0:00

Hugh and Betty and the Nancy's

0:02

and Bill's and Joe's and James will

0:04

find in the study of science a

0:07

richer more rewarding life.

0:11

Welcome to inquiring minds. I'm Andrei

0:13

DeSantis. This is a pod cast that

0:15

explores the space for science and society

0:17

collide. We wanna find out what's true,

0:19

what's left to discover, and why

0:21

it matters.

0:31

It's not often that a book about numbers

0:33

finds a publisher and is released to the

0:35

general public. But listeners of

0:37

this show, I'm sure, will agree that

0:40

math and equations and numbers

0:42

in general, have the ability to

0:44

explain almost anything we can conceive

0:46

of in the universe. Sometimes though,

0:49

it takes a bit of translation. and

0:51

i for one often need a lot of help.

0:53

So I was delighted to talk to Tony Padilla.

0:56

He's a leading theoretical physicist and cosmologist

0:58

at the University of Nottingham. And in

1:00

twenty sixteen, he and his collaborators shared

1:03

the Buchalter cosmology prize for

1:05

their work on the cosmological constant.

1:08

He's also a YouTube star. creating

1:11

videos for numberphile, many

1:13

of which have been viewed millions of times.

1:16

So he seemed like just the right person

1:18

to explain some of these amazing

1:20

numbers to me and

1:22

also to show how

1:24

understanding these numbers gives us a

1:26

glimpse not just of

1:29

how we measure the universe, but ultimately

1:32

the

1:32

nature of reality itself.

1:37

Tony

1:37

Padilla, welcome to inquiring wines.

1:40

Hi,

1:40

lovely to be here.

1:42

So I have to say that I'm kind

1:44

of scared of numbers whenever I have like

1:46

mathematician or a theoretical physicist

1:49

on the show, I feel totally out of my

1:51

element. except that, like,

1:54

there are times when I can if I can kind

1:56

of visualize a number, I feel

1:58

like then I I'm okay. I can understand it.

2:00

But even in the book jacket, you recommend

2:02

that there are some numbers that I really even shouldn't

2:05

try to visualize because it

2:07

might lead my head to

2:09

become a black hole. Black

2:11

hole head. Okay. So so

2:14

let's let's start there. Why

2:17

is it that some numbers can make my

2:19

head explode,

2:20

literally? Well, they they they they yeah.

2:22

They would they would get your head collapsed into a

2:24

black hole. So he's kind of the opposite of his throat,

2:26

actually. Yeah. So it

2:28

it's all to do with the fact. So what what I'm talking

2:31

about there is is that there's a number well,

2:33

very big numbers, but a very big number like

2:35

this number, Graham's number, which was, for

2:38

a long time, you know, the sort of largest

2:40

number ever to have been used in a mathematical

2:43

proof and finite number, of course.

2:45

And it's really big. It's bigger than any of the sort

2:47

of numbers that you wouldn't normally talk about,

2:49

you know, you know, even when you talk about

2:51

big numbers like a billion or a trillion

2:53

or a quad trillion, it's way bigger

2:55

than any of those guys. Right? So

2:57

it it it's just like you wouldn't come

2:59

across it in any sort of everyday everyday

3:02

existence. It just wouldn't happen. It's completely out

3:04

that but it's still number that that

3:06

exists and has been used by mathematicians.

3:09

So I what I thought was a real really nice

3:11

way to sort of picture how big it was was

3:13

Well suppose you actually imagine this number

3:15

in your head. Literally, it's sort

3:17

of digits that that make it up sort

3:19

of one by one written out in your

3:21

head. What would happen? And what would

3:23

happen is that your head would collapse into

3:25

a black hole long before you ever

3:27

got anywhere near seeing the whole

3:29

number. And the reason is

3:32

it's to do with the fact that each

3:34

individual digit in that number carries some

3:37

information about the number. Right? It's just

3:39

like It tells you something. It tells you that that

3:41

digit is in the number. So it gives you some information.

3:44

And

3:44

one of things we know in physics is

3:46

that is

3:46

that information actually weighs it

3:49

actually weighs it has mass, it has

3:51

energy. mean, an intuitive way

3:53

to see that is like in your mobile phone and,

3:55

you know, sort of when you add some information

3:57

to your mobile phone, some data

3:59

or something, the energy levels in the electron

4:02

track will will move and actually

4:04

they move up and and that makes the

4:06

the phone ever so slightly heavier. So

4:08

when you when you upload a photo to your own, you're

4:10

making it It's a slightly heavier. I mean, it's

4:12

imperceptible, of course. But but the point is

4:15

that information weighs. And so

4:17

because there's so much information in

4:19

Graham's number. You're adding an awful

4:21

lot of mass to your head if you're

4:24

trying to picture in your head. And if you add

4:26

a lot of mass to very you know, to a small area,

4:28

then the only thing that can store

4:30

that mass is a black hole. It's

4:33

literally gonna collapse your head into a black

4:35

hole and, well, Good

4:36

luck with that. Yeah. I mean,

4:38

that makes a lot of sense, and I can actually

4:41

visualize that happen. But I won't I won't do it

4:43

too long. Less all that information

4:45

gets into my head. But that sort of makes

4:47

me wonder as you're talking about this

4:50

and as someone who's really interested in the brain,

4:53

we think about information in

4:56

the brain as being stored,

4:58

and that's actually in some ways that

5:00

it's not really true. It's not like there are

5:02

cells that permanently I

5:04

mean, maybe they change a little bit, but it's still a biological

5:07

organ that is like always changing, always

5:09

active. And if you take away its

5:11

biological ability to

5:13

medap apologize, it no longer functions and so

5:16

the information is gone. And so I wondered like,

5:18

what do you think about sort of how our

5:20

brains then add information

5:23

to themselves? Yeah.

