Latest / Daniel and Kelly’s Extraordinary Universe / Why is the three-body problem so hard?

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Why is the three-body problem so hard? · Daniel and Kelly’s Extraordinary Universe

0:08
Speaker 1: Hey, Daniel, when you are teaching, are you the kind
0:10
Speaker 1: of professor that assigns super hard homework in your classes?
0:14
Speaker 1: You mean, like, find the motion of a banana tied
0:17
Speaker 1: to a string held by a squirrel riding on a
0:20
Speaker 1: roller coaster, all of that in orbit around a black hole?
0:23
Speaker 1: Like that kind of problem? What are you, professor, Rube Goldberg? No,
0:29
Speaker 1: that was just a joke. I actually like to make
0:31
Speaker 1: the homework just a little bit harder than what we
0:34
Speaker 1: work on in class. You know, that's where the concepts
0:37
Speaker 1: really come together in your mind. Right, right, you're an
0:40
Speaker 1: evil professor. Basically you never assigned unsolved research problems to
0:44
Speaker 1: first year students. Know that only happens in the movies. Man,
0:48
Speaker 1: Goodwill Hunting is not a documentary. You're not Matt Damon.
0:51
Speaker 1: I don't have the looks for it. Yes, there's always
0:55
Speaker 1: room for improvement. Hi am more hamming cartoonists and the
1:12
Speaker 1: creator of PhD comics. I'm Daniel. I'm a particle physicist,
1:16
Speaker 1: and I've never solved an outstanding math problem. Not yet,
1:20
Speaker 1: do you mean? Right? Like if you had solved it, it
1:22
Speaker 1: it wouldn't be an an outstanding math problem. That's true. Yeah,
1:26
Speaker 1: there are these famous, outstanding problems, and it's cool when
1:28
Speaker 1: they stand for hundreds of years and then somebody comes
1:31
Speaker 1: along and figures them out. What do you think happens?
1:33
Speaker 1: Like somebody just comes up with the right way to
1:35
Speaker 1: look at it, or like they see something nobody else
1:38
Speaker 1: has seen before, or the history was just waiting for
1:41
Speaker 1: the right intellect. Yeah, sometimes it's a slow construction of
1:44
Speaker 1: ideas over hundreds of years. When you look at the
1:47
Speaker 1: history of it and be like, problem proposed in sixteen nineteen,
1:50
Speaker 1: progress has made in eighteen fourteen, and then Samantha figures
1:55
Speaker 1: it out, and it's pretty awesome to see the stretch
1:58
Speaker 1: of history there. I'm waiting for people to solve some
2:00
Speaker 1: pretty intractable parenting problems. Didn't sometimes they had Those are eternal, man,
2:05
Speaker 1: they will never be solved. They will never be solved.
2:09
Speaker 1: It's part of being human, I guess. Welcome to our
2:11
Speaker 1: podcast Daniel and Jorge Explain the Universe, a production of
2:14
Speaker 1: our Heart Radio in which we tackle the hardest problem,
2:17
Speaker 1: which is understanding the nature of this universe we find
2:21
Speaker 1: ourselves in. How does it work, where did it come from,
2:24
Speaker 1: why is it the way that it is, and is
2:26
Speaker 1: it even possible to understand it. We dive right into
2:30
Speaker 1: the biggest, hardest, deepest questions. We explain the answers and
2:34
Speaker 1: our ignorance to you. What if that's the harder problem,
2:36
Speaker 1: Daniel explaining something to other people. We do our best here,
2:40
Speaker 1: but um, it's pretty hard to wrap your head around
2:43
Speaker 1: all the amazing and incredible stuff that is happening in
2:46
Speaker 1: the universe. And one of my favorite things about doing
2:48
Speaker 1: this podcast is exercising that part of my brain that
2:51
Speaker 1: translates these ideas from like the cutting edge of physics,
2:54
Speaker 1: two things everybody can understand, because to do that you
2:57
Speaker 1: have to have a really good grasp on what's going on. See,
3:00
Speaker 1: you actually have to understand it first before explaining into people.
3:03
Speaker 1: So what am I doing here? Then? Well, sometimes when
3:05
Speaker 1: you try to explain something, you realize whole lot of second,
3:08
Speaker 1: I don't really understand how this works as well as
3:10
Speaker 1: I thought it did sometimes only sometimes, though that never
3:13
Speaker 1: happens on our podcast. It happens to me all the
3:15
Speaker 1: time when I'm teaching and also on this podcast, And
3:17
Speaker 1: that's one reason why it's so fun, because not only
3:19
Speaker 1: are we explaining stuff, we're also learning as we go.
3:22
Speaker 1: But that is a pretty good parenting lesson. Also, it's
3:25
Speaker 1: good to share what you know when you learn what
3:27
Speaker 1: you love about this crazy beautiful costmas. Yeah, how does
3:30
Speaker 1: that help you with your parenting? Well, it's just good
3:32
Speaker 1: to share. I think it's good. Well, you have to
3:33
Speaker 1: share with your children. I think it's a law, that
3:35
Speaker 1: is a rule. But it's also good to teach it
3:37
Speaker 1: to share, you know. It's just everyone's more generous with
3:40
Speaker 1: their what they have in their knowledge. We're all happy.
3:42
Speaker 1: I thought you were going to use the wondering glamor
3:44
Speaker 1: of the universe to convince your kids to do their chores,
3:47
Speaker 1: like take out the trash because stars are amazing? Are
3:51
Speaker 1: you are insignificant in this universe? You're a tiny speck
3:54
Speaker 1: of dust in the floating and vast vacuum of perhaps
3:57
Speaker 1: infinite space, and therefore you should do your homework. I
4:00
Speaker 1: think that will work against you. So then why should
4:02
Speaker 1: I bother taking out the trash if nothing matters? Because
4:06
Speaker 1: if nothing matters children, everything matters. Like that that trended
4:11
Speaker 1: philosophical use that PhD for something. But anyways, we do
4:14
Speaker 1: like to talk about not only what scientists know about
4:17
Speaker 1: this universe and all of the wonderful stuff in it,
4:20
Speaker 1: but also what scientists are struggling with understanding about how
4:24
Speaker 1: things work. That's right, because we have this amazing mental
4:27
Speaker 1: machinery of science that lets us build up a body
4:31
Speaker 1: of knowledge. Things we do understand about the universe has
4:34
Speaker 1: a machinery to it, and that machinery is mathematical. It's
4:37
Speaker 1: incredible in me sometimes that mathematics can describe the way
4:41
Speaker 1: the world works at all. You know, you throw a
4:43
Speaker 1: baseball and it follows a parabola, which is a very
4:46
Speaker 1: simple mathematical relationship. So it's incredible when you can use
4:49
Speaker 1: mathematics to describe what's really very complex behavior, all sorts
4:54
Speaker 1: of zillions of particles moving through the air altogether. But
4:57
Speaker 1: sometimes it's easier than other times. And the cool thing
5:00
Speaker 1: about sciences is that it's always at the sort of
5:02
Speaker 1: the leading edge of human knowledge, right, Like that's what
5:05
Speaker 1: science is. It's sort of like asking the questions nobody's
5:08
Speaker 1: ever asked, or finding the answers nobody that has so far.
5:11
Speaker 1: And so sometimes you run into things that are just
5:14
Speaker 1: really really extra hard or maybe even impossible. Yeah, and
5:17
Speaker 1: sometimes they are impossible because the physics is really hard,
5:21
Speaker 1: and sometimes they're impossible because we just don't have the
5:23
Speaker 1: mathematics yet. Like, there's been lots of times in history
5:26
Speaker 1: when mathematicians have developed tools, not because they thought they
5:29
Speaker 1: were gonna be useful for physics, but just because they
5:31
Speaker 1: thought it was fun, and then later on physicists were
5:34
Speaker 1: like a whold on a second. That totally helps me
5:36
Speaker 1: solve this problem I've been struggling with for twenty years.
5:39
Speaker 1: A great example is general relativity, which is built on geometry,
5:43
Speaker 1: which was developed just ten years before. Without all that
5:46
Speaker 1: work developing geometry, there's no way Einstein could have developed relativity.
5:50
Speaker 1: Is this really fascinating dance between mathematics and physics? Yeah?
5:54
Speaker 1: What kind of dance? How would you describe that dance?
