take
an infinite amount of time, for example,
in my imagination of infinity,
to go from one side of the ball
to the other side.
But, you know, it's not infinite, right?
For me, it's not infinite.
So you're not holding infinity
in your hand?
Well, poetically, I am.
I'm holding infinity in my hand.
I see everything in this room
reflected in this sphere.
If we didn't have walls in this room,
I'd be able to see
the entire universe in this sphere.
Well, the entire universe
that's behind me,
because there's a path from everything
to this sphere and then to my eye.
The one thing we cannot do in space-time
is look down on the universe like this.
And this is one of the,
in some terms, mistakes we make,
uh, when we try to imagine
a finite universe.
We imagine being in a space higher up,
an extra dimension out,
and looking down on it.
But, of course,
that would be part of the universe.
If light could get to me,
that's part of the universe.
So there is never such a thing.
You can't jump out of the universe
and look down on it. Ever.
You're holding infinity. It's real.
It's not.
Do you know the old story from Plato,
the prisoners in the cave?
Right. So it's an old bit of philosophy,
that the prisoners
are trapped in the cave,
their backs are to the opening
of the cave,
light is streaming into the cave,
but all the prisoners can see
is shadows on the wall of the cave
of things happening
out there in the world.
To me, this is the shadow.
This is not the real sphere.
This is not the perfect sphere.
The perfect sphere would have infinitely
many points on its surface and inside.
This thing is made of atoms.
There's a lot of 'em,
but not infinitely many.
It's a shadow of infinity.
I love this shadow...
...because it gives me
a glimpse of infinity.
It... feels almost inconceivable.
We're finite creatures,
we have access to finite things.
We can only do so much in a lifetime.
Could we somehow nonetheless
get a glimpse
into something that is truly infinite?
And I think this is not impossible.
An example that I've spent
quite a lot of time thinking about is,
"What would happen to a physical system
if you just wait
an infinite amount of time?"
So let's imagine we take a box.
It's an excellent box.
Nothing can come in. Nothing can go out.
So we put an apple in the box,
close the box.
We might come back in a month
and the apple is looking
kind of mealy and decayed.
Come back in a year,
the apple is a real mess.
The apple is rotted.
Bacteria have done their thing.
Come back in, you know, a hundred years...
the apple is probably a kind of dust.
The apple contains chemical energy,
the same kind of energy you'd get
if you ate the apple or burned an apple.
That energy will eventually come out,
and so the apple inside the box
will get very hot,
uh, probably thousands of degrees.
Those particles can start
to nuclear-fuse together.
This will take a really long time,
because nuclear reactions happen
incredibly slowly at thousands of degrees,
but eventually it will happen.
Your apple has turned into millions
of degree plasma of fundamental particles
and, you know,
burning into higher and higher things.
Eventually, you'll end up
with probably some iron nuclei
and lots of photons.
Billions and billions of years later...
neutrons will decay into protons
and other fundamental particles,
and then it'll sit there
for a very, very long time.
Let's think about what the particles,
the protons and neutrons,and stuff.
What do they...
How do they experience this?
They are just cranking along,
obeying the laws of physics.
The state of the box is changing
from one to the other, to the other.
So, if there's 10 to the 24 particles
in an apple,
there's something like
10 to the 10 to the 24 different states
that those particles can be in.
That's a gigantic number.
But it isn't infinite.
And what that means is that,
if you let the box sit there
for an infinite amount of time,
it will use them all up.
It will go through
every possible state that it can,
all 10 to the 10 to the 24
or whatever of them.
And eventually,
it will start having toreuse
states that it's been in before
because there just aren't any more
that it can evolve into.
And so, eventually,
if you wait a long time,
something will happen.
And this is the power
that infinity has over the finite.
At some point,
you could open the box
and there's your apple again.
How did that happen?
How did this hot gas turn into an apple?
But eventually, it has to.
In fact, every possible thing
that could exist in the box will exist.
And they will each exist
an infinite number of times.
Why do we care?
Well, we might be in the box.
In any finite region of space,
like the observable universe
that we now inhabit,
there's a finite amount of energy,
which is carried
by a finite number of particles.
