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more at uh1.com. We're

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the show which explores the numbers which govern

0:57

life, the universe and everything. And

1:00

today we're focusing on the universe. You

1:04

might have heard of The Three-Body Problem,

1:07

a new Netflix show from the makers

1:09

of Game of Thrones, based on the

1:11

hugely successful sci-fi novel by Chinese author

1:14

Lu Xixin. They

1:17

are coming and there's nothing

1:19

you can do to stop them. But

1:23

if you've studied physics, the three-body

1:25

problem brings to mind something else

1:27

entirely. It's a classic

1:30

issue in astrophysics, where scientists often

1:32

want to predict the paths and

1:34

orbits of groups of celestial bodies,

1:37

like stars, planets or moons. And

1:39

it's that concept which forms part of the

1:41

premise of the new Netflix show. The

1:44

plot is, well, complicated. And

1:47

at More or Less, we are dedicated

1:49

to remaining spoiler-free. But it's

1:51

not giving too much away to say the

1:53

three-body problem is at the centre of everything.

1:56

This is how it's explained in one

1:58

promotional clip. If our planet

2:01

revolves around one of the suns in

2:03

a stable orbit, that's a stable

2:05

era. However, if one

2:07

of the other suns snatches

2:09

our planet away, we wander

2:11

through the gravitational fields of all three

2:14

suns. That's a

2:16

chaotic era. Essentially,

2:18

there's an alien planet which

2:20

flips between periods of stable

2:22

climate and apocalyptic weather, as

2:24

it unpredictably and erratically moves

2:26

close to or far from

2:28

three stars. So there's

2:31

a literal three-body problem for the

2:33

aliens to solve. Well, technically

2:35

it's four, but what's an extra

2:37

body between friends? Enough

2:39

science fiction, though. To learn the

2:41

science facts, I spoke to Dr

2:43

Anna-Lisa Vary, who studies mathematics and

2:45

astronomy at the University of Edinburgh

2:47

in Scotland. And we started with

2:50

the building block. Two body problems.

2:52

This is the problem of

2:55

determining the position and the

2:57

velocities of two bodies

2:59

that can be stars or planets

3:01

in astronomical terms, starting

3:03

from their initial condition at

3:06

any point in time. So we

3:08

know that at a certain

3:10

moment we have a specification of

3:12

position and velocities, and we want

3:15

to compute their orbit as resulting

3:17

from the gravitational interaction between

3:19

these two bodies. So basically how

3:21

the Earth and the Moon will

3:24

move? Yes, under their mutual gravitational

3:26

interaction. So you can do this really

3:28

pen and paper. A series of

3:30

equations were developed hundreds of years ago

3:32

to solve how two bodies will move

3:34

around the centre of mass for millions

3:37

of years. Add just one

3:39

more celestial body, and you've got a

3:41

three-body problem. In reality,

3:44

the Earth and the Moon aren't just sitting there in

3:46

a void in space on their own. There's

3:49

other things just in our solar system. There's

3:51

the Sun, there's seven other planets, asteroids, moons,

3:53

Pluto, whatever we decide that is. How

3:56

much more complicated does it get when you

3:58

add those other factors in? significantly more.

4:00

So the moment in which you step

4:03

up from two and we even consider

4:05

the three-body problem, things are getting complicated

4:07

to the point that in some

4:09

special cases we can still have an

4:11

analytical solution, so something that we can

4:13

compute pen and paper, and these

4:16

are relying on particular

4:18

simplification or restriction as we call it.

4:21

But if you want to consider the fully

4:23

general statement even just at the level of

4:25

the three-body problem, we don't have a general

4:27

solution for it, and certainly it's not something

4:29

that can be achieved analytically or pen and

4:31

paper. When we're making these predictions there of

4:33

how these things are going to move, I

4:35

mean surely we still

4:37

know how the earth and

4:40

the moon and the sun are going to

4:42

move around each other by next week, for

4:44

example. We're not going to be totally surprised

4:46

by what happens next month. Can we still

4:48

make short-term predictions or is this a long-term

4:50

problem? Very good. So this is the essence

4:53

of the problem in some sense.