5:56
Speaker 1: Is it like a Charleston or more like a waltz?
5:59
Speaker 1: Or like hip hop breakdancing competition? What would you call it?
6:03
Speaker 1: The mathematicians carefully build their tools and we just sneak
6:06
Speaker 1: in and steal them, So maybe it's more like a
6:08
Speaker 1: cat Burglar dance. Oh man, I can't wait for that,
6:14
Speaker 1: you know, interpretive dance History of Science Broadway play that
6:18
Speaker 1: you're working on. Yeah, you know, I wish it was
6:19
Speaker 1: more back and forth. Sometimes I feel like, shouldn't the
6:22
Speaker 1: mathematicians be excited when their tools actually get used to
6:26
Speaker 1: describe the real universe? But a lot of times they
6:28
Speaker 1: don't seem to care at all, and they're like, whatever,
6:31
Speaker 1: who cares about the real universe? I'm walking the halls
6:34
Speaker 1: of truth. You're selling their halls with like reality and
6:38
Speaker 1: like red and dirt, Like that's just dirt. Adams are
6:41
Speaker 1: just dirt. If they cared about getting dirty, they would
6:43
Speaker 1: have been physicists instead of mathematicians. I see, physicis are
6:48
Speaker 1: are the down and dirty of of scientists. I think
6:50
Speaker 1: physicists are to mathematicians what engineers are to physicists. Oh,
6:53
Speaker 1: I see the better the better people, right, the true
6:57
Speaker 1: heroes on the hierarchy of useless pure the hierarchy of usefulness.
7:02
Speaker 1: You mean, depending on what you put in the top? Yes,
7:06
Speaker 1: exactly right. Yes, if you turn upside down, we're actually
7:10
Speaker 1: at the top. Yes, it's all about your perspective, that's right.
7:13
Speaker 1: There is no up in space anyway. Well, there are
7:15
Speaker 1: interesting problems in physics, some of them which are even intractable,
7:19
Speaker 1: and so in this episode we'll be talking about one
7:21
Speaker 1: such problem that maybe affects are very movement through space,
7:25
Speaker 1: and it affects how planets revolve around their suns, and
7:28
Speaker 1: which we may never find the answer for. So to
7:31
Speaker 1: be on the podcast, we'll be asking the question, what's
7:38
Speaker 1: so hard about the three body problem? Now, Daniel, this
7:43
Speaker 1: is not something that's not safe for work, is it?
7:47
Speaker 1: I mean, I see something here at three bodies? Is
7:49
Speaker 1: this about? You know? No, this is not about being
7:52
Speaker 1: exploratory in your relationships at all. It's what's so mathematically
7:56
Speaker 1: difficult about three gravitationally attracting objects? Is the safe preparatory
8:02
Speaker 1: in the heavenly bodies relationships? You know, some bodies here
8:06
Speaker 1: on Earth are quite heavenly as well, but we're talking
8:08
Speaker 1: about celestial bodies, that's right, the real stars. Alright, So
8:12
Speaker 1: the three button. More specifically, this is kind of about
8:15
Speaker 1: what is the three body problem at all? Because I
8:17
Speaker 1: imagine that a lot of people have heard of him,
8:19
Speaker 1: although it is the title of sort of a well
8:21
Speaker 1: known science fiction novel out there, right, that's fairly recent,
8:26
Speaker 1: that's right. Yeah, it's like one of the biggest novels
8:28
Speaker 1: in the last few years. It's a whole trilogy written
8:30
Speaker 1: by a fantastic Chinese author. A lot of people are
8:32
Speaker 1: really into this book, and a lot of our listeners
8:34
Speaker 1: have written in asking us to talk about this book.
8:37
Speaker 1: But I thought, first maybe be more fun to talk
8:40
Speaker 1: about like the physics problem that's at the heart of
8:42
Speaker 1: the novel, that we can talk about the actual problem itself. Yeah,
8:45
Speaker 1: I think. I try to read the novel. It's it's
8:47
Speaker 1: pretty dense, it's kind of thick. Yeah, there's a lot
8:50
Speaker 1: of physics in that book, which is pretty fun for
8:52
Speaker 1: people who like really well thought out physics novels. And
8:56
Speaker 1: so it's a good idea to try to get an
8:57
Speaker 1: understanding for like what is the underlying problem at the
9:00
Speaker 1: core of the story? Right? And it was like a
9:03
Speaker 1: bestseller and want all the awards right in science fiction.
9:06
Speaker 1: M So you can check that out if you like.
9:08
Speaker 1: But the title of it refers to kind of an
9:10
Speaker 1: old and famous problem in physics about I imagine three bodies.
9:15
Speaker 1: That's right, it's really old problem, and old problems are
9:18
Speaker 1: the funniest problems because it means that like a lot
9:20
Speaker 1: of smart people have been butting their heads against this
9:23
Speaker 1: problem for decades or even centuries, and nobody has figured
9:27
Speaker 1: it out. And doesn't mean it's impossible. There are other
9:29
Speaker 1: mathematical problems that have existed for hundreds of years and
9:32
Speaker 1: then all of a sudden, some dude in a cabin
9:34
Speaker 1: in Russia comes out with like a hundred page proof
9:36
Speaker 1: of it. So it might be possible to be solved,
9:38
Speaker 1: but nobody's cracked this one. Yeah, just a book on Airbnb,
9:41
Speaker 1: that cabin in Russia, and you know, book it for
9:45
Speaker 1: for a couple of years, and that you might solve
9:47
Speaker 1: a famous problem. That's the real answer. That wasn't a metaphor.
9:51
Speaker 1: That was that really happened to you, not to me. No,
9:55
Speaker 1: there really is a Russian mathematician who worked all by
9:57
Speaker 1: himself for a decade and saw the famous problem in math,
10:01
Speaker 1: the remon conjecture. Wow. And he was in a cabin,
10:04
Speaker 1: using a cabin. He worked all by himself, and he
10:06
Speaker 1: just sent in the solution and they tried to give
10:08
Speaker 1: him the Fields Medal for it and he wouldn't even
10:10
Speaker 1: show up. Wow. That feels like such a fine line
10:14
Speaker 1: between like, you know, genius and you know, socially unacceptable behavior.
10:21
Speaker 1: He's well on one side of that line. But anyways,
10:25
Speaker 1: let's talk about this problem, the three body problem. And so,
10:28
Speaker 1: as usually we were wondering how many people out there
10:30
Speaker 1: we knew what this was, if they had heard of
10:32
Speaker 1: it before beyond the novel, or how important it is
10:36
Speaker 1: to sort of predicting the movement of our planets in
10:40
Speaker 1: our solar system. So Daniel as usually went out there
10:42
Speaker 1: into the wilds of the internet to ask people what
10:45
Speaker 1: is the three body problem? So, while we are still
10:48
Speaker 1: pandemically shut down, I am very grateful to all of
10:51
Speaker 1: you who are willing to participate via email on the
10:54
Speaker 1: person on the virtual street interviews. So if you would
10:58
Speaker 1: like to participate and hear your speculation on the podcast,
11:00
Speaker 1: please don't be shy. Send us a message to questions
11:03
Speaker 1: at Daniel and Jorge dot com. Think about it for
11:06
Speaker 1: a second. Do you know what the three body problem is?