And those finite number of particles
can only be arranged
in finitely many distinct patterns.
Because there are only
finitely many distinct ways
that the particles can be arranged,
if space does go on infinitely far,
the particle pattern
has to ultimately repeat.
And that would mean
there'd be copies of us out there.
There'd be copies of us.
- An infinite number of copies.
- Out there.
- An infinite number of copies.
- Of us.
Infinitely many of us
at very far parts of the universe
doing exactly the same thing
that this copy of us is doing.
Copies of me that continue,
and copies of me that die at any moment.
Anything that can happen will happen
an infinite number of times.
Suddenly, we're in a wild...
- So somewhere there's an Earth...
- ...inhuman...
- ...where I'm having this conversation...
- ...place.
Where instead of being very hot right now,
it would be air-conditioned.
An infinite number of copies where...
An elephant suddenly appears
in front of me.
There could be
our exact universe,
but with a different history.
Hillary Clintonwon the election.
Germany won the war.
And on that Earth,
the dinosaurs might still rule.
I think when a lot of people
hear some of these ideas,
they're like, "God, they were just up late
drinking and having a good time
and came up with this crazy idea
'cause they wanted to think it
in science fiction."
But this is reality-based.
If the universe is infinite
in extent,
there would be an infinite number
of Einsteins in our universe.
And some of them would be talking to you
and probably be giving much better answers
that I'm giving.
According to
the general theory of relativity,
it is probable
that the universe is not infinite
but closed in upon itself.
Something like the surface of a sphere.
One thing I have learned in a long life...
But those other Einsteins,
they're very far away.
We may never be
in contact with them,
because, according
to his theory of relativity,
nothing can go faster
than 186,000 miles per second,
which is the speed of light.
We have this view of reality that...
We look at it in front of us, right?
I mean, I see you,
I see that white screen,
I see the camera, as they are now, right?
Which means if I see them
as all you are now,
I see immediately.
So the light
that comes from all these objects to me
arrives instantaneously at infinite speed.
Once upon a time, we did think that
perhaps things happened instantaneously
and that information
between one point and another
could be conveyed in the blink of an eye,
in a single instance.
Well, no, of course.
It doesn't come at infinite speed.
It takes some time to come.
So I don't see the now.
I see the past in reality.
Why? Because there's no infinite speed.
Ladies and gentlemen, there he is.
The whizzingest wave,
the peppiest particle. Philo T. Photon!
Move over, Magellan.
Philo is primed to perform
his most fabulous feat of derring-do yet.
Circumnavigating the globe
eight times in a single second.
On your mark, Philo.
He did it, ladies and gentlemen.
The son of a gun did it!
Oh...
Let's see that again in real-time.
Do it again! Encore!
And now I'm sure Philo is pooped.
What's this?
He's going to fly
to the next galaxy and back?
No one has ever attempted
a stunt like this before.
Ladies and gentlemen, I can't watch!
The speed of light is
the maximum speed
at which anything can travel in the
universe.
The speed of light, it's...
it's incredibly fast.
And the speed of light
is horrendously slow.
If we wanna travel in the galaxy,
it's hard enough, uh,
but if you want to travel in the universe
from galaxy to galaxy,
we just cannot, because we cannot...
We're too slow.
And light is too slow. Incredibly slow.
So is the universe infinite?
It's hard to think
what is the universe.
We know that we see the universe
as many billion light years,
uh, and we know
the universe is larger than what we see.
We have indications of that.
But it could be maybe ten times larger.
Maybe a hundred times larger.
There are parts of the universe
most probably
in which, even if we send a signal now,
it will never get there.
So the universe is very,
very, very, very, very big.
And it makes our heads spin.
I was looking up at the sky one night
when I was about ten years old.
And...
I felt like my life didn't matter.
And I guess it was converting
large space to large time.
One star after another star
after another star...
...and wondering whether
that would keep going...
...forever.
I had this sense that the universe,
it existed a long time before I was born...
and it would exist
a long time after I was dead.
And I was just a speck...
that didn't matter.
I don't matter. My parents don't matter.
Nothing matters.
We're all just specks.
We're just living in this brief moment.
None of us were here a million years ago.