4:55

We do have the ability to

4:58

make computations that are on short

5:00

time scale, as you said. The

5:02

concerning element is on the long-term

5:04

predictability of the behavior, meaning that

5:07

we don't know whether a certain

5:09

configuration will remain stable on certain

5:11

time scale or will

5:13

change dramatically, for example, by

5:16

ejecting one of the body or by

5:18

flipping the orbital plane or doing

5:20

other violent events that can have really

5:23

a very signature of instability in

5:25

that sense. Changing the starting

5:27

configuration of a sailor system even

5:29

very slightly will result in a

5:31

radically different outcome further down the

5:33

line, and we're not just

5:35

talking about a few meters of difference.

5:37

Simulations of the future of our sailor

5:39

system find a small chance of mercury

5:41

either colliding with the sun or

5:44

being flung into Venus. Why

5:46

is it so much harder to

5:48

predict things over a longer time

5:51

period rather than shorter ones? Is

5:53

it just that we've got so many

5:56

more things to think about? It's actually

5:58

the effect of the build-up. of

6:00

this tiny variation over a long period

6:03

of time. So there

6:05

is an exponential divergence in

6:07

the behavior of the solution that corresponds

6:10

to the orbit of these different

6:12

objects or stars or planets that

6:15

as a function of time becomes significant

6:17

because of that exponential nature.

6:20

Now when we talk about a long time,

6:22

astronomers in my experience have a different understanding

6:24

of what a long time is to me.

6:27

Are we talking about someone's lifetime, centuries or

6:29

like hundreds of millions of years? So

6:32

just to be specific about

6:34

computation concerning the stability of our

6:37

solar system, we know now

6:39

for a good degree of accuracy that

6:41

60 million years is the time scale

6:44

for which we can claim that we

6:46

have a stable solution to our solar

6:48

system. So we're okay for the

6:50

next 60 million years we can relax. Correct. Let's

6:53

move then from our solar system

6:55

to a fictional universe and

6:58

the three-body problem, the books and the TV

7:00

show. There it describes a system

7:02

with three stars. Is

7:04

that something that we see in the universe? Actually

7:08

yes and it's incredible to

7:10

realize that the closest star

7:12

or stellar system to us,

7:15

Alpha Centauri, is actually a

7:17

triple system so has three stars. The

7:26

show and the book, they depict

7:28

this planet which goes through rapid

7:31

changes of climate as they move

7:33

its position around their stars quite

7:35

quickly in this unpredictable manner and

7:38

yet here in real life we're

7:41

talking about a predictability over thousands

7:43

of years and an unpredictability over

7:45

possibly tens of millions. Is

7:47

what's described in this book

7:49

that short-term unpredictability possible? Not

7:52

really, mostly because we

7:55

still have good enough computers and

7:57

good enough numerical algorithms and the possibility

7:59

of computing. thing on short time

8:01

scale, the position and the velocity of

8:03

all the bodies, in particular in this

8:05

case three stars, to high degree

8:08

of reliability. So there

8:10

is this distinction between being able to make

8:12

a prediction on short time scale versus long

8:14

time scale. There might be

8:16

a catch if the system described in

8:18

the book is not hierarchical, so it's

8:20

not having the structure of having an

8:22

inner binary plus a faraway body,

8:25

but it's more democratic

8:27

in that sense. So all

8:29

the bodies are just interacting

8:31

without underlying structure. This

8:34

can make the overall configuration more

8:36

chaotic than the example that we

8:38

just discussed. So the time scale

8:40

for predictability can be shorter in

8:42

their respect, but to be

8:44

able to claim that over seconds

8:47

or minutes there is the

8:49

impossibility of determining the position

8:52

and velocity and therefore the

8:54

characteristics of the planet seems

8:56

to be a bit of a stretch to me. I

8:59

love the fact that your conclusion is these aliens are

9:01

bad at maths. Thanks to Dr.

9:03

Anna-Lisa Vary from the

9:15

University of Edinburgh. That's all

9:17

we've got time for on More or

9:19

Less this week, but please continue scouring

9:21

the darkest corners of the universe for

9:23

mathematical conundrum for us to solve. No

9:26

question is too big or too small

9:28

for us to take on, so send

9:31

them in to More or Less at

9:33

bbc.co.uk. Until next

9:35

week, goodbye. Hey

9:45

folks, I'm Mark Maron from the WTF

9:47

podcast and this episode is brought to

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