11:09
Speaker 1: Here's what people have to say. I don't know what
11:11
Speaker 1: the three body problem is, I'm afraid so I'm barely
11:14
Speaker 1: aware of what the three body problem is. I did
11:18
Speaker 1: read as you should use three body problem trilogy. My
11:22
Speaker 1: understanding is that it's a problem with how three bodies
11:27
Speaker 1: orbit one another and how it could continue to do
11:30
Speaker 1: that and be stable without cuestion into one another. A
11:34
Speaker 1: lot of people spend a fair amount of time calculating
11:38
Speaker 1: how two massive bodies interacts due to the gravitational field
11:42
Speaker 1: surrounding them. But actually, if you add a third body,
11:45
Speaker 1: the system becomes unstable, it becomes chaotic, so you can't
11:51
Speaker 1: determine an exact solution. And also if you make a
11:56
Speaker 1: small change let's say in the initial positions of the bodies, um,
12:01
Speaker 1: you can't actually determine how let's say the forces between
12:06
Speaker 1: the three bodies will be affected. I think that's to
12:09
Speaker 1: do when you've got three bodies that rotatue interacts, usually
12:12
Speaker 1: like the Sun, the Earth and the Moon, for example,
12:16
Speaker 1: would be that would be three bodies, and I think
12:19
Speaker 1: you can solve two bodies. Any more than a few
12:22
Speaker 1: more and you can't solve it. I think is it
12:23
Speaker 1: is one of the issues. Wow, that is something I
12:27
Speaker 1: am not sure where it is. I don't know what
12:31
Speaker 1: the three body problem is m unless it's relating to
12:36
Speaker 1: a previous question where if you have three bodies acting
12:42
Speaker 1: on each other gravitationally, um, you haven't got sort of
12:47
Speaker 1: one orbiting another or one with a joint orbit with
12:50
Speaker 1: another that that will be probably quite at random implication
12:56
Speaker 1: to their orbits. I have never heard of the three
13:00
Speaker 1: body problem before. But if I were to guess, I
13:04
Speaker 1: think it is three bodies interacting with each other, and
13:08
Speaker 1: something unusual happens, like something that doesn't happen between two
13:12
Speaker 1: bodies of four bodies. It just happens between these three
13:16
Speaker 1: bodies for some reason, and for some reason the number
13:20
Speaker 1: is three. Actually, I've studied physics before, so I know
13:23
Speaker 1: that the three body problem is this problem where if
13:26
Speaker 1: you have two objects pulling on each other, then those
13:31
Speaker 1: equations can be solved pretty easily. But if you add
13:33
Speaker 1: in a third body, now you have three different interactions
13:36
Speaker 1: between A B, A C and C B. And when
13:40
Speaker 1: you have interactions of that order that that many interactions,
13:45
Speaker 1: it becomes sort of an unsolvable math problem. And so
13:48
Speaker 1: we don't have like good solutions for those sort of situations.
13:51
Speaker 1: We have to essentially come up with approximations and simulate it.
13:55
Speaker 1: All right, There not a lot of knowledge about this,
13:58
Speaker 1: But someone did read the True Gene. Yeah, exactly three
14:02
Speaker 1: books in the three Body Problem trilogy. It's nice. It
14:04
Speaker 1: must have been good because he read all three or
14:06
Speaker 1: I wonder if your completest, you know, tendencies would kick
14:09
Speaker 1: in after you rerund well, I can't just read one
14:11
Speaker 1: three body problem book. I gotta read all three depends
14:14
Speaker 1: if they leave a cliffhanger at the end of the
14:15
Speaker 1: first novel. You should title all your trilogies with the
14:18
Speaker 1: number three in it. But it seems like most people
14:20
Speaker 1: here are guessing it has to do with bodies in
14:22
Speaker 1: space and then specifically three bodies of course, But a
14:26
Speaker 1: lot of people are saying maybe it's about it becoming
14:29
Speaker 1: unsolvable or chaotic or unstable. Are they sort of in
14:32
Speaker 1: the right track. They are exactly on the right track.
14:35
Speaker 1: It's really interesting. There's a problem which is easy if
14:38
Speaker 1: there's only two objects involved, and then becomes basically unsolvable
14:41
Speaker 1: if you have three objects involved, right, like real human relationships,
14:47
Speaker 1: which can be tricky even when there are two bodies involved,
14:51
Speaker 1: even if everyone is open minded, it gets tricky. Al Right, Well,
14:55
Speaker 1: let's dig into Daniel, how would you describe the three
14:57
Speaker 1: body problems? I think the best way to describe it
15:00
Speaker 1: is to first talk about what we can do and
15:03
Speaker 1: simply said, if you have two objects in space, and
15:06
Speaker 1: you know where they are, how heavy they are, and
15:09
Speaker 1: the direction they're going in, then you can predict their motion.
15:12
Speaker 1: You can say at some time in the future, I
15:15
Speaker 1: know where they are going to be. So, for example,
15:18
Speaker 1: imagine just the Sun and the Earth. These are two
15:20
Speaker 1: objects that pull on each other. There are forces involved.
15:23
Speaker 1: And if you know where the Sun and the Earth
15:25
Speaker 1: are at some moment in time, in which direction they're heading,
15:28
Speaker 1: and their masses, you can write down a very simple
15:30
Speaker 1: formula that will tell you where they will be in
15:33
Speaker 1: the future. Like you say, where will the sun be
15:35
Speaker 1: in a year, or in a thousand years or in
15:37
Speaker 1: a million years. It's like a very simple mathematical expression.
15:40
Speaker 1: You plug in the time, it tells you where the
15:42
Speaker 1: Sun will be. So that's the two body problem, and
15:45
Speaker 1: we have a solution for that. We can crank through
15:48
Speaker 1: the mathematics and get a very nice simple formula that
15:50
Speaker 1: tells us where they will be at any moment in
15:52
Speaker 1: the future. Right, But you have to kind of assume
15:54
Speaker 1: that they're alone in the in the whole universe, like
15:56
Speaker 1: there's nothing else in the universe pulling on them. Right,
15:59
Speaker 1: that's right, only two bodies. And as usual, you know,
16:02
Speaker 1: physics is telling a story, and that story is always approximate.
16:05
Speaker 1: The reality never matches the approximate stories we try to
16:08
Speaker 1: use when we tell physics stories because in reality, there's
16:11
Speaker 1: an infinite number of bodies out there in space, and
16:13
Speaker 1: gravity works for over infinite distances, and so everything in
16:16
Speaker 1: the universe is hugging on things all the time. But
16:20
Speaker 1: usually you can get away with disregarding that. You don't
16:23
Speaker 1: have to care about what's happening in Andromeda when you're
16:25
Speaker 1: doing in the calculation of whether your satellite is going
16:27
Speaker 1: to go around the Earth, because it's basically zero contribution.
16:30
Speaker 1: So here we're talking about the scenario where you have
16:33
Speaker 1: two bodies and everything else can be ignored without changing
16:36
Speaker 1: anything down to like, you know, the tenth decimal place
16:38
Speaker 1: or something. Yes, so in the sort of simplified universe
16:41
Speaker 1: of exactly two things in your universe, you can predict
16:44
Speaker 1: the motion of two objects, all right, So then I'm
16:46
Speaker 1: guessing when you get to three bodies, it gets a
16:49
Speaker 1: little harder. When you get to three bodies, it doesn't
16:51
Speaker 1: just get a little harder, it becomes impossible. If you
16:54
Speaker 1: know where three objects are. You know, so you have,
16:56
Speaker 1: for example, the Sun, the Earth, and then another object.
17:00
Speaker 1: Now you just have three objects and you know exactly
17:02
Speaker 1: where they are, what direction they're going in, and you
17:04
Speaker 1: know their masses. You cannot write down a simple formula
17:07
Speaker 1: that tells you where they're going to be in a week,
17:10
Speaker 1: or in a year or in a thousand years. Well,
17:13
Speaker 1: it gets really complicated. Suddenly, it gets really complicated. We
17:16
Speaker 1: don't have a solution. Now, we have an understanding for
17:19
Speaker 1: what's going on, Like we know the forces involved, We
17:22
Speaker 1: know what the gravity is between two objects given their distance. Right,
17:26
Speaker 1: that's a pretty simple formula. Newton told us how to
17:28
Speaker 1: do that. But that doesn't mean we know how to
17:30
Speaker 1: find the solution. Doesn't mean we can take those forces
17:33
Speaker 1: and predict the motion. Right. Well, I think this might
17:35
Speaker 1: be kind of a subtle subject for a lot of
17:37
Speaker 1: people out there, which is like what you mean in
17:39
Speaker 1: physics as a solution, because it doesn't mean that you
17:43
Speaker 1: can't predict where they're going to be. You just don't
17:44
Speaker 1: have an easy solution to the equations to predict this. Right.
17:48
Speaker 1: It means that we know what the constraints are. Like
17:50
Speaker 1: physics tells you what the rules are, tells you like,
17:52
Speaker 1: for example, how two objects pull on each other. It
17:55
Speaker 1: doesn't tell you how those objects are going to move.