5:24

So this is a really interesting question. I mean, I'm

5:27

not a biologist or or in your side. So

5:29

so this is probably gonna come come across a little

5:31

bit additive, but but it certainly it it

5:33

it is interesting. And obviously, I think, you know, the brain

5:36

stores information with leaves, you know, sort

5:38

of sign ups is going off and and so on and

5:40

so forth. And and you're inspiring

5:42

and and and that. And you

5:44

can sort of count how much information that the brain

5:47

could star. But actually, there's a paper by a physicist

5:49

and from Munich, a very steam

5:51

physicist called Gheer de Valle. And

5:53

he sort of speculated that maybe the brain

5:56

could store information in

5:58

a way that was more akin to how a black

5:59

hole stores information. Now if it can do that,

6:02

then it might have a much more powerful

6:04

storage capacity then in the naive

6:06

way that sort of storing it through the way

6:08

the neurons fire, you know, just

6:10

sort of like sort of massive information if

6:13

you like. I don't think we fully know is is

6:15

my understanding. We we don't think we fully know how

6:17

the brain stores information and how

6:19

effective it can be at storing information. And

6:21

as I said, on a gears ideas is actually it

6:23

could be much more effective than we realize and it could

6:25

try to store information a bit more like a black hole

6:27

like he claims a black hole stores information.

6:30

actually don't know There's no consent to somehow

6:32

that our call starts information either. So there's a lot

6:34

of speculation on all sides with this with

6:36

this discussion. So

6:38

and keeping on to the, you know, topic

6:40

of weight and adding weight, you know, one

6:42

of one of the things that when I was reading your book that

6:44

made me laugh out loud was that you start

6:46

your course about gravity with

6:49

a simple sentence that gravity is fake.

6:52

So So, I mean, you know, I kind of

6:54

expect people who are more

6:56

on the new age, you know,

6:58

sort of bent to sort of make comments

7:00

like that. So okay. So tell me

7:01

about it. Why why is gravity an illusion?

7:04

Why is it fake? How can it not exist?

7:06

It is fake. Right? So whatever whatever I say that,

7:08

am I am I grammarously classic, you know.

7:10

It's one of the first things I come out with and the students

7:12

get very upset. It's like, you know, this call is basically

7:15

fake. What are you even doing? but

7:18

it's completely true. And and the reason the reason

7:20

you know it's true is that you could sort of do away

7:23

with gravity. And one

7:24

of things you could do, for example, is a really radical

7:26

experiment you could try out. Now, I'm not suggesting

7:28

any of your listeners try this, but it's something you could

7:30

try. Right? You could climb to the top

7:32

of the Berge Khalifa. I talk about this in the book.

7:35

which is the tallest building in the world in in Dubai.

7:38

And you could get into a blacked out box so you

7:40

have no windows. You can't see outside. And

7:42

then somebody chocks this this box

7:44

of

7:44

the building. Now, what's gonna happen?

7:47

Now, that let's just neglect

7:49

their resistance to keep things simple. Right?

7:52

that box is gonna accelerate downwards

7:54

due to gravity. But so are you?

7:56

Okay. So you're both gonna be going in tandem.

7:59

and you can't see outside

7:59

the box and you don't know that it's gonna

8:02

crash to earth in some horrible event.

8:04

All you can see is that you're inside this box

8:07

Both you and the box and the and the floor

8:09

of the box are accelerating at the same rate. And what

8:11

will happen is you will feel weightless. You

8:13

will actually become weightless. in

8:15

that box. So effectively,

8:18

you've gone away with gravity. So

8:20

in that sense, gravity really is faith.

8:22

And

8:22

this with the sort of insight, thinking about

8:24

experiments like this as well, what led

8:26

Einstein to really realize that gravity wasn't

8:28

a force like the other forces that we talk about,

8:31

like the forces of electromagnetism or

8:33

the nuclear forces to go on deep inside

8:35

atoms. It's somehow different.

8:37

And what he speculated and and showed

8:39

was that was

8:40

that it's actually the coverage here of

8:43

space and time. It's the shape of space

8:45

and time. So it's not a force in the traditional

8:47

sense of the other ones. It really is the shape of

8:49

space time. And the reason it's fake

8:52

is

8:52

that you can zoom in to

8:54

a very small region of space time

8:56

and

8:56

you cannot see that it's bent or

8:58

twisted. You can sort of eliminate that bending

9:00

and twisted by zooming in. It's

9:02

very much the same concept that

9:05

the ancients thought that the earth was flat.