None of us will be here
a million years from now.
And the universe doesn't care.
It just goes on and on and on.
So...
why are we wasting time,
you know, going to school,
having dentist appointments?
All of that.
Why are we wasting our time?
Because none of it matters.
And then...
...I fell in love.
And that changed everything.
That mattered.
Even though we might both
be specks in the cosmos.
One of the oldest questions
that thinkers puzzled on
is what happens in the universe
if I could fly forever?
What would happen?
In the past, it seemed
that there were two alternatives.
Both too strange.
One is that the universe is infinite
and I could go forever.
And the other is that it's finite
and there is a wall.
But if there is a wall,
then I could go through the wall,
and so what's next?
And Einstein published
this spectacular paper.
He said, "No, no, no.
The universe can be finite,
but without walls,
because if I go in one direction,
I keep going, and I come back
from the other direction."
Like it happens on the Earth.
If I walk on the Earth towards east,
I walk, walk, walk, walk.
Do I find a wall? No.
Is Earth infinite? No. What happened?
I just come back from the other side.
And it's very possible today
that the universe in fact has this shape.
Namely, has no boundary, there's no wall
at the end of the universe,
but it's finite.
Huge, but finite.
There's actually way more ways
to make the universe finite,
just geometrically, abstractly playing
around with whatever you want,
than there are to make it infinite.
In fact, there's an infinite number
of ways to make the universe finite,
and there's really only a couple of ways
to make it infinite.
We do know
that the universe could be infinite,
but we don't actually have a mechanism
to measure an infinite amount of length.
And because light travels
at a finite speed
and the age of the universe is finite,
there will only ever be
a finite subset of the universe
that we'll ever be able to observe.
Whether beyond that
it's finite or infinite,
we just will never
be able to experimentally know.
When we talk about infinity,
we can certainly talk about infinity
in the extent of the spatial domain.
We can also talk about infinity
in the temporal domain.
The duration of the universe.
It's possible that the universe
will continue on expanding
into an infinite time in the future.
That's what
the equations predict, actually.
In 1998,
we discovered that the universe
is not only expanding,
but the rate of expansion is accelerating.
The galaxies are moving away
from each other with increasing speed.
And what this means
is that, eventually, we will be cut off
from other galaxies.
And so, as the stars in our galaxy
eventually burn out...
as they will,
'cause all of them
have a limited amount of nuclear fuel...
there eventually will not be
any new energy sources in our galaxy.
And since we will be cut off
from all other galaxies eventually,
maybe about 100 billion years from now...
there will not be
any energy sources at all
and life will completely...
end.
And so, roughly 100 billion years
from now...
that will be the end of life.
And if we keep on going along
the cosmological timeline,
galaxies, planets, black holes,
everything that we know about,
it will all disintegrate.
So all that would be left at that point
are particles wafting
through the darkness.
Now, if the universe exists
in an infinite amount of time,
as we now think that it will,
the era of life is just a sliver of time
when you look at the full unfolding
of the universe and time.
Even though 100 billion years
seems like a long time,
it's nothing compared to infinity.
Even if human beings make it
past this particular...
...immediate crisis,
or other sentient life emerges,
there will be a last sentient being.
There will be a last living creature.
Even if the universe is infinite,
there will be a last thought.
A lot of people have kind of
this visceral anxiety about not existing.
But, personally,
I don't have this feeling.
I'm like, you know,
once I didn't exist, before I was born.
There will be a point in time
when I don't exist because I'll die.
And the same is true for our species.
And all life.
Um,
It's, it's... You know,
even physicists have feelings.
And so we can ask,
"How does that make you feel?"
"Are you...
As a physicist, is it daunting?"
"Is it, you know, an existential crisis?"
I... I have never...
I've always had the opposite reaction,
even to some of
the most apocalyptic predictions
for the future of the universe.
It gives me a great sense
of meaning and connectedness
to appreciate that you're part
of this grand picture.
Nothing is permanent in that sense.
And to... to my mind, that's freeing.
It frees us
from this focus on the permanent
as the place
where value ultimately resides,
to a focus
on the brief moment that we have,
in which we can understand things,
and create beauty,
and experience wonder, regardless
of how fleeting that experience may be.