17:58
Speaker 1: To figure out how the objects are to move, which
18:00
Speaker 1: is what you need to predict their emotion. You need
18:03
Speaker 1: to be able to solve all of those equations and
18:05
Speaker 1: get the answer out. So physics gives you, like all
18:08
Speaker 1: the equations you need to solve. It doesn't mean you
18:10
Speaker 1: know how to solve the equations, Like not every equation
18:13
Speaker 1: you get is solvable, or we don't necessarily have the
18:16
Speaker 1: mathematical tools to solve an arbitrary equation. Turns out, in
18:20
Speaker 1: physics there are only like five problems we do know
18:23
Speaker 1: how to solve and everything else is intractable. Well, that
18:27
Speaker 1: probably makes for a short workday there free. But I
18:30
Speaker 1: think what you mean is, like, for example, like a ball,
18:32
Speaker 1: if I throw a ball here at my son in
18:35
Speaker 1: our backyard here, like I know that that ball, I
18:39
Speaker 1: know the constraints on it, like I know the forces
18:41
Speaker 1: pulling on it, the force of gravity, and I know
18:43
Speaker 1: that F equals m A for example. So I can solve,
18:45
Speaker 1: for example, for its exceloration very easily. But maybe getting
18:50
Speaker 1: like a formula for what its position is going to
18:53
Speaker 1: be is a little tricky. It's different than knowing what
18:56
Speaker 1: it's acceleration is going to be exactly. The acceleration just
18:58
Speaker 1: tells you how is momentums and change in a given moment.
19:02
Speaker 1: Right to know where it's going to be, you need
19:04
Speaker 1: to then solve the equations of motion, which incorporate all
19:07
Speaker 1: these forces and is affected by that acceleration. But it
19:10
Speaker 1: requires actually solving the equation. You know. It's like if
19:13
Speaker 1: I have an equation that says X plus five equals ten. Right,
19:17
Speaker 1: that's an equation that constrains X. It limits what X
19:20
Speaker 1: can be, but it's not actually the solution. The solution
19:23
Speaker 1: is X equals five. That's a very simple one, right.
19:26
Speaker 1: You know exactly how to go from the equation X
19:29
Speaker 1: plus five equals tend to the solution, But you don't
19:31
Speaker 1: necessarily know how to do that for an arbitrary equation.
19:34
Speaker 1: Take another simple example, like X squared equals forty nine.
19:38
Speaker 1: How do you find the solution to that? You know
19:40
Speaker 1: off the top of your head that x equals seven works,
19:43
Speaker 1: You can plug it in and check it. But how
19:45
Speaker 1: do you find the solution? If I tell you X
19:47
Speaker 1: square equals an arbitrary number? How do you find the
19:51
Speaker 1: square root of an arbitrary number? There actually is no
19:53
Speaker 1: way to do that. There is no mechanism for solving
19:56
Speaker 1: that equation other than guessing and checking us like my
20:00
Speaker 1: parenting strategy right there. And I think what you mean is, like,
20:04
Speaker 1: you know, in physics, you have equations to tell you,
20:06
Speaker 1: for example, like the acceleration of x, which is like
20:09
Speaker 1: how the velocity changes, which is like how the position
20:12
Speaker 1: is changing. Like you have equations for that. But to
20:14
Speaker 1: actually get the pocsisition, you have to kind of backtrack
20:17
Speaker 1: from acceleration to velocity to position. And that's where the
20:20
Speaker 1: trickiness comes from, right yeah, because the acceleration changes through time,
20:25
Speaker 1: and so to figure out how all those accelerations add
20:27
Speaker 1: up to describe the motion of the object is not
20:30
Speaker 1: always easy. And then what you want is a simple
20:33
Speaker 1: formula that describes it, and that doesn't necessarily exist, right
20:37
Speaker 1: because I guess when you go from two bodies to
20:39
Speaker 1: three bodies, then the formula just get too complicated. The
20:42
Speaker 1: formula gets too complicated. Exactly, the system gets really complicated
20:47
Speaker 1: because now you have these three different objects pulling on
20:50
Speaker 1: each other, and it actually becomes chaotic. All right, Well,
20:53
Speaker 1: let's dig into why exactly it is so hard and
20:56
Speaker 1: how it becomes pure chaos when you add a third
20:59
Speaker 1: cell steel body into the mix, and what consequences it
21:03
Speaker 1: has for our ability to predict the universe. But first,
21:06
Speaker 1: let's take a quick break. All right, Daniel, we're talking
21:21
Speaker 1: about the three body problem, and I guess we're not
21:24
Speaker 1: just talking about like what happens if your spouse moves
21:26
Speaker 1: to another city, right, this is more cosmic. I can't
21:29
Speaker 1: solve that problem for you. There is no equation that
21:31
Speaker 1: tells you how to live your life. That's the one
21:35
Speaker 1: body problem is already pretty hard. Now we're talking about
21:38
Speaker 1: the three body problem. One is the loneliest number. But
21:40
Speaker 1: this is not a relationship helpline, and this is not
21:43
Speaker 1: a podcast about human emotions. We are trying to solve
21:46
Speaker 1: the much easier problem of motion of objects through space.
21:49
Speaker 1: And so you're saying that when I have two objects
21:52
Speaker 1: in space, it's easy enough to sort of predict where
21:54
Speaker 1: they're going to be once you have three. It because
21:56
Speaker 1: there's no easy solution to that problem. Yeah, there's no
21:59
Speaker 1: easy solution. There's no like short mathematical answer when you
22:03
Speaker 1: like is something like x f T or x is
22:05
Speaker 1: the position of the object, and then a simple formula
22:08
Speaker 1: where you can plug in the time and it will
22:10
Speaker 1: tell you exactly the position of the object. That's what
22:13
Speaker 1: you're looking for because you'd like to be able to
22:15
Speaker 1: take that system and say, I want to know where
22:18
Speaker 1: the moon is going to be, where I want to
22:19
Speaker 1: know where the sun is going to be in a
22:21
Speaker 1: thousand years. The problem is that there is no such
22:23
Speaker 1: simple formula. We haven't found one at least, and we
22:25
Speaker 1: suspect that it might not exist because the system of
22:28
Speaker 1: three objects is much much more complicated than a system
22:32
Speaker 1: of just two objects, right, And it gets really complicated
22:35
Speaker 1: because now you have three objects in three D? Is
22:38
Speaker 1: it kind of about going to the third dimension? That
22:40
Speaker 1: makes it hard because I imagine if you have two
22:42
Speaker 1: bodies in space, you can just treat him as like
22:44
Speaker 1: a two D problem, right, like you just imagine the
22:47
Speaker 1: plane where these two bodies are. But once you have
22:49
Speaker 1: three and then it's like, now it's a three D problem.
22:51
Speaker 1: It's true that two objects in space you can always
22:53
Speaker 1: define a plane between them. You can also put three
22:55
Speaker 1: objects on a plane though, right, three points define a plane,
22:58
Speaker 1: so there's always a plane for three jects. I think
23:00
Speaker 1: the problem is that when you have three objects, a
23:03
Speaker 1: small change in their location leads to a big change
23:07
Speaker 1: in where they're going to be in the future. At
23:09
Speaker 1: least for gravitational interactions, whereas if you have two objects,
23:13
Speaker 1: a small change and where the Earth is going to be,
23:15
Speaker 1: it will mostly settle back into the same answer. And
23:18
Speaker 1: so in terms of like finding an equation that describes it,
23:21
Speaker 1: there's a whole family of equations that can describe stable solutions.
23:24
Speaker 1: We don't really have functions that are very good describing
23:27
Speaker 1: chaotic situations, whereas very small change in the angle or
23:31
Speaker 1: the velocity of the moon means it's now suddenly over here,
23:34
Speaker 1: or it's suddenly on the other side of the sun,
23:36
Speaker 1: or it flies off in a completely different direction. Our
23:39
Speaker 1: equations are not good at describing chaotic mathematics. But I
23:42
Speaker 1: guess maybe the question is, like, what is it that
23:44
Speaker 1: about going from two to three that actually makes the
23:47
Speaker 1: equations unsolvable? Like before, with two, I can solve the equations,
23:51
Speaker 1: but with three, there's no solution for them. Does it
23:54
Speaker 1: become nonlinear? Is that what it is? It's already nonlinear,
23:57
Speaker 1: right that even with an equals to it's nonlinear as
24:00
Speaker 1: these distances go like one over radius squared, so there's
24:03
Speaker 1: an inverse are squared there, So it's already nonlinear. I
24:06
Speaker 1: think something you said earlier is really the right way
24:08
Speaker 1: to think about it. We know the forces F and
24:11
Speaker 1: the mass M, and we have F equals m A,
24:14
Speaker 1: so we can get the acceleration. That's a very simple formula.
24:17
Speaker 1: But how do you go from knowing the acceleration, which
24:19
Speaker 1: is how much the speed is changing, to knowing the
24:22
Speaker 1: actual location. What you have to do is add up
24:25
Speaker 1: the effects of lots of little accelerations over time, which
24:29
Speaker 1: means you have to integrate. You have to use calculus.
24:32
Speaker 1: But just like there aren't that many physics problems that
24:35
Speaker 1: are solvable, not every function can be integrated, at least
24:39
Speaker 1: not into a simple formula you can write down. So
24:41
Speaker 1: just because you know the force and the acceleration doesn't
24:44
Speaker 1: mean you know how to integrate it into getting the location.
24:48
Speaker 1: And we can go a little bit further if you
24:50
Speaker 1: look at the structure of the problem. Mathematicians call these
24:52
Speaker 1: problems non integrable, which just means that, like the possible
24:56
Speaker 1: trajectories for these objects in this three D space don't
25:00
Speaker 1: follow simple paths right like, they diverge very quickly. It's
25:04
Speaker 1: not like it can be easily simplified from a whole
25:06
Speaker 1: big set of possible solutions down to just a few,
25:09
Speaker 1: and with any equals too. With the two body problem,
25:11
Speaker 1: there are a bunch of simplifications you can make that
25:13
Speaker 1: separate the problem so that, for example, the distance between
25:17
Speaker 1: the objects is independent of their relative angle, because for
25:20
Speaker 1: two objects, you know, the angle doesn't really matter. What
25:23
Speaker 1: only matters is really just the distance. But for three
25:26
Speaker 1: objects you have not just the relative distances, but you
25:28
Speaker 1: also have the relative angles. And so now all the
25:31
Speaker 1: problems are still tied together. You know, when you try
25:34
Speaker 1: to solve a set of equations, sometimes it's helpful to
25:36
Speaker 1: try to separate them and solve them independently, but that's
25:39
Speaker 1: not always possible, and when they're all entangled up with
25:42
Speaker 1: each other, you can't always find a solution. Now, I see,
25:45
Speaker 1: there's something sort of magical about the number two that
25:47
Speaker 1: then you lose once you get more than two, right,
25:49
Speaker 1: because it's not just three bodies that are hard, it's
25:51
Speaker 1: also four and five and six and infinite. Right. Yes,
25:54
Speaker 1: you might have thought, oh, well, two bodies are solvable,
25:56
Speaker 1: so then why not three? It's actually the other direction.
25:59
Speaker 1: Two is the the one that is solvable. Right. All
26:02
Speaker 1: the problems are unsolvable except for this one magic special
26:05
Speaker 1: case of two bodies which we have been able to
26:08
Speaker 1: separate using this special trick and solve. So it's sort
26:12
Speaker 1: of lucky that any of them are solvable. Well, the
26:15
Speaker 1: zero body problem is solvable too, and the one body problem,
26:18
Speaker 1: I imagine is solvable. It's just that it's just gets
26:21
Speaker 1: more complicate. Real equations start to like interact with each other,
26:24
Speaker 1: and then you can't like fit a simple formula as
26:27
Speaker 1: a solution, right, yeah, exactly. And in addition, there's something
26:31
Speaker 1: about chaos here, right, that's right, The results become chaotic.
26:35
Speaker 1: As we said before, if you change a little bit
26:37
Speaker 1: the initial conditions, if Earth is a little bit further
26:39
Speaker 1: away or pointing in a slightly different direction, you can
26:43
Speaker 1: get completely different outcomes. So Earth can be like tossed
26:46
Speaker 1: out of the Solar System, or it can fall into
26:49
Speaker 1: another orbit or something like that. Whereas if you just
26:52
Speaker 1: have two bodies, things tend to be pretty stable. That
26:55
Speaker 1: means that if you perturb it, something comes along, gives
26:57
Speaker 1: the Earth a little push, will probably roll back into
26:59
Speaker 1: a initial orbit, whereas in a three body system, things
27:03
Speaker 1: get out of hand very quickly. And that's you know,
27:05
Speaker 1: not just like is it complicated motion. That's one of
27:08
Speaker 1: the reasons why we don't have a simple formula because
27:11
Speaker 1: we don't have functions that describe that, like sign and
27:15
Speaker 1: co sign and logarithm. These things are mostly well behaved,
27:18
Speaker 1: and so it's very difficult to describe chaotic motion using
27:22
Speaker 1: the sort of mathematical language that we have developed. Oh,
27:25
Speaker 1: I see, because there's no function that is chaotic kind
27:28
Speaker 1: of is that what you're saying, like, chaotic motion is
27:31
Speaker 1: not easily kind of captured in a formula. Yeah, it's
27:35
Speaker 1: not easily captured in a formula. It's possible to describe
27:38
Speaker 1: chaotic motion, but usually our solutions there are numerical, they're approximate,
27:43
Speaker 1: use simulations. You know, we can describe chaotic systems like
27:47
Speaker 1: you build a computer system, you put three objects in it,
27:50
Speaker 1: and then what you do is you say, all right,
27:52
Speaker 1: what happens in the first second, and you say, well,
27:55
Speaker 1: the Earth's gonna move this way, the Sun is gonna
27:56
Speaker 1: move that way, and the moon is going to move
27:58
Speaker 1: this other direction, and then you update everything and then
28:00
Speaker 1: you do it again. So you slice the problem in
28:02
Speaker 1: time and you say, what if I only want to
28:04
Speaker 1: predict a half second from now or a milli second
28:07
Speaker 1: from now, then you can really simplify and say I
28:10
Speaker 1: know what to do for a half second. Then you
28:12
Speaker 1: just do that over and over and over again. That's
28:14
Speaker 1: the way we can describe a chaotic system is like
28:16
Speaker 1: slicing it in time and then try to move our
28:19
Speaker 1: stimulation forward, just one time slice at a time. But
28:23
Speaker 1: that doesn't mean that we can then look at that
28:25
Speaker 1: motion and say, oh, look it follows a sign wave,
28:27
Speaker 1: or oh look it follows a logarithm of a sign wave.
28:30
Speaker 1: We can't find a solution. We can't find a mathematical
28:33
Speaker 1: description of the motion, even if we can describe it
28:35
Speaker 1: in the simulation I see. So like we can maybe
28:39
Speaker 1: predict what the system is going to do, what these
28:41
Speaker 1: three bodies are going to do, but we have to
28:43
Speaker 1: do it step by step. We can't just say, like, hey,
28:46
Speaker 1: twenty years from now, this is what it's going to be.
28:47
Speaker 1: There's no formula that will tell you that. You have
28:50
Speaker 1: to like simulate it a little by little until you
28:52
Speaker 1: get to ten years from now. Yeah, and even those
28:54
Speaker 1: simulations are difficult because it's chaotic. Like if you don't
28:58
Speaker 1: make those calculations very very very precise, then your simulation
29:02
Speaker 1: is going to be wrong. As you try to predict
29:03
Speaker 1: further and further into the future, because small mistakes really
29:08
Speaker 1: add up the snowball into big mistakes. It's just like
29:11
Speaker 1: you know, the butterfly problem. Butterfly flaps its wings in
29:14
Speaker 1: China and that has cascading effects on the weather, which
29:17
Speaker 1: causes eventually a storm in Central Park in New York.
29:21
Speaker 1: And these things are real. They're real physical systems that
29:23
Speaker 1: behave this way where if you give them a very
29:26
Speaker 1: small nudge, it can have a very big effect downstream.
29:29
Speaker 1: And that makes them very very challenging even to simulate,
29:32
Speaker 1: as we talked about, because if you get something wrong
29:34
Speaker 1: very early on, your results in ten years are nonsense.
29:38
Speaker 1: We much prefer to have like a simple we call
29:40
Speaker 1: it an analytical formula, like a very short math expression
29:44
Speaker 1: that we can just plug numbers into, because it can
29:45
Speaker 1: be exact and it can tell us exactly what's going
29:47
Speaker 1: to happen in ten years or in a hundred years.
29:50
Speaker 1: I think what you're saying is that these numerical approaches
29:52
Speaker 1: or simulations, they're just an approximation basically, right Like you're
29:56
Speaker 1: looking at the equations like the f equals amaze or
29:59
Speaker 1: the you know, the horses between the three bodies, and
30:02
Speaker 1: you're saying, well, let's not try to get the exact solution.
30:04
Speaker 1: Let's just pretend that for the next millisecond everyone has
30:07
Speaker 1: the same acceleration or something like that. Exactly. You make
30:10
Speaker 1: a bunch of simplications and you say, well, I only
30:12
Speaker 1: want to predict a millisecond in the future, so can
30:14
Speaker 1: I do that? And then you just keep doing that
30:17
Speaker 1: over and over again. You're saying that if I'm wrong
30:19
Speaker 1: a little bit because of that implication, then in a
30:22
Speaker 1: chaotic system, I could be really wrong. Yeah, and that's
30:25
Speaker 1: a big deal. If you're doing something like planning a
30:27
Speaker 1: trip to the stars or sending your probe to Jupiter
30:31
Speaker 1: or whatever, you definitely want to get that right right, Yeah.
30:34
Speaker 1: You don't want to be off by a few light years. Yeah.
30:37
Speaker 1: Or even if you're just flying through the Solar System,
30:39
Speaker 1: if you get it wrong, you could end up crashing
30:41
Speaker 1: into the Sun or getting tossed out of the Solar
30:44
Speaker 1: System in the wrong direction. You're trying to make it
30:46
Speaker 1: to Pluto from here, right, Pluto is very far away
30:49
Speaker 1: in a very very small target. Imagine firing a gun
30:52
Speaker 1: from l A to New York and trying to hit
30:55
Speaker 1: a tiny and the tiny target, it's very difficult. They're
30:57
Speaker 1: very small. If you're off by a tiny little angle
31:00
Speaker 1: in l A, you're definitely not going to hit that
31:02
Speaker 1: target in New York. But I guess that. You know,
31:04
Speaker 1: we are pretty good these days with you know, supercomputers,
31:07
Speaker 1: we are pretty good at simulating things and kind of predicting.
31:10
Speaker 1: You know, maybe not the storm that comes from the
31:12
Speaker 1: butterfly wings, but you know, the weather is you know,
31:15
Speaker 1: predictable sort of up to like a week, right or
31:18
Speaker 1: a couple of weeks, which is super impressive because they
31:20
Speaker 1: have to simulate all of those you know, air molecules
31:24
Speaker 1: and pockets of hot air that are out there in
31:25
Speaker 1: the atmosphere. It's not that it makes the problem impossible,
31:29
Speaker 1: it's just makes it harder. Or you know kind of storms,
31:32
Speaker 1: how much we can predict it. Yeah, if you had
31:33
Speaker 1: an infinitely powerful computer, then we could solve these problems
31:37
Speaker 1: because we could simulate them with really high resolution. We
31:39
Speaker 1: could take like really really short time steps in our simulation.
31:43
Speaker 1: Instead of stepping forward a millisecond, we could step forward
31:45
Speaker 1: in nanosecond and then correct. And so if you had
31:48
Speaker 1: infinite computing resources, you could do these things very effectively.
31:52
Speaker 1: And some of the reasons why these problems which seem
31:54
Speaker 1: to be impossible for a long time, like predicting the weather,
31:57
Speaker 1: seem to be getting easier, and not because humans are
31:59
Speaker 1: getting smarter, but because our computers are getting more powerful,
32:03
Speaker 1: and so now we have a lot more computing power
32:05
Speaker 1: available to do things like predicting the weather and trying
32:08
Speaker 1: to predict earthquakes and all these really really hard problems
32:11
Speaker 1: that are really important. Like today we can predict how
32:14
Speaker 1: the whole Solar system works, right, We mostly can, And
32:17
Speaker 1: a lot of that is because mostly the Solar system
32:19
Speaker 1: is a bunch of two body problems, like the Earth
32:22
Speaker 1: moving around the Sun. Technically it's you know, it's an
32:24
Speaker 1: eight body problem because the Earth is pulled on by
32:27
Speaker 1: the Moon and Jupiter and Neptune and whatever. But mostly
32:29
Speaker 1: it's just the Sun. You can ignore everything else when
32:32
Speaker 1: you're calculating the Earth to some degree. If you want
32:35
Speaker 1: to get it exactly right, then yes, you need to
32:37
Speaker 1: include effects from Mars and Venus, and then you can't
32:40
Speaker 1: use Kepler's laws. You can't use the simple formulas that
32:43
Speaker 1: we have for a two body problem. You have to
32:45
Speaker 1: get down and dirty and do the simulations using very
32:48
Speaker 1: powerful computers. But then I guess, would you say that
32:51
Speaker 1: our Solar system is chaotic as well? Like is our
32:53
Speaker 1: Solar system a chaotic system? Because it seems sort of
32:56
Speaker 1: stable right now, but are you saying maybe, like if
33:00
Speaker 1: you give it enough time, it is kind of a
33:01
Speaker 1: little unpredictable. Yeah, definitely, the Solar System is chaotic, but
33:05
Speaker 1: on the cosmological time scales, not on like a year
33:08
Speaker 1: or ten years, but unlike millions and billions of years,
33:12
Speaker 1: and it was more chaotic in the beginning. We sort
33:14
Speaker 1: of settled into something that's more stable. But when the
33:17
Speaker 1: Solar System began, it was a big hot mess and
33:19
Speaker 1: things were flying everywhere. Planets were colliding into each other
33:23
Speaker 1: and making new planets and throwing things out of the
33:26
Speaker 1: Solar System. We probably had a different number of planets
33:29
Speaker 1: a billion or two billion years ago. People suspect there
33:32
Speaker 1: might have been like another giant planet which was tossed
33:35
Speaker 1: out of the Solar System by Jupiter and Saturn. So, yeah,
33:38
Speaker 1: that sounds pretty chaotic to me. Solar system was like,
33:41
Speaker 1: you know, I have enough to deal with with the
33:43
Speaker 1: nine bodies, possibly eight, let's get someone out. But you
33:47
Speaker 1: can take a very complicated system like the Solar system
33:49
Speaker 1: and find approximately stable solutions things which will last for
33:53
Speaker 1: a long long time. But how stable are they? Something
33:56
Speaker 1: which flies through the Solar system can perturb it a
33:58
Speaker 1: little bit, and then things can very quickly go out
34:00
Speaker 1: of whack. So if you have like another star and
34:03
Speaker 1: that gets a little close to our Solar system, it
34:06
Speaker 1: could change the orbit of Jupiter, which could have knock
34:08
Speaker 1: on effects about changing the orbit of Saturn, and then
34:10
Speaker 1: the asteroid belt and Mars, and pretty soon we could
34:13
Speaker 1: have craziness. All right, Well, let's get into that craziness
34:17
Speaker 1: of our Solar system and what the consequences are of
34:19
Speaker 1: this three body problem and our ability to understand the
34:24
Speaker 1: rest of the cosmos. But first let's take another quick break.
34:40
Speaker 1: All right, we're talking about the three body problem, and
34:44
Speaker 1: it's hard to find an analytical solution to it, as
34:48
Speaker 1: opposed to the two body problem, which you can find
34:50
Speaker 1: a nice, neat formula for it. But I wonder then
34:52
Speaker 1: if this is sort of like a physicist frustration, because
34:55
Speaker 1: as an engineer, I'm pretty much used to like things
34:57
Speaker 1: not having an analytical solution, like from day one, like
35:00
Speaker 1: nothing only like throwing a ball up in the air
35:03
Speaker 1: has an analytical solution. Everything else you have to do
35:05
Speaker 1: with numerical simulations or approximating, you know, the Navy, your
35:08
Speaker 1: Stokes equations and having non linear stuff that you can't solve,
35:12
Speaker 1: and so you know like it. As an engineer you
35:14
Speaker 1: always rely on simulations, but maybe in physics you get
35:17
Speaker 1: more frustrated for not having like a neat, you know,
35:21
Speaker 1: clean formula to predict the future. Well, the thing that's
35:23
Speaker 1: tantalizing is that there are a few cases when you
35:26
Speaker 1: can find a neat formula where you can start with
35:29
Speaker 1: just pencil and paper, describe the pushing and the pulling
35:32
Speaker 1: of your system, and then get out a formula that
35:35
Speaker 1: tells you where everything is going to be basically for
35:37
Speaker 1: all time. That's amazing, it's beautiful, and it's tempting. It
35:41
Speaker 1: makes you think, Wow, why can't I do this for
35:44
Speaker 1: other systems? Why can't I do this for every system? Right?
35:47
Speaker 1: Because if they exist for some systems, it gives you
35:49
Speaker 1: the sense that, like, if we had the right mathematics,
35:52
Speaker 1: if we knew the right language to talk about this stuff,
35:55
Speaker 1: maybe even really complicated problems would be simpler. So it's
35:58
Speaker 1: sort of aspirational yeah, I can imagine that frustration. You're
36:01
Speaker 1: in your cabin in the middle of Russia, in Siberia,
36:04
Speaker 1: in the middle of nowhere, and you're like, oh, shoot,
36:06
Speaker 1: I need a computer I didn't bring one, or oh shoot,
36:09
Speaker 1: I need to talk to somebody else, I don't have
36:11
Speaker 1: a phone. That's frustrating, right, It is frustrating. And you know,
36:15
Speaker 1: it's something funny about teaching freshman physics. I teach mechanics
36:18
Speaker 1: often here you see irvine, and you know there are
36:21
Speaker 1: not a lot of problems that really are solvable, like
36:24
Speaker 1: very few problems can you actually sit down with pencil
36:27
Speaker 1: and paper and say, here's the situation, here's the solution.
36:30
Speaker 1: And so, in teaching this class for like almost twenty
36:32
Speaker 1: years now, I've noticed that basically every physics Hormemork problem
36:36
Speaker 1: in every textbook is one variation on like one of
36:39
Speaker 1: these five solvable problems. And so as soon as you
36:42
Speaker 1: look at when you're like, oh, this is that one problem,
36:44
Speaker 1: or this is a problem number four, except they're using
36:46
Speaker 1: a squirrel instead of a ball of rolling down a
36:48
Speaker 1: plane or something, and so it all boils down to
36:51
Speaker 1: like a few solvable problems because there are only a
36:54
Speaker 1: few that can actually be solved. I mean, there's an
36:56
Speaker 1: analytical simple solutions to what Professor Whitesen is gonna have.
37:00
Speaker 1: But on the final test, I hope students are taking notes.
37:03
Speaker 1: I say, if you take my class for twenty years,
37:05
Speaker 1: it becomes pretty easy. I guess even physics professors are predictable.
37:09
Speaker 1: Is that what you're saying they're going to do. It's
37:13
Speaker 1: hard to invent new solvable problems in physics. And you
37:16
Speaker 1: know it's not just like motion of two objects. There
37:20
Speaker 1: are lots of places in physics where the problems are
37:22
Speaker 1: not solvable. Einstein developed general relativity, right, which means he
37:25
Speaker 1: wrote down the equations for how space curves when masses around.
37:30
Speaker 1: He wrote down the equations, which means those are the
37:32
Speaker 1: constraints that space has to follow. It doesn't mean he
37:35
Speaker 1: can tell you how space behaves when masses around. Those
37:39
Speaker 1: are the solutions to the Einstein equation. And he couldn't
37:42
Speaker 1: solve his own equations. Like he developed general relativity and
37:45
Speaker 1: he's like, here the equations, I don't know how to
37:47
Speaker 1: solve this. He wasn't even the first person to solve
37:50
Speaker 1: the Einstein equation that was short styled. Because these equations
37:53
Speaker 1: are like famously impossible to solve. Now, if you have
37:56
Speaker 1: a solution, you can check it. You can say I
37:59
Speaker 1: think space ends in this way when there's massed around.
38:02
Speaker 1: You can plug it into the equations, and if it works,
38:04
Speaker 1: you're like, cool, I found it. But again, just because
38:06
Speaker 1: you have the equations doesn't mean you know how to
38:08
Speaker 1: find the solution. Anybody who's done differential equations knows that's true.
38:12
Speaker 1: We have like no general mechanism for saying, here's a
38:15
Speaker 1: differential equation, I can go from the equation to finding
38:18
Speaker 1: the solution. And so there's lots of places in physics
38:21
Speaker 1: where we just don't know how to solve these things.
38:23
Speaker 1: Even still for general relativity, we only know how to
38:26
Speaker 1: solve it for a few cases, like an empty universe,
38:29
Speaker 1: a universe that's smoothly filled with matter like no lumps
38:33
Speaker 1: at all, or a black hole. Basically everything else is unsolvable.
38:37
Speaker 1: Then that's why before Sheeld found right like Evan found
38:40
Speaker 1: the solution for general relativity in the case of a
38:43
Speaker 1: simple black hole. Yeah, exactly. He was the first person
38:45
Speaker 1: to ever solve these equations, and he actually did it
38:48
Speaker 1: while he was a soldier in World War One. What
38:51
Speaker 1: was he like fighting in a cabin in Russia. Also,
38:55
Speaker 1: never fight a land war in Russian man, especially while
38:57
Speaker 1: you're trying to solve question. Extra difficulty points. Unless he
39:02
Speaker 1: was fighting for the Russians. Maybe I don't know, maybe
39:04
Speaker 1: he's Russian, and then he had a lot of time
39:06
Speaker 1: because the other team was doomed. No, but it's a
39:10
Speaker 1: great story. You should look up how short Starts solved
39:12
Speaker 1: this problem. I see. So it's not he solved general
39:14
Speaker 1: relativity for all time in all cases. He just found
39:17
Speaker 1: a solution for general relativity in this special case of
39:20
Speaker 1: a simple black hole. Yeah, of a universe that has
39:22
Speaker 1: nothing but a black hole in it. He figured out
39:25
Speaker 1: the solution how space bends in that scenario. And then
39:28
Speaker 1: later people figured out, Okay, well, if I assume that
39:31
Speaker 1: the universe is totally empty, can I solve the equations? Oh,
39:34
Speaker 1: I can do that? Or if I assume the universe
39:36
Speaker 1: is like filled smoothly with matter, can I do that?
39:39
Speaker 1: But like, nobody has solved general relativity for like our
39:42
Speaker 1: solar system, or even just for like the Sun and
39:45
Speaker 1: the Earth together. It's too complicated. Nobody has figured out
39:48
Speaker 1: how to go from those equations to say, here's how
39:51
Speaker 1: space has to bend in this situation. Oh wait, so
39:55
Speaker 1: not even like the two body problem has a solution
39:58
Speaker 1: in general relativity. Yeah, that's right. General auctivity much much
40:01
Speaker 1: harder than Newtonian mechanics. We can do things like numerical relativity,
40:05
Speaker 1: like we can describe how black holes orbit each other
40:08
Speaker 1: and collide and generally gravitational waves. Because we can do
40:11
Speaker 1: it numerically, we can use computers to do approximate solutions
40:15
Speaker 1: to these things. But nobody can like write down simple
40:17
Speaker 1: formulas to tell you like how black holes orbit each
40:20
Speaker 1: other and collapse. Oh, I see. All this time we've
40:23
Speaker 1: been talking about the two body probably being solvable. It's
40:25
Speaker 1: only solvable in the Newtonian case, right, Like if you
40:28
Speaker 1: assume the simplest or the simple physics of Newton, then
40:33
Speaker 1: you can find a solution, but not for three. But
40:35
Speaker 1: if you assume, like what we actually know what's going
40:38
Speaker 1: on general relativity, then it's we can't even start, Like
40:41
Speaker 1: there's no solution, Yeah exactly. You know, Einstein lays out
40:44
Speaker 1: the equations the constraints, but he doesn't tell you, and
40:46
Speaker 1: he doesn't know how to go from the constraints to
40:49
Speaker 1: a solution. You know, it's sort of like if you're
40:52
Speaker 1: driving down the highway with your family and you ask
40:54
Speaker 1: somebody what they want for dinner, and everybody says, I
40:56
Speaker 1: want a salad, or I want pizza, or I want
40:58
Speaker 1: hot dogs, Like those are the con straints. Doesn't necessarily
41:01
Speaker 1: mean you know how to find a restaurant that satisfies
41:03
Speaker 1: those constraints, right, Having the constraints doesn't tell you how
41:07
Speaker 1: to find a solution. Wow, it sounds like something from
41:10
Speaker 1: personal experience with data. You're trying to events, Yes, I'm
41:13
Speaker 1: looking for a restaurant the search salads and hotdogs and pizza.
41:18
Speaker 1: Let me know if you find one that's not even
41:21
Speaker 1: the general relativity solution. Like if you add relatives to
41:23
Speaker 1: this card, right, then it gets impossible, right, because then
41:27
Speaker 1: you have all these relative dynamics exactly, very chaotic, very quickly. Well,
41:31
Speaker 1: I think what's interesting is that this is not just
41:34
Speaker 1: difficult for us as physicists to like predict these things
41:39
Speaker 1: and kind of like know what's going to happen, but
41:41
Speaker 1: it's also kind of hard for the universe to know
41:42
Speaker 1: what's going to happen. Right, Like, if something is chaotic,
41:45
Speaker 1: it also means that things are kind of unpredictable in general,
41:48
Speaker 1: like crazy things can happen in our solar system. Yes,
41:51
Speaker 1: systems with three objects don't last very long because they
41:54
Speaker 1: are chaotic. They don't tend to fall into stable patterns
41:58
Speaker 1: and survive for very long. So if you have like
42:01
Speaker 1: three stars orbiting each other, then pretty quickly two of
42:05
Speaker 1: them will eject the third one out into the universe.
42:08
Speaker 1: Because there are not very many stable solutions to the
42:11
Speaker 1: three body problem. And this is different from like can
42:14
Speaker 1: human mathematicians write down a simple formula to predict what
42:17
Speaker 1: will happen? That's one question. Another question is like how
42:20
Speaker 1: long can three stars orbit each other before two of
42:23
Speaker 1: them kick out the other one. I guess you mean
42:25
Speaker 1: like three stars of about the same size, right, Yeah,
42:28
Speaker 1: three stars about the same size and about the same
42:31
Speaker 1: distance from each other at a real like three body system.
42:33
Speaker 1: Because the only way for that to really happen, for
42:36
Speaker 1: it to become stable is to sort of turn it
42:38
Speaker 1: into a double two body system. Take your three stars,
42:43
Speaker 1: group two of them together, make them really close, and
42:46
Speaker 1: put them far away from the third star, and then
42:48
Speaker 1: what you have is like a little two body system
42:50
Speaker 1: of two stars. And then you have that two body system.
42:53
Speaker 1: You can treat it sort of like as a single
42:55
Speaker 1: object when you're talking about the third star which is
42:58
Speaker 1: now orbiting that pair. And so when we do find
43:01
Speaker 1: trinary systems out there in the universe, they're typically this
43:04
Speaker 1: like two body system. In a hierarchy, we have a
43:07
Speaker 1: two body system, and then one of those bodies turns
43:09
Speaker 1: out to have two things inside of it, right, And
43:12
Speaker 1: I think this hierarchy we sort of talked about it
43:14
Speaker 1: in the last podcast, but it's acidly with distance, right, Like,
43:17
Speaker 1: if two of them are out here, you know, interacting
43:20
Speaker 1: and orbiting around each other, then to another body that's
43:24
Speaker 1: fairly far away, our two little bodies here, I feel
43:27
Speaker 1: like one. And so then that makes it more stable. Exactly, if,
43:30
Speaker 1: for example, we had two sons at the center of
43:32
Speaker 1: our solar system, if they were really close to each other,
43:35
Speaker 1: and they were much closer to each other than we
43:38
Speaker 1: were to them, we could treat it like it was
43:40
Speaker 1: just one object. It wouldn't matter to us that it
43:42
Speaker 1: was two objects. But if we got closer to them,
43:45
Speaker 1: or if we even like trying to get between them,
43:47
Speaker 1: then it would make a big difference on our trajectory
43:50
Speaker 1: that there were two objects instead of one, and so,
43:52
Speaker 1: for example, in that novel we talked about at the
43:55
Speaker 1: top of the episode, that's exactly what's going on. There's
43:57
Speaker 1: a solar system with two stars and a plan that's
44:00
Speaker 1: whizzing all around right through them in a very crazy,
44:03
Speaker 1: unstable orbit. And so not only does it have like
44:05
Speaker 1: really weird night and day patterns, but it has a
44:08
Speaker 1: very chaotic trajectory, and so you can't necessarily predict exactly
44:12
Speaker 1: where it's going to be. It's kind of like a
44:14
Speaker 1: real couples, I guess, you know, like from a distance,
44:18
Speaker 1: you can sort of assume they think and act as one,
44:20
Speaker 1: but once you get go up close to them easily,
44:22
Speaker 1: there's a lot of disagreement there. But you never want
44:24
Speaker 1: to get between them exactly. That's right. It soundstable. Yeah,
44:27
Speaker 1: you don't want to be the third body there, you
44:30
Speaker 1: definitely don't. You can get tossed out of your solar
44:32
Speaker 1: system or maybe eject the one of the others. But then, yes,
44:38
Speaker 1: it sounds like we're writing a romcom now involving a
44:40
Speaker 1: trip to the woods in Russia. All right, Well, this
44:43
Speaker 1: is kind of an interesting question here, and an interesting
44:45
Speaker 1: problem because it doesn't just tell you that some things
44:47
Speaker 1: are hard to solve in nature, but some things are
44:51
Speaker 1: hard and unpredictable themselves in nature, right, Like some of
44:55
Speaker 1: these things out in nature they just don't last long
44:58
Speaker 1: they been out of control, or they a settle into
45:01
Speaker 1: things that are more stable, like to body solar systems. Yeah,
45:04
Speaker 1: and it could be that in the future somebody events
45:07
Speaker 1: mathematics that makes it easier to describe that crazy chaotic
45:10
Speaker 1: motion and that you know, in twenty years or in
45:13
Speaker 1: fifty years, we have like a a new basic function,
45:15
Speaker 1: you know, like we have signed and coson. These were
45:17
Speaker 1: invented functions by human mathematicians. Somebody might come up with
45:21
Speaker 1: a new function which turns out to be really useful
45:23
Speaker 1: to describing three body motion and and allows us to
45:27
Speaker 1: find some expression. A lot of mathematicians are skeptical because
45:31
Speaker 1: they can sort of express these solutions is like an
45:33
Speaker 1: infinite series, and they showed that it's very complicated, and
45:37
Speaker 1: they suspect that there isn't a simple function. But you know,
45:39
Speaker 1: future mathematicians are usually smarter than today's mathematicians, and so
45:43
Speaker 1: I hold out hope or maybe like there are aliens
45:45
Speaker 1: who have figured this out, you know, like they'll come
45:48
Speaker 1: to us and be like, yes sign and cosap we
45:49
Speaker 1: don't have, you know, chaos sign or something that describes
45:53
Speaker 1: chaos motion. Yeah, exactly, And maybe somewhere some mathematicians is
45:57
Speaker 1: developing the tools and they don't even realize how it's
45:59
Speaker 1: going to useful. I love those stories of mathematicians developing
46:02
Speaker 1: these ideas and then them later being co opted by physicists.
46:06
Speaker 1: And so maybe those ideas exist right now and all
46:09
Speaker 1: you have to do is go out and read the
46:10
Speaker 1: right math paper and you're like, oh, this is exactly
46:13
Speaker 1: the hammer we need to hit this physics nail. Or
46:15
Speaker 1: maybe the answer is in some cabin in Russia, but
46:18
Speaker 1: the you know, the poor soul ran out of food
46:20
Speaker 1: or something and it's lost to us, but it's written
46:24
Speaker 1: down on a frozen sheet of paper in that cabin.
46:27
Speaker 1: It exists. But anyways, I guess the good news is
46:31
Speaker 1: that it's an open problem and there could be somebody
46:33
Speaker 1: listening to this podcast right now that might solve it
46:35
Speaker 1: in the future, maybe even you. Well we hope you
46:38
Speaker 1: enjoyed that. Thanks for joining us, see you next time.
46:49
Speaker 1: Thanks for listening, and remember that Daniel and Jorge explained
46:51
Speaker 1: the universe is a production of I heart Radio. For
46:55
Speaker 1: more podcast from My heart Radio, visit the I heart
46:58
Speaker 1: Radio app, Apple Podcasts, or wherever you listen to your
47:01
Speaker 1: favorite shows.