9:07

Why did they think it was flat? It's because

9:09

they were zoomed in. Right? If you step

9:11

back from the Earth and look at it from far away, you can

9:14

see it's very clearly a sphere. Right? Or -- Mhmm.

9:16

-- a sphereoid. But if you

9:18

zoomed in, you might be tricked into thinking it's

9:20

flat. It's

9:21

the same as space time. If you zoom into

9:23

space time, you can be tricked into

9:25

thinking it isn't curved. And if it's not curved,

9:28

and gravity is that curvature, then you can

9:30

sort of see that you can do away with

9:32

gravity. And

9:33

that's exactly what's happening when you

9:36

jump off the bed to califra in a black belt. looks.

9:38

You're eliminating gravity altogether.

9:40

So if you can eliminate it, then

9:42

it's kind of fake. Right? Yeah.

9:43

I mean, it's a really interesting way to think about

9:45

it. You know, I struggle with this idea of of

9:47

gravity bending, spacetime, sort

9:50

of just because it's hard for me to picture,

9:52

but the image of the person in the box

9:54

really gives me something to, like, hang on

9:56

to. But you also have this

9:58

really interesting example of you

10:00

saying Bolt and slowing

10:03

down time and the Twin Paradox. So

10:05

I wonder if you could kind of walk us

10:07

through the logic of that example

10:09

because that too I found really compelling. One

10:12

of the things that Einstein taught us was that

10:15

there

10:15

isn't like a a giant clock in the

10:17

sky that tells everybody this time.

10:19

That thing just doesn't exist. Yeah. Don't don't

10:21

tell my son that because it it's

10:24

an important part. Yeah.

10:27

That's true though. True though. Right.

10:29

So so so there there is no giant clock at this

10:31

guy. There's just what it is is everybody has

10:33

their own clock, and that ticks it better at

10:35

their rates. Right?

10:36

And so if somebody's moving

10:39

relative to somebody else, then their

10:41

clock you know, the the the

10:43

the watch on their wrist will actually tick

10:46

more slowly. Okay? So it's the

10:48

times actually moving more slowly. So

10:50

the one way that you can think people normally

10:52

talk about this in terms of spaceships going

10:54

really, really fast and how their clocks

10:57

are ticking more slowly and all that. But

10:59

I like to talk about it in the context of Usain

11:01

Bolt because he's the fastest man on Earth. Right?

11:03

So so, therefore, let's think about that

11:05

because that's fun. Right? So he was, of course,

11:07

he when he broke the world record, I think it was

11:09

in in Berlin. And

11:13

he

11:13

was running very fast And then everybody

11:15

in the stadium was essentially still

11:17

relative to him. Right? So Ty was

11:19

actually moving more slowly for him.

11:21

this is incredible. So actually so then you

11:23

can ask the question. Has he actually

11:25

sort of jumped forward in time in a way? Is

11:27

at the end of the race? So you could ask the questions,

11:30

entire moving world slowly for him. So at the end of

11:32

the race, he's actually aged

11:35

less than everybody in the stadium.

11:37

So they all get back together. He meets everybody

11:39

in the stadium, but he's actually aged less.

11:42

Now, this isn't just sort of magic

11:44

This isn't just some equations that Einstein

11:46

wrote down. This is We've experimentally tested

11:49

these things, and we've tested them not

11:51

on you saying bolt. No. We've bothered to do that,

11:53

but We've

11:54

sent atomic clocks whitting

11:56

around the earth at very high speeds, and

11:58

we've seen that they've actually

11:59

aged less than their counterbox

12:02

box. on Earth. So it's incredible.

12:04

This is real phenomenon. So when you apply it to you

12:06

saying, boy, you can apply it to you saying, boy, and

12:08

you see that actually, actually aged

12:10

a lit by running so fast, he aged a

12:12

little bit less than everybody watching in the stadium

12:15

that day, all due to the effects of relativity.

12:18

So

12:18

I don't know if you've seen the new Pixar

12:20

movie Buzz Lightyear, but

12:22

that's essentially the plot of the movie that

12:24

this this toy that was the inspiration

12:26

for Toy Story or one of them one of the characters.

12:29

Now, okay, maybe I'm spoiling it for some people,

12:31

but basically gets on a spaceship and

12:34

it goes so fast that when he comes

12:36

back, everyone else is like four years older

12:38

and he's the same age. And he does this over and over

12:40

and over again as he's trying to get people off of this

12:42

planet. And like, reading

12:44

the Usain Bolt example made me realize

12:46

that obviously the the geniuses at Pixar

12:50

were using this idea

12:52

and taking it to its extreme. And

12:54

so, like, if we did take it to the

12:56

extreme, do you think that we as

12:58

humans would ever get to a point where our

13:01

astronauts or cosmonauts would actually

13:03

come back to Earth. White,

13:05

like, significantly observably

13:08

younger than their,

13:10

you know, twins than their counterparts. So

13:12

that's a really really good question. I mean, I I

13:14

think if you're just using the the the effects

13:16

we were talking about in the case of of

13:19

you saying bolt and just going faster

13:21

or or buzz light or or whatever something

13:23

like that. the only thing would be challenging. And

13:25

the the reason is that to have anything there was a sort

13:27

of, you know,

13:27

a really significant amount. And

13:29

the the reason simple is is that it costs

13:31

a lot of energy to accelerate somebody

13:34

up to speeds that

13:36

are kind of close to the speed of light,

13:38

which is where that this kind of effect starts

13:40

to become really meaningful. know, I talk about

13:42

the number the the amount of difference it makes for you saying

13:44

about the speed. He was going and you can calculate

13:47

it. It's a it's a small deviation. But

13:49

if you really wanted to be meaningful where you're coming

13:51

back and you're significantly younger

13:53

than the people that stayed at home on earth,

13:55

then

13:56

you need to be going up a very

13:58

relative speeds closer to speed of the light.