That the universe itself
gets to have its window of life,
its window of consciousness
and beauty and love,
and then, poof.
It's sort of like the universe as a whole
is living the way we do.
We're only here for a short time
compared to infinity,
and, to me, that's a holy thought.
I mean, that's...
as close as I can get to being religious.
The gift that you have of consciousness
for the short time that you're here.
Wait, what was I trying to say?
Something popped into my head.
There are interesting concepts
in abstract math
where you can take something
that appears to have one characteristic,
but you can put it inside something else
or put it around something else
and it will look different
from that point of view.
And, in a way, I think that the universe
is infinite in some sense,
compared with our own lives,
because we just won't be there.
We won't be there to see it.
Whether it's really infinite or not,
I don't know,
and I think that's wonderful.
Not knowing doesn't make me sad.
As a scientist,
for me, not knowing is exciting.
There are things that I believe
that our minds can't know,
but they are real and they exist.
If we want to call that the infinite,
if we want to call that spirit,
if we want to call that God,
whatever you want to call that thing,
I believe thatthing is for real,
but not knowable.
Infinity's very large.
It's too big, infinity.
To me, infinity isan emotion that we get
in front of the immensity of nature.
We are little teeny things.
We do science. It's great.
I love to do science.
Try to figure out
the quantum properties of gravity,
trying to figure out
what is the shape of the cosmos.
But the reality is
we are, you know, like a little cat
trying to understand quantum mechanics.
The cat isn't going
to understand quantummechanics
because he has the brain it has.
A poor human like me won't understand
everything about the universe
because of the poor brain I have.
The number of neurons in our brain
is comparable to the number of stars
in the galaxies.
It is immense.
Which means that the space
of thinkable thoughts
is a fantastically big number.
It's a one followed by billions of digits.
It's an incredibly large number.
Larger than anything we have encountered.
But, look, our brain,
it's a kilogram of meat
which can be in one configuration
or the other, and that's it.
Uh, you can list all of them in principle.
Once again, there's no Infinity here,
and we have to confront
the fundamental finiteness,
not of nature, but of ourselves.
One, two, three, four, five...
Do you think
that human creativity is infinite?
- ...eight, nine, ten...
- Uh...
...eleven, twelve, thirteen...
I sort of recoil at that suggestion.
I don't know. Oh, good gracious. I...
I don't know.
I don't know that we are infinite.
Twenty-one, twenty-two,
twenty-three. Seven, eight, nine,
ten, eleven, twelve.
Ninety-one, ninety-two, ninety-three,
ninety-four, ninety-five, ninety-six...
For some reason, thinking about
anything about human beings being infinite
doesn't seem right to me.
We feel very bounded, to me.
Bounded in our rationality,
bounded in our creativity.
Yeah, I don't even really know
how to visualize infinity.
One, two, three...
Can I even picture a thousand?
...nine, five, two...
Even that number
is too big for me to properly imagine.
I find that...
it's hard for me to really imagine
numbers bigger than ten.
Is it real or fantasy?
Is it just a game we play
To pass the time while slips away
In front of me
Possibilities to find
As we walk the line
Faster and slower
And over and over
We tumble and we intertwine
Solving the riddle
And little by little we find
It goes on and on
Forever and ever and ever and ever
Forever and ever and ever and ever
Forever and ever and ever and ever
Forever and ever and ever and ever
Love it's all that matters in the end
At the end of forever
Space is staring back at me
It's not easy to explain
Where all just links in the daisy chain
Will you recognize just what you see?
Search and you won't miss the signs
The ones the universe left behind
From the beginning
We're spinning and spinning
And spiraling out of control
It's never-ending
We never know where we will go
It's goes on and on
Forever and ever and ever and ever
Forever and ever and ever and ever
Forever and ever and ever and ever
Forever and ever and ever and ever
Faster and slower
And over and over
We tumble and we intertwine
It's never-ending
We never know what we'll find
It goes on and on
Forever and ever and ever and ever
Forever and ever and ever and ever
Forever and ever and ever and ever
Forever and ever and ever and ever
Love isall that matters in the end
At the end of forever
Forever