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Studios. Wait,

1:00

you're listening. OK. All

1:02

right. OK. All

1:05

right. You're listening

1:07

to Radiolab. Radiolab.

1:09

From WNYC. The

1:12

C. The C. Yeah. Hey.

1:17

Hello. I have to find

1:19

your window. Hi. Are you tired? No. No,

1:21

I'm all right. Oh. How are you? Oh, good. I'm

1:24

good. I'm excited for this

1:26

random little thing. Hey, I'm Luttev Nasser.

1:29

I'm Lula Miller. This is Radiolab. OK.

1:31

Well, a mystery guest is going to appear

1:33

momentarily. Oh,

1:37

we see you. Hey. I can

1:39

hear you both. Perfect. Good

1:41

work. Hi. Well, OK.

1:43

So Karim Lhatev. Hi.

1:45

It's very nice to meet you. My pleasure.

1:47

Where are you? I'm in Alexandria, outside

1:50

of DC. OK. So I guess

1:52

the best way to set you up is

1:55

that Karim is here because he

1:57

has broken. one

2:00

of the most forbidden

2:02

rules of the

2:04

universe. Are you a cannibal? Is that what I'm

2:06

about to learn? I

2:09

haven't broken anything. It's the question of- You haven't

2:11

yet. No, no, no, well, that's the question. It's

2:13

the question of whether to break it and how

2:15

to break it. What are the consequences

2:17

of breaking it? Could you break it? Should I? Should

2:20

I try to? Should I? Whoa. You

2:23

seem like you're on a precipice. Brother. Okay,

2:27

so what is this rule

2:29

that- Yeah, what's the rule? In

2:32

mathematics, you're allowed to do

2:34

everything for the most part.

2:36

You can multiply, you can divide, but

2:38

as you may recall from school, there's

2:41

one thing in mathematics you're not allowed

2:43

to do. Do you remember?

2:46

It's dividing by zero? Dividing by zero. We

2:49

have this entire structure of mathematics

2:51

that is incredibly useful. It's incredibly

2:53

powerful, but it all

2:56

kind of hinges upon our

2:58

agreeing to not go

3:01

through this one door that has on

3:03

it. There is

3:05

a sign on this door that says,

3:08

division by zero, don't open this door because what's on

3:10

the other side of this door is- To

3:13

infinity. All sorts of craziness. And

3:15

beyond. An infinite loop. To see

3:17

a world in the grain of

3:19

sand. Where everything is the same.

3:21

Don't divide by zero. When you

3:23

make the two into one, and

3:25

when you make the inner like

3:27

the outer, then

3:33

you will enter the kingdom. It's

3:37

like this sign you hang on the elevator

3:39

that's not working, you know? Like it's like

3:41

out of order. Like please do not go

3:43

through here. Well, here's the thing though. It

3:45

isn't that the elevator is out of order.

3:47

It's that the elevator goes to a dimension

3:50

that is so problematic to our

3:52

way of thinking in this dimension that

3:55

as long as you agree to not

3:57

go into that kind of elevator shaft

3:59

wormhole. We're good. You can have

4:01

your airplanes. You can have your computers. So

4:04

today we've got a story about a

4:06

paper that Kareem Ani wrote almost

4:09

20 years ago about

4:11

dividing by zero. I

4:13

happened to cross it about 10 years ago,

4:15

and it really tickled something

4:17

in me. Over the years, I would think

4:19

about it. I'd wonder whatever happened

4:21

to this guy who wanted to divide by

4:24

zero. I'd wonder if there

4:26

were consequences for math. I'd wonder if

4:28

there were real consequences for reality. For

4:30

my reality, for his reality, I didn't

4:32

know. But I thought

4:34

that as we ourselves are

4:37

rounding the clock of a calendar year,

4:39

passing through zero to start anew, I

4:42

thought now might be a nice time to call him up

4:45

and try to understand. So,

4:47

my friends, leave

4:50

your calculators at the door, because

4:52

we are going to try to enter a new

4:54

kind of math. Here we

4:57

go. Well, I think what a

4:59

mathmatician would say is, by all means. Are

5:01

you a mathmatician? Yeah, sorry. We should say who

5:03

you are, by the way. Who are you, Kareem?