14:00

And to do that, you've got to accelerate

14:02

up to that speed and it's really hard. And the

14:04

reason it's hard to accelerate up to speed

14:06

of light is that you can't go faster So

14:08

there's there's something physically that

14:11

stops you from going faster

14:13

than light. And it starts that process

14:16

of trying to stop you from going faster

14:18

than light, kicks in even

14:20

before you reach light speed. because

14:22

it's the growth of your resistance

14:24

to acceleration, which is you're inertia,

14:27

which is your mass. So your

14:29

mass grows and grows and grows as

14:31

you accelerate up to higher and higher speeds,

14:33

And eventually, it just grows so big that it's just impossible

14:36

to accelerate you. You

14:37

just don't have the energy resources to do it.

14:39

So I think it's unlikely But a way that you

14:41

could possibly achieve it, which think you're seeing in

14:43

the filming to stellate, is by going

14:45

and wondering off close to a black hole if you dare.

14:48

And if you do that, then you get a similar effect,

14:50

but through gravity, even though gravity's

14:52

fake.

14:53

Yeah. So I think you're trying to tell me that Star Wars

14:55

is wrong. I don't

14:58

know. Anyway, it's like

15:00

fake, but they can't get light speed.

15:02

So maybe we should move on to

15:04

before you destroy, like, my love of

15:07

of event science fiction. You

15:09

have talked about though that

15:12

you don't have to be a customer's time travel

15:14

in this way. You talked about a Cabbie driver.

15:16

Is that more along

15:18

the same lines? Or are we talking

15:21

about something, you know, fundamentally

15:23

different? now

15:24

that's exactly the same effect. The Kabi drive

15:26

is going around. And, you know, for every

15:28

every second that that that people have stood

15:30

still relative to the to the curb, is

15:32

aging that little bit less. And of course, you're

15:34

accumulated. This guy's driving through New

15:37

York City for forty,

15:39

fifty years of their life and constantly driving,

15:41

then you can you can can add up. The effect

15:43

can add up. Now it's not gonna add up to to four

15:45

or five years, unfortunately, for the Kabi.

15:47

But

15:47

it might add up to a few microseconds. It's

15:50

just still okay. Well done.

15:59

Speaking more of about sort of

16:02

twins, you also spent

16:04

a long time talking about the existence of

16:06

doppelgangers. And this gets

16:08

to a contemplation of

16:10

just the vastness of the universe

16:13

and these, like, really big numbers. And

16:15

so I I wanted to talk to you a little bit about that

16:17

about sort of like it's sometimes

16:19

hard for me to imagine how we

16:23

define the universe with a

16:25

with a number because it seems to

16:27

change in terms of like, you know,

16:29

what constitutes the universe and

16:31

how we measure it. So tell me a little bit

16:33

about like what is the current thinking about how

16:36

big the universe is, how that

16:38

corresponds to some of these numbers and how we

16:40

can actually visualize it. Yeah.

16:42

So when you when you think about how big the

16:44

universe is, there's kind of two ways that you can

16:46

you can think about it. The first is you can talk

16:48

about the observable universe, which is

16:50

the kind

16:51

of the parts of the universe that we could

16:53

see even in principle because ultimately,

16:56

light has a finite speed. Right? It's not an

16:58

infinite speed. So and nothing to go faster

17:00

than light. And

17:01

the universe is only thirteen point eight

17:03

billion years old. And so there's a

17:05

limit to how far light can have traveled.

17:08

And so that puts us sort of bound on on

17:10

the sort of size of the universe that we could even

17:12

see. That's what

17:13

we call the observable universe. that's

17:15

about ten to the twenty six

17:17

meters, so one with twenty six

17:19

zeros meters. That's how big

17:21

the observable universe is.

17:23

Now you can ask the question, what

17:25

happens when you get to that ten

17:27

to the twenty six meters? There's not there's not a

17:29

wall there. There's not some sort of, you know, wall which

17:31

says this is the end of the universe. Now Now

17:33

turn back. That's that's not the case.

17:35

We

17:35

don't know. Right? We don't know what's

17:38

beyond there. It's We we can't see it.

17:40

And it

17:41

could be that the universe extends much, much

17:43

further than that. It's entirely possible.

17:46

One of the things we we do try to

17:48

measure

17:49

is how bent the universe is.

17:51

So you could imagine that the universe might

17:53

be like a giant ball so

17:55

that you could go all all the way around and come

17:57

back where you started and you could ask, well, how

17:59

big is that

17:59

born? Well,

18:01

you can sort of guess just

18:03

by measuring how bendy it is.

18:05

So

18:05

the less bendy it is, the bigger it is.

18:07

the more bend it is, the smaller it is.

18:09

So

18:10

we plan to measure that bendiness. And

18:12

what that bendiness tells us is that the universe,

18:14

I think it's at least two hundred and fifty times

18:16

larger than that that

18:18

sort of, you know, observable size.

18:20

It's at least two fifty times bigger

18:22

than that. But it may be many, many more

18:24

times bigger. We don't know. two things we don't

18:26

know. And one of the things we can think about,

18:28

there are theories of the early universe,

18:30

for example, that solve interesting cosmological

18:33

problems that

18:34

actually predict that the universe

18:36

could be truly gargantuan, like,

18:39

way beyond the sort of the observable realm.

18:42

You know, perhaps even a Googleplex

18:44

in size, which it it meters, which is

18:46

which is the thing I talked about in the book and and

18:48

what leads me to to speculate about duffle

18:50

peppers. Yeah. So, well, you wanna talk about

18:52

that. But before we talk about that, you

18:55

know, I just have like a a really stupid

18:57

question. Like, why

18:58

can't anything be faster than light? What's

19:00

this special about light that makes it the fastest

19:02

thing in the known universe? Yeah.

19:04

That's a that's that's a good question. So so

19:07

what

19:07

makes light special is not so much that

19:09

it's the fastest thing. It's that

19:11

everybody agrees that

19:13

it sort of goes at that speed, that it goes

19:15

at roughly three hundred millimeters per

19:18

second. that that's the light speed. So the

19:20

speed of light is

19:21

the speed of light. It never changes. Now

19:23

you might say, well, it's not obvious, but no, it's

19:25

not obvious because if you're sort of

19:27

driving down a motorway at

19:29

at seventy miles per hour. Now you're

19:31

driving at seventy miles per hour relative to the

19:33

road, but relative to cars going in

19:35

the opposite direction at seventy miles

19:37

per hour. You're

19:38

driving at hundred and forty miles per hour.

19:40

Right? Mhmm. So the the that's how

19:42

speed seemed to be, velocity seemed

19:44

to work, but not when light is involved.

19:47

Whoever

19:47

is looking at a light so the light from

19:49

your headlamps is moving away from

19:51

you at speed of light, but

19:53

it's also moving away from the guys

19:55

going in the opposite direction at the

19:57

speed of light. it's the same speed.

20:00

And so

20:00

if it's always the same speed, that's what makes

20:02

light special.

20:03

And

20:04

why is that true? And it comes from the fact

20:06

that Light, the speed of light is

20:08

an intrinsic part of the laws of

20:11

of electricity and magnetism. It tells

20:13

us how far an

20:14

electromagnetic wave goes. And I

20:16

started to realize that you can't change those

20:18

laws. Those laws shouldn't depend on whether you're

20:20

moving or not. So the speed of light must

20:22

be the same for everybody. regardless

20:24

of their motion or rather of, you know,

20:27

if if they're just moving at some constant velocity

20:29

relative to one another. So this is

20:31

what's special about it. And a consequence

20:33

of that is that nothing can go faster

20:35

than life. It's just the mathematics then

20:37

leads you to this is a barrier that should not

20:39

be crossed. But

20:40

the key really key thing is not the

20:43

light, it's the fastest speed.

20:44

It's that it's always the same thing.

20:46

But the speed of light is always the

20:48

speed of light. That's what

20:51

Einstein

20:51

has always said that he he rather his

20:54

theory had been called the theory of invariant. This

20:56

in other words, the theory had been varied to speed

20:58

of light, but the speed of light is the same for everybody

21:01

rather

21:01

than the theory of relativity. So,

21:03

yeah,

21:03

that's what's important about light. I

21:05

mean, there's something really comforting about that. And

21:07

so I kinda wanna hold on to that. And as we

21:09

go into this question about big

21:11

the universes. So a Google.

21:13

So that's like one followed by a hundred

21:15

zeros. Right? That's

21:17

right. Yeah. Yeah. Yeah. But then it

21:19

gets even bigger than that if you

21:21

add the suffix plex to it. Right?

21:23

That's right. Then you got a Google Zeros.

21:25

And if you do the Google Duplex, that has

21:27

a Google Play Xeroes. And you have Google

21:29

Triple X, that has a Google Duplex

21:31

zero, and you can go on like that, really, go

21:34

really crazy, written big, very quickly. I

21:36

mean, it seems

21:36

like eventually there it would be fine.

21:38

I you know, like I mean, well, I guess I guess no.

21:40

I guess I guess there would you could never

21:42

stop that. Right? So you would just keep adding

21:45

Google's to whatever

21:47

you have, and it just goes on forever.

21:50

Yeah. You could build up larger and larger

21:52

objects. So as I said, you start off with a Google.

21:54

said that's got a hundred one with a hundred zeros.

21:56

You don't say I've got a Google plex. That's

21:58

a one followed by

21:59

a Google series. And then Google Tube place

22:02

is a one followed by Google plex series. And

22:04

yet, you could iterate that process forever and

22:06

ever. Actually,

22:06

the original definition of the Google

22:08

PlayX wasn't wasn't as clean as that.

22:10

was the person that came up with it who

22:12

was who was a Edward Casnet, who was a

22:15

physicist

22:15

at Columbia University. And

22:17

he was getting his nephew to to help him with

22:19

some of these names and So and

22:22

when he said, what should the Google plex be? I

22:24

want it to be this really big number that's much bigger

22:26

than a Google. And so his his nephews,

22:28

his nine year old, Boy at a time

22:31

called Milson Serato, and he said, well,

22:33

it should be a one followed by zeros

22:36

until you get tired. which is just

22:38

a bit it is a bit precise for a mathematician.

22:40

Right? So it's a so he said, well,

22:42

I'm not in that. So he he went with a with a

22:44

Google Play should be a one funded by a Google

22:47

Okay.

22:47

So now that we know it's a very large number,

22:50

tell us about your theory or your consideration

22:52

about sort of how this relates to the size of

22:54

the of the universe, not the

22:56

observable one, but the entire one.

22:58

So

22:59

one of the themes of the book is to try to bring

23:01

these numbers, which I heard some level

23:03

just numbers. Right? And Googleplex is just a number.

23:06

It's it's it's a very big number. And

23:08

is it beautiful, you know, there's some beautiful message

23:10

in thinking about how you get there. But at the

23:12

same time, I can't even picture it. It comes back

23:14

to like what we did with grains number. How

23:16

can I really imagine it? And the way

23:18

to do that for me is always try to bring it into

23:20

the physical world try to sort of imagine it

23:22

in in our physical realm somehow. And

23:24

so what are the things thought about was, what what

23:26

about a a universe that was a Googleplexer

23:29

crossing in, say, meters,

23:31

whatever, kilometers or miles. It doesn't

23:34

really make a lot difference. What with that

23:36

universe? I mean, the universe could be that big.

23:38

what would its properties be? What would be some

23:40

interesting phenomena you'd find? And one

23:42

of the things you would find is that indeed

23:44

doppelgangers existed. And I

23:46

really mean genuine doppelgangers as

23:48

an exact copies of viewing

23:50

or exact copies of me, exact

23:52

copies of president Biden, you

23:55

know, there's there's there's there's literally exact copies

23:57

of I mean, really exact copies as in

23:59

not just

23:59

lookalikes, but as

24:01

Tim has arranged in exactly the same way

24:04

neurons firing in the same way so they've got

24:06

the same thoughts and really

24:08

exact copies right down to the sort of quantum

24:11

DNA, the same quantum state. So

24:13

truly, I mean, almost indistinguishable from

24:15

it nonsense. And

24:16

that's just because the number is so large

24:18

that the universe would have to repeat

24:20

itself. I mean, that was kind of where I didn't quite get,

24:23

like, why would this be AAA

24:25

necessary consequence? Isn't there, like, an infinite

24:27

number of ways in which these atoms

24:29

can collect themselves?

24:31

Exactly. So so the answer to that

24:33

is no. Right? And and it's because gravity

24:36

stops it being true. and gravity plays

24:38

a really important role there. So you can ask the question,

24:40

right, exactly what you've just done is, if

24:42

we look at sort of the volume and space that that

24:44

you occupy and you can ask how many

24:46

different ways are to arrange all the building

24:49

blocks of that space. Now you can call them at them

24:51

or you can call them, you know, whatever you wanna call

24:53

them. But but but let's say atoms. So the

24:55

building blocks of that space, how

24:57

can I many many different ways can I

24:59

arrange them? The

25:00

answer is not infinite. You might

25:01

think it is, but but it's not gravity prevents

25:04

it being infinite, basically because black

25:06

or because of black holes. Black

25:08

holes present this sort of cutoff

25:10

they they sort of guarantee that there's only

25:13

a finite number of arrangements that you could possibly

25:15

have in a small region of space. And

25:17

so that it's just from the

25:19

fundamental about gravity that

25:21

we learned from this. And so the consequences

25:23

is there are only finite number arrangements for

25:26

the atoms that that make up make up you

25:28

or or make up any sort of

25:31

volume of space the same size.

25:33

And so as you move across space,

25:35

you just each point, you're gonna sample one

25:37

of them. So so you take the volume of space you're

25:39

occupying and the arrangement of atoms are

25:42

a very intro like and that's it. That's

25:44

great. then you look at the space next to you

25:46

and that's different. It's a different arrangement.

25:48

Fine. When you go to the one next to you, you

25:51

know, two along that it's different again. and then

25:53

you go all the way across this Google Playa

25:55

and Universe.

25:56

And the

25:57

number of arrangements that you could have in principle

25:59

is less than a number of samplings that you

26:01

make and it's actually way less.

26:04

So

26:04

it's inevitable you get repetitions and actually

26:06

it's it's it's essentially inevitable you get repetitions

26:08

of even unlikely things like like

26:10

you or me or

26:11

president Biden, so they might be quite

26:14

rare arrangements compared to say empty

26:16

space. But nevertheless, there's some

26:18

probability of them happening and the

26:20

size of the universe is so much

26:22

bigger than the number of arrangements that's,

26:25

you know, you just overwhelm the odds of emphatically.

26:27

So you're gonna not just gonna get double count, but you're

26:29

gonna get many double counts. Okay.

26:31

Before we leave these big numbers and

26:33

and go into the the tiny ones. I

26:35

just have one last question. Do

26:37

we know the universe as a ball?

26:39

Or, like, I mean, I can imagine it could be

26:42

an infinite variety of shapes? Or

26:44

is there some physical reason why

26:47

we would think that that's the most likely

26:49

case? because when you talk about the bendiness,

26:52

I can think, well, that's just

26:52

maybe a curve. Like, I mean, maybe it's bumpy.

26:55

You know? And maybe we're just seeing this one

26:57

little part of it. Yeah. No. No. No. So

26:59

no. We don't know that. Right? And it's definitely gonna be

27:01

bumpy on some sort of local, you know. They're definitely

27:03

local bumps that we the sun creates a

27:05

a local bump in our solar system in the shape

27:07

of of it. So it's definitely got a little local

27:10

books. But what you what we're talking about is

27:12

on on very, very large scales. You know,

27:14

when we look at the when we really step back from the

27:16

universe, does it look approximately like a ball?

27:19

because we expect there's something called the the

27:21

sort of cosmological principle, which says

27:23

that no point is special in the universe.

27:25

And if that's the case, then you can argue that it's it

27:27

could be a ball, but it doesn't have to be.

27:29

It could also be just like a a flat

27:31

plane, like sort of an analog a three-dimensional

27:33

analog of it. of a flat piece of paper.

27:36

So something like rather than a ball, it's like flat.

27:38

Or it could even be saddle shapes. So it's shaped

27:41

like a like a horse's saddle. So

27:43

these are the three possibilities that people

27:45

normally talk about most common ones.

27:47

We don't know which of those it is.

27:50

Right? We know that it's if it it could

27:52

be a ball, but if it is a ball, it's a very large

27:54

ball. But

27:55

it's hard to tell the difference between a

27:57

very large ball and something which is totally

27:59

a plane. Right?

28:01

They you know, unless you zoom right out,

28:03

hard to tell the difference, and we we haven't

28:05

been able to tell the difference. We we

28:07

don't know the answer to that. Instinctively, I

28:09

like the idea that it's a ball because that's finite.

28:12

And

28:12

I just like the idea that universe is

28:14

finite. But

28:15

that's pure protease. That's that's

28:17

pure anti anti infinite prejudice,

28:19

which is not really acceptable. But but

28:21

it's not like a hotdog. It's got to be one

28:23

of these three things. like we know, it's not just

28:25

like a cylinder. Well, that would break

28:27

the cosmological principle, so it wouldn't look the same

28:29

everywhere. But Right. Right. Right.

28:32

you can imagine it's certainly a torus which is

28:34

like a doughnut. Okay. Alright.

28:36

That's a genuine possibility and a real, really

28:39

interesting one. So

28:39

let's talk now about, like, the tiny

28:42

numbers. I I mean, I understand the

28:44

mind fascination with thinking about numbers that

28:46

are bigger, bigger, bigger, and bigger, But

28:48

when you get smaller and smaller and smaller and smaller, you also come

28:50

up to the same problem that you can, like,

28:52

you can chisel away at a number infinitely

28:55

until it it it's like just, you know,

28:57

gets so so so so

28:59

so small. But in terms of,

29:01

like, the little numbers, Which

29:04

one is your favorite? And what does it

29:06

tell us?

29:07

So it's it's my favorite is the one that's dominated

29:10

my my whole career, which is which is ten

29:12

to the minus one hundred and twenty see.

29:14

You know, which is zero point and then you've got

29:16

a hundred and nineteen zeros and then

29:18

a one. Right?

29:19

It's a really, really small number. And somehow,

29:21

it's it's it's a measure of how unlikely

29:24

our universe is.

29:26

So so there's this crazy problem

29:28

in in physics with nobody really well,

29:30

outside of physics. We talk about we don't

29:32

talk about it that much because it's really embarrassing. But

29:34

within physics is one of the biggest problems in theoretical

29:37

physics today, and that's it's called the cosmological

29:39

constant problem. And what it says is is

29:41

you can ask, how much does the universe

29:44

weigh? Right?

29:44

How much does it does it weigh?

29:47

And okay. Well, what do I really mean by that?

29:49

Well, let's let's remove Take out all the stars

29:51

and planets. Let's take it and all the people

29:53

and all the aliens and all the little green men. Take

29:56

out all that stuff. And

29:57

so you've just got empty space left over.

30:00

you say, well, how much does that weigh?

30:02

And

30:03

the answer you

30:04

would think is, well, nothing. Right? It's empty

30:06

space. But

30:07

that's not true. And

30:09

the reason is because of quantum mechanics. quantum

30:11

mechanics tells us that empty space is not really

30:14

a dull and uninteresting place that you

30:16

would imagine. It's actually a sort of

30:18

seething breath of of virtual

30:20

particles popping in and out of existence.

30:23

And this this sort of bubbling and

30:25

struggling answer is really actually

30:27

causes the universe to sort of to

30:29

weigh a bit. And of course,

30:32

that weight will in turn cause the universe

30:34

to bend. and

30:35

we can use our best

30:37

theories that we have that describe

30:39

other

30:39

areas of physics amazingly well,

30:42

and we could try to calculate how

30:44

much weight this vacuum

30:46

of space has that the the

30:48

empty space of our universe, how much weight

30:50

does it have? And the answer we get is

30:52

a huge number. And then we can say,

30:55

okay. So that's what our theory tells

30:57

us. Now let's actually try to measure how much

30:59

it's bending space. and we can

31:01

measure that. And it comes out as a really,

31:03

really small number. And the ratio of the

31:05

two, the the small and the big, is ten to the

31:07

minus a hundred and twenty. it's a horrendously

31:10

bad estimate. The one that our theoretical

31:12

estimate is horrendous compared to the actual

31:15

observed value. And so

31:17

It's a great mystery. Why are we

31:19

getting this crazy big answer? And

31:22

the universe is actually showing us this really

31:24

tiny. observed

31:24

answer. And

31:26

so those two things don't seem to line up at

31:29

all. It's a huge mystery. And

31:31

as I said, it's considered one of the biggest

31:33

problems in in their escrow visits today.

31:35

Even

31:35

in your book, you highlight the fact that

31:37

in some ways, a lot of us find

31:40

it despiring to think

31:42

that we live in this vast, vast

31:44

universe and we're you know, our lives

31:47

are, you know, essentially meaningless blips.

31:49

But in in the book, like, right at point

31:51

where you go from the large numbers of the little numbers,

31:53

you warn us that it's actually the little numbers

31:56

that are gonna be even more frightening

31:59

in terms of our existential crisis.

32:01

And I is that and I kinda get what

32:03

you're saying with here now, like, in this

32:05

in the sense, it's like, this so unlikely that the universe

32:07

would have existed to to begin with. So

32:10

how do you reconcile that

32:12

with the fact that the universe does exist,

32:15

at least so we think it does? And

32:18

then there's like this whole certainty

32:21

of if it's as big as we think it is or as

32:23

you think it is, there's dope you know, everything's

32:25

like repeated. It's like how do you reconcile

32:27

that paradox?

32:28

Yeah.

32:29

So so, I mean, it it is a great mystery.

32:31

So so why why the universe doesn't

32:34

weigh anything like as much as we we

32:36

expect. It's it's a good job. It

32:38

doesn't. Because if it did, it

32:40

would have bent itself into oblivion

32:42

within a moment of creation. I literally

32:44

universe would have been born and it had just gone straight

32:47

away because it was just crushing itself

32:49

under its own weight. So it's a huge relief

32:51

that it it isn't as heavy

32:53

as our calculations predicted should be.

32:55

But maybe in there lies the answer to the

32:57

question. Right?

32:58

Maybe

32:59

the reason it's actually much

33:02

lighter than we thought which allows much larger

33:04

universe. Maybe

33:05

the reason is precisely because

33:07

we exist And this this comes down

33:09

to something called the anthropic principle, which says,

33:11

imagine a multiverse, imagine a

33:13

whole great many universes They

33:16

have huge numbers of different weights,

33:19

if you like. Some are very heavy like our calculations

33:21

predict. The vast majority will

33:23

be very heavy like our calculations predict.

33:25

And that's why our calculations predict them.

33:27

But occasionally, you can get really cute cancellations.

33:31

And when those cute cancellations

33:33

kick in.

33:34

They make the universe light. And when they make

33:36

the universe light, they give it the chance to

33:38

grow and get big. The minute they

33:40

do that, they have a chance for stars

33:42

and planets to form, and

33:44

then little green man and

33:46

eventually humans can form around

33:48

on those planets and

33:49

that's why we're here to measure it. So maybe our existence

33:51

and existence of complex life is very much linked

33:54

to the fact that we measure a very

33:56

very light

33:57

the universe compares a very heavy one.

33:59

So

33:59

now listeners, you know why

34:02

Tony Padilla's book is called Fantastic Numbers

34:05

and where to find them. A cosmic quest from

34:08

zero to infinity available now

34:10

at your favorite book seller. Twenty fifth year, thank

34:12

you so much for being on inquiring minds.

34:14

Thank

34:14

you. It's being a lot fun.

34:16

So

34:18

that's it for another episode. Thanks for

34:20

listening. And if

34:21

you wanna hear more, please subscribe.

34:23

If you'd like to get an ad free version of the show,

34:26

consider supporting us at patreon dot

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com slash inquiring lines. I want

34:30

to especially thank David Noelle Hering

34:32

Chang, Sean Johnson, Jordan Miller,

34:34

Kai Ryhala, Michael Galgul, Eric

34:36

Clark, Yuchy Lynn, Clark Lindgren, Joel,

34:39

Stefan Meyer, Eyewall, Dale Amaster, and

34:41

Charles Blyle. Enquiring Minds produced

34:43

by Adam Isaac. This episode was

34:45

edited by Daniel Link. And I'm your

34:47

host, Andreyvus Contus. See you next

34:49

time.