5:05

What do you do? What do you do? I

5:09

am the founder of CitizenMath, and what we do is

5:12

we write lessons for

5:14

middle and high school classrooms around real

5:16

issues. So, students are using mathematics to

5:18

discuss, great, should the federal government increase

5:20

the minimum wage? Or,

5:22

why do airlines oversell their flights? Using

5:24

mathematics is a tool for discussing and

5:26

analyzing the world around us. Love it.

5:28

But coming back to this

5:31

idea of division by zero. Yeah,

5:33

okay. So, maybe we just

5:35

start with, why can't you divide

5:37

by zero? Like, why is that

5:39

such a hard and fast rule? So,

5:42

one reason is because it violates

5:44

a mathematical principle that every operation

5:46

needs to be undoable. Anything you

5:48

do, you need to be able

5:50

to undo. Okay.

5:54

Let's say you start with ten, and

5:56

you divide by five, and so now you

5:58

are at two. Now you need

6:00

to be able to get back to 10 though. And so

6:02

you can go from 2 and multiply it by 5 to

6:04

get back to 10. 10

6:06

divided by 5 gives you to 2. 2

6:09

times 5 gets you back to 10. But if

6:11

you now try that with 0. 10

6:14

divided by 0 is some

6:17

number. Well, to go backwards, now

6:19

that's some number times 0. How

6:21

can that get you back to 10? So it

6:23

violates. Because 0 times

6:25

anything is 0. It's kind of sucked into the black

6:28

hole of 0-ness. So

6:31

that's the it violates this

6:33

custom, let's say, or law. Because there'd be no

6:35

thing you can multiply by 0 to get to

6:37

the number 10. Exactly. Once you divide by 0.

6:40

So mathematicians created this

6:43

rule, this kind of barricaded

6:45

door, that basically says, do not

6:48

try to divide by 0 because

6:50

the answer is undefined. There

6:53

is no answer. You can't do

6:55

it. However, there have

6:57

been people who have gone

7:00

through that door. Hi there. Hi, Steve.

7:03

Lulu, I don't think we've ever done this together.

7:05

I know. Isn't that wild? I have never actually

7:07

gotten to meet you. This is so nice. Oh,

7:09

nice. Yeah, hi. OK. This

7:12

is Steve. Steve Strogatz. And I'm

7:14

a mathematician and a math professor

7:16

at Cornell University. And Steve has

7:18

not walked through the door of dividing by 0.

7:21

But he says that these sorts

7:23

of rules, these sorts of

7:25

barricades, in math, it's always

7:28

been important to break them. Exactly.

7:30

That's actually some of the most fruitful parts

7:32

of math, that when

7:35

you try to do something that seems

7:37

impossible, it often leads to the creation

7:39

of whole new universes. So for

7:42

example, Steve was like, OK, let's think

7:44

about square roots. So if you take

7:46

a number, like the number 3. OK,

7:48

so 3 times 3, that'd

7:50

be in the jargon 3 squared. 3

7:53

times 3, 3 squared is 9. So

7:56

the undoing of that is that the square root of

7:58

9 is 3. But now,

8:00

let's say you wanted to take the square root

8:02

of negative 9. You know, your first thought would

8:05

be negative 3 maybe is the square root of

8:07

negative 9, but it doesn't work. If you do

8:09

negative 3 times negative 3, you

8:12

get positive 9, not negative 9. Because

8:14

in math, and we're not going to go into Y,

8:16

if you multiply two negative numbers, you get a

8:18

boom, positive number. So you

8:20

can't do it. You can't take the square root of

8:22

negative 9. There is no number that will

8:24

work. So a long, long time ago,

8:26

mathematicians were like, okay, there is a

8:29

rule, no square roots of negative numbers.

8:31

But then, in like the late

8:33

1500s, a bunch of new

8:36

rambunctious, upcoming, disobedient mathematicians said,

8:38

well, what if we just

8:40

broke that rule? And

8:43

to make the math work,

8:45

we just invented a whole

8:47

universe of new numbers. That is

8:50

so bizarre that mathematicians called these

8:52

imaginary numbers. Numbers that are not

8:54

technically negative, and they're not technically positive.

8:56

They were sometimes called fictitious numbers. But

8:58

they allow the math to work in

9:00

such a way that you can start doing

9:02

square roots of negative numbers. Because

9:04

you just wish it to be

9:07

so. Just invent some new numbers? Yeah,

9:09

it's invention. Exactly. It's invention in the

9:11

artistic sense. You can invent something that

9:14

didn't previously exist. But was anyone

9:16

like, no, we have a

9:18

rule. You can't take a

9:20

square root of a negative number. Yes, absolutely.

9:22

It's like anything else that human beings

9:24

do. They're always reactionaries. There

9:27

are always people who say, you're muddying the

9:29

waters. You're messing up the pristine and beautiful

9:31

world of math with your ugly

9:33

ideas. Because these ideas have a

9:36

lot at stake intellectually, and there's

9:38

always resistance. But that's

9:40

where the breakthroughs happen. You take something that

9:42

earlier generations say was impossible, and you say,

9:44

what if? And then you try it,

9:46

and you figure out a way to do it. That's

9:49

where the progress happens. What

9:52

does an imaginary number give us?

9:56

That gives us the modern world. Like concrete stuff. I'm

9:58

going to tell you. OK. I

10:00

mean, imaginary numbers – okay,

10:02

so if we fast forward to the 20th century, this is

10:05

not why imaginary numbers are invented. They're invented

10:07

much earlier than that. But in the 20th

10:09

century, when the theory of

10:11

the atom starts to be worked out, we

10:14

learn how to describe what's

10:17

going on with hydrogen atoms

10:19

and helium and how light

10:21

works. In other words, we

10:23

invent – we, the collective

10:25

of scientists in the 1920s, invent quantum mechanics.

10:30

So it's our most accurate physical theory there

10:32

is. It gives us today

10:34

everything. It gives us what we're doing right

10:36

now, talking over the internet. It

10:38

gives us lasers. It gives us transistors,

10:41

chips. Everything in the modern

10:43

world has an underpinning

10:46

in quantum theory and the electronic

10:48

revolution that it made possible. The

10:51

math of quantum theory is built on

10:53

imaginary numbers. You can't

10:55

do quantum mechanics without comfort with

10:58

imaginary numbers. And it's crazy in

11:00

that what was thought to be imaginary a few

11:04

decades or really more like a few

11:06

centuries later turns out to be the

11:08

mathematics of reality. And

11:14

to Steve, this is sort of the beauty

11:17

and the artistry of math.

11:19

I mean that in math, we have

11:21

creative freedom. We can

11:23

do anything we want as

11:25

long as it's logical. Mathematics

11:28

in many ways is a

11:31

chronicle of human's understanding of

11:33

reality and logic, kind

11:36

of a chronicle of how we

11:38

think. Like, it began with early humans

11:40

coming up with the idea of what we

11:42

call natural numbers – one, two, three, and

11:44

so on. Then the Sumerians

11:46

in Mesopotamia and the Mayans each

11:49

independently came up with the idea

11:51

of zero, which blows

11:53

its way around the globe. And then

11:55

a few thousand years later, the third

11:57

century in China, negative numbers show up.

12:00

up and they too spread across the

12:02

world and math gets more and more

12:04

complicated. And so we start

12:06

to come up with rules and

12:09

then we try to break those

12:11

rules. And in the wake of

12:13

that breakage, we often invent new

12:15

numbers like imaginary numbers or rational

12:17

numbers or real numbers or complex

12:19

numbers. We come

12:21

up with all these different tools

12:23

that we've invented by pushing at

12:25

the rules, pushing at the boundaries

12:27

of math that then help

12:29

us to better understand the

12:31

world around us. But

12:34

this is where division by zero is different, categorically

12:38

different, because it's so

12:40

beyond the like

12:43

it leads to these results that

12:46

would undermine all of mathematics. It

12:48

would break math as we know it.

12:52

And this is where, for me, this

12:55

becomes actually quite existential.

13:02

When we come back, we are

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What if? Radio

14:58

Lab. We are back with Kareem and...

15:00

Dividing by zero. All

15:04

right, friends. It is time

15:06

now to break the

15:08

rule. We are going to

15:10

divide by zero. We are

15:12

going to grab our calculators and

15:15

watch what happens when

15:17

we do. If divide by zero, does

15:19

it catch fire? Because there are actually all

15:21

these videos on YouTube. Try

15:23

to divide by zero is awesome

15:25

and dangerous. We're sweet. Where we

15:27

show the machine dividing by zero.

15:29

Nerdy men. We're going to watch

15:31

as this calculator tries to divide

15:33

by zero. We'll take these old

15:36

mechanical calculators. I will just input

15:38

a... Punch in some numbers. Dividend

15:40

of one, two, three. Divided by

15:43

zero, we hit equals. Here we go. And

15:49

what happens is the numbers

15:51

on these calculators just

15:53

keep rolling over and over

15:57

and over. and

16:01

over. It will never stop and

16:05

I guess it keeps up to eventually

16:07

end with catch fire. Like the mechanisms

16:09

driving that calculator just gets stuck. In

16:12

an infinite loop. And

16:17

it is right here, for

16:20

Kareem. Where this becomes actually

16:22

quite existential.

16:25

Because he explains to understand what is

16:27

driving that looping. You have to think

16:30

about the math going on. He said,

16:32

you know, take for example the number 10.

16:35

If you take 10 and divide it by 10 you get 1. 10

16:37

divided by 5 is 2. 10 divided by half is 20. The

16:40

smaller the number on the bottom, the number

16:42

that you are dividing by, the

16:44

larger the result. And so by

16:46

that reasoning. If you divide

16:48

by zero, the smallest nothingness

16:51

number we can conceive of, then

16:54

your answer would be infinity.

16:59

Why isn't it infinity? Infinity feels like a

17:01

great answer. Because infinity in mathematics isn't

17:03

actually a number. It's

17:05

a direction. It's a direction that

17:07

we can move towards.

17:11

But it isn't a destination that we can get to.

17:15

And the reason is because

17:17

if you allow for

17:19

infinity, then you get really weird

17:21

results. For instance, infinity

17:24

plus zero is infinity.

17:27

Infinity plus 1 is infinity. Infinity

17:31

plus 2 is infinity. Infinity plus

17:33

3 is infinity. And what

17:35

that would suggest is zero is

17:37

equal to 1, is equal to 2, is equal to 3,

17:40

is equal to 4. And

17:43

that would break math as we

17:45

know it. Again, Steve Strogatz. Because then

17:47

as your friend says, all numbers

17:49

would become the same number. Which, you

17:52

know, for math, the whole vast

17:54

interconnected web of it would be a

17:56

problem. The world of fluid dynamics,

17:58

calculus, geometry, physics, all sorts of things. But all

18:00

this stuff depends on numbers

18:02

being individual, discrete things.

18:05

But if you allow

18:07

for division by zero, that all

18:09

goes away. And you get into

18:11

all of these strange consequences like

18:13

1 equaling zero, equaling 2, equaling

18:15

infinity, equaling 4. And

18:17

so in order to protect math and

18:20

all the things we use it for, like

18:22

making computers and planes and

18:24

all modern technology, mathematicians said

18:26

that when you try to divide by

18:29

zero, the answer is undefined.

18:34

It's undefined. There's no

18:36

sensible definition. And that's why they

18:39

put up that barricaded door. Because what's

18:41

beyond the door is it

18:43

just seems impossible. It

18:45

seems very difficult to get our heads around.

18:48

Because effectively what we're saying is everything

18:50

is one thing. Now

18:54

Karim says, when I first started thinking about

18:57

this 10 years ago or however long that it

18:59

was, it was something fun to think about. It

19:01

was something fun to write a grad school paper

19:03

about. But he says

19:05

more recently he's had this feeling

19:07

that's grown and grown of this

19:10

isn't complete. There's something

19:12

else here. Now,

19:15

maybe this is something you have felt at

19:18

some point in your life. Maybe

19:20

you're even feeling it right now that the

19:22

daily stuff of it isn't

19:25

all there is. But there's

19:27

something else out

19:29

there. And for

19:31

Karim, he's like, look, I'm not religious. He's

19:33

devoted basically his whole life to math. And

19:36

mathematics is kind of a representative of one

19:38

way of thinking about not just the world,

19:40

but one way of thinking about reality. And

19:43

so to Karim, it perplexes him. It sort

19:45

of tugs at him to see

19:47

math itself saying, when you

19:49

actually follow out the operation

19:52

of dividing by zero, you

19:54

end up in a completely different. Realm,

19:57

where one equals two equals.

20:00

3 equals infinity. That all of these

20:02

numbers are one and the same. That

20:05

everything is effectively one thing. Everything

20:07

is equal to everything else. And

20:09

this world of division, I don't mean

20:12

political division, but that too. This

20:14

world of duality,

20:17

of differences, of things being discrete

20:20

from one another. That

20:22

all goes away. And

20:25

Kareem can't help but to notice that's

20:27

the sort of stuff you hear from. Jesus said

20:29

to them, Jesus, when

20:31

you make the two into one,

20:33

and Buddha, or people who follow

20:36

Taoism, or people who have

20:38

done intense meditation, or intense holy

20:40

synogenics. Often times those people come

20:42

back, and the thing that they say

20:44

is, I felt like I was one

20:46

with everything. So

20:50

you see in these religious texts, you see literally

20:52

the collapse of the integer system. I'm

20:55

seeing math being a way of

20:57

thinking about reality, and thinking about the nature of

20:59

nature. And to Kareem,

21:01

because the math itself leads to

21:03

this undefined place where

21:06

numbers work really differently. Where all of

21:08

these numbers are one and the same. To

21:10

him? That suggests that

21:12

there is something else. And

21:17

I'm not saying that's God, or whatever it

21:19

is, it's just there's something else here.

21:22

And I can't, by death and fiction, I

21:25

cannot on this side of the door, articulate

21:29

what that reality would look like.

21:32

But... I'm middle

21:34

aged. Now that Kareem

21:36

is rolling into his mid 40s. I

21:39

don't have children, a spouse. He

21:41

finds himself unable to stop wondering

21:43

about what that something else could really look like.

21:45

I look at my life and I think, well,

21:49

after 44 years you're still not content

21:51

with this. That must be a sign. That

21:55

either you're doomed to be discontented,

21:59

or you're not. That's

22:01

a sign that like you're not going to find it here.

22:05

You need to go through the door because honestly,

22:08

what's your alternative? But how do

22:10

you actually do it? Like

22:12

what? How do you, I don't guess

22:14

how you, how do you actually divide by zero

22:16

and go through the door? I don't know.

22:18

Whatever that means. I have no idea what it

22:21

would mean practically to divide by zero. But

22:23

he says he does know it would

22:25

have to start with some pretty major

22:27

changes. Like he would definitely need to

22:29

quit his job. He would need to

22:31

leave behind his house in the DC

22:33

burbs. Look, I'm Arab. I feel this weird

22:36

like attraction to the

22:38

desert. Like

22:40

I would probably go take camping gear

22:42

and go find a desert and sit in the desert. And

22:45

then, well, he's

22:47

not entirely sure. All

22:49

he knows is that he would need to

22:51

connect with that mathy part of his brain

22:53

he has been using for decades, thinking

22:56

about numbers as these discrete and

22:59

different things. And

23:01

then try to turn

23:04

it up. That is the thing that

23:06

I will need to put down. And

23:08

then maybe if he

23:11

listened really close, he

23:13

could begin to hear or feel

23:15

the something else

23:18

behind all of this. Now,

23:22

okay, so what's my personal

23:24

reaction to that? By the

23:27

way, there's a guy named Steve Strogab. Yeah,

23:29

sure. We talked to him about you. We were

23:31

behind your back and we talked to him about

23:33

you. And we

23:35

told him about how you were

23:37

thinking about trying to access

23:40

a world where there are no

23:42

differences in numbers. I

23:45

would say you can do that. If you want

23:47

to do that, you can do it. You

23:49

can make a universe in your mind where all numbers are

23:51

the same number. Let me describe

23:54

that universe. There's

23:56

a universe I'm going to call zero world. Welcome

24:00

to Zero World. Okay.

24:04

Where in fact there's only one number. Zero.

24:07

And here are the properties of

24:09

the mathematical Zero World. Zero plus

24:12

zero. Equals zero. And

24:15

that's true no matter how many times you add

24:17

zero. You can't get any new numbers in this

24:20

world. Because there are no additional numbers. There's only

24:22

zero. Zero plus zero

24:25

plus zero plus zero. As

24:27

far as the eye can see. Yes. And

24:30

that's it. That's

24:32

your universe. It's the universe of zero. All

24:35

numbers are the same because they're all zero.

24:38

And are you happy now? He

24:42

keeps going. He

24:44

says to me. That's like such a

24:46

solipsistic, aesthetic little universe. That

24:49

is the ultimate in navel gazing.

24:51

That does nothing for anybody. But

24:53

it's self-consistent. You can live in that

24:55

universe if you want to pretend there's

24:57

nothing but zero. Oh, okay. And

25:00

let me respond to that then. Yeah. Because

25:02

Steven Strogatz is a really smart dude. But

25:05

the question, that first question of are you

25:07

happy now? I would say well, Steven,

25:11

if you live in one world or where every

25:13

number is distinct from

25:15

one another, like if you're happy in that

25:17

world, great. I'm not

25:19

because I have this question in the back

25:21

of my mind. This question of what

25:25

is actually on the other side of that door? To

25:27

me, it is zero world and I

25:29

just find it incredibly stultifying. It's

25:32

a very impoverished little self-contained

25:34

logical place. Stultifying

25:36

but mathematically sound? I

25:38

think it is. It's defensible. You can have

25:41

it. There's nothing wrong with it. It's just

25:43

as minimal as a thing can be. It

25:46

has no potential for anything beyond itself.

25:48

But it's just a fine little solipsist looking

25:51

at its own belly button. And

25:53

I... Your belly button inside your

25:55

belly button is everyone and everything. It's

25:57

like... It's like... I don't know. I'm just trying to...

26:00

I'm going to send him because he's not here. I don't know if I want to

26:02

go there, but ... You can try. I'm not

26:04

buying it. No, but it's like division. He

26:06

kept saying like division goes away, political division,

26:08

spiritual division, duality goes away. Right.

26:11

Let me try to make the case for it. The

26:14

case for it, I guess, is

26:16

this is a noble impulse to see

26:18

the unity. It's also a productive impulse.

26:21

Scientifically, looking for unified

26:23

theories has

26:25

historically been the way to great

26:27

progress in physics. To

26:29

recognize that electricity and magnetism are

26:32

actually two sides of the same

26:34

coin that we now call electromagnetism,

26:36

that was a great invention, a

26:39

great breakthrough of the middle 1800s

26:41

that gave us modern things like

26:43

wireless and telegraphs

26:45

and telephone, and then

26:48

Einstein unifying space and time, matter

26:50

and energy. This is

26:52

a trend. We've been doing this unification

26:54

program in physics for the past 150 years, and

26:56

it's very, very

26:58

successful, and it reveals these underlying

27:02

deep commonalities among things

27:04

that are superficially different. The

27:06

idea that there's great insight to

27:09

be had by realizing that things that

27:11

look different are actually deep down the

27:13

same, that's a good move. That is

27:15

historically a very good move much of

27:17

the time, but there's

27:20

also the move that, along with

27:22

the unifying impulse, you also have

27:24

to have the diversifying impulse. You

27:26

have to realize that not all

27:28

things are the same, that there

27:30

is great abundance in the world,

27:32

all kinds of diversity, whether of

27:34

people or biological species or

27:36

phenomena. There

27:39

are two kinds of scientists, or more

27:41

than two, but there are unifiers and

27:43

diversifiers, and there's a need for both.

27:47

I guess I want to argue for the happy

27:50

middle that if you're all

27:52

about diversity, you won't see patterns.

27:55

If you're all about unity, you won't

27:57

see richness. Both

28:00

are blinkered visions of the world. I just

28:02

don't believe in either extreme. And

28:06

someone's talking to Steve and

28:09

talking to Cream. I

28:11

think the question we were

28:13

really kicking around is, does

28:16

your experience of the world

28:18

feel fulfilling and

28:21

complete, even true? And

28:23

I think for Steve, there is

28:25

a deep pleasure and joy and

28:27

a benefit, like a real tangible

28:29

benefit to accepting math exactly as

28:31

it is and reveling in

28:34

how it describes reality. And

28:36

for Cream? Every day I sit at

28:39

my computer. There isn't. Kind

28:41

of rewriting our lessons to tighten things up.

28:43

The one I was working on yesterday was

28:45

about concert tickets and about all the fees

28:49

and like our secondary ticket brokers, Scurge,

28:51

or are they actually like correcting kind

28:53

of a market failure? That sounds interesting.

28:55

Oh yeah. All of our

28:57

lessons are interesting. I mean, I think. It's

29:00

so based on math and

29:02

it sounds like every day you're

29:04

staring at these things that you

29:06

believe are confining you, these numbers.

29:09

And you're literally not just staring at them.

29:11

You're like working with them even more intimately

29:13

than most people because you're trying to like fit

29:15

them around the universe and explain that back

29:17

to kids. Like, you're playing

29:19

with these tools that sound

29:22

like they have, you

29:24

feel like are failing you or maybe not failing

29:26

you, but they aren't all that's there. I sort

29:28

of feel like I'm spinning my wheels needlessly. I

29:31

feel like I'm ready for something. I feel like I'm ready

29:33

for whatever is the next step. But

29:37

what's crazy to me is like, but to do

29:40

that because of the nature of what you do

29:43

and what your passion has been, you have

29:46

to turn your back

29:49

on math. It sort of sounds like.

29:51

I mean, I think, look, I think

29:53

we live our lives in phases and

29:55

that isn't. I'm not going to put it down

29:58

and then stomp all over it. It's

30:00

a gentle pudding town. It's not throwing it

30:03

on the ground, but I

30:05

feel like I've sucked all the

30:07

juice out of that orange for me. Okay,

30:10

one last question. When you

30:12

think about the world, when

30:14

you think about zero world mathematically,

30:18

where one equals two equals zero equals infinity.

30:20

Everything gets sucked into black hole zero. Yeah,

30:22

this place that you, it sounds like you

30:24

yearn for that you want to go experience

30:26

and understand and feel right? I mean, is

30:28

that okay? What does

30:31

has it has thinking

30:34

about it and spending time there

30:36

theoretically? Has it

30:38

changed your understanding of numbers or math at

30:40

all? Has it expanded math for you at

30:42

all? I

30:45

respect that more. Is it true?

30:47

Is it? Lighting the

30:50

sign. Lighting the sign? Yeah. What

30:54

does that mean? Mathematics saying, mathematics saying,

30:57

there's something we can't account for. I admire

31:01

that. Why? Why? Why? Because

31:04

everybody, I am Christian. This is

31:06

the truth. There is no

31:09

truth but for this. I am Muslim.

31:11

This is the truth. There is no

31:13

truth but for this mathematics is an

31:15

incredibly powerful tool. And for the institution

31:17

or for mathematics personified to say, I'm

31:20

an exceptionally powerful tool. If

31:23

you master me, and if you use me,

31:25

you're going to be able to do so much. But

31:29

I'm not complete. There is

31:31

something I can't account for. I think

31:34

that humility. I really, I

31:37

think that is end level. When

31:39

I first wrote that paper about division by zero,

31:41

I was like, I'm

31:43

really going to stick it to math. And

31:49

now it's more like, what

31:52

a wonderful gift for this

31:54

powerful tool that we use to

31:56

do so much to say, but

31:59

if If you want to go further, you

32:02

need to put me down now. This

32:42

episode was produced by Matthew Hilfey,

32:45

with help from my catty Foster Keith

32:47

and Alyssa Jean Perry. Mixing

32:50

help from Arianne Wack, backtracking

32:52

by Diane Kelly. It was

32:54

edited by Pat Walters. Uh...

33:00

Steve Strogatz, by the way, also

33:03

hosts a podcast all about math,

33:06

where he zips and zazzles through different

33:08

puzzles and questions with all kinds of fun

33:11

guests. It is called The Joy of Y. W-H-Y,

33:14

The Joy of Y. And Kareem

33:17

wrote a book all about how to get kids talking

33:20

about how math interplays with

33:22

real-world puzzles. It's called

33:24

Dear Citizen Math. And

33:27

you can check out citizenmath.com to

33:29

see all sorts of neat lessons he and his team have dreamed up

33:31

over the years for middle

33:33

school and high school classrooms. That'll

33:36

do it for today. That'll

33:39

do it for this year. Thank

33:42

you so much for listening to Radiolab.

33:45

I hope you all get

33:47

a little bit of zero world over the break, like

33:50

where nothing is happening. Just,

33:52

uh, low

33:55

stress, low thought.

33:58

Rest? Dare we say rest? Welcome

34:03

back to Zero World. Where

34:10

there are no phones. Yes,

34:16

your precious little phone is gone. Going

34:19

somewhere? I

34:23

don't think so. There are no

34:25

cars. There's no planes. Motorcycles or

34:27

bicycles? None of it.

34:32

No money. Oh, how good. Freedom.

34:35

No money. You can't even count here.

34:39

Just easy. In

34:42

but zero. As

34:44

far as the eye can see. Ha

34:48

ha ha ha. Ha

34:53

ha ha ha ha ha. Are

34:59

you happy now? Hi,

35:27

I'm Ram from India. Leadership

35:49

support for Radiolabs. Science

35:51

programming is provided by the Gordon and

35:53

Betty Moore Foundation. Science

35:55

sandbox, a Simon Foundation initiative,

35:58

and the John Templeton Foundation. Foundation

36:01

support for Radio Lab was provided

36:03

by the Alfred P. Sloan Foundation.

36:30

To find out more about the season,

36:32

visit moma.org to join today and make

36:34

the most of the season as a

36:36

member. And enter code WNYC at checkout

36:38

for a special holiday